THE EFFECT OF MICROHYDRATION ON IONIZATION ENERGY AND
PROTON TRANSFER IN NUCLEOBASES. ANALYSIS AND METHOD
DEVELOPMENT.
by
Kirill Khistyaev
A Dissertation Presented to theFACULTY OF THE USC GRADUATE SCHOOLUNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of theRequirements for the Degree
DOCTOR OF PHILOSOPHY(CHEMISTRY)
May 2013
Copyright 2013 Kirill Khistyaev
Acknowledgements
I am very grateful to my advisor Prof. Anna Krylov for the chance to work in her
wonderful group. She is not only a good mentor but a great manager who carefully
choose promising students and raise them into real scientists. She cares a lot about
interests and talents of her students. In her group you can work on a projects that you are
really interested in and capable to do them well. That is exactly how it was in my case. I
really enjoyed projects I was working at in Anna’s group. I was able to fully dedicate my
time and thoughts to these projects because I shared their goals and importance. During
my work in Anna’s group I was given a chance not only to fulfill the requirements for
PhD in Chemistry but also to learn materials far beyond this requirements and to grow
professionally. In many respects it was thanks to the fact that Anna always encourages
her students desire to learn the newest methods and technologies. I strongly believe that
my experience and knowledge obtained in Anna’s group will be invaluable my future
career.
I want to thank all my colleagues of our wonderful group. The staff of our group
changed significantly during my 5-year PhD term but all members of our group always
ii
were very kind and helpful. They were always open to interesting discussions and
reached me a lot. I am very grateful to Dr. Evgeny Epifanovskiy for teaching me a
lot about electronic structure methods and how they actually work on computers hard-
ware. Without his implementation of ccman2 and libtensor libraries the GPU-related
part of this work would not be possible. His help with discussions and implementation
of GPU-enabled ccman2 library cannot be overestimated. I would like to acknowledge
Dr. Ksenia Bravaya for helping me with microhydrated thymine and dimethyluracil
projects. Without her deep knowledge of the quantum chemistry field, both theory and
application, it would be much harder to succeed with this projects. I am grateful to
Vadim Mozhayskiy who taught me the basics of coupled-cluster methods and Q-Chem
package. I would like to thank Dmitry Zuev and Nikolay Plotnikov for useful discus-
sions on computational chemistry and technical questions.
I am grateful to Prof. Aiichiro Nakano who taught me the basics of GPU program-
ming and inspired me to do the GPU part of this work.
I gratefully acknowledge our collaborators Dr. Musahid Ahmed and his group from
Lawrence Berkeley National Laboratory for providing us with great experimental data
and discussions that was used in this work.
I thank my wife Olga for all understanding and support during my work on my
thesis. Without her I would not be able to spend so much time on my research. Finally,
I would like to thank my family in Russia for making me who I am and making it all
possible, especially my parents, grandparents and my brother.
iii
Table of contents
Acknowledgements ii
List of tables vi
List of figures vii
Abbreviations xii
Abstract xiv
Chapter 1: Introduction and overview 11.1 Computational study of microhydration effects . . . . . . . . . . . . . . 11.2 Electronic structure methods . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Methods for the ground electronic state . . . . . . . . . . . . . 41.2.2 Methods for excited electronic states . . . . . . . . . . . . . . . 91.2.3 Density functional theory methods . . . . . . . . . . . . . . . . 11
1.3 Chapter 1 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 2: The effect of microhydration on ionization energy of thymine 172.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2 Experimental and computational techniques . . . . . . . . . . . . . . . 21
2.2.1 Electronic structure calculations . . . . . . . . . . . . . . . . . 212.2.2 Calculation of the Franck-Condon factors and PIE curves . . . . 272.2.3 Experimental details . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 312.3.1 Ionization-induced geometry changes in thymine hydrates . . . 312.3.2 Vertical ionization energies . . . . . . . . . . . . . . . . . . . . 322.3.3 The origin of IE changes . . . . . . . . . . . . . . . . . . . . . 352.3.4 Adiabatic ionization energies and FCFs . . . . . . . . . . . . . 382.3.5 Theory versus experiment . . . . . . . . . . . . . . . . . . . . 40
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.5 Chapter 2 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
iv
Chapter 3: The effect of microhydration on proton transfer in 1,3-dimethyluraciland 1,3-dimethyluracil dimers 52
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.2 Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.1 Proton transfer in thymine-water clusters . . . . . . . . . . . . . 623.3 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 633.4 Computational results . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1 Proton transfer in monohydrate . . . . . . . . . . . . . . . . . . 703.4.2 Proton transfer in dihydrated species . . . . . . . . . . . . . . . 75
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.6 Chapter 3 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Chapter 4: The implementation of the coupled-cluster family of methods ongraphics processing unit 84
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.2 GPU architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904.3 GPU programming languages by the example of CUDA C . . . . . . . 94
4.3.1 Thread organization . . . . . . . . . . . . . . . . . . . . . . . . 954.3.2 Memory organization . . . . . . . . . . . . . . . . . . . . . . . 95
4.4 Review of existing quantum chemistry methods accelerated with GPU. . 974.5 Challenges of the implementation of the CCSD method on GPU . . . . 1014.6 Implementation details . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.6.1 Overview of the code structure and libraries design . . . . . . . 1034.6.2 Description of the GPU-enabled code . . . . . . . . . . . . . . 1074.6.3 Results and conclusions . . . . . . . . . . . . . . . . . . . . . . 110
4.7 Chapter 4 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Chapter 5: Future work 1155.1 Chapter 5 references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Appendix: Tensor algebra library graphical processing unit implementation 118
v
List of tables
2.1 Vertical and adiabatic IEs (eV) of thymine and thymine-water clusterscomputed by EOM-IP-CCSD/cc-pVTZ. . . . . . . . . . . . . . . . . . 34
3.1 Vertical and adiabatic ionization energies (eV) of mU, (mU)2, water,and various hydrated species. All energies are computed by EOM-IP-CCSD/6-311+G(d,p) except for (mU)2 and (mU)2·H2O which are com-puted with 6-31+G(d,p) basis set. . . . . . . . . . . . . . . . . . . . . 71
vi
List of figures
1.1 Action of different flavors of the EOM excitation operator forms differ-ent sets of target states giving rise to a suite of EOM-CC methods. . . . 12
2.1 Structures and binding energies (De, kcal/mol) of the considered thymine-water monohydrates, dihydrates and trihydrates, CCSD/cc-pVTZ at RI-MP2/cc-pVTZ geometry. . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Equilibrium structures of thymine and three thymine monohydrates opti-mized by RI-MP2/cc-pVTZ. Bondlengths and changes in bond lengthsdue to interactions with water are shown (in A). . . . . . . . . . . . . . 23
2.3 Equilibrium structures of thymine dihydrate and trihydrate optimizedby RI-MP2/cc-pVTZ. Bondlengths and changes in bond lengths due tomicrohydration are shown (in A). . . . . . . . . . . . . . . . . . . . . 24
2.4 Equilibrium structures of ionized thymine and thymine monohydratesoptimized by ωB97X-D/cc-pVTZ. Bondlengths and changes in bondlengths due to ionization are shown (in A). . . . . . . . . . . . . . . . 25
2.5 Equilibrium structures of ionized thymine and thymine di- and trihy-drates optimized by ωB97X-D/cc-pVTZ. Bondlengths and changes inbond lengths due to ionization are shown (in A). . . . . . . . . . . . . 26
2.6 Coordinates describing relative water-thymine motion. . . . . . . . . . 28
2.7 Mass spectrum of microhydrated thymine recorded at a photon energyof 10 eV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.8 VIEs (eV) and the corresponding MOs of thymine and thymine-waterisomers, EOM-IP-CCSD/cc-pVTZ. Changes in VIEs due to microhy-dration and the leading EOM-IP amplitude are given in parentheses. . . 33
2.9 VIEs versus the degree of charge transfer to water in different ionizedstates of the three thymine monohydrates. . . . . . . . . . . . . . . . . 36
vii
2.10 Changes in VIEs versus the degree of charge transfer to water in differ-ent ionized states of T1. . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.11 Changes in VIEs versus charge-dipole interaction energy between thecharges on thymine and the dipole moment of water molecule. . . . . . 37
2.12 Calculated FCFs for the first ionized state of T1 (lower panel). Upperpanel: FCFs due to water-thymine motion (undefined scale); middlepanel: FCFs due to thymine moiety. . . . . . . . . . . . . . . . . . . . 39
2.13 Calculated FCFs factors for the first ionized state of T2 (lower panel).Upper panel: FCFs due to water-thymine motion (undefined scale); mid-dle panel: FCFs due to thymine moiety. . . . . . . . . . . . . . . . . . 40
2.14 The experimental (raw and smoothed data, and error bars) and calculated(T1 and T2) PIE curves. The respective adiabatic 0←0 transitions arealso shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.15 The differentiated PIE (DPIE) curves and calculated VIEs for thymineand thymine clusters with one, two, and three water molecules. . . . . . 42
2.16 The PIE curves and calculated AIEs for thymine and thymine clusterswith one, two, and three water molecules. . . . . . . . . . . . . . . . . 43
3.1 Schematic of experimental apparatus. . . . . . . . . . . . . . . . . . . 55
3.2 Mass spectra of hydrated (with H2O) mU and its dimer using 12 eVphotons with different backing pressure and temperature. . . . . . . . . 56
3.3 The percentage of different dimer forms relative to the all forms of mUpresent in the beam. The percentage is calculated as the ratio betweenthe signal of the indicated form and the signal of all forms of mU presentin the beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4 Structures of 1,3-dimethyluracil and its dimer hydrated with one or twowater molecules. In all structures, water acts as a proton donor. Hydra-tion of the dimer does not lead to considerable changes in the relativeposition of the two mU moieties, e.g., the distances between C=O andC-CH3 groups in dry and hydrated (mU)2 clusters are around 3.3-3.5A. Temperature increase results in higher concentration of mU clusters,whereas backing pressure controls degree of hydration. . . . . . . . . . 58
viii
3.5 Mass spectrum of hydrated mU and the dependence of the yield of various pro-tonated species on photon energy and backing pressure. A. Mass spectrum ofhydrated (with D2O) mU and its dimer using 12 eV photons. The inset showsthe region at mass to charge (m/z) 180 corresponding to [mU(D2O)2]+. Thedashed lines indicate two additional peaks at m/z 181 and 182 arising due tonatural isotope abundance (13C) and due to protonated and deuterated species.The intensity ratios between the peaks marked by the arrows at different photonenergy for mU(D2O)2 are shown in panel B. The constant behavior of the m/z181 peak confirms that it arises from isotopic contributions and is not due to PT.Panel C shows similar ratios (for N+1 and N+2 m/z peaks) for N=182 corre-sponding to [DmU(H2O)2]+. In this case, the N+2 peak is constant, revealingthat there is no deuteron transfer between the bases. Panel D: The effect ofbacking pressure (Ar gas) on PT. The black curve (mU-D2O PT) character-izes deuteron transfer from D2O to uracil; the red curve [mU-D2O PT (nor-malized)] — deuteron transfer from D2O to uracil divided by the sum of mUand (mU)2 hydrates, ∑
n,m[(mU)n(D2O)mD]+/ ∑
n,m 6=0∑
k+l=0,1[(mU)n(D2O)mHkDl]+.
The blue curve (mU-mU PT) corresponds to PT between the mU molecules,
∑n
[mU(D2O)nH]+/∑m
[(mU)2(D2O)m]+. E: The appearance energies of deuter-
ated species [mU(D2O)nD]+ for different cluster sizes n. . . . . . . . . . . . 60
3.6 Yield of protonated thymine (TH) and thymine-water (T(H2O)H+) clus-ters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.7 Monohydrated structures. Distances in angstroms and binding energiesin kcal/mol are given for each structure. The lowest-energy isomer ismUW1-1a. mUW1-1b, mUW1-2a, and mUW1-2b are 1.59, 1.58 and3.06 kcal/mol higher, respectively. . . . . . . . . . . . . . . . . . . . . 65
3.8 Dihydrated structures. Distances in angstroms and binding energiesin kcal/mol are given for each structure. The lowest-energy isomer ismUW2-1a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.9 MOs corresponding to the lowest ionized state in mU·H2O, (mU)2, and(mU)2·H2O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.10 Photoionization efficiency curve (black) of [(mU+D2O)]+ and its deriva-tive (red), observed using 8 eV to 12 eV photons. The derivative plotreveals multiple ionized states derived by removing the electron fromdifferent MOs. Black arrows points towards the calculated ionizationenergies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
ix
3.11 Structural changes in ionized mUW1-1a. Left: optimized neutral state.Top right: Franck-Condon optimized structure of the 1st (1A”) adiabaticstate of the cation. Bottom right: optimization of the 5th (3A”) adiabaticstate of the cation gives optimized proton-transferred structure of thecation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.12 Potential energy profiles for low-lying states of [mU·H2O]+ along thePT reaction coordinate. The proton is moved from the water moleculeto the mU oxygen site. The 5th ionized state, 3A′′, in which the holeis on the water molecule (see Fig. ??), shows no barrier facilitatingdownhill PT. PT from lower ionized states are possible, however thisinvolves changes in the electronic wave function character and requiresmore than 10.6 eV photon energy. The left panel shows the experimentalratio between the [mU(D2O)2]+ signal (m/z 180) and [mU(D2O)2D]+
the deuterated species at m/z 182; it shows dramatic enhancement in PTwhen the 3A′′ state is accessed. . . . . . . . . . . . . . . . . . . . . . 73
3.13 Energy diagram describing relevant ionized states and their ordering atdifferent geometries along PT coordinate. All energies are given in eVand are calculated with EOM-IP-CCSD/6-311+G**. . . . . . . . . . . 74
3.14 Possible proton-transferred structures in [mU(H2O)2]+. Left panels showmanually distorted structures used as staring points for optimization.Right panels show the final optimized structures of the ionized species.Distances are in Angstroms. . . . . . . . . . . . . . . . . . . . . . . . 76
4.1 Calculations per second per $1000, logarithmic plot. . . . . . . . . . . 85
4.2 The evolution of computing platform’s peak performance and CPU fre-quency demonstrates CPU frequency standstill around 2004. . . . . . . 87
4.3 Theoretical peak performance for the CPU and GPU, floating-point oper-ations per second. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.4 Sketchy representation of CPU and GPU architectures. . . . . . . . . . 91
4.5 NVIDIA Kepler GK110 architecture. 2880 CUDA cores organized in15 SMXs are shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6 NVIDIA Kepler GK110 streaming multiprocessor (SMX) architecture.192 singleprecision CUDA cores, 64 doubleprecision units, 32 specialfunction units (SFU), and 32 load/store units (LD/ST). . . . . . . . . . 93
4.7 Kepler Memory Hierarchy. . . . . . . . . . . . . . . . . . . . . . . . . 94
x
4.8 Grid structure. Thread blocks form a grid that correspond to one kernel. 96
4.9 Speedup for various *GEMM calls as a function of square matrix size(averaged over 10 runs). MGEMM correspond to the heterogeneousmodel with different thresholds. Times are scaled relative to runningDGEMM on the CPU. . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.10 Overview of CC/EOM-CC code architecture. . . . . . . . . . . . . . . 104
4.11 Overview of the libtensor library structure. A multi-layer design allowsfor various extensions in terms of new algorithms and data types as wellas new hardware architectures. The layers interact through well-definedinterfaces; any layer can be substituted by an alternative implementationwithout the need to modify the code in the layers above or below. . . . 105
4.12 Diagram of classes in libtensor. For each type of tensors there are spe-cialized tensor operations. General block tensors and operations on themare generic implementations. Concrete block tensors use the genericstructures and algorithms within, but provide a simplified interface. Thetemplate argument in gen block tensor allows to use different types oftensors, e.g., real, complex or CUDA dense tensors, sparse tensors, ortensors with special properties. Any such implementation of tensor haveto provide tensor operation classes (tod add, tod contract2, etc.). . . . . 106
4.13 Memory layers of GPU implementation of VMM. Multiple copies of thetensor can be stored in all three layers. VMM keeps track of the latestcopy of the tensor and updates older version as needed. . . . . . . . . . 109
A.1 Schematic order of execution of tensor contraction operation. . . . . . 119
xi
Abbreviations
QM quantum mechanics
QM/MM quantum mechanics/molecular mechanics
CC coupled-cluster
CCSD coupled-cluster with single and double substitutions
EOM equation-of-motion
EOM-IP-CC equation-of-motion coupled-clusters
EOM-IP-CCSD equation-of-motion coupled-clusters single and double substitutions
TD-CISD time-dependent configuration interaction with single and double
excitations
HOMO highest occupied molecular orbital
LUMO lowest unoccupied molecular orbital
IE ionization energy
AIE adiabatic ionization energy
VIE vertical ionization energy
PIE photoionization efficiency
xii
VUV vacuum ultraviolet
FCF Franck-Condon factor
PT proton transfer
NAB nucleic acid base
mU 1,3-dimethyluracil
DmU d6-1,3-dimethyluracil
GPU graphics processing unit
EFP effective fragment potential
xiii
Abstract
Quantum mechanics can predict basic properties of molecules such as relative energies,
electronic charge distributions, dipoles, ionization and excitation energies. By solving
the Schrodinger equation with the electronic molecular Hamiltonian we can determine
the electronic structure of the molecule that implies physical and chemical properties of
the molecule.
In this thesis we use quantum mechanics to study basic properties of microhydrated
nucleobases – essential building blocks of DNA. Water plays a central role in chemistry
and biology by mediating the interactions between molecules, altering energy levels of
solvated species, modifying potential energy profiles along reaction coordinates, and
facilitating efficient proton transport through ion channels and interfaces. The effect of
hydration on different properties of molecules and chemical reactions has been inten-
sively studied for many years both theoretically and experimentally. Numerous sol-
vation models were developed in an effort to simulate the properties and reactions in
the bulk water. However, even the interaction between several water molecules are not
completely understood. This work demonstrates how microhydration can affect such
properties as ionization energies and control proton transfer mechanisms. It explains
the experimental results and proposes mechanisms of observed effects.
xiv
In order to facilitate theoretical studies the development of new quantum chemistry
programs that are able to utilize the resources of modern high-performance hardware is
required. An exact solution for the Schrdinger equation can only be obtained for the
species with just a few electrons. However, there are a number of quantum chemistry
methods that give approximate solutions. Among the most widely used and accurate
methods are coupled-cluster methods. In the last chapter the details of the GPU enabled
implementation of the post-HartreeFock ab initio quantum chemistry methods is given.
In Chapter 2 a combined theoretical and experimental study of the effect of micro-
hydration on ionization energies (IEs) of thymine is presented. The experimental IEs
are derived from photoionization efficiency curves recorded using tunable synchrotron
VUV radiation. The onsets of the PIE curves are 8.85±0.05, 8.60±0.05, 8.55±0.05, and
8.40±0.05 eV for thymine, thymine mono-, di-, and tri-hydrates, respectively. The com-
puted (EOM-IP-CCSD/cc-pVTZ) AIEs are 8.90, 8.51, 8.52, and 8.35 eV for thymine
and the lowest isomers of thymine mono-, di-, and tri-hydrates. Due to large structural
relaxation, the Franck-Condon factors for the 0←0 transitions are very small shifting the
apparent PIE onsets to higher energies. Microsolvation strongly affects IEs of thymine
— addition of each water molecule reduces the first vertical IE by 0.10-0.15 eV. The
adiabatic IE decreases even more (up to 0.4 eV). The magnitude of the effect varies for
different ionized states and for different isomers. For the ionized states that are localized
on thymine the dominant contribution to the IE reduction is the electrostatic interaction
between the delocalized positive charge on thymine and the dipole moment of the water
molecule.
In Chapter 3 proton transfer in a model system comprising dry and microhydrated
clusters of nucleobases is investigated. Experiments with mass spectrometry and tunable
vacuum ultraviolet synchrotron radiation show that water shuts down ionization-induced
xv
proton transfer between nucleobases, which is very efficient in dry clusters. Instead, a
new pathway opens up in which protonated nucleobases are generated by proton trans-
fer from the ionized water molecule and elimination of a hydroxyl radical. Electronic
structure calculations reveal that the shape of the potential energy profile along the pro-
ton transfer coordinate depends strongly on the character of the molecular orbital from
which the electron is removed, i.e., the proton transfer from water to nucleobases is bar-
rierless when an ionized state localized on water is accessed. The computed energetics
of proton transfer is in excellent agreement with the experimental appearance energies.
Possible adiabatic passage on the ground electronic state of the ionized system, while
energetically accessible at lower energies, is not efficient. Thus, proton transfer is con-
trolled electronically, by the character of the ionized state, rather than statistically, by
simple energy considerations. Proton transfer from ionized outer water to nucleobases
in dihydrated cluster through the Grotthuss-like mechanism is barrierless and the most
energetically favorable mechanism.
Chapter 4 describes an implementation of coupled-cluster (CC) post-HartreeFock
ab initio quantum chemistry methods, which are widely used in the research, includ-
ing the research described in previous chapter, on GPU with CUDA C language. The
implementation of these methods is based on the ccman2 and libtensor libraries and is
part of the Q-Chem 4 electronic structure package. These libraries use layered modular
architecture which allows relatively easy addition and replacement of low-level modules
without changing high-level code (such as CC equations). Developed layered architec-
ture make possible a fast adaptation of the existing code in the ccman2 library to other
languages and technologies, such as OpenCL with AMD GPUs or Intel Xeon Phi copro-
cessor. The development of CC code for new massively parallel architectures is crucial
for future research of larger systems with higher accuracy and for QM/MM methods.
xvi
Chapter 1: Introduction and overview
1.1 Computational study of microhydration effects
Computational chemistry is a rapidly developing subfield of theoretical chemistry that
uses principles of computer science to solve chemical problems by calculations. Among
computational chemistry methods ab initio quantum chemistry methods play a very spe-
cial role. These methods are based on the systematic application of the principals of
quantum mechanics to chemical systems. The uniqueness of these methods is in the
fact that they derive complex physical and chemical properties of molecules from the
first principles, that is, the basic physical properties of such simple particles as electron
and atomic nucleus and quantum mechanics laws. It is amazing that one can calculate
with high accuracy complex properties of such large systems as nucleobases tetramers
or porphyrines by just knowing the positions and types of atoms.
Experiments can give us certain information about molecular properties and yields
of chemical reactions. However, they typically are not able to explain why the properties
have certain values and what is the nature of the observed phenomena. Without theory
it is often hard to even assign the experimental signals to certain species. However, the-
ory can do much more than interpretation of experimental results. It can help develop
a mechanism of an observed phenomena and understand the fundamental physical prin-
ciples behind it. It is extremely important to understand the fundamental principles
1
because only then it is possible to extend the obtained knowledge to other systems. For
example, in the research presented in Chapter 2 of this thesis we had from the experiment
unassigned photoionization efficiency (PIE) curves of microhydrated thymine clusters
with certain masses. At first, quantum chemistry calculations allowed us to match the
differentiated PIE peaks to ionization energies of microhydrates. Further theoretical
investigation led us to a conclusion that the effect of the microhydration on IE energies
in these clusters can be explained by simple electrostatic interaction. It gave an insight
into the nature of interaction between the water and other molecules. Thus by applying
quantum chemistry methods we were able to go beyond just the statement of the experi-
mental facts about the studied system and derive a broader pictures that have implication
to other systems and methods.
Major part of this work is dedicated to the study of the effects of microhydration
of nucleobases. It is hard to overestimate the importance of water in chemistry and
life sciences. Almost all chemical reactions in living organisms and many of the indus-
trial chemical processes occures in water solutions. Thus it is no surprise that water
and its effects on other molecules and reactions has been intensively studied for a long
period of time. Many methods were developed in attempt to model the solvation effects.
However, we are still far from complete understanding of the behavior of water and its
interactions with other molecules. One of the reason is that it is very difficult to model
such a complex environment as bulk water. Isolating limited number of water shells and
studying them with accurate QM methods does not give the correct properties of the bulk
water because of the long-range and many-body effects and polarization. From the other
side, simpler and cheaper methods, such as various molecular mechanics methods and
semi-empirical methods, typically are not able to capture all important interactions. A
2
number of hybrid QM/MM methods were developed in attempts to overcome the short-
falls of individual QM and MM techniques. However, the results of QM/MM methods
can drastically differ between methods and even within a single method with different
parameters. In this thesis instead of the study of a complex molecule (such as DNA)
in the complex environment of bulk water, the small building blocks of DNA in the
smallest possible water environment - microhydrates of nucleobases in the gas phase -
were studied. Both precise experimental techniques and accurate theoretical methods
were applied to discover the exact mechanisms of interaction between water and nucle-
obases. The results obtained for microhydrated nucleobases are not limited to these
systems only but should be similar for other molecules as well. They can be used in
other models such as QM/MM and be further extended to large systems and bulk water.
Quantum chemistry provides us with powerful tools for understanding the proper-
ties of molecules. Unfortunately, the exact solution for the Schrdinger equation – the
basis of all quantum chemistry methods – can only be obtained for the species with
only few electrons. However, there are a number of quantum chemistry methods that
give approximate solutions. Among the most widely used and accurate methods are
coupled-cluster (CC) methods. Most of the computations performed in this research
were based on the CC methods. However, the CC methods have a high computational
cost and steep scaling factor (e.g. N6 for CCSD). In order to be able to apply these meth-
ods to larger systems such as microhydrated nucleobases clusters with more than first
solvation shell it is crucial to use a faster hardware. Unfortunately, it is no longer possi-
ble to get better performance with just a single CPU core as it was before. Any modern
architecture requires parallel programs for efficient execution. One of the most efficient
computation hardware architectures is the Graphical Processing Unit architecture. Many
computational science programs have been recently ported to GPU to benefit from their
3
performance. Note that there are two main vendors - AMD and NVIDIA, that produce
GPUs and there are several languages (e.g. CUDA C, OpenCL, OpenACC) designed to
program for GPU. To complicate matters further, there are different competing archi-
tectures such as Intel Xeon Phi coprocessor, multicore CPUs, APUs, vector processors,
etc. It is hard to predict which technologies will better work with the CC methods in
the future and it is very time-consuming to develop a separate programs for every tech-
nology. The goal of the research presented in Chapter 4 was not just develop a GPU
capable implementation of the CC methods but to design a library architecture that can
be used for implementations with other architectures with minimal efforts.
1.2 Electronic structure methods
1.2.1 Methods for the ground electronic state
The ground state is of particular interest in electronic structure theory because most of
chemical reactions occur on the lowest-energy PES. One of the conventional approaches
to approximately solve for the ground-state energy is to use Hartree–Fock method,
which employs variational principle and is based on the mean-field description of
electron–electron interactions. Using a set of one-electron basis set functions, one solves
a system of Roothaan equations self-consistently to obtain molecular orbitals and their
energies.
The Hartree–Fock method can be roughly described as taking the following steps.
The reader is encouraged to consult electronic structure texts1, 2 for more details.
1. A one-electron basis set is selected for each atom of the molecule. In this work
we use Pople’s split-valence3–5 and Dunning’s6 collections of basis sets, which
are based on the Cartesian Gaussian representation of Slater-type orbitals. Using
4
the basis set, orbitals of each type (s, p, d, etc.) are created. They are called
atomic orbitals φµ.
2. Initial molecular orbital matrix C and Fock matrix F are formed using core Hamil-
tonian, superposition of atomic densities, Huckel theory or another similar strat-
egy. The orbital overlap matrix S is computed.
3. Roothaan equation
FC = SCE
is solved for the matrix C and the diagonal matrix E. Because Fock matrix F itself
depends on C, the equation has to be solved self-consistently. Iterations continue
until the convergence criterion (usually |C(i)−C(i−1)|< ε) is met.
Resulting from this procedure, the C matrix contains in its rows the expansion coef-
ficients for obtaining molecular orbitals ψi in terms of atomic orbitals
ψi = ∑µ
ciµφµ (1.1)
and the diagonal matrix E contains corresponding molecular orbital energies.
Hartree–Fock theory does not include electronic correlation, but provides a starting
point for correlated methods.
Coupled-cluster theory
It is well known that the inclusion of electron correlation is essential for the accurate
determination of molecular properties. Among the various approaches to the correlation
problem, coupled-cluster theory has proven to be very powerful and accurate. Since
the first application of the CC methods to the electron correlation problem by Cizek in
5
19667, 8, they have become one of the most successful and widely used tools of quan-
tum chemistry. Although the CC equations are more complicated than the configuration
interaction equations, they have significant benefits over CI methods. One of the main
advantages of CC methods is size extensivity which assures that the results of calcula-
tions scale properly with the size of the system. This is a very important property for
calculations of interaction energies, chemical reactions and potential energy surfaces.
Similar to the CI method, CC theory represents the wave function of the ground state
as an expansion in terms of the reference determinant, then all determinants with sin-
gle substitutions, followed by double substitutions, and so on. Unlike CI, which uses a
linear excitation operator to generate the expansion, in CC theory the wavefunction is
written in the following exponential form8:
|ΨCC〉= exp(T )|Φ0〉
where |Φ0〉 is a single Slater determinant (usually Hartree-Fock determinant) called the
reference determinant and T is a cluster operator, which consists of a series of n-tuple
excitation operators:
T = T1 +T2 +T3 + . . .
Each term in the series can be expressed in the second quantization form:
T1 = ∑ia
tai a†
aai T2 =14 ∑
i jabtabi j a†
aa†ba jai T3 =
16 ∑
i jkabcT abc
i jk a†aa†
ba†caka jai
and so on. These equations follow the conventional notation: i, j, . . . stand for occupied
in the reference determinant |Φ0〉 spin-orbitals, a,b, . . . designate virtual (unoccupied)
spin-orbitals. The creation and annihilation operators a†p and ap create or remove an
6
electron from the spin-orbital |p〉. When T includes all excitation operators up to Tn for
n electrons, the result is equivalent to that from full-CI(FCI) calculations as all possible
excited determinants are present in the expansion. The CC energy in that case contains
100% of the electronic correlation energy within the given basis set. Using the full
expansion of the cluster operator T , however, is impractical because the computational
complexity of the method grows exponentially with the size of the system. FCI results
have only been reported for di- and triatomic molecules in rather small basis sets. To
reduce the scaling of the CC method, the T operator is truncated. Because of the expo-
nential form of the wave function ansatz, CC theory retains size-extensivity even with
the truncated cluster operator. This is unlike CI, in which only the full expansion is
size-extensive. Advantages of the CC approach are apparent from the fact that for any
truncation of T such as T≈T2,
exp(T2) |Φ0 〉= 1+T2+12
T22+
13!
T32+. . .
still introduces certain types of quadruple, hextuple and higher excitations into the calcu-
lations via the T22 ,T3
2, etc. terms. This argument is applicable to any level of truncation
of the T operator. These two qualities make the truncated CC models superior to their
CI counterparts.
Limiting the expansion of T to the first two terms, for example, gives rise to coupled-
clusters with single and double excitations (CCSD) method, initially implemented by
Purvis and Bartlett9
|ΨCCSD〉= exp(T1+T2) |Φ0 〉
Among all iterative CC methods, CCSD provides the most attractive balance
between the computational cost and accuracy. When chemical accuracy is desired (of
7
the order of a few kcal/mol), the energy can be further improved using a non-iterative
CCSD(T) correction via perturbation theory10.
The wave function and energy are obtained by solving the system of CC equations
for the T amplitudes:
〈Φ0|exp(−T )H exp(T )|Φ0〉= ECC
〈Φ0|exp(−T )H exp(T )−ECC|Φi〉= 0
In practice the CC equations are solved numerically using the Jacobi method for the
system of linear equations in the matrix form. The vector solution is the CC amplitudes
and the update procedure is formulated as a recurring expression for the T vector11.
To improve the convergence of the scheme, the direct inverse of the iterative subspace
(DIIS)12 method is applied. For example, The Schrodinger equation for CCSD is:
(H−ECCSD)ΨCCSD=(H−ECCSD)exp(T1+T2) |Φ0 〉= 0
A set of equations sufficient for determining the tai and tab
i j coefficients can be obtained
from the projections onto a reference determinant |Φ0 〉 and all excited determinants
generated by the action of T on |Φ0 〉9 . When this set of equations is appropriately
factorized, all terms involve the contraction of a cluster operator T with either two- or
four-index quantities13. In the case of CCSD, the quantities that are contracted with the
amplitudes tai and tab
i j are one- and two-particle intermediates in which the correspond-
ing Fock matrix element fpq or antisymmetrized molecular orbital integral 〈pq‖rs〉 is
the leading term of an expansion which also contains contractions between Fock matrix
elements and integrals with T amplitudes. The calculations of these intermediates and
in particular the contractions of the amplitudes with the intermediates have the largest
8
computational cost in CCSD method. The addition of triples correction in CCSD(T)
method besides tensor contraction adds a specific operation similar to dot-product oper-
ation in matrix algebra but requires an elementwise division by the sum of elements of
delta-matrices. This operation is used in the triples correction to the converged CCSD
energy expression10:
∆E = ∑i jkabc
t(a)i jkabct(b)i jkabc
∆ia +∆ jb +∆kc
1.2.2 Methods for excited electronic states
Equation-of-motion method
Equation-of-motion approach is a powerfull and versatile electronic structure method
allows the description of many multi-configurational wavefunctions within a single-
reference formalism. The formal starting point for this method is the CC wavefunction
for a convenient reference state with N electrons. Applying the general linear excitation
operator R on the ground state CC wave function yields the excited state wave function
|Ψ(m)〉= R(m)|ΨCC〉= R(m) exp(T )|Φ0〉 (1.2)
(the integer m identifies the excited state). The structure of the excitation operator R is
the same as in CI. It can be expanded as
R = R1 +R2 +R3 + . . . (1.3)
where R1 generates all possible singly excited determinants with respect to the reference
determinant, R2 generates all doubly excited determinants, and so on.
9
In the limit of the zero cluster operator T = 0, this approach becomes regular CI as
the excitation operator R acts directly on the reference determinant. If the series for R
is not truncated, the operator generates all possible excitations. In this case the full CI
result is recovered, no matter what the cluster operator T is.
The idea can be reformulated and generalized by introducing a similarity transfor-
mation for the electronic Hamiltonian H using the cluster operator:
H = exp(−T )H exp(T ) (1.4)
Regardless of the choice of T, the similarity transformed Hamiltonian H has the same
spectrum as the original Hamiltonian H. That allows us to “fold” the electronic corre-
lation in the form of the cluster operator into the Hamiltonian and find the eigenvalues
(target state energies) and eigenvectors (target state wave functions) in various subspaces
of the Fock space. When T and R are truncated (e.g. at single and double excitation),
the EOM models are numerically superior to the corresponding CI models, because cor-
relation effects are “folded in” in the transformeds Hamiltonian. This approach is called
equation-of-motion coupled-clusters (EOM-CC) method14–22.
If the excitation operator R promotes one or more electrons from occupied to virtual
orbitals, it can be written in the second quantization form as
R(m)0 = r0 R(m)
1 = ∑ia
rai a†
aai R(m)2 =
14 ∑
i jabrab
i j a†aa†
ba jai (1.5)
This form of R preserves the number and spin of electrons. It is used in EOM-CC for
excitation energies (EOM-EE-CC), which yields the energies and wave functions for
electronically excited states.
10
Operator R can be designed to remove or attach electrons, and change their spin
(Fig. 1.1). This gives rise to a suite of EOM-CC methods: for ionization energies
(EOM-IP-CC), for attachment energies (EOM-EA-CC), spin-flip (EOM-SF-CC). It is
a powerful toolkit that allows one to start with a convenient well-behaved reference
state, and form target states by applying the different flavors of the operator R23.
EOM operator R is written in the tensor form in the basis of molecular orbitals. The
elements of this tensor (rai , rab
i j in Eq. 1.5) are called EOM amplitudes. They are found
by solving the eigenproblem
〈Φµ|H−E(m)|R(m)Φ0〉= 0 (1.6)
where 〈Φµ| are all µ-tuply excited with respect to the reference determinants.
Just like the cluster operator T in CC, the operator R can be truncated at different
excitation levels. In EOM-CCSD16, 17, 24, 25, both T and R include terms up to T2 and
R2. The EOM-CCSD methods give an error in the range of 0.1–0.3 eV for excitation
energies.
1.2.3 Density functional theory methods
Long-range-corrected density functionals
In long-range-corrected functionals, a range-separated representation of the Coulomb
operator26, 27 is used to mitigate the effects of the self-interaction error. The contribu-
tion from the short-range part is described by a local functional, whereas the long-range
part is described using the exact Hartree-Fock exchange. The separation depends on a
parameter γ. In ωPB97X28, γ and other parameters are optimized using standard training
sets. Benchmark results have demonstrated consistently improved performance relative
11
EOM-EE-CC (excitation energies)
EOM-IP-CC (ionization potential)
EOM-EA-CC (electron attachment)
EOM-SF-CC (spin-flip)
Figure 1.1: Action of different flavors of the EOM excitation operator forms dif-ferent sets of target states giving rise to a suite of EOM-CC methods.
12
to non-long-range-corrected functionals. In ωPB97X-D29 functional parameters were
reoptimized to include empirical atom-atom dispersion corrections. Tests show that
for non-covalent systems, ωPB97X-D shows slight improvement over other empirical
dispersion-corrected density functionals, while for covalent systems and kinetics it per-
forms noticeably better. Relative to ωPB97X, the new functional is significantly superior
for non-covalent interactions, and very similar in performance for bonding interactions.
13
1.3 Chapter 1 references
[1] A. Szabo and N.S. Ostlund. Modern Quantum Chemistry: Introduction toAdvanced Electronic Structure Theory. McGraw-Hill, New York, 1989.
[2] T. Helgaker, P. Jørgensen, and J. Olsen. Molecular electronic structure theory.Wiley & Sons, 2000.
[3] W.J. Hehre, R. Ditchfield, and J.A. Pople. Self-consistent molecular orbital meth-ods. XII. Further extensions of gaussian-type basis sets for use in molecular orbitalstudies of organic molecules. J. Chem. Phys., 56:2257, 1972.
[4] P.C. Hariharan and J.A. Pople. Theor. Chim. Acta, 28:213, 1973.
[5] R. Krishnan, J.S. Binkley, R. Seeger, and J.A. Pople. Self-consistent molecularorbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys.,72:650, 1980.
[6] T.H. Dunning. Gaussian basis sets for use in correlated molecular calculations.I. The atoms boron through neon and hydrogen. J. Chem. Phys., 90:1007–1023,1989.
[7] J. Cizek. On the correlation problem in atomic and molecular systems. Calcu-lation of wavefunction components in Ursell-type expansion using quantum-fieldtheoretical methods. J. Chem. Phys., 45:4256–4266, 1966.
[8] J. Cizek. Adv. Chem. Phys., 14:35, 1969.
[9] G.D. Purvis and R.J. Bartlett. A full coupled-cluster singles and doubles model:The inclusion of disconnected triples. J. Chem. Phys., 76:1910–1918, 1982.
[10] K. Raghavachari, G.W. Trucks, J.A. Pople, and M. Head-Gordon. A fifth-orderperturbation comparison of electron correlation theories. Chem. Phys. Lett.,157:479–483, 1989.
[11] J. Gauss, J.F. Stanton, and R.J. Bartlett. Coupled-cluster open-shell analytic gra-dients: Implementation of the direct product decomposition approach in energygradient calculations. J. Chem. Phys., 95:2623–2638, 1991.
[12] P. Pulay. Chem. Phys. Lett., 73:393, 1980.
[13] J.F. Stanton, J. Gauss, J.D. Watts, and R.J. Bartlett. A direct product decompositionapproach for symmetry exploitation in many-body methods. I. energy calculations.J. Chem. Phys., 94:4334–4345, 1990.
14
[14] D.J. Rowe. Equations-of-motion method and the extended shell model. Rev. Mod.Phys., 40:153–166, 1968.
[15] K. Emrich. An extension of the coupled-cluster formalism to excited states (I).Nucl. Phys., A351:379–396, 1981.
[16] J. Geertsen, M. Rittby, and R.J. Bartlett. The equation-of-motion coupled-clustermethod: Excitation energies of Be and CO. Chem. Phys. Lett., 164:57–62, 1989.
[17] J.F. Stanton and R.J. Bartlett. The equation of motion coupled-cluster method.A systematic biorthogonal approach to molecular excitation energies, transitionprobabilities, and excited state properties. J. Chem. Phys., 98:7029–7039, 1993.
[18] S.V. Levchenko and A.I. Krylov. Equation-of-motion spin-flip coupled-clustermodel with single and double substitutions: Theory and application to cyclobu-tadiene. J. Chem. Phys., 120(1):175–185, 2004.
[19] D. Sinha, D. Mukhopadhyay, and D. Mukherjee. A note on the direct calculation ofexcitation-energies by quasi-degenerate MBPT and coupled-cluster theory. Chem.Phys. Lett., 129:369–374, 1986.
[20] S. Pal, M. Rittby, R.J. Bartlett, D. Sinha, and D. Mukherjee. Multireferencecoupled-cluster methods using an incomplete model space — application toionization-potentials and excitation-energies of formaldehyde. Chem. Phys. Lett.,137:273–278, 1987.
[21] J.F. Stanton and J. Gauss. Analytic energy derivatives for ionized states describedby the equation-of-motion coupled cluster method. J. Chem. Phys., 101(10):8938–8944, 1994.
[22] M. Nooijen and R.J. Bartlett. Equation of motion coupled cluster method for elec-tron attachment. J. Chem. Phys., 102:3629–3647, 1995.
[23] A.I. Krylov. Equation-of-motion coupled-cluster methods for open-shell and elec-tronically excited species: The hitchhiker’s guide to Fock space. Annu. Rev. Phys.Chem., 59:433–462, 2008.
[24] H. Sekino and R.J. Bartlett. A linear response, coupled-cluster theory for excitationenergy. Int. J. Quant. Chem. Symp., 26:255–265, 1984.
[25] H. Koch, H.J.Aa. Jensen, P. Jørgensen, and T. Helgaker. Excitation energies fromthe coupled clusters singles and doubles linear response functions (CCSDLR).Applications to Be, CH+, CO, and H2O. J. Chem. Phys., 93(5):3345–3350, 1990.
15
[26] H. Iikura, T. Tsuneda, T. Yanai, and K. Hirao. A long-range correction schemefor generalized-gradient-approximation exchange functionals. J. Chem. Phys.,115:3540, 2001.
[27] R. Baer and D. Neuhauser. Density functional theory with correct long-rangeasymptotic behavior. Phys. Rev. Lett., 94:043002, 2005.
[28] J.-D. Chai and M. Head-Gordon. Systematic optimization of long-range correctedhybrid density functionals. J. Chem. Phys., 128:084106, 2008.
[29] J.-D. Chai and M. Head-Gordon. Long-range corrected hybrid density function-als with damped atom-atom dispersion interactions. Phys. Chem. Chem. Phys.,10:6615–6620, 2008.
16
Chapter 2: The effect of
microhydration on ionization energy of
thymine
2.1 Introduction
Ionization of nucleic acid bases is involved in DNA radiation and photo-damage and
may eventually lead to dangerous mutations with a risk for cancer and neurodegenerative
deceases. Due to their relatively low ionization energies, individual nucleobases are the
most likely components of DNA to be oxidized. Their IEs, however, are affected by cou-
pling to DNA’s sugar-phosphate backbone, hydrogen-bonding and π-stacking between
neighboring bases, as well as interactions with solvating water molecules and counter
ions. Quantifying the exact nature of these effects has proven difficult, and even the val-
ues of IEs of solvated DNA are still controversial. For example, a recent computational
study1 that attempted to compute the IE of guanine in solvated DNA by a QM/MM
approach reported a large increase (4 eV) of guanine’s IE, contrary to the conclusions
drawn from experimental studies2.
As part of our effort to understand the role played by different interactions of NABs
with the environment3–8, we recently characterized the effect of hydrogen bonding and
17
π-stacking on the ionized states of the gas-phase dimers of AA, TT, AT, and CC in a
combined experimental and theoretical study7, 8. We found that stacking and h-bonding
can reduce the IEs by 0.4-1 eV via two distinct mechanisms: hole delocalization and
electrostatic charge-dipole interactions. We also analyzed ionization-induced structural
changes in isolated nucleic acid bases9 and in uracil dimers4, 5. Consistent with delo-
calized character of the highest occupied molecular orbital (HOMO), structural changes
involve several CC and CN bonds, the largest change being for the double CC bond.
In bare NABs the relaxation energy is 0.2-0.4 eV, whereas in the dimers the difference
between adiabatic and vertical IEs is larger. To quantify the effect of structural relax-
ation on photoionization efficiency curves, we computed Franck-Condon factors (FCFs)
for the lowest-energy tautomers of NABs9. In all cases, we observed that the 0←0 tran-
sitions have non-negligible FCFs and that the onsets of the PIE curves indeed represent
AIEs.
Microsolvation has been found to decrease the IEs of nucleobases by about 0.1 eV
per water molecule6, 10. The absolute values of IEs reported in VUV6 and electron
impact10 studies are slightly different. An excellent agreement of the IE of isolated
thymine determined from the PIE curve (8.90±0.05 eV)6 with the value derived from
MATI spectra (8.9178±0.0010 eV)11 validates the accuracy of the synchrotron VUV
measurements6.
The computational studies12, 13 performed with B3LYP predicted similar magnitude
shifts and pointed out substantial geometric relaxation in hydrated species leading to
even larger changes in AIEs. These studies were motivated by differences between the
results obtained by the two experimental approaches, i.e., using electron impact ioniza-
tion and VUV photoionization6, 10. A number of tautomers were calculated to interpret
18
the early electron impact results, while attempts were made to fit the appearance energy
measurements to various vertical and adiabatic values.
In other nucleobases, microhydration leads to similar effects6, although the magni-
tude of the IE drop varies. For example, the changes in AIE in adenine-water clusters6, 14
are smaller than those for thymine.
The effect of microsolvation on electronically excited states and photoinduced
dynamics in nuclear bases and other model chromophores has been investigated theo-
retically and experimentally15–22. In addition to perturbations to the electronic spectrum
and differential stabilization of excited states, microsolvation can open up new relax-
ation channels including, among others, hydrogen/proton and electron transfer, charge-
transfer-to-solvent states, and zwitter-ion formation.
The theoretical treatment of ionized species is challenging owing to their open-shell
character and electronic near-degeneracies23, 24. Wave-function approaches using dou-
blet references often suffer from spin-contamination and symmetry-breaking, which
result in hole over-localization23. DFT methods are affected by self-interaction error
leading to charge over-delocalization. Owing to these defects, computational studies
often observe artifacts of electronic structure methodology rather than real physical
properties of these systems. We employ the EOM-IP method that is free from the above
problems and is the method of choice for these systems. EOM-IP describes open-shell
target states as ionized states derived from well behaved closed-shell neutral reference
wave functions (see Section 2.2.1). We also use DFT with a range-separated functional
(ωB97X-D) that greatly reduces self-interaction errors25, 26.
The appearance energies of microhydrated thymine ions [T(H2O)n, n=1-3)] have
been reported previously by our collaborators from Dr. Musahid Ahmed group6. In
the present work they have performed the measurements with a broader energy range
19
and report improved error bars. Furthermore, derivation of the PIE curves as reported
by us for NABs and their dimers, allows for qualitative interpretation of the VIEs for
thymine and hydrated thymine as maxima at obtained curves. In the earlier experimental
work6, the beam contained mixed adenine-thymine and water clusters, and in the new
experiments reported here thymine alone was microhydrated with water.
OOO
OO
H3CO
H3CN
O
H3CON
O
H3C
N
N
O
H3C
N
N
O
N ON O
N O
OO
T1 (11.3) T2 (9.1) T3 (8.9) T4 (6.7)
O OO O
N
O
H3C
N
O
H3C
O
N
O
H3C
N
O
H3C
O
N ON
N
ON O
N O
O OO
O OO O O
T11 (23.4) T12 (20.1) T111 (32.8) T112 (31.0)
Figure 2.1: Structures and binding energies (De, kcal/mol) of the consideredthymine-water monohydrates, dihydrates and trihydrates, CCSD/cc-pVTZ at RI-MP2/cc-pVTZ geometry.
Previous experimental and theoretical studies on the microhydration of thymine did
not provide a detailed physical picture of the ionization processes. Hence, the focus of
this work is on quantifying the effect of microsolvation on IEs and on understanding its
origin. We consider several isomers of the microhydrates shown in Fig. 2.1 (all struc-
tures correspond to the lowest-energy tautomer of thymine). In order to unambiguously
compare with the experimental measurements, we also perform modeling of the FCFs
20
for the lowest electronic state of the cations. Accurate FCF calculations for hydrogen-
bonded systems of such complexity are rare and provide important benchmarks as well
as insight into the spectroscopy of biologically relevant species.
All experimental data presented in this chapter were obtained by Dr. Musahid
Ahmed group from Lawrence Berkeley National Laboratory.
2.2 Experimental and computational techniques
2.2.1 Electronic structure calculations
Open-shell doublet wave functions can be formally derived from a closed-shell systems
by addition or subtraction of an electron. As such, they can be described accurately
and efficiently by the ionization potential (IP) and electron affinity (EA) variants of
equation-of-motion coupled-cluster (EOM-CC) methods27–30. EOM-IP, which relies
on the N-electron closed-shell reference, is free from the symmetry breaking and spin-
contamination problems that are ubiquitous in open-shell calculations, and is capable of
describing charge localization patterns in ionized clusters4, 7, 23, 31. EOM-IP simultane-
ously includes dynamical and non-dynamical correlation, describes multiple electronic
states in one calculation, and treats states with different number of electrons on the
same footing. Using the EOM-CC family of methods, electronically excited, ionized,
or attached states of the thymine-water clusters can be computed starting from the same
closed-shell CCSD (coupled-cluster with singles and doubles) reference wave function
of the neutral24, 32.
21
The target open-shell wave functions are generated by a Koopmans-like excitation
operator R acting on the reference CC wave function:
ΨEOM−IP(N−1) = ReT
Φ0(N) (2.1)
where Φ0(N) is the reference determinant of the N-electron neutral system, T is the
coupled-cluster excitation operator including single and double substitutions, and R
consists of 1h and 2h1p (1-hole and 2-hole-1-particle) operators generating (N − 1)-
electron determinants from the N-electron reference. Amplitudes T are found by solv-
ing CCSD equations for the ground-state wave function of the neutral, while amplitudes
R are obtained by subsequent diagonalization of the similarity transformed Hamiltonian,
H = e−T HeT .
EOM-IP-CCSD yields accurate energy splittings and smooth potential energy sur-
faces along charge transfer coordinates23. This method has been successfully applied
to describe electronic structure of ionized benzene dimers31, 33, water clusters34–36 and
dimers of nucleobases3–5, 7, 8.
We also employed DFT with the long-range and dispersion-corrected ωB97X-
D functional26 (for geometry optimization and frequency calculations). Long-range
Hartree-Fock exchange included in ωB97X-D mitigates the effect of self-interaction
error yielding accurate structures and frequencies7, 9.
There are several tautomers of thymine; however, the energy gap between the canon-
ical form and next most stable tautomer is more than 10 kcal/mol37 in the gas phase.
Since we used thermal vaporization to generate thymine in the gas phase, there is not
enough energy to populate higher-lying tautomers. Thus, the canonical form should be
predominantly present in the molecular beam.
22
O
H3C 1.399
1.221
1.459N
O
H3C1.456
(-0.003)
1.221(0.000) 1.400
(0.001)1.011
(0 000)
N
N
O
1.350
1.374 1.381
1.216
1.381
N
N
O
1.375(-0.006)
1.227(0.011)
1.371(-0.010)
1.372(-0.002)
1.352(0.002)
1.017
1.011 (0.000)
1 8711.006
O
(0.011)
1.8710.972
0.958
1.871
T1 0.958
O1.221
(0.000) 1 399
OO
1 455
1.232(0.011)
1 3881.896
0.957
0.971
1.020
NH3C
O
1.460(0.001)
( ) 1.399(0.000)
1.372(-0.009)
1.227(0.011)
1.350(0.000)
1.915
0.970
0.958N
CH31.455
(-0.004)1.388
(-0.011)
1.381(0.000)
1.215(-0.001)
1.351(0.001)
1.021(0.010)
(0.009)
N O1.375(-0.006)
1.375(0.001)
N O( 0.001)
1.383(0.002)
1.371(-0.003)
1.006(0.000)
1.006(0.000)
T2 T3
Figure 2.2: Equilibrium structures of thymine and three thymine monohydratesoptimized by RI-MP2/cc-pVTZ. Bondlengths and changes in bond lengths due tointeractions with water are shown (in A).
We considered the three most stable monohydrated thymine isomers (T1-T3, see
Fig. 2.1) and the two thymine-(H2O)2 structures (T11, T12) obtained by Hobza et al.
using the molecular dynamics/quenching technique (MD/Q)37. The forth most stable
monohydrate structure (T4) shown in Fig. 2.1 is 4.4 kcal/mol higher in energy than
the most stable T1. Therefore we excluded T4 from further consideration. Thymine
trihydrate structures (T111 and T112) were obtained by addition of a water molecule to
dihydrate structures. All ground-state geometries were optimized using the RI-MP2/cc-
pVTZ and ωB97X-D/cc-pVTZ methods, which yielded similar results. For example,
the differences in all bond lengths for the thymine molecule in T1 is less than 0.01 A;
23
O
H C1.455
( 0 004)
1.222(0.001)
1.400(0 001)
OO
1 452
1.232(0.011)
1 390 1.891
0.9570.971
N
N
O
H3C (-0.004) (0.001)
1.375(-0.006)
1.229(0.013)
1.372
1.352(0.002)
1.011(0.000)
NH3C
1.452(-0.007)
1.390(0.009)
1.375(-0.006)
1.227(0.011)
1.353(0.003)
1.021(0.010)
N O
O O
1.365(-0.016)
(-0.002)1.024
(0.018)
1.764 0.975
1.784N O
O
1.374(-0.007)
1.368(-0.006)
1.017(0.011)
1.8650.973
1.871
O0.9750.957 1.761
0.957
O0.958
T11
0.958
T12
N
O
H3C
O
1.451(-0.008)
1.232(0.011)
1.390(-0.009)
1.375( 0 006)1 353
1.020(0.009)
1.901
0.972
N
O
H3C1.454
(-0.005)
1.222(0.001) 1.401
(0.002)
1.373( 0 008)
1.353( )
1.011(0.000)
N O
(-0.006)1.229
(0.011)
1.368(-0.013)
1.368(-0.006)
1.353(0.003)
1.024(0.018)
1.781
N O
(-0.008)1.233
(0.017)1.361
(-0.020)
1.372(-0.002)
(0.003)
1.034(0.028)
1.722
O O
( )
1.763
0.975
0.957 1.755 0.957
0.976O O
O
1.871
T111 T112T111
Figure 2.3: Equilibrium structures of thymine dihydrate and trihydrate optimizedby RI-MP2/cc-pVTZ. Bondlengths and changes in bond lengths due to microhy-dration are shown (in A).
the hydrogen bond between the N-H group of thymine and the oxygen of water is 0.028
A shorter and the hydrogen bond between C=O of thymine and the hydrogen of water
is 0.026 A shorter for RI-MP2 (1.871 and 1.903 A respectively) than for ωB97X-D
(1.899 and 1.929 A, respectively). Figs. 2.2 and 2.3 show the RI-MP2 ground states
geometries. The respective Cartesian geometries as well as ωB97X-D structures are
given in Supplementary Materials for Ref. 38.
24
N
O
H3C
1.198(-0.023)1.486
(0.030)1.391
(-0.009)
1 366 N
O
CH3O
1.201(-0.031)
1.490(0.048)
1.383(-0.005)
1.670( 0 226)
0.958(-0.013)
0.958(0.001)
1.044(0.023)
N
O
H3C
1.197(-0.024)
1.490(0.031)
1.391(-0.008)
1.365
1.013(0.002)
1.012(0.001)
N
N
O1.051
(0.023)
1.433(0.062)
1.192(-0.035)
1.404(0.052)
1.308(-0.064)
1.366(-0.009)
1 626
N
N
O1.015
(0.009)
1.446(0.063)
1.190(-0.025)
1.401(0.050)
1.312(-0.059)
1.357(-0.024)
(-0.226)
N O1.015
(0.023)
1.441(0.011)
1.187(-0.027)
1.402(0.052)
1.313(-0.032)
(-0.016)
2.764(0.893)
O1.626
(-0.245)
0.958(0.000)
0.961(-0.011)
T1 T2 and T3T
Figure 2.4: Equilibrium structures of ionized thymine and thymine monohydratesoptimized by ωB97X-D/cc-pVTZ. Bondlengths and changes in bond lengths due toionization are shown (in A).
The equilibrium structures of the cations were computed with ωB97X-D/cc-pVTZ
(see Figs. 2.4 and 2.5). This functional, when used with 6-311++G(3df,3pd) basis set,
was shown to describe geometries and binding energies of the weakly bound complexes
with mean absolute errors of 0.064 A and 0.22 kcal/mol, respectively26. For the ionized
thymine monohydrates, this functional (with the cc-pVTZ basis) yields structures that
are similar to those obtained with EOM-IP-CCSD/6-311+G(d,p), i.e., the mean absolute
errors are 0.01 A for the thymine moiety and 0.11 A for thymine-water hydrogen bond.
All IEs were calculated using EOM-IP-CCSD/cc-pVTZ at the equilibrium geome-
tries described above. The cc-pVTZ basis set provides a good balance between accu-
racy and computational efficiency. The first IE of thymine computed using EOM-
IP-CCSD with the extended cc-pVTZ basis [augmented by diffuse s and p functions
from 6-311++G(d,p) as was done in Ref. 39] is 9.20 eV, which is 0.07 eV higher than
the cc-pVTZ value. Zero point energy (ZPE) correction lowers AIEs of thymine and
thymine monohydrates (T1 and T2) by 0.08 eV. Thus, due to error cancellation, non
ZPE-corrected AIEs computed with cc-pVTZ are very close to the ZPE-corrected AIEs
obtained with the extended cc-pVTZ basis set.
25
O
O1 486
1.202(-0.030) 1.040 0 957
0.957O1.199(-0.023)
1 482 1.390
NH3C
O1.486(0.026)
1.383(-0.007)
1.359(-0.016)
1.196(-0.031)
1.401(0.048)
(0.019)1.688
0.957
NH3C
1 425
1.195(-0.034)
1.403(0.051)
1 307
1.482(0.027) (-0.010)
1.367(-0.008)
1.012(0.001)
N O
O
1.434(0.060)
1.308(-0.060)
1.049(0.032)
1.636 1.871
N O
O
1.084(0.060)
1.425(0.060)
1.307(-0.065)
1.486(-0.278)
0.983(0.008)
0.958
2.575(0.491)
O
O
0.9590.957
T12
O0.955(-0.002)
1.671(-0.090)
0.958(-0.017)
0.956(-0.001)
T11 0.958(-0.014) 0.957
(-0.001)
N
O
H3C
O
N
O
H3C1.480
(0.026)
1.200(-0.022) 1.393
(-0.008)
1.365( 0 008)
1.405( )
1.012(0.001)
1 402
1.203(-0.029)
1.483(0.032)
1.383(-0.007)
1 359
1.038(0.018)
1.703(-0.198)
( )
N ON O
(-0.008)1.201
(-0.032)1.416
(0.045)
1.307(-0.065)
(0.052)
1.167(0.133)
2.046 1.074(0.050)
1.429(0.061)
1.198(-0.031)
1.402(0.049)
1.307(-0.059)
1.359(-0.016)
2.277(0.496)
O OO OO
1.336
T111
1.517(-0.246)
0.955(-0.002)
0.981(0.006)
1.683(-0.072)
0.959(-0.017)
0.956(-0.001)
T112T111
Figure 2.5: Equilibrium structures of ionized thymine and thymine di- and trihy-drates optimized by ωB97X-D/cc-pVTZ. Bondlengths and changes in bond lengthsdue to ionization are shown (in A).
The charge distribution analysis were performed using Natural Bond Orbital Pack-
age (NBO, v. 5.0)40. All calculations were conducted using the Q-CHEM electronic
structure package41. Molecular structures, frequencies, and relevant total energies are
given in Supplementary Materials for Ref. 38.
26
2.2.2 Calculation of the Franck-Condon factors and PIE curves
Unambiguous comparison with the experimental PIE curves requires calculation of
FCFs. While in molecular systems (i.e., ionized NABs), FCFs can be reliably com-
puted using the double-harmonic approximation with Duschinsky rotations42, as was
done in Ref. 9, the calculations in clusters are more challenging due to large structural
relaxation of soft (and anharmonic) inter-fragment degrees of freedom. To correctly
describe these effects, we combine double-harmonic treatment of the thymine moiety
and water with a one-dimensional quantum treatment of the inter-fragment coordinate
assuming that the water-thymine and intramolecular thymine vibrations are uncoupled
and that the respective FCFs are multiplicative.
Using the ezSpectrum program43, we first compute FCFs for the thymine moiety
using double-harmonic approximation with Duschinsky rotations42 at the Cs geometry
using normal modes and frequencies for the non-planar structures with one hydrogen of
water out of the plane. The water molecule itself was excluded from this calculation and
only the geometry of the thymine moiety (from the monohydrate) was used. Duschinsky
rotations are important because the normal-mode overlap matrix for the neutral and the
ionized states is significantly non-diagonal. In these calculations, we used harmonic
frequencies and structures computed by ωB97X-D/cc-pVTZ for both the neutral and
the 1st ionized states of the monohydrates.
The effect of water-thymine degrees of freedom on FCFs is described by a one-
dimensional model, which takes into account anharmonicity and large structural relax-
ation. This treatment is similar to the intrinsic reaction coordinate connecting the initial
and final state. Water-thymine motion is defined by three coordinates: r, the distance
between the water oxygen and the nearest hydrogen in thymine, θ, the angle formed by
27
O
H3CN
3
N O
O
rθ Oθ
φ
Figure 2.6: Coordinates describing relative water-thymine motion.
the NH bond in thymine and the oxygen in water, and ϕ, the rotation of the water center-
of-mass relative to the axis defined by r (Fig. 2.6). In the neutral thymine monohydrate
(T1), these coordinates obtain the values r = 1.923 A, θ = 36.7◦, and ϕ = 40.6◦, while
in the cation they equal r = 1.668 A, θ = 1.6◦, and ϕ = 2.2◦. Along the simplest path,
each coordinate is described by a linear equation connecting the values in the neutral
and in the cation. This path is used to evaluate two potential surfaces, V(r), one with the
thymine held at its equilibrium neutral geometry and the second with thymine held at
its equilibrium cation geometry. The effective one-dimensional Hamiltonian describing
this motion is:
H =− 12m
∂
∂r− 1
2m∂2
∂r2 −1
2mr2∂2
∂θ2 −12I
∂2
∂ϕ2 +V (r), (2.2)
28
where m is the mass of water and I is the moment of inertia of water rotating in the plane
of the molecule. This equation was then solved to obtain vibrational eigenstates for the
water motion on the neutral and cation surfaces which, in turn, were used to compute
FCFs. Within the approximation that the vibrational mode corresponding to the water
motion is decoupled from the vibrational modes of the thymine, the energy associated
with the water-water vibrational transitions is additive to the thymine-only spectra and
the FCFs are multiplicative. Each peak appearing in the spectrum associated with the
thymine moiety thus has the spectrum for the water fragment superimposed on top of it.
This leads to both qualitative and quantitative changes in the theoretical spectrum, since
the peaks with the largest FCFs in the water vibrational motion are the 1←0 and 2←0
peaks.
2.2.3 Experimental details
The experiments were performed on a molecular beam apparatus coupled to a 3 meter
VUV monochromator on the Chemical Dynamics Beamline at the Advanced Light
Source (ALS). The thermal vaporization source has been described recently in a pub-
lication detailing the microsolvation of DNA bases6. The nozzle consisted of a 0.953
cm diameter disk (1 mm thick) with a 100 µm diameter center hole welded on to one
end of a closed stainless steel tube of 0.953 cm OD and 15.24 cm long. This front end
of the stainless steel tube contained thymine and could be heated to between 298 and
700 K with a cartridge heater mounted in an aluminum heating block. The temperature
of the tube was monitored with a thermocouple to the heating block. To produce the
water complexes, Ar carrier gas at 58.7 kPa was passed over a water reservoir held at
room temperature and directed into the stainless steel nozzle. The temperature utilized
for generating thymine vapor was 503 K.
29
100 150 200 250 3000
100
200
300
400
500
600
700
Cou
nts
a.u.
T2W4T2W3T2W2
T2WT2TW5
TW4
TW3
TW2
m/z
T
TW
Figure 2.7: Mass spectrum of microhydrated thymine recorded at a photon energyof 10 eV.
Shown in Figure 2.7 is a representative mass spectrum of microhydrated thymine
recorded at a photon energy of 10 eV. The main peak is thymine followed by thymine-
water clusters, where up to five waters clustered around thymine are detectable. Also
observed are the thymine dimer with up to four water clusters connected to the dimer.
The clusters are ionized by tunable synchrotron radiation in the 8.0-13.0 eV region,
and the ions are detected by a time-of-flight mass spectrometer. For each mass, the yield
of the ions is measured as a function of photon energy, which produces PIE spectra. The
typical step size for the PIE scans is 50 meV with a dwell time of 30 s at a repetition
rate of 10 kHz. The differentiation of the PIE curves, following the method used by
Berkowitz in interpreting the photoionization of methanol44, produces a spectrum sim-
ilar to a photoelectron spectrum from which information about vibrational progressions
and other electronic states can be extracted. The differentiation is performed numeri-
cally after taking a five points nearest-neighbor average to reduce the effects of noise in
the PIE. The accuracy of reported onset energies in the PIE spectra is 0.05 eV.
30
2.3 Results and Discussion
2.3.1 Ionization-induced geometry changes in thymine hydrates
We begin with an overview of the structures of thymine and thymine/water clusters
summarized in Figs. 2.2 and 2.3.
The minimum energy structures of the thymine monohydrates (see Fig. 2.1) are non-
planar with the hydrogen atom of water out of the plane of thymine (the dihedral angle
is 780 for T1). However, the energy difference between the planar (optimized with Cs
constraint) and non-planar structures is less than 0.5 kcal/mol. Moreover, the effect of
non-planarity on VIE is also small (about 0.02 eV). Thus, we employed planar (Cs)
geometries in all calculations of thymine monohydrates for computational efficiency.
The binding energy per hydrogen bond increases with addition of each water
molecule. Binding energies (non ZPE-corrected, De) are 11.3, 9.1, 8.9 kcal/mol for
the T1, T2, and T3 monohydrates, respectively. For the dihydrates they are 23.4 and
20.1 kcal/mol for T11 and T12, and for the trihydrates (T111 and T112) they are 32.8
and 31.0 kcal/mol. The optimized geometries reveal that the only structural parame-
ters affected by hydration are those of the thymine part which is in close proximity to
the water molecule (Figs. 2.2 and 2.3). The hydrogen bonding with water results in
an increase in the bond length of the N-H and C-O groups, and a decrease in the C-N
bond length. With the addition of each water molecule the induced structural changes
increase, with the largest changes in bond lengths being 0.011, 0.018 and 0.028 A for
the monohydrate, dihydrate and trihydrate, respectively.
The ionization-induced structural relaxation of thymine hydrates is much larger than
that of isolated thymine9. For example, the largest change in bond lengths of the thymine
moiety in clusters is 0.062 A, whereas for isolated thymine it is only 0.032 A. A possible
31
explanation is a large shift of water molecules towards the positively charged N-H group
and away from the negatively charged oxygen. This results in a shorter hydrogen bond
between the N-H group and oxygen of water (0.245 A for T1), and a longer hydrogen
bond between the C=O and the hydrogen of water (0.893 A for T1). As discussed below,
this large structural relaxation results in vanishing FCFs for the 0←0 transition.
2.3.2 Vertical ionization energies
The VIEs of all lowest ionized states summarized in Table 2.1 and Fig. 2.8 are affected
by water. The first VIE in all clusters is reduced relative to thymine, and the addition
of each water molecule leads to a roughly 0.1 eV drop in VIE (except for T11-T111);
however, the magnitude of the effect varies for different clusters. The changes in higher
VIEs also vary for different states and cluster structures from -0.24 to 0.74 eV. For
monohydrates, the largest change in the first VIE is 0.12 eV observed in T1.
32
9.13(0.961)
9.01(0.12; 0.960)
9.05(0.08; 0.961)
9.08(0.05; 0.960)
10.13 10.10 10.179.97
(0.16; 0.951)10.13(0.952)
10.52
10.10(0.03; 0.951)
10.51
10.17(-0.04; 0.951)
10.36(0.16; 0.957)
(0.16; 0.951)
10.34(0 18; 0 956)
, eV
10.52(0.957)
11.04(0.951)
10.51(0.01; 0.956)
11.10(-0.06; 0.951)
(0.16; 0.957)
10.87(0.17; 0.949)
(0.18; 0.956)
11.03(0.01; 0.951)
VIE
12.39(0.972)
( ; )
12.30(0.09; 0.962)
11.94(0.45; 0.965)
11.97(0.42; 0.946)
( )
12.67(0.939)
12.53(0.14; 0.939)
12.58(-0.19; 0.940)
12.63(-0.24; 0.923)
13.82(0.832)
13.70(0.12; 0.905)
13.60(0.22; 0.802)
13.55(0.27; 0.829)
Thymine T1 T2 T3
Figure 2.8: VIEs (eV) and the corresponding MOs of thymine and thymine-waterisomers, EOM-IP-CCSD/cc-pVTZ. Changes in VIEs due to microhydration andthe leading EOM-IP amplitude are given in parentheses.
33
Tabl
e2.
1:Ve
rtic
alan
dad
iaba
ticIE
s(e
V)
ofth
ymin
ean
dth
ymin
e-w
ater
clus
ters
com
pute
dby
EO
M-I
P-C
CSD
/cc-
pVT
Z.
Stat
eT
T-H
2OT
(H2O
) 2T
(H2O
) 3T
1T
2T
3T
11T
12T
111
T11
21
9.13
9.01
(0.1
2)9.
05(0
.08)
9.08
(0.0
5)8.
89(0
.24)
8.93
(0.2
0)8.
88(0
.25)
8.83
(0.3
0)2
10.1
310
.10(
0.03
)10
.17
(-0.
04)
9.97
(0.1
6)10
.10
(0.0
3)10
.15
(-0.
02)
10.0
3(0
.10)
10.0
8(0
.05)
310
.52
10.5
1(0
.01)
10.3
6(0
.16)
10.3
4(0
.18)
10.4
4(0
.08)
10.3
6(0
.16)
10.4
8(0
.04)
10.3
0(0
.22)
411
.04
11.1
(-0.
06)
10.8
7(0
.17)
11.0
3(0
.01)
11.0
4(0
.00)
10.9
2(0
.12)
11.0
8(-
0.04
)10
.88
(0.1
4)5
(H2O
)12
.39
12.3
0(0
.09)
11.9
4(0
.45)
11.9
7(0
.42)
11.9
3(0
.74)
11.9
3(0
.74)
11.9
711
.85
612
.67
12.5
3(0
.14)
12.5
8(-
0.19
)12
.63
(-0.
24)
12.3
8(0
.01)
12.2
1(0
.18)
12.1
811
.87
713
.82
13.7
0(0
.12)
13.6
0(0
.22)
13.5
5(0
.27)
13.5
0(0
.32)
13.5
2(0
.60)
12.3
112
.31
1stA
IE8.
908.
51(0
.39)
8.65
(0.2
5)8.
64(0
.26)
8.52
(0.3
8)8.
30(0
.60)
8.35
(0.5
5)8.
21(0
.79)
∆E
a0.
230.
500.
400.
440.
370.
630.
530.
62a
Rel
axat
ion
ener
gyfo
rthe
first
ioni
zed
stat
e,∆
E=V
IE-A
IE
34
The first six occupied molecular orbitals of thymine monohydrates and the four MOs
of di- and trihydrates are localized on either thymine or water. The shapes of these MOs
are almost the same as in bare thymine/water. The corresponding ionized states are of
Koopmans character, e.g., the leading R1 amplitude values are greater than 0.94 (Fig.
2.8). However, for the states with IEs close to water IEs, the respective MOs (e.g.,
the sixth orbitals of monohydrate, fifth orbital of dihydrate) become delocalized, and
the corresponding wave functions become multiconfigurational (there are several R1
amplitudes with values greater than 0.15).
2.3.3 The origin of IE changes
We considered several possible explanations for the observed changes of the VIE in
thymine clusters: the geometry change of thymine molecule in clusters, charge transfer
from thymine to water resulting in hole delocalization, and electrostatic (charge-dipole)
interaction between the ionized thymine moiety and water. Below we evaluate differ-
ent effects and conclude that the dominant contribution to the VIE changes is due to
electrostatics.
To estimate the effect of the change in the geometry, we computed IEs of bare
thymine at the equilibrium geometry of thymine in the T1 monohydrate. The first VIE
at this geometry is 9.16 eV, which is 0.03 eV higher than that of thymine at its own
equilibrium geometry (9.13 eV). Therefore the geometry change does not explain the
change of VIEs.
The degree of charge transfer between the thymine and water was evaluated using
the NBO analysis. We found that the distribution of the positive charge is consistent with
the shape of the corresponding Hartree-Fock orbitals. The hole is localized on thymine
and the maximum charge transfer in monohydrates is only 0.027 a.u. Moreover, there
35
0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024 0.026 0.028
-0.05
0.00
0.05
0.10
0.15
0.20
T1 T2 T3
ΔVIE
, eV
Δq(H2O)
Figure 2.9: VIEs versus the degree of charge transfer to water in different ionizedstates of the three thymine monohydrates.
0.15
0.10
0.05 , eV
0.00
ΔIE
-0.05
0.010 0.012 0.014 0.016 0.018 0.020 0.022 0.024 0.026 0.028
Δq(H2O)q( 2 )
Figure 2.10: Changes in VIEs versus the degree of charge transfer to water indifferent ionized states of T1.
36
is no correlation between charge transfer and the change in the IE (Fig. 2.9); in fact, for
T1 there is even the opposite dependence, the larger the charge transfer the smaller the
change in the IE, as shown in Fig. 2.10.
To calculate the charge-dipole interaction energy, we employed a simple classical
model following the analysis in Ref. 7. The energy was calculated as the sum of interac-
tion energies between the dipole of water and the partial (NBO) charges on the thymine
atoms using the following equation:
E =−∑i
µ ·qi
r2i
cosΘ (2.3)
where µ is the dipole moment of water, qi is the charge of the ith thymine atom calculated
by the NBO analysis, r is the distance between the atom and the center of the dipole,
and Θ is the angle between the dipole vector and the vector connecting the center of the
dipole and the atom.
0 25
0.20
0.25
0.15
0 05
0.10
E, e
V
T1 T2T3
0.00
0.05
ΔIE T3
-0.05
-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-0.10
Δ E VΔ Ecd, eV
Figure 2.11: Changes in VIEs versus charge-dipole interaction energy between thecharges on thymine and the dipole moment of water molecule.
37
The ionization introduces a net positive charge on the thymine resulting in a new
charge distribution. This leads to the change in electrostatic interaction energy, which
is calculated as the difference of the interaction energy in the neutral and the ionized
states. Fig. 2.11 shows computed IEs for different states and structures versus these
charge-dipole interaction energies. There is a strong correlation between the change in
the electrostatic interaction energy and the change in VIE.
We conclude that the change in VIE is explained by a simple charge-dipole interac-
tion between the partial charges on thymine and the water dipole, which either stabilize
or destabilize the ionized states relative to the neutral ground state.
2.3.4 Adiabatic ionization energies and FCFs
Due to large geometry relaxations of the ionized states (see Figs. 2.4 and 2.5), the
AIEs are significantly lower that VIEs. The relaxation energies for different structures
are in the range of 0.4-0.6 eV, which is considerably larger than the relaxation energy of
bare thymine (0.23 eV)9. The structures that undergo greater structural relaxation in the
ionized states are characterized by a larger relaxation energy. Compare, for example,
T11 and T12 (Fig. 2.5). The AIEs of the clusters are considerably lower than that of
bare thymine and are reduced by about 0.1 eV with addition of each water molecule.
To compare the calculated AIEs with the experimental PIE onsets, we calculated
FCFs for T1 and T2, as described in Section 2.2.2. The computed intensities are convo-
luted by a Gaussian with width of 0.05 eV which corresponds to the experimental width,
and are shown in Fig. 2.12 and 2.13. As one can see, the relaxation in the water-thymine
degrees of freedom affects the FCFs resulting in negligible intensity for the 0←0 tran-
sitions and shifting the spectra to higher energies. The resulting PIE curves obtained
by integration of FCFs are shown in Fig. 2.14. The computed PIE onsets are shifted by
38
8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.5
1.0
0.0
0.1
0.2
0.3
Energy, eV
overall
Inte
nsity
, a.u
. thymine
water-thymine motion
Figure 2.12: Calculated FCFs for the first ionized state of T1 (lower panel). Upperpanel: FCFs due to water-thymine motion (undefined scale); middle panel: FCFsdue to thymine moiety.
0.03 eV to higher energies relative to the 0←0 transitions. Moreover, the intensities at
the computed onsets are so small that the apparent onsets are shifted by about 0.1 eV to
higher energies.
39
8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4
0.0
0.2
0.4
0.6
0.8
1.0
0.00
0.05
0.10
0.15
0.0
0.1
0.2
0.3
0.4
Inte
nsity
, a.u
.
Energy, eV
overall
thymine
water-thymine motion
Figure 2.13: Calculated FCFs factors for the first ionized state of T2 (lower panel).Upper panel: FCFs due to water-thymine motion (undefined scale); middle panel:FCFs due to thymine moiety.
2.3.5 Theory versus experiment
Figs. 2.15 and 2.16 show differentiated and raw PIE spectra for T, T(H2O), T(H2O)2,
T(H2O)3 as well as the computed VIEs and AIEs for different structures. The com-
puted IEs for different structures are summarized in Table 2.1. For bare thymine, the
experimental and computed IEs are in excellent agreement9.
40
8.4 8.5 8.6 8.7 8.8 8.9
-5000
5001000150020002500300035004000450050005500600065007000
0 → 0 T20 → 0 T1In
tens
ity, a
.u.
T1 T2 raw experiment smoothed exp.
Energy, eV
Figure 2.14: The experimental (raw and smoothed data, and error bars) and cal-culated (T1 and T2) PIE curves. The respective adiabatic 0←0 transitions are alsoshown.
Our present experimental results from the differentiated PIE for thymine are in
agreement with the previous experimental results and calculations9. The onset is
8.85±0.05 eV. The small peak at the onset arising at 8.80 eV could come from frag-
mentation of higher clusters. The two peaks at 11.8 eV and 12.2 eV do not have theoret-
ical counterparts (Fig. 2.15, T). The peak at 11.8 eV is an experimental artifact because
argon used in the gas filter to remove higher harmonics in the incident radiation has
absorption lines at 11.62 eV and 11.83 eV. These lines strongly perturb PIE intensities
and were removed from the experimental data.
For thymine monohydrates, the experimental PIE curve onset at 8.60 eV is in per-
fect agreement with the calculated AIEs for T2 (8.65 eV) and T3 (8.64 eV), but 0.09
eV higher that the calculated AIE for T1 (8.51 eV) (Fig. 2.16, T-H2O). This discrep-
ancy is due to the unfavorable FCFs for T1 ionization obscuring the onset, as evidenced
by the simulated PIE curves (computed by integrating Franck-Condon progressions as
41
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.50.0
1.0
2.0
T
Inte
nsity
, a.u
.
Photon energy, eV
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.50.0
0.2
0.4
0.6
0.8
1.0
1.2
exp. DPIE T1 T2 T3
T-H2O
Inte
nsity
, a.u
.
Photon energy, eV
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.50.0
0.1
0.2
0.3
0.4
0.5 exp. DPIE T11 T12
T(H2O)2
Inte
nsity
, a.u
.
Photon energy, eV
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.50.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16 exp. DPIE T112 T111
T(H2O)3
Inte
nsity
, a.u
.
Photon energy, eV
Figure 2.15: The differentiated PIE (DPIE) curves and calculated VIEs for thymineand thymine clusters with one, two, and three water molecules.
described in Section 2.3.4) shown in Fig. 2.14. We used our best estimate of adiabatic
energies, i.e., including the ZPE (-0.08 eV) and extended basis (+0.07 eV) corrections.
The calculated onsets are 8.53 eV and 8.70 eV for T1 and T2. They are shifted from
the respective AIEs by 0.03 eV (AIE is 8.50 eV) and 0.06 eV (AIE is 8.64 eV). The
apparent onsets are shifted even more (by ≈ 0.1 eV), as the intensity of the calculated
PIE for T1 below 8.6 eV is significantly smaller than at higher energies which makes it
difficult to observe low energy signal in the experiment (8.60 eV). Overall, the experi-
mental onset at 8.60 eV agrees very well with the computed PIE curves for T1 and T2
42
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.50
1
2
3
4
5
6 T
Inte
nsity
, a.u
.
Photon energy, eV
8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.20.00
0.01
0.02
0.03
0.04
0.05
Inte
nsity
, a.u
.
Photon energy, eV
8.85 eV
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.50.0
0.5
1.0
1.5
2.0
2.5
3.0
8.60 eV
T-H2O
Inte
nsity
, a.u
.
Photon energy, eV
T2T3
T1 T2T3
T1
8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.20.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
T2T3
Inte
nsity
, a.u
.
Photon energy, eV
T1 T2T3T1
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.50.0
0.2
0.4
0.6
0.8
1.0
T11
T(H2O)2
Inte
nsity
, a.u
.
Photon energy, eV
T12
T12T11
8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.00.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
0.020
8.55 eV
Inte
nsity
, a.u
.
Photon energy, eV
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.50.00
0.05
0.10
0.15
0.20
0.25
0.30
T111
8.40 eV
T(H2O)3
Inte
nsity
, a.u
.
Photon energy, eV
T112
T111T112
8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.90.000
0.001
0.002
0.003
0.004
0.005
Inte
nsity
, a.u
.
Photon energy, eV
Figure 2.16: The PIE curves and calculated AIEs for thymine and thymine clusterswith one, two, and three water molecules.
and the AIE of 8.56 eV (T1). We also note that the experimental PIE rises much faster
after the calculated T2 PIE onset (8.70 eV).
The VIEs for thymine monohydrate are in good agreement with the peaks maxima
in the experimental differentiated PIE curves, which correspond to experimental VIEs
(Fig. 2.15, T-H2O). From the comparison of the experimental differentiated PIE and
calculated VIEs, we conclude that all three isomers may be present in the beam because
for evry calculated VIE there is a peak in diffirentiated PIE that could be assigned to this
VIE.
43
For thymine dihydrate, the experimental onset at 8.55 eV is in good agreement with
the calculated AIE for T11 (8.52 eV) [see Fig. 2.16, T(H2O)2]. The calculated AIE for
the T12 structure is 8.30 eV, which is 0.25 eV lower than the experimental onset. A
possible explanation is that T12 undergoes a larger geometry relaxation upon ionization
than T11. The VIEs of T11 and T12 are very close (8.89 and 8.93 eV respectively), but
T12 has a much larger relaxation energy (0.63 eV versus 0.37 eV for T11). This can
lead to a small FCF for T12, so it is not clear if these isomers can be seen at the onset.
The sharp rise of the experimental PIE curve suggests more favorable FCFs, as in T11.
Finally, T12 is 3.3 kcal/mol higher in energy than T11 and is not likely to be populated
much in the molecular beam.
The theoretical VIEs for both thymine dihydrate structures agree well with the exper-
imental differentiated PIE peaks [Fig. 2.15, T(H2O)2]. There are a few experimental
peaks that do not have theoretical VIE counterparts suggesting that more than the two
T(H2O)2 isomers considered here are present in the beam.
The theoretical AIE for thymine trihydrate T111 is 8.35 eV, which is close to the
experimental onset at 8.40 eV [(Fig. 2.16, T(H2O)3]. The theoretical AIE for the T112
structure is 8.21 eV, which is 0.19 eV lower than the experimental value. Possible expla-
nations of the difference are unfavorable FCFs and smaller concentration of T112 in the
molecular beam relative to T111. The theoretical VIEs for both trihydrates are in good
agreement with the experimental PIE curve, which can be seen in Fig. 2.15, T(H2O)3.
As suggested for T(H2O) and T(H2O)2, there could also be minor contributions from
other structures which are not considered here.
44
2.4 Conclusions
We have presented a combined theoretical and experimental study of the ionized clusters
of thymine with one, two and three water molecules. The PIE onsets are 8.85±0.05 eV,
8.60±0.05 eV, 8.55±0.05 eV, 8.40±0.05 eV for bare thymine, thymine monohydrate,
dihydrate and trihydrate, respectively. The computed EOM-IP-CCSD AIEs are 8.90 eV,
8.51-8.64 eV, 8.30-8.52 eV and 8.21-8.35 eV for bare thymine, thymine monohydrates,
dihydrates and trihydrates, respectively.
All thymine microhydrates undergo significant structural relaxation upon ioniza-
tion, which results in higher relaxation energies for microhydrates than for the bare
thymine molecule, e.g., the computed relaxation energies for thymine, T-H2O, T(H2O)2
and T(H2O)3 are 0.23, 0.40-0.50, 0.37-0.63, 0.53-0.62 eV, respectively.
We found that due to the large structural relaxation in hydrated species, the FCFs for
the 0←0 transitions are small thus shifting the apparent onsets to higher energy (0.03-
0.10 eV). The agreement between theoretical and measured PIEs is good, however, due
to unfavorable FCFs the PIE onsets overestimate the AIEs. The theoretical VIEs are in
good agreement with the maxima of the differentiated PIE curves.
There is a significant effect of microhydration on the AIE of thymine. Addition
of the first water molecule decreases the AIE as much as 0.39 eV, the second water
molecule decreases the AIE as much as 0.35 eV, and the third one — as much as 0.31
eV. VIEs also are affected by the addition of water. The effect is different for different
structures and ionized states. The change of VIE depends on the shape of the corre-
sponding MOs and the position of the water and is dominated by electrostatic (charge-
dipole) interactions. We found that there is no significant charge transfer from thymine
45
to water, and that the changes of VIEs due to hydration-induced structural changes in
the thymine moiety are small.
46
2.5 Chapter 2 references
[1] E. Cauet, M. Valiev, and J.H. Weare. Vertical ionization potentials of nucleobasesin a fully solvated DNA environment. J. Phys. Chem. B, 114:5886–5894, 2010.
[2] P. Slavıcek, B. Winter, M. Faubel, S.E. Bradforth, and P. Jungwirth. Ioniza-tion energies of aqueous nucleic acids: Photoelectron spectroscopy of pyrimidinenucleosides and ab initio calculations. J. Am. Chem. Soc., 131:6460–6467, 2009.
[3] A.A. Golubeva and A.I. Krylov. The effect of π-stacking and H-bonding on ion-ization energies of a nucleobase: Uracil dimer cation. Phys. Chem. Chem. Phys.,11:1303–1311, 2009.
[4] A.A. Zadorozhnaya and A.I. Krylov. Ionization-induced structural changes inuracil dimers and their spectroscopic signatures. J. Chem. Theory Comput., 6:705–717, 2010.
[5] A.A. Zadorozhnaya and A.I. Krylov. Zooming into pi-stacked manifolds of nucle-obases: Ionized states of dimethylated uracil dimers. J. Phys. Chem. A, 114:2001–2009, 2010.
[6] L. Belau, K.R. Wilson, S.R. Leone, and M. Ahmed. Vacuum-ultravioled photoion-ization studies of the microhydration of DNA bases (guanine, cytosine, adenine,and thymine). J. Phys. Chem. A, 111:7562–7568, 2007.
[7] K.B. Bravaya, O. Kostko, M. Ahmed, and A.I. Krylov. The effect of π-stacking,h-bonding, and electrostatic interactions on the ionization energies of nucleic acidbases: Adenine-adenine, thymine-thymine and adenine-thymine dimers. Phys.Chem. Chem. Phys., 12:2292–2307, 2010.
[8] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed. Ionization of cytosinemonomer and dimer studied by VUV photoionization and electronic structure cal-culations. Phys. Chem. Chem. Phys., 12:2860–2872, 2010.
[9] K.B. Bravaya, O. Kostko, S. Dolgikh, A. Landau, M. Ahmed, and A.I. Krylov.Electronic structure and spectroscopy of nucleic acid bases: Ionization energies,ionization-induced structural changes, and photoelectron spectra. J. Phys. Chem.A, 114:12305–12317, 2010.
[10] S.K. Kim, W. Lee, and D.R. Herschbach. Cluster beam chemistry: Hydration ofnucleic acid bases; Ionization potentials of hydrated adenine and thymine. J. Phys.Chem., 100:7933–7937, 1996.
47
[11] K.-W. Choi, J.-H. Lee, and S.K. Kim. Ionization spectroscopy of a DNA base:Vacuum-ultraviolet mass-analyzed threshold ionization spectroscopy of jet-cooledthymine. J. Am. Chem. Soc., 127:15674–15675, 2005.
[12] D.M. Close, C.E. Crespo-Hernandez, L. Gorb, and J. Leszczynski. Influence ofmicrohydration on the ionization energy thresholds of thymine: Comparisons oftheoretical calculations with experimental values. J. Phys. Chem. A, 110:7485–7490, 2006.
[13] D.M. Close, C.E. Crespo-Hernandez, L. Gorb, and J. Leszczynski. Theoreticalelucidation of conflicting experimental data on vertical ionization potentials ofmycrohydrated thymine. J. Phys. Chem. Lett., 112:4405–4409, 2008.
[14] V.R. Smith, E. Samoylova, H.H. Ritze, W. Radloff, and T. Schultz. Excimer statesin microhydrated adenine clusters. Phys. Chem. Chem. Phys., 12:9632–9636,2010.
[15] A.L. Sobolewski and W. Domcke. Computational studies of aqueous-phase pho-tochemistry and the hydrated electron in finite-size clusters. Phys. Chem. Chem.Phys., 9:3818–3829, 2007.
[16] A. L. Sobolewski, W. Domcke, C. Dedonder-Lardeuxc, and C. Jouvet. Excited-state hydrogen detachment and hydrogen transfer driven by repulsive 1πσ∗ states:A new paradigm for nonradiative decay in aromatic biomolecules. Phys. Chem.Chem. Phys., 4:1093–1100, 2002.
[17] A.L. Sobolewski and W. Domcke. Photoinduced electron and proton transfer inphenol and its clusters with water and ammonia. J. Phys. Chem. A, 105:9275–9283,2001.
[18] H.-H. Ritze, H. Lippert, E. Samoylova, V.R. Smith, I.V. Hertel, W. Radloff, andT. Schultz. Relevance of πσ∗ states in the photoinduced processes of adenine,adenine dimer, and adeninewater complexes. J. Chem. Phys., 122:224320, 2005.
[19] Y. He, C. Wu, and W. Kong. Photophysics of methyl-substituted uracils andthymines and their water complexes in the gas phase. J. Phys. Chem. A, 108:943–949, 2004.
[20] M.K. Shukla and J. Leszczynski. Interaction of water molecules with cytosinetautomers: An excited-state quantum chemical investigation. J. Phys. Chem. A,106:11338–11346, 2002.
[21] A. Yoshikawa and S. Matsika. Excited electronic states and photophysics of uraciland water complexes. Chem. Phys., 347:393–404, 2008.
48
[22] C.M. Marian, F. Schneider, M. Kleinschmidt, and J. Tatchen. Electronic excita-tion and singlet-triplet coupling in uracil tautomers and uracil-water complexes - aquantum chemical investigation. Eur. Phys. J. D, 20:357–367, 2002.
[23] P.A. Pieniazek, S.A. Arnstein, S.E. Bradforth, A.I. Krylov, and C.D. Sherrill.Benchmark full configuration interaction and EOM-IP-CCSD results for proto-typical charge transfer systems: Noncovalent ionized dimers. J. Chem. Phys.,127:164110, 2007.
[24] A.I. Krylov. Equation-of-motion coupled-cluster methods for open-shell and elec-tronically excited species: The hitchhiker’s guide to Fock space. Annu. Rev. Phys.Chem., 59:433–462, 2008.
[25] J.-D. Chai and M. Head-Gordon. Systematic optimization of long-range correctedhybrid density functionals. J. Chem. Phys., 128:084106, 2008.
[26] J.-D. Chai and M. Head-Gordon. Long-range corrected hybrid density function-als with damped atom-atom dispersion interactions. Phys. Chem. Chem. Phys.,10:6615–6620, 2008.
[27] D. Sinha, D. Mukhopadhyay, and D. Mukherjee. A note on the direct calculation ofexcitation-energies by quasi-degenerate MBPT and coupled-cluster theory. Chem.Phys. Lett., 129:369–374, 1986.
[28] S. Pal, M. Rittby, R.J. Bartlett, D. Sinha, and D. Mukherjee. Multireferencecoupled-cluster methods using an incomplete model space — application toionization-potentials and excitation-energies of formaldehyde. Chem. Phys. Lett.,137:273–278, 1987.
[29] J.F. Stanton and J. Gauss. Analytic energy derivatives for ionized states describedby the equation-of-motion coupled cluster method. J. Chem. Phys., 101(10):8938–8944, 1994.
[30] M. Nooijen and R.J. Bartlett. Equation of motion coupled cluster method for elec-tron attachment. J. Chem. Phys., 102:3629–3647, 1995.
[31] P.A. Pieniazek, S.E. Bradforth, and A.I. Krylov. Charge localization and Jahn-Teller distortions in the benzene dimer cation. J. Chem. Phys., 129:074104, 2008.
[32] C.M. Oana and A.I. Krylov. Dyson orbitals for ionization from the ground andelectronically excited states within equation-of-motion coupled-cluster formalism:Theory, implementation, and examples. J. Chem. Phys., 127:234106, 2007.
[33] P.A. Pieniazek, A.I. Krylov, and S.E. Bradforth. Electronic structure of the benzenedimer cation. J. Chem. Phys., 127:044317, 2007.
49
[34] P.A. Pieniazek, J. VandeVondele, P. Jungwirth, A.I. Krylov, and S.E. Bradforth.Electronic structure of the water dimer cation. J. Phys. Chem. A, 112:6159–6170,2008.
[35] P.A. Pieniazek, E.J. Sundstrom, S.E. Bradforth, and A.I. Krylov. The degree ofinitial hole localization/delocalization in ionized water clusters. J. Phys. Chem. A,113:4423–4429, 2009.
[36] E. Kamarchik, O. Kostko, J.M. Bowman, M. Ahmed, and A.I. Krylov. Spectro-scopic signatures of proton transfer dynamics in the water dimer cation. J. Chem.Phys., 132:194311, 2010.
[37] J. Rejnek, M. Hanus, M. Kabelac, F. Ryjek, and P. Hobza. Correlated ab initiostudy of nucleic acid bases and their tautomers in the gas phase, in a microhydratedenvironment, and in aqueous solution. Part 4. Uracil and thymine. Phys. Chem.Chem. Phys., 7:2006–2017, 2005.
[38] K. Khistyaev, K.B. Bravaya, E. Kamarchik, O. Kostko M. Ahmed, and A.I. Krylov.The effect of microhydration on ionization energies of thymine. Faraday Discuss.,150:313–330, 2011.
[39] A. Landau, K. Khistyaev, S. Dolgikh, and A.I. Krylov. Frozen natural orbitalsfor ionized states within equation-of-motion coupled-cluster formalism. J. Chem.Phys., 132:014109, 2010.
[40] E.D. Glendening, J.K. Badenhoop, A.E. Reed, J.E. Carpenter, J.A. Bohmann, C.M.Morales, and F. Weinhold. NBO 5.0. Theoretical Chemistry Institute, Universityof Wisconsin, Madison, WI, 2001.
[41] Y. Shao, L. Fusti-Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown,A.T.B. Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neill, R.A. Distasio Jr,R.C. Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. VanVoorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P. Maslen, P.P. Koram-bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen,A. Dreuw, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S.Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z.Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee, J.Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. WoodcockIII, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel,W.J. Hehre, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon.Advances in methods and algorithms in a modern quantum chemistry programpackage. Phys. Chem. Chem. Phys., 8:3172–3191, 2006.
50
[42] R. Berger, C. Fischer, and M. Klessinger. Calculation of the vibronic fine structurein electronic spectra at higher temperatures 1. Benzene and Pyrazine. J. Phys.Chem. A, 102:7157–7167, 1998.
[43] V.A. Mozhayskiy and A.I. Krylov.ezSpectrum, http://iopenshell.usc.edu/downloads/.
[44] J. Berkowitz. Photoionization of CH3OH, CD3OH, and CH3OD: Dissociative ion-ization mechanisms and ionic structures. J. Chem. Phys., 69:3044–3054, 1978.
51
Chapter 3: The effect of
microhydration on proton transfer in
1,3-dimethyluracil and
1,3-dimethyluracil dimers
3.1 Introduction
Excited-state proton transfer is ubiquitous in chemistry1–3 and biology, occurring, for
example, in photoactive proteins such as green fluorescent4 and photoactive yellow pro-
teins5. In DNA, excited-state proton transfer between the nucleobases is a pathway
contributing to photoprotection6, 7. The driving force for excited-state proton transfer in
DNA is the increased acidity of electronically excited nucleobases. Likewise, oxidized
nucleobases, in which a valence electron is completely removed, also exhibit enhanced
acidity leading to PT between the strands of DNA7 and competes with electron hole
(positive charge) migration along the strands8. Studies of isolated model systems, such
as clusters of nucleobases9, 10, reveal that ionization-induced PT is very facile, even
in systems with no h-bonds such as the methylated π-stacked uracil dimer10. Elec-
tronic structure calculations show that ionization-induced PT between nucleobases is
52
endothermic in the neutral ground state (e.g., 0.8 eV uphill in AT), while it is exother-
mic in ionized species by 0.4-0.8 eV. Furthermore, ionization-induced PT in h-bonded
pairs is barrierless suggesting a high efficiency for this process. Interestingly, even in
π-stacked systems that have no h-bonds, PT is only slightly endothermic and involves a
moderate barrier (0.2 eV in methylated uracil dimer); consequently, this channel opens
up very close to the ionization threshold. A very recent study11 of one-electron oxida-
tion of DNA in solution has found that the initial steps involve proton transfer from a
methyl group of thymine; thus, providing experimental evidence of the facile PT from
non-hydrogen bonded moieties in realistic environments.
Water is believed to be instrumental for PT in biological systems12, such as in water-
filled ion channels, as well as through interfaces, membranes and in aerosols13. The
ability of water to form so-called “water wires” facilitating a relay-type transport of
protons, the Grotthuss mechanism, is essential in all these processes14, 15. The proton-
coupled electron transfer in DNA also involves water wires11. Notwithstanding the
importance of water-mediated ground- and excited-state PT, these processes are not well
understood, and only a few studies have emerged to shed light on the underlying mech-
anistic details and dynamics. For example, a recent study of small NO+(H2O)n clusters
investigated how the shape of h-bonded network controls proton-coupled water activa-
tion in HONO formation in the ionosphere16. Sequential PT through water bridges in
acid-base reactions has been studied by time-resolved experiments in which the reaction
has been initiated by an optical trigger exciting the photoacid17. Resonant ionization
spectroscopy of gas-phase h-bonded clusters was employed to investigate proton versus
hydrogen transfer pathways18. Various experimental techniques, most notably ion based
infrared spectroscopy, have been used to quantify important energetics and dynamics of
ionization-induced PT, and the catalytic action of solvating waters on tautomerization
53
equilibria via PT19–22. However a detailed understanding of the reaction pathways and
directionality of PT in model systems, let alone in real biological and chemical systems
remains elusive.
In this work, we report that water has a dramatic effect on the PT in ionized species.
We focus on methylated uracil clusters, capitalizing on our previous experience with this
model system and absence of low energy tautomers10, 23; however, similar effects were
also observed in microhydrated thymine species. We consider 1,3-dimethyluracil (mU,
structure shown in Fig. 3.4) and its deuterated analog, d6-1,3-dimethyluracil (DmU).
Mass spectrometry coupled with tunable VUV radiation molecular beam experiments
show that microhydration changes the branching ratio between different relaxation chan-
nels and entirely shuts down PT between the bases. Instead, a new pathway opens up,
where protonated nucleobases are produced via PT from the ionized water molecule
and elimination of the hydroxyl radical. Electronic structure calculations reveal that the
shape of the potential energy profile along the PT coordinate depends strongly on the
character of the molecular orbital from which the electron is removed, i.e., the PT from
water to nucleobases becomes barrierless upon access of an ionized state localized on
water. The computed energetics of PT is in excellent agreement with the experimental
appearance energies. We also note that the possible adiabatic processes, which become
energetically accessible at lower energies, are not efficient. Thus, PT is controlled elec-
tronically, by the character of the ionized state, rather than statistically, by simple energy
considerations.
All experimental data presented in this chapter were obtained by Dr. Musahid
Ahmed group from Lawrence Berkeley National Laboratory. Ananlysis of the raw expe-
rimantal data was done jointly by me and Dr. Musahid Ahmed.
54
3.2 Experimental details
1 Experimental results
The experiments were performed on a molecular beam apparatus coupled to a 3 meter
VUV monochromator on the Chemical Dynamics Beamline at the Advanced Light Source. The
experimental apparatus is described in Fig. S1. To generate monomers and dimers in a
supersonic jet expansion, a small sample is placed in a thermal vaporization source ( 3/8" tube
with 100 µm orifice) and heated to generate sufficient vapor pressure. U and 1,3-mU from
Sigma-Aldrich where heated to 320oC and 112oC, respectively. Argon gas at 220 Torr carries the
vapors through the orifice and passes a 2 mm skimmer to produce a molecular beam at the
interaction region of a reflectron mass spectrometer (R. M. Jordan) where it is ionized by the
VUV light. The rotational and vibrational temperature of the molecular beam is calculated to be
Trot 7 K and Tvib<50 K compared to the molecular beam results of Amirav et, al.1 For the
effusive beam the sample is placed in a heated oven attached to the repeller plate of the mass
spectrometer. Since the sample is about 5 mm from the ionization region of the mass
spectrometer, sufficient vapor pressure was reached at much lower sample temperatures; 100oC
and 35oC, for U and 1,3-mU respectively. The vapors then pass through a 1 mm orifice in the
repeller plate to reach the interaction region of the mass spectrometer where they are interrogated
by the light.
Figure S1: Schematic of experimental apparatus.
Page | 2
Figure 3.1: Schematic of experimental apparatus.
The experiments were performed on a molecular beam apparatus24 coupled to a
3 meter VUV monochromator on the Chemical Dynamics Beamline at the Advanced
Light Source by our collaborators from Musahid Ahmed group from Lawrence Berke-
ley National Laboratory. The experimental apparatus is described in Fig. 3.1. To gen-
erate monomers and dimers in a supersonic jet expansion, a small sample is placed in
a thermal vaporization source (3/8” tube with 100 µm orifice) and heated to generate
sufficient vapor pressure.
Argon gas at 600 Torr was bubbled through water (D2O) and then passed over the
sample vapors (1,3-mU from Sigma-Aldrich, at 112 oC) before expanding to vacuum
through a 100 µm orifice and a 2 mm skimmer (1 cm downstream) to produce a molecu-
lar beam at the interaction region of a reflectron mass spectrometer (R. M. Jordan) where
it is ionized by the VUV light. As the synchrotron light is quasi-continuous (500 MHz),
55
pulsing the electrical fields of the ion optics forms the ion packet in the mass spectrom-
eter. Measurements are taken at photon energies between 8 eV and 12 eV with a step
size of 50 meV. The ion signals from the microchannel plate detector are collected with
a multichannel-scalar card (FAST Comtec 7889) and accumulated over multiple (e.g.
300,000) sweeps at each point of the scan24. We repeated the experiments with H2O
vapors and d6-1,3-mU, the latter is unavailable commercially, and therefore it was syn-
thesized according to the procedure developed by Davidson and Baudisch (Davidson
and Baudisch 1926) and we described in detail in our previous paper10.
Figure 3.2: Mass spectra of hydrated (with H2O) mU and its dimer using 12 eVphotons with different backing pressure and temperature.
A judicious combination of experimental source conditions (backing pressure and
reservoir heater temperature) allowed us to vary the population of dimethyl uracil
monomers, dimers, and their microhydrated clusters with up to 7 water molecules in
the molecular beam (Fig. 3.2). The origin of transferred proton is determined by using
various combinations of deuterated and non-deuterated species, such as DmU-H2O ver-
sus mU-D2O.
56
100 200 300 400 500 600 700 800
5
10
15
20
25
30
35
Perc
en
t fr
om
all
ura
cil
sig
na
ls, %
Pressure (Torr)
All hydrated forms of mU dimer
(mU)2
+
All forms of mU dimer
Figure 3.3: The percentage of different dimer forms relative to the all forms of mUpresent in the beam. The percentage is calculated as the ratio between the signal ofthe indicated form and the signal of all forms of mU present in the beam.
Fig. 3.3 shows the percentage of different dimer forms of mU relative to all forms
of mU present in the beam. The percentage of all (mU)2 is roughly constant beyond
250 Torr, with the value above 25%. However, the percentage of bare mU dimers sig-
nificantly decreases, while the percentage of the hydrated mU dimers increases. Thus,
increased pressure does not inhibit the formation of the mU dimer, rather, it increases
its hydration. Higher mU clusters (trimers, etc) are not present in the beam in any sig-
nificant amount according to the low signal of the respective m/z.
The structures of the representative isomers of mU and its dimer hydrated with one
or two water molecules are shown in Fig. 3.4. Because of methylation, only uracil’s
oxygens, O(mU) are available for h-bonding. Consequently, in mono-hydrated struc-
tures, water acts as a proton donor. The H(H2O). . .O(mU) bond length are 1.87 A and
1.80 A in mU-H2O and (mU)2-H2O, respectively. The second water molecule forms
57
T
backin
g
pre
ssure
T
1.87
2.37
1.781.80
2.16
3.41
3.44
3.32 3.46
3.46 3.44
1.82
1.93
2.03
1.80
2.48
Figure 3.4: Structures of 1,3-dimethyluracil and its dimer hydrated with one or twowater molecules. In all structures, water acts as a proton donor. Hydration of thedimer does not lead to considerable changes in the relative position of the two mUmoieties, e.g., the distances between C=O and C-CH3 groups in dry and hydrated(mU)2 clusters are around 3.3-3.5 A. Temperature increase results in higher con-centration of mU clusters, whereas backing pressure controls degree of hydration.
an h-bond with the first water molecule in mU-(H2O)2. In hydrated (mU)2, the second
water forms an h-bond with the second uracil ring.
58
Previously10, we demonstrated that PT between the bases in mU dimers occurs from
a methyl group. Thus, the following PT reactions are possible in ionized (mU)2(D2O)
clusters:
(mU)2(D2O)+→ (mU)2D++OD→ mUD++mU +OD (3.1)
(mU)2(D2O)+→ (mU)2H++D2O→ mUH++mU +D2O (3.2)
Likewise, in (mU)n(D2O)m clusters, the appearance of protonated species is due to the
PT between the bases, whereas the deuteron transfer will signify PT from the solvent
to uracil. By considering the ratios of the respective m/z peaks, one can quantify the
efficiency of these competing PT channels.
Fig. 3.5A shows a VUV single photon ionization mass spectrum of the molecular
beam with ion signals corresponding to the mU monomer (at m/z 140), dimer (at m/z
280), and their clusters with D2O. The inset in Fig. 3.5A shows an enlarged portion of
the spectrum around m/z 180 where the main feature corresponds to the mU(D2O)2 ion,
a cluster of one mU and two deuterated waters. The two adjacent smaller peaks (at m/z
N+1 and N+2, marked by solid and dashed arrows, respectively, where N=180) arise
either due to the natural isotope abundance (13C) or from protonated/deuterated species.
As discussed below, similar spectra were obtained for the DmU-H2O mixture. The iso-
topes account for 7.5 % and 1 % of the peaks at m/z 181 and m/z 182, respectively; sim-
ilar values are obtained for the other hydrated species. Contrary to the PT yield, the nat-
ural isotope contributions do not depend on the photon energies, thus, the energy depen-
dence of the ratio between N+1 and N+2 peaks to the parent peak [N=180 for mU(D2O)2
or N=182 for DmU(H2O)2] allows us to distinguish between proton/deuterium trans-
fer versus natural isotopes. As illustrated in Fig. 3.5B, the (N+1)/N ratio (solid line)
is constant in the mU-D2O beam, whereas the (N+2)/N (dashed line) exhibits a clear
59
140 280 4200.0
800.0
1.6k
2.4k
14k
176 180 1840.0
500.0
1.0k
1.5k
9.5 10.0 10.5 11.0 11.5
0.0
0.1
0.2
9.5 10.0 10.5 11.0 11.5 12.00.0
0.2
0.4
A
Ion
co
un
ts
m/z
(N+2)/N
(N+1)/NR
atio
Photon energy (eV)
B (N+1)/N
(N+2)/N
Ra
tio
Photon energy (eV)
C
200 400 600 800
0
1
2
D mU-D
2O PT(normalized)
mU-mU PT
Ratio
Pressure (torr)
0.02
0.04
0.06
0.08
200 400 600 800
0
1
2
D Ratio2
Ratio3
Ratio
Pressure (torr)
0.02
0.04
0.06
0.08 Ratio1
mU-D2O PT
9.5 10.0 10.5 11.0 11.5
0.0
0.2
0.4 n=5
n=4
n=3
n=2
n=1
Ra
tio
Photon energy (eV)
E
Figure 3.5: Mass spectrum of hydrated mU and the dependence of the yield of var-ious protonated species on photon energy and backing pressure. A. Mass spectrum ofhydrated (with D2O) mU and its dimer using 12 eV photons. The inset shows the regionat mass to charge (m/z) 180 corresponding to [mU(D2O)2]+. The dashed lines indicatetwo additional peaks at m/z 181 and 182 arising due to natural isotope abundance (13C)and due to protonated and deuterated species. The intensity ratios between the peaksmarked by the arrows at different photon energy for mU(D2O)2 are shown in panel B.The constant behavior of the m/z 181 peak confirms that it arises from isotopic con-tributions and is not due to PT. Panel C shows similar ratios (for N+1 and N+2 m/zpeaks) for N=182 corresponding to [DmU(H2O)2]+. In this case, the N+2 peak is con-stant, revealing that there is no deuteron transfer between the bases. Panel D: Theeffect of backing pressure (Ar gas) on PT. The black curve (mU-D2O PT) character-izes deuteron transfer from D2O to uracil; the red curve [mU-D2O PT (normalized)] —deuteron transfer from D2O to uracil divided by the sum of mU and (mU)2 hydrates,∑n,m
[(mU)n(D2O)mD]+/ ∑n,m6=0
∑k+l=0,1
[(mU)n(D2O)mHkDl]+. The blue curve (mU-mU PT) cor-
responds to PT between the mU molecules, ∑n
[mU(D2O)nH]+/∑m
[(mU)2(D2O)m]+. E: The
appearance energies of deuterated species [mU(D2O)nD]+ for different cluster sizes n.
60
onset (followed by a sharp rise) at about 10.8 eV. This demonstrates that there is no PT
between the bases; rather, there is a deuterium transfer from the solvating D2O to the
mU dimer.
To confirm that the proton/deuterium transfer can only occur from the solvent, we
repeated the experiment with DmU and non-deuterated water (H2O). Fig. 3.5C shows
(N+1)/N and (N+2)/N ratios (solid and dashed lines, respectively) for N=182, which
corresponds to the DmU(H2O)2 cation. Here we observe that the N+1 peak (proton
transfer) exhibits a threshold behavior (at 10.8 eV, as in the mU-D2O experiments, Fig.
3.5B), while (N+2)/N remains constant. Thus, there is no deuterion transfer between the
DmU species. Note, that the kinetic isotope effect on the inter-base PT was found to be
minor for the stacked mU dimer10, and, therefore, the constant behavior of the (N+2)/N
peak in the DmU-H2O is not due to H/D exchange in the base. Essentially water shuts
down PT between the mU bases, which opens up at 8.9 eV in the absence of water10.
In Fig. 3.5A, there is evidence of mU dimers in the molecular beam. Furthermore,
we can control the degree of dimerization relative to solvation by varying the backing
pressure of the carrier gas (Ar), as illustrated in Fig. 3.2.
Fig. 3.5D shows the effect of backing pressure on the relative efficiency of PT in
the mU-D2O beam. The increase of backing pressure increases the yield of hydrated
species, at the expense of bare mU dimer and monomer. However the total amount of all
forms of the mU dimers (bare dimer plus all hydrated dimers) remains roughly the same
(Fig. 3.3).The yield of interfragment PT is given by the signal of all protonated species
(dominated by mUH+, more than 85%). When normalized to the total dimer population,
the yield of protonated species decreases with backing pressure (Fig. 3.5D mU-mU
PT blue curve). This suggests that the interfragment PT is suppressed by hydration of
dimers rather than reducing the population of dimers via monomer hydration (hence
61
reducing the number of molecules available for clustering). The yield of all deuterated
forms of mU increases upon hydration, as shown by the ratio of all deuterated forms
to all forms of mU present in the beam (black line). Finally, upon normalization to
the population of the hydrated species, we observe a constant ratio of all deuterated
forms to all hydrated forms of mU (mU-D2O (normalized) red line around 0.25), hence
confirming that the increased yield of PT is proportional to the degree of hydration. This
suggests that the rate of PT in the hydrated clusters (and, possibly, its mechanism) does
not depend on degree of hydration.
3.2.1 Proton transfer in thymine-water clusters
Fig. 3.6 shows the yield of protonated thymine (TH+) and thymine- water (T(H2O)H+)
clusters as a function of ionization energy. We observe that the onsets for TH+ and
T(H2O)H+ are the same, which is similar to the mU(H2O)nH+ appearance energies that
do not depend on the cluster size. Note that in the absence of water, PT in thymine
occurs at 9.20 eV, with a major rise in signal between 9.7 and 9.9 eV9.
Thymine provides an interesting comparison since it was demonstrated previously9,
hydrogen bonded and π-stacked dimers populate the molecular beam in contrast to
dimethyluracil, where only π-stacked dimers exist. The calculations suggest that it is
hydrogen bonded thymine dimers which give rise to this signal, while the lower onset
is explained by a dimer with π-stacked geometry. Upon solvation, PT switches off at
these lower energies, as is evidenced in the signal for TH+ and T(H2O)H+ shown in
Fig. 3.6. Using a similar analysis as performed for mU, a constant ratio of 0.073 is due
to isotopes while the onset of PT begins around 10.6 eV, with a major rise at 11.2 eV.
Both the onset and the shapes of the appearance curves are very similar to those for mU
shown in Fig. 2 of the main manuscript, suggesting that a similar PT mechanism from
62
9.5 10.0 10.5 11.0 11.5 12.0 12.50.05
0.10
0.15
0.20
0.25
TH+
T(H2O)H
+
Ra
tio
Photon energy (eV)
Figure 3.6: Yield of protonated thymine (TH) and thymine-water (T(H2O)H+)clusters.
the solvent is occurring. This means, whether one has hydrogen bonded or π-stacked
nucleobase dimers and higher clusters, upon solvation, PT which was quite effective
from cluster fragmentation shuts down completely from the base itself. It is only when
the solvent is ionized that PT begins again.
3.3 Computational details
To understand the mechanism by which water shuts down PT between the bases, we turn
to electronic structure calculations. Electronic structure calculations were performed
following the computational protocols developed and validated in our previous studies
of ionized species9, 10, 23, 25–28. All calculations were performed using Q-Chem29 and
employed methods ranging from EOM-CC to DFT with range-separated functionals
and dispersion correction (ωB97X-D).
63
For accurate description of the ionized states we employed EOM-IP-CCSD in which
problematic target open-shell wave functions are derived by Koopmans-like operators
acting on well-behaved closed-shell reference states30. EOM-IP-CCSD simultaneously
includes dynamical and non-dynamical correlation, describes multiple electronic states
in one calculation, and treats states with different numbers of electrons on the same
footing. It is free from artificial symmetry breaking and spin-contamination.
All neutral ground-state structures and ionized protonated structures were optimized
using DFT with the ωB97X-D functional and the 6-311+G(d,p) basis set. Ionization
energies were calculated using EOM-IP-CCSD with the 6-311+G(d,p) basis set. Ionized
excited states geometries were optimized at the EOM-IP-CCSD/6-31+G(d,p) level of
theory.
Mono- and di-hydrated structures were obtained by placing the water at positions
that are most favorable for h-bonding and optimizing these structures. Previous stud-
ies9, 28, 31 and chemical intuition point out that in the most stable microhydrates water
forms a hydrogen bond with either C=O or N-H group of a nuclear base. mU has two
C=O groups and there are two possible water positions for every group. This gives rise
to four monohydrated structures shown in Fig. 3.7. Dihydrated structures were obtained
by adding a water molecule to monohydrated structures, with a subsequent optimization
(Fig. 3.8).
3.4 Computational results
Previous theoretical studies of microhydrated nucleobases28 reported a small red-shift
(∼ 0.4 eV) in the lowest IE, in excellent agreement with experiments20, 28. The calcula-
tions revealed that the character of the ionized state remains the same as in the isolated
base (πCC orbital); the red-shift was explained by the fact that in the lowest-energy
64
1.89 2.37
mUW1-1a 9.17
mUW1-1b 7.58
2.37
1.87
1.87
2.29
1.88
2.46
mUW1-2a 7.59
mUW1-2b 6.12
Figure 3.7: Monohydrated structures. Distances in angstroms and binding ener-gies in kcal/mol are given for each structure. The lowest-energy isomer is mUW1-1a. mUW1-1b, mUW1-2a, and mUW1-2b are 1.59, 1.58 and 3.06 kcal/mol higher,respectively.
microhydrated structures, the nucleobase is acting as a proton donor. Using similar
computational protocols described in the Computational Details section, we conducted
electronic structure calculations of micro-hydrated mU dimers.
We observe that the hydration by one or two water molecules does not change the
relative distance between the two mU moieties (see Fig. 3.4), e.g., the distance between
C(=O) and C(-CH3) moieties, which are involved in inter-base PT, in the mU dimer is
3.4 A, whereas in (mU)2(H2O) and (mU)2(H2O)2 it varies between 3.3-3.5 A.
65
mUW2-2b 14.21
mUW2-2a 14.72
mUW2-1b 18.25
mUW2-1a 20.93
1.88 2.45
1.90
2.28
1.90 2.41
2.79
1.90
1.79 1.81
2.42
1.78 1.80
2.16
Figure 3.8: Dihydrated structures. Distances in angstroms and binding energies inkcal/mol are given for each structure. The lowest-energy isomer is mUW2-1a.
The effect on the lowest ionized state is small, both in terms of energy and the
character of the state (Table 3.1). We observe a moderate blue shift (∼0.1-0.3 eV)
in the VIE, which is consistent with the structures of hydrated species (see Fig. 3.4)
where uracil acts as a proton acceptor. The character of the lowest ionized state is
also unaffected, as evidenced by the wave function composition and the shapes of the
respective MOs (Fig. 3.9).
66
mUW1 mU2 mU2W1
Figure 3.9: MOs corresponding to the lowest ionized state in mU·H2O, (mU)2, and(mU)2·H2O.
Thus, neither structure nor energetics of the lowest IE explains the observed behav-
ior. However, we note that water blocks the proton-accepting sites in mU; it may also
add structural rigidity to the system. The analysis of higher ionized states (see Table
S1) reveals that while hydration has relatively small effect on the lowest ionized states
of mU, the ionized states localized on water are affected much more strongly by the
interaction with mU. Specifically, the state corresponding to ionization from a lone pair
in water appears at 10.9-11.5 eV in mU mono- and dihydrates, which is 1-1.5 eV lower
compared to the bare water monomer. The lower bound of the energy range is remark-
ably close to the observed onset of PT in microhydrated clusters (10.8 eV). These results
suggest that the PT channel opens up when the lowest ionized state on solvated water
which corresponds to an excited ionized state of the mU(H2O)n cluster becomes acces-
sible. These results are consistent with the experimentally observed onsets of PT, which
are independent of the cluster size (see Fig. 3.5E), in stark contrast to the lowest IE of
microhydrated nucleobases which show notable dependence on the number of hydrated
waters (∼ 0.1 eV drop in IE per water molecule)20, 24, 28.
To gain further insight into the electronic structure of hydrated species and to validate
theory, we focus on the PIE curve (obtained by integrating the area under the respective
67
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.00
10
20
30
40
50
60
3A" (11.2 eV)
Ion
coun
ts
Photon energy (eV)
1A" (8.9 eV)
2A" (9.9 eV)
1A' (10.0 eV)
2A' (10.8 eV)
8.6 eV (AIE)
Figure 3.10: Photoionization efficiency curve (black) of [(mU+D2O)]+ and itsderivative (red), observed using 8 eV to 12 eV photons. The derivative plot revealsmultiple ionized states derived by removing the electron from different MOs. Blackarrows points towards the calculated ionization energies.
m/z peak) of the smallest hydrated cation, mU(D2O). The differentiation of the PIE
curve allow identification of multiple ionized states (the peaks on the differentiated PIE
curve correspond to the VIEs). The PIE (black) and the differentiated (red) curves are
shown in Fig. ??, along with the computed VIEs. The curve features the ionization
onset at ∼ 8.6 eV and a series of peaks between 8.5 and 11.5 eV. The computed AIE is
in excellent agreement with the experimental onset, whereas the computed VIEs match
well the peaks of the differentiated curve. Thus, the peaks at 8.9, 9.9, 10.0, 10.8 and
11.2 eV correspond to vertical ionizations from the 1A′′, 2A′′, 1A′, 2A′, and 3A′′ states,
respectively. The character of these states are illustrated by the respective molecular
orbitals which are also shown in Fig. ??. As Fig. ?? clearly illustrates, low-lying
68
electronic ionized states correspond to the ionization from mU, whereas the 3A′′ state
at 11.2 eV is localized on water, and is similar to the water-localized states observed in
microhydrated dimers.
69
3.4.1 Proton transfer in monohydrate
To understand proton transfer in microhydrated mU, we consider the lowest energy
monohydrated mU (t1b) as a model structure. The first and fifth ionized states (which
correspond to the first ionizations of the mU and water moieties, respectively) were
optimized using EOM-IP-CCSD/6-31+G(d,p). The resulting geometries are presented
in Fig. 3.11. In the first ionized state, in which the hole is localized on mU, the elec-
trostatic interactions push water away from the C=O group (the H-O distance increases
by 1.13 A); this displacement acts against PT. In contrast, in the fifth ionized state (the
hole is localized on water), electrostatic forces pull water closer to mU resulting into a
barierless PT and gives optimized proton-transferred structure of the cation.
1.74 0.99
2.37
1.87 0.97
1.94
2.90 0.96
1A”
3A”
2.63
Figure 3.11: Structural changes in ionized mUW1-1a. Left: optimized neutralstate. Top right: Franck-Condon optimized structure of the 1st (1A”) adiabaticstate of the cation. Bottom right: optimization of the 5th (3A”) adiabatic state ofthe cation gives optimized proton-transferred structure of the cation.
70
Tabl
e3.1
:Ver
tical
and
adia
batic
ioni
zatio
nen
ergi
es(e
V)o
fmU
,(m
U) 2
,wat
er,a
ndva
riou
shyd
rate
dsp
ecie
s.A
llen
ergi
esar
eco
mpu
ted
byE
OM
-IP-
CC
SD/6
-311
+G(d
,p)e
xcep
tfor
(mU
) 2an
d(m
U) 2·H
2Ow
hich
are
com
pute
dw
ith6-
31+G
(d,p
)ba
siss
et.
Stat
eH
2Om
U(m
U) 2
mU·H
2Om
U·(H
2O) 2
(mU
) 2·H
2Om
UW
1-1a
mU
W1-
1bm
UW
1-2a
mU
W1-
2bm
UW
2-1a
mU
W2-
1bm
UW
2-2b
mU
2W1-
1am
UW
1-1b
112
.22
8.87
8.40
8.93
9.01
9.03
9.08
8.89
9.00
9.18
9.24
8.41
8.72
214
.42
9.74
8.81
9.93
9.91
9.95
9.94
9.95
9.87
10.1
110
.08
8.85
9.11
318
.93
9.77
9.42
10.0
010
.02
9.91
9.92
10.0
310
.03
10.1
910
.20
9.52
9.76
410
.66
9.66
10.7
710
.77
10.9
110
.90
10.7
410
.74
11.0
311
.05
9.61
9.96
512
.16
9.69
11.2
111
.14
11.4
111
.24
11.2
410
.92
11.1
911
.14
9.88
9.98
69.
8512
.19
12.2
612
.16
12.2
211
.61
11.6
311
.51
11.1
99.
9610
.14
710
.46
13.2
313
.12
13.3
313
.23
12.1
412
.24
12.3
112
.37
10.4
110
.39
810
.51
13.6
313
.67
13.7
313
.68
13.0
112
.73
13.2
213
.10
10.6
310
.82
911
.67
13.7
613
.85
13.8
713
.86
13.5
913
.65
13.4
413
.27
11.4
510
.84
1011
.88
14.2
014
.14
14.2
514
.27
13.6
613
.65
13.9
113
.93
11.7
311
.90
1114
.27
14.2
114
.16
14.1
314
.11
13.8
714
.03
13.9
411
.89
12.1
612
14.5
914
.614
.52
14.5
414
.17
14.0
514
.31
14.2
513
.22
12.6
21s
tAIE
8.59
8.59
8.56
8.61
71
To further understand PT in solvated systems, we analyze the potential energy pro-
files along the PT coordinate in [mU(H2O)]+. In order to analyze potential energy pro-
files along the PT coordinate we generated ten structures using the following expression
for the Cartesian coordinates32:
xn = xinitial +(x f inal− xinitial) ·n/10 (3.3)
The initial and final structures are optimized structures of the neutral mU·H2O and
proton-transferred system, mUH+·OH. Thus, n can be interpreted as a step along the
PT coordinate.
The profiles are shown in Fig. 3.12. The energy of the ionized states that are local-
ized on mU (1A′′ and 2A′′, see Fig. ??) increases along the PT coordinate (the PT is
also endothermic in the neutral state). In contrast, the energy of the fifth state (3A′′)
corresponding to the ionization of water decreases showing that PT from this state is
a barrierless downhill process. A similar behavior is observed for other states, in that
energetically, water-ionized states go down, whereas uracil-localized states go up. Alter-
natively, one can consider a possibility of adiabatic PT, e.g., on the lowest ionized state
(1A′′). This will of course involve changes in the electronic state character from the
mU-localized one to the water-ionized one and a barrier. The analysis of energy pro-
files shows that PT is energetically accessible at ∼10.6 eV (upper bound), i.e., at this
energy the system has enough energy to overcome the barrier on the adiabatic PES cor-
responding to the lowest ionized state of the system. Yet, the onset of PT yield occurs
only at 10.8 eV thus suggesting that such an adiabatic process is inefficient. This can
be readily rationalized by analyzing the respective electronic wave functions. The low-
est ionized state corresponds to the ionization of mU, which reduces the proton affinity
of mU. Hence the short-time dynamics will involve structural changes which are not
72
0
1
2
9
10
11
12
neutral
1A"
2A"
3A"
mUH+
OH*
En
erg
y (
eV
)
2.61 eV
2.19 eV
ionization from water
8.93 eV
11.21 eV
[mU H2O]
+
Figure 3.12: Potential energy profiles for low-lying states of [mU·H2O]+ along thePT reaction coordinate. The proton is moved from the water molecule to the mUoxygen site. The 5th ionized state, 3A′′, in which the hole is on the water molecule(see Fig. ??), shows no barrier facilitating downhill PT. PT from lower ionizedstates are possible, however this involves changes in the electronic wave functioncharacter and requires more than 10.6 eV photon energy. The left panel shows theexperimental ratio between the [mU(D2O)2]+ signal (m/z 180) and [mU(D2O)2D]+the deuterated species at m/z 182; it shows dramatic enhancement in PT when the3A′′ state is accessed.
favorable for PT from water. Indeed, in the Franck-Condon optimized structures of the
lowest electronic state of [mU·H2O]+ (Fig. 3.11) the distance between O(mU) and water
hydrogen increases from 1.87 A to 2.90 A. In contrast, PT is barrierless starting from
the Franck-Condon point in the fifth ionized state. Thus, even though the system may
have enough energy to overcome the barrier on the lowest ionized state adiabatic PES,
this pathway is not favored dynamically because the gradients in the Franck-Condon
region point away from the PT coordinate. In contrast, when the right electronic state is
73
accessed, the PT may occur ballistically on the respective diabatic surface. We observe
that PT in hydrated mU species is controlled electronically, by the character of the state,
rather than statistically, by energy considerations alone.
mU•H2O
mUH•*OH
VIE = 11.21 (3A”) 2.19 mUH + *OH
0.60
VIE = 8.93 (1A”)
0.09
Figure 3.13: Energy diagram describing relevant ionized states and their orderingat different geometries along PT coordinate. All energies are given in eV and arecalculated with EOM-IP-CCSD/6-311+G**.
Relevant energy differences in mUW1-1a are summarized in Fig. 3.13. VIEs for
the 1st and 5th ionized states are 8.93 and 11.21 eV, respectively. The energy difference
between the final PT structure (fully relaxed mUH+·OH in the lowest ionized state) and
initial ionized state is 2.18 eV (50.4 kcal/mol). This can be described as energy gain
due to PT on the diabatic surface corresponding to a water ionized state. The PT struc-
ture is 0.09 eV (2.13 kcal/mol) above the lowest ionized state at the Franck-Condon
geometry. Thus, for the lowest ionized state, the PT is an uphill process adiabatically.
74
Finally, energy required for PT structure to dissociate producing mUH+ and OH is 0.6
eV (13.76 kcal/mol). Thus, adiabatically, the energy difference for the following pro-
cess: [mU·H2O]+ → mUH+ + OH is 0.69 eV or 15.9 kcal/mol (for the lowest ionized
state). Combining this value with VIE we arrive at 9.62 eV — this would be mUH+
appearance energy on the lowest ionized state assuming no barrier. However, as illus-
trated by Fig. 5 of the main manuscript, we anticipate a barrier on the lowest adiabatic
PES. The experimental onset for mUH+ is much higher (∼ 11 eV) and agrees well with
VIE corresponding to the 5th ionized state of mU·H2O.
3.4.2 Proton transfer in dihydrated species
The appearance energies of mU(H2O)nH+ does not depend on the cluster size, as illus-
trated in Fig. 3.5E, and to understand this, we consider a dihydrated system mUW2-1a
(see Fig. 3.8). In this structure, one (inner) water forms a hydrogen bond with the C=O
group of mU and the second (outer) water acts as proton donor forming an h-bond with
the first water (and a weaker h-bond with the C-H group of mU).
We consider three possible PT structures that can be formed upon ionization. The
first structure with the H3O+ moiety (Fig. 3.14A) can be obtained by PT from the outer
water molecule to the inner water molecule. The second structure (Fig. 3.14C) that
has protonated mU and an inner OH radical can be derived by direct PT from the inner
ionized water to mU. The third structure with protonated mU and an outer OH radical
(Fig. 3.14E) can be described as a result of Grotthuss-like double PT from ionized outer
water to the inner water, and from the inner water — to mU. The first structure can be
described as an intermediate for the double PT.
To gain insight into possible PT pathways in dihydrates, we prepared such struc-
tures by manually displacing the parent structure and optimized them by using protocols
75
Initial Optimized
Single Transfer Single Transfer
Single Transfer
Double Transfer
Double Transfer Double Transfer
D
B
F
1.55 1.90
1.55 1.90
1.80
2.35
C
A
E
Figure 3.14: Possible proton-transferred structures in [mU(H2O)2]+. Left panelsshow manually distorted structures used as staring points for optimization. Rightpanels show the final optimized structures of the ionized species. Distances are inAngstroms.
described above. The initial structures are shown in the left panel of Fig. 3.14, whereas
the resulting optimized structures are shown on the right.
The lowest ionization energy of water in this dihydrate correspond to the state with
a hole localized on the outer water. Thus, we expect this state to relax via PT to either
the first or the third structures. However, the optimization of the structure shown in Fig.
3.14A converged to the double PT structure (see Fig. 3.14B) indicating that there is no
76
local minimum corresponding to the first structure (with H3O+). Thus, ionization of
water in a dihydrate leads to the double PT structure via a Grotthuss-like pathway. The
energetics of this process is in agreement with a higher proton affinity of mU compared
with water. However, it is interesting that there is apparently no barrier along the double
PT reaction coordinate (the optimization of the state with the hole localized on the outer
water converges to doubly proton-transferred state). We also note that energy differences
between the structures corresponding to the single and double PT (Fig. 3.14B and Fig.
3.14D, respectively) is 22.7 kcal/mol (computed by ωB97X-D). This is in agreement
with known facts that in clusters more stable structures are the ones with OH radical
on the outside. These energy differences can be rationalized by counting the number of
h-bonds in the two structures. The energy difference between 5th ionized state at the
initial Franck-Condon geometry and lowest ionized state at double PT stricture is 53.4
kcal/mol.
In large water clusters, the lowest ionized states correspond to the surface states,
where there are waters that serve only as proton donors33. Thus, the IEs corresponding
to the surface states should be relatively independent of the cluster size (and even the
chemical nature of its core). The experimental onsets for protonated mU(H2O)n clus-
ters are remarkably insensitive to the cluster size (Fig. 3.5E); this suggest that in larger
clusters the surface-ionized states lead to multiple barrierless PT yielding solvated pro-
tonated uracil with the OH radical on the surface. Thus, such clusters of water with
molecules with relatively high proton affinity could serve as model systems for studying
directionality in Grotthuss-like PT through water wires and membrane interfaces34, 35.
While most of the experiments in this work focused on mU, this nucleobase is by
no means unique in that water has a significant effect on PT. Similar experiments per-
formed on thymine show that in the absence of water, PT begins at 9.20 eV, with a
77
major rise in signal between 9.7 and 9.9 eV9. Thymine provides an interesting com-
parison, because both h-bonded and π-stacked dimers populate the molecular beam9, in
contrast to mU which forms only π-stacked dimers10. The calculations suggested that
it is h-bonded thymine dimers which give rise to this signal at 9.7 eV, while the lower
onset was explained by a dimer with π-stacked geometry9. Upon solvation, PT switches
off at these lower energies, as is evidenced in the signal for TH+ and T(H2O)H+ shown
in Fig. 3.6. The onset for PT is around 10.6 eV, with a major rise at 11.2 eV, which
is very similar to the onsets observed in mU. The shapes of the curves for protonated
thymine species are also very similar to those in Fig. 3.5B and C. This suggests that a
similar PT mechanism from the solvent is occurring.
3.5 Conclusions
We conclude that both in h-bonded and π-stacked nucleobase dimers and larger clusters,
solvation shuts down PT between the bases, which is rather efficient in “dry” clusters.
It is only when the solvent is ionized that PT begins again. Our findings illustrate that
water has a dramatic effect on PT pathways, not only by serving as a wire for proton
transport, but also by shutting down other PT routes. In our model systems, an outer-
most ionized water molecule acts as an acid (activated by an ionization event), and the
nucleobase — as a base, whereas other waters may participate in PT either as spectators
or as intermediate proton acceptors, as shown recently in photo induced acid-base reac-
tions17. We explain the remarkable similarity between the appearance onsets in solvated
mU and thymine, as well as insensitivity of the onsets and shapes of the appearance
curves on the cluster sizes to the fact that the lowest ionized states in which the hole
is localized on the solvent correspond to the surface states, i.e., water molecules acting
as proton donors only. Electronic structure calculations show that these IEs are rather
78
insensitive to the size and/or chemical identity of the cluster core (mU versus mU dimer
versus thymine). Thus, these states become accessible at very similar energies initiat-
ing facile PT to the accepting base, either directly (in monohydrates), or through the
mediating water molecules.
While our study focuses on PT in a simple model system, one can anticipate that
some of these mechanisms may be operational in solution or in biological environments.
A growing body of studies illustrating the central role of PT has led to a paradigm shift
in the discussion of water and its active role in biology and chemistry. Water is no
longer seen as just a solvent, but is an active participant in a variety of processes such
as enzyme catalysis and membrane transport. Water has also been shown to catalyze
reactions36 which are important in biology and atmospheric chemistry16, 37. Proton-
coupled electron transfer in DNA is mediated by water chains11. Autoionization in
water also drives a variety of processes which are critical to life and biology12, while
PT through nanopores, artificial membranes and structures have major ramifications in
energy conversion and storage technologies. PT in nano confined geometries38 have
implications for catalysis and solar energy conversion, while ions have been shown to
enhance the transfer of protons through aqueous interfaces39. In this work we have
shown that PT can be very effectively controlled by subtly changing how DNA bases
hydrogen bond and stack within themselves and upon solvation and thus can provide a
template for novel dynamical studies in the temporal, spatial, and spectroscopic domain.
79
3.6 Chapter 3 references
[1] A. Rosspeintner, B. Lang, and E. Vauthey. Ultrafast photochemistry in liquids.Annu. Rev. Phys. Chem., 64:247, 2013.
[2] L.M. Tolbert and K.M. Solntsev. Excited-state proton transfer: From constrainedsystems to ”super” photoacids to superfast proton transfer. Acc. Chem. Res., 35:19–27, 2002.
[3] S.J. Formosinho and L.G. Arnaut. Excited-state proton transfer reactions ii.intramolecular reactions. J. Photochem. Photobiol., 75:21–48, 1992.
[4] J.J. van Thor. Photoreactions and dynamics of the green fluorecent protein. Chem.Soc. Rev., 38:2935–2950, 2009.
[5] E.C. Carroll, S.-H. Song, M. Kumauchi, I.H.M. van Stokkum, A. Jailaubekov,W.D. Hoff, and D.S. Larsen. Subpicosecond excited-state proton transfer preced-ing isomerization during the photorecovery of photoactive yellow protein. J. Phys.Chem. Lett., 1:2793–2799, 2010.
[6] T. Schultz, E. Samoylova, W. Radloff, I.V. Hertel, A.L. Sobolewski, and W. Dom-cke. Efficient deactivation of a model base pair via excited-state hydrogen transfer.Science, 306:1765–1768, 2004.
[7] A.K. Ghosh and G.B. Schuster. Role of the guanine N1 imino proton in themigration and reaction of radical cations in DNA oligomers. J. Am. Chem. Soc.,128:4172–4173, 2006.
[8] T. Charkaborty, editor. Charge Migration in DNA. Springer, 2007.
[9] K.B. Bravaya, O. Kostko, M. Ahmed, and A.I. Krylov. The effect of π-stacking,h-bonding, and electrostatic interactions on the ionization energies of nucleic acidbases: Adenine-adenine, thymine-thymine and adenine-thymine dimers. Phys.Chem. Chem. Phys., 12:2292–2307, 2010.
[10] A. Golan, K.B. Bravaya, R. Kudirka, S.R. Leone, A.I. Krylov, and M. Ahmed.Ionization of dimethyluracil dimers leads to facile proton transfer in the absenceof H-bonds. Nature Chem., 4:323–329, 2012.
[11] R.N. Barnet, J. Joseph, U. Landman, and G.B. Schuster. Oxidative thymine muta-tion in DNA: Water-wire-mediated proton-coupled electron transfer. J. Am. Chem.Soc., 135:3904–3914, 2013.
80
[12] P. Ball. The importance of water. In I.W. M. Smith, C.S. Cockell, and S. Leach, edi-tors, Astrochemistry and Astrobiology, Physical Chemistry in Action, pages 169–210. Springer Berlin Heidelberg, 2013.
[13] G.A. Voth. Computer simulation of proton solvation and transport in aqueous andbiomolecular systems. Acc. Chem. Res., 39:143–150, 2006.
[14] N. Agmon. The Grotthuss mechanism. Chem. Phys. Lett., 244:456–462, 1995.
[15] D. Chandler, C. Dellago, and P. Geissler. Wired-up water. Nat. Chem., 4:245–247,2012.
[16] R.A. Relph, T.L. Guasco, B.M. Elliott, M.Z. Kamrath, A.B. McCoy, R.P. Steele,D.P. Schofield, K.D. Jordan, A.A. Viggiano, E.E. Ferguson, and M.A. Johnson.How the shape of an h-bonded network controls proton-coupled water activationin HONO formation. Science, 327:308–312, 2010.
[17] O.F. Mohammed, D. Pines, J. Dreyer, E. Pines, and E.T.J. Nibbering. Sequentialproton transfer through water bridges in acid-base reactions. Science, 310:83–86,2005.
[18] C. Manca, C. Tanner, and S. Leutwyler. Excited state hydrogen atom transfer inammonia-wire and water-wire clusters. Int. Rev. Phys. Chem., 24:457–488, 2005.
[19] L. F. Sukhodub. Interactions and hydration of nucleic acid bases in a vacuum.experimental study. Chem. Rev., 87:589–606, 1987.
[20] S.K. Kim, W. Lee, and D.R. Herschbach. Cluster beam chemistry: Hydration ofnucleic acid bases; Ionization potentials of hydrated adenine and thymine. J. Phys.Chem., 100:7933–7937, 1996.
[21] N.J. Kim, H.M. Kim, and S.K. Kim. Ionization-induced proton transfer inthymineammonia van der Waals clusters. Int. J. Mass. Spectr., 261:32, 2007.
[22] K. Mizuse, J.-L. Kuo, and A. Fujii. Structural trends of ionized water networks:Infrared spectroscopy of water cluster radical cations (H2O)n+ (n=3-11). Chem.Science, 2:868–876, 2011.
[23] A.A. Zadorozhnaya and A.I. Krylov. Zooming into pi-stacked manifolds of nucle-obases: Ionized states of dimethylated uracil dimers. J. Phys. Chem. A, 114:2001–2009, 2010.
[24] L. Belau, K.R. Wilson, S.R. Leone, and M. Ahmed. Vacuum-ultravioled photoion-ization studies of the microhydration of DNA bases (guanine, cytosine, adenine,and thymine). J. Phys. Chem. A, 111:7562–7568, 2007.
81
[25] A.A. Golubeva and A.I. Krylov. The effect of π-stacking and H-bonding on ion-ization energies of a nucleobase: Uracil dimer cation. Phys. Chem. Chem. Phys.,11:1303–1311, 2009.
[26] O. Kostko, K.B. Bravaya, A.I. Krylov, and M. Ahmed. Ionization of cytosinemonomer and dimer studied by VUV photoionization and electronic structure cal-culations. Phys. Chem. Chem. Phys., 12:2860–2872, 2010.
[27] K.B. Bravaya, O. Kostko, S. Dolgikh, A. Landau, M. Ahmed, and A.I. Krylov.Electronic structure and spectroscopy of nucleic acid bases: Ionization energies,ionization-induced structural changes, and photoelectron spectra. J. Phys. Chem.A, 114:12305–12317, 2010.
[28] K. Khistyaev, K.B. Bravaya, E. Kamarchik, O. Kostko M. Ahmed, and A.I. Krylov.The effect of microhydration on ionization energies of thymine. Faraday Discuss.,150:313–330, 2011.
[29] Y. Shao, L. Fusti-Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown,A.T.B. Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neill, R.A. Distasio Jr,R.C. Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. VanVoorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P. Maslen, P.P. Koram-bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen,A. Dreuw, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S.Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z.Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee, J.Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. WoodcockIII, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel,W.J. Hehre, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon.Advances in methods and algorithms in a modern quantum chemistry programpackage. Phys. Chem. Chem. Phys., 8:3172–3191, 2006.
[30] A.I. Krylov. Equation-of-motion coupled-cluster methods for open-shell and elec-tronically excited species: The hitchhiker’s guide to Fock space. Annu. Rev. Phys.Chem., 59:433–462, 2008.
[31] D. Ghosh, O. Isayev, L.V. Slipchenko, and A.I. Krylov. The effect of solvationon vertical ionization energy of thymine: From microhydration to bulk. J. Phys.Chem. A, 115:6028–6038, 2011.
[32] P.A. Pieniazek, S.A. Arnstein, S.E. Bradforth, A.I. Krylov, and C.D. Sherrill.Benchmark full configuration interaction and EOM-IP-CCSD results for proto-typical charge transfer systems: Noncovalent ionized dimers. J. Chem. Phys.,127:164110, 2007.
82
[33] P.A. Pieniazek, E.J. Sundstrom, S.E. Bradforth, and A.I. Krylov. The degree ofinitial hole localization/delocalization in ionized water clusters. J. Phys. Chem. A,113:4423–4429, 2009.
[34] A. Springer, V. Hagen, D.A. Cherepanov, Y.N. Antonenko, and P. Pohl. Pro-tons migrate along interfacial water without significant contributions from jumpsbetween ionizable groups on the membrane surface. Proc. Nat. Acad. Sci.,108(35):14461–14466, 2011.
[35] O.-H. Kwon and O.F. Mohammed. Water-wire catalysis in photoinduced acid-basereactions. Phys. Chem. Chem. Phys., 14:8974–8980, 2012.
[36] Y. Matsuda, A. Yamada, K. i. Hanaue, N. Mikami, and A. Fujii. Catalytic actionof a single water molecule in a proton-migration reaction. Angew. Chem. Int. Ed.Engl., 49(29):4898–4901, 2010.
[37] R.J. Buszek, J.R Barker, and J.S. Francisco. Water effect on the OH + HCl reaction.J. Phys. Chem. A, 116(19):4712–4719, 2012.
[38] J. Kofinger, G. Hummer, and C. Dellago. Single-file water in nanopores. Phys.Chem. Chem. Phys., 13:15403–15417, 2011.
[39] H. Mishra, S. Enami, R.J. Nielsen, M.R. Hoffmann, W.A Goddard, and A.J.Colussi. Anions dramatically enhance proton transfer through aqueous interfaces.Proc. Nat. Acad. Sci., 109(26):10228–10232, 2012.
83
Chapter 4: The implementation of the
coupled-cluster family of methods on
graphics processing unit
4.1 Introduction
From early days of computational chemistry quantum chemistry calculations have been
limited by the available computational resources. Quantum chemistry started from
calculations of very simple diatomic molecules with simple and inaccurate methods.
Nowadays quantum chemistry tools can easily be used to compute systems which con-
sist of more than 20 heavy atoms, such as DNA bases dimers, with accurate corre-
lated methods. However, there are many important molecular systems, such as pho-
toactive proteins, porphyrin and chlorin-based molecules (e. g. heme and chlorophyll),
carotenoids, molecules in organic solar cells, solvated molecules and others, for which
the calculations with desirable accuracy are still practically inaccessible. Other impor-
tant systems that require large computational resources are DNA bases clusters and DNA
nucleotides that are model systems for interactions in DNA. There are methods that
allow splitting complicated systems apart and applying different levels of theory to sep-
arate parts to achieve reasonable computational costs and accuracy. These are QM/MM,
embedding, and fragment-based approaches. Other approaches neglect some high-level
84
interactions between distant parts of the system. For example, local correlation methods
eliminate the steep scaling of traditional CC methods for molecules with well localized
electronic structures1. However, such methods perform less well for genuinely delocal-
ized systems, systems with strong nontrivial interactions between fragments, or for basis
sets augmented with diffuse functions. Thus we can see that there are numerous com-
putational projects in quantum chemistry which require large computational resources.
Figure 4.1: Calculations per second per $1000, logarithmic plot.
During the last century there was a dramatic decrease in the price of computations
(Fig. 4.12). From the beginning of microprocessors era this decrease was mostly due to
the increasing computational performance of a single microprocessor. From the 1970th
till the beginning of 21st century microprocessors (and central processors units (CPU) in
85
particular) performance gains were in many respects achieved by increasing micropro-
cessor clock frequency: from 2 MHz in Intel 8080 to 3.8 GHz in Pentium 4 (Fig. 4.23).
Higher CPU frequency means more operations per second. Thus the increase of the
CPU frequency allows faster execution of the same code without any modification. For
many years theoretical chemists were able to compute properties of bigger and bigger
systems using basically the same algorithms due to increasing CPU frequency. How-
ever, around 2004 CPU frequency speedup has come to an end with Pentium 4 reaching
a frequency of 3.8 GHz. At this point CPUs have hit the “power-wall”: higher CPU
frequency requires more power consumption and cause more power dissipation that can
lead to a CPU overheating and requires special cooling systems. This made further
increase of the CPU frequency commercially impractical. Further performance gains
were achieved through the development of multiple cores on a single die CPU. Starting
from the production of dual-cores Pentium D and Athlon X2 in 2005 manufactures have
increased the number of cores in one CPU up to 16 processors (e.g. AMD Opteron 6200
“Interlagos”).
Multiple-core CPUs are able to execute more than one instruction stream simultane-
ously (“in parallel”). However, a code designed for sequential execution with a one-core
processor cannot be executed in parallel on multiple-cores, unless the compiler auto-
matically parallelizes this code. Despite decades of work by compiler researchers, auto-
matic parallelization has had only limited success4. Thus multiple-cores CPUs require
an existing code to be rewritten with explicit parallelism in the most time-consuming
parts.
Parallelism has been employed for many years in high-performance computing that
uses supercomputers and computer clusters. One of the main problems of such sys-
tems is slow communication between the nodes. Another disadvantage is a very high
86
Figure 4.2: The evolution of computing platform’s peak performance and CPUfrequency demonstrates CPU frequency standstill around 2004.
price of supercomputers and powerful computer clusters which limits its availability to
theoretical chemists.
Another type of systems that had employed parallelism for a relatively long time is
graphical processing unit. GPUs are co-processors that have been heavily optimized for
computer graphics processing. In a computer graphics processing numerous uniform
operations are applied to large 2D and 3D arrays of data, which correspond to pixels.
To handle such computations the single instruction, multiple data (SIMD) approach was
utilized. SIMD devices have multiple processing elements that perform the same oper-
ation (e.g. multiplication) on multiple data units simultaneously. Modern GPUs have a
highly parallel structure with up to 2880 (NVIDIA GK110 architecture) arithmetic logic
units (ALUs) or cores able to perform simple math operations. The nature of many sci-
entific computational problems allows efficient use of high parallelism and power of
87
GPUs. For example matrix operations can be calculated using GPU with a significant
speedup compared to the CPU. The technique of using a GPU to perform computation
in applications traditionally handled by CPU is called General-purpose computing on
GPU (GPGPU). GPGPU is a fairly recent trend and for a long time was constrained
by limited programmability of GPU and supported data types. First attempts to imple-
ment GPGPU had to use the standard graphics application programming interface (API)
and high-level shading languages such as DirectX, OpenGL and Cg, which made the
developing of GPGPU programs a challenging task. Release of the Compute Unified
Device Architecture (CUDA) developed by NVIDIA in 2007 and later the Khronos
Group’s Open Computing Language (OpenCL), Microsoft’s DirectCompute, OpenACC
and other GPGPU oriented languages have made the development of the GPGPU pro-
grams much easier and realistic.
However, GPUs made prior to 2010 either didn’t support double precision data types
or double precision operations were very slow because they have very limited number
of ALUs capable of performing double precision operations. Until recently, the lack of
double precision support has made GPGPU inapplicable to quantum chemistry problems
due to large computational errors5–8. The production of NVIDIA Tesla C2050/C2070
GPUs with a new Fermi architecture with up to 512 stream processors in 2010 changed
that. Each stream processor on this chip is able to perform one double-precision floating-
point operation per every other cycle. The latest release in 2012 of the NVIDIA Tesla
K20x GPU with 2688 ALUs made it very promising to use GPUs of this type in quantum
chemistry calculations.
To benefit from the implementation on GPU a computational chemistry method
must be able to utilize the high parallelism of the GPU architecture. The example of
such methods is coupled-cluster family of methods. Such methods as CCSD, CCSD(T)
88
and many others are widely used for high accuracy quantum chemical computations.
Some of the most accurate calculations for small to medium sized molecules use these
methods9. One of the main disadvantages of these methods is that they have very high
computational costs and a scaling of N6 for CCSD and N7 for CCSD(T) where N is
the system size. The most computationally expensive operations in these methods are
tensor contractions, which can be reduced to matrix operations. It is known that matrix
operation can be very efficiently parallelized on SIMD devices as they mostly include
the same arithmetic operation on the large set of data. It was shown that matrix multipli-
cation operations can be executed on GPU with high efficiency10, 11. For example, the
latest NVIDIA Tesla GPU (K20x) reaches impressive 1.22 Teraflop double-precision
performance in DGEMM matrix-multiplication12. In addition, the performance of the
CPUs increases much faster that the performance of CPUs (Fig. 4.311). Thus, it is very
promising to implement CC methods with a GPGPU technique.
In addition, it is important to keep in mind that there are several competing massively
parallel architectures, such as NVIDIA Tesla and AMD FirePro GPUs and Intel Xeon
Phi Coprocessor. Modern CPUs with 16 cores and integrated GPUs could potentially
also be used as massively parallel processors. Thus the implementation model should
be flexible in order to quickly adapt to different technologies.
This chapter explains our approach to the implementation of the CC family of meth-
ods on GPU using CUDA C including working implementation of the CCSD(T) method.
Our implementation is part of the ccman2 and libtensor libraries of Q-Chem electronic
structure package13. It is based on a modular and layered architecture which allows to
adapt the library to different underlying technologies.
89
Figure 4.3: Theoretical peak performance for the CPU and GPU, floating-pointoperations per second.
4.2 GPU architecture
This chapter gives a brief description of GPU architectures by the example of the newest
NVIDIA Kepler GK110 architecture. ATI GPUs architecture has the same basics con-
cepts but organization of processors and memory structure are different. Most scientific
application for GPU and all known quantum chemistry programs used NVIDIA GPUs,
mostly because of the NVIDIA CUDA C language support.
GPUs, initially designed for graphics rendering, represent a single instruction, mul-
tiple data (SIMD) class of devices. They have multiple processing elements that perform
the same operation on multiple data simultaneously. GPU is specialized for compute-
intensive, highly parallel computations and therefore designed such that more transistors
90
Figure 4.4: Sketchy representation of CPU and GPU architectures.
are devoted to data processing rather than data caching and flow control as in CPU. This
is illustrated in Fig. 4.411.
AnOverviewoftheGK110KeplerArchitecture
Kepler GK110 was built first and foremost for Tesla, and its goal was to be the highest performing
parallel computing microprocessor in the world. GK110 not only greatly exceeds the raw compute
horsepower delivered by Fermi, but it does so efficiently, consuming significantly less power and
generating much less heat output.
A full Kepler GK110 implementation includes 15 SMX units and six 64‐bit memory controllers. Different
products will use different configurations of GK110. For example, some products may deploy 13 or 14
SMXs.
Key features of the architecture that will be discussed below in more depth include:
The new SMX processor architecture
An enhanced memory subsystem, offering additional caching capabilities, more bandwidth at
each level of the hierarchy, and a fully redesigned and substantially faster DRAM I/O
implementation.
Hardware support throughout the design to enable new programming model capabilities
Kepler GK110 Full chip block diagram
Figure 4.5: NVIDIA Kepler GK110 architecture. 2880 CUDA cores organized in15 SMXs are shown.
91
Kepler GK110 based GPUs consist of up to 2880 stream processors called cores
(Fig. 4.514). Each core has a fully pipelined arithmetic logic unit (ALU) and float-
ing point unit (FPU) and able to perform one fused multiply-add (FMA) instruction
for single precision arithmetic (with IEEE 754-2008 floating-point standard) per cycle.
Cores are organized in 15 groups of 192, called streaming multiprocessor (SMX) (Fig.
4.614). Besides 192 single-precision cores each SMX has 64 double-precision units
and 32 load/store units allowing source and destination addresses to be calculated for
32 threads per clock and supporting units load and store the data at each address to
cache or DRAM. Each SM has 32 special function units (SFUs) able to execute one fast
approximate transcendental instruction such as sin, cosine, reciprocal, and square root
per thread, per clock.
Each SMX has 64 KB of on-chip memory that can be configured as either 48 KB
of Shared memory with 16 KB of L1 cache, 32 KB Shared with 32 KB L1 cache or as
16 KB of shared memory with 48 KB of L1 cache. Shared memory is available for all
SMX cores and can be used for cooperation between the cores. SMX has a register with
a capacity of 65536 by 32 bits shared by all threads. Besides 15 SMXs Kepler based
GPU can have up to 6 Gb of local DRAM memory and 1536 KB L2 cache (shared
by all SMXs). Kepler architecture introduces new Read-only cache that previously (in
Fermi architecture) could be used only by the Texture units. Kepler memory hierarchy
is represented in Fig. 4.714
GPUs are connected to the northbridge chip (or directly to the CPU in latest models)
through the PCI Express bus. Northbridge is connected to the CPU and CPU DRAM.
The bandwidth between the CPU and northbridge and CPU DRAM on modern systems
is typically higher than the bandwidth of the PCI Express bus. Moreover, most mod-
ern CPUs have integrated PCI express and RAM controllers. Thus the communication
92
Streaming Multiprocessor (SMX) Architecture
Kepler GK110’s new SMX introduces several architectural innovations that make it not only the most
powerful multiprocessor we’ve built, but also the most programmable and power‐efficient.
SMX: 192 single‐precision CUDA cores, 64 double‐precision units, 32 special function units (SFU), and 32 load/store units (LD/ST).
Figure 4.6: NVIDIA Kepler GK110 streaming multiprocessor (SMX) architecture.192 singleprecision CUDA cores, 64 doubleprecision units, 32 special function units(SFU), and 32 load/store units (LD/ST).
between CPU and GPU and memory transfer between CPU DRAM and GPU DRAM
is limited by the PCI Express bandwidth. Latest GPUs use PCI Express 3.0 with a 16
Gb/s bandwidth.
93
Kepler Memory Subsystem – L1, L2, ECC
Kepler’s memory hierarchy is organized similarly to Fermi. The Kepler architecture supports a unified
memory request path for loads and stores, with an L1 cache per SMX multiprocessor. Kepler GK110 also
enables compiler‐directed use of an additional new cache for read‐only data, as described below.
64 KB Configurable Shared Memory and L1 Cache
In the Kepler GK110 architecture, as in the previous generation Fermi architecture, each SMX has 64 KB
of on‐chip memory that can be configured as 48 KB of Shared memory with 16 KB of L1 cache, or as 16
KB of shared memory with 48 KB of L1 cache. Kepler now allows for additional flexibility in configuring
the allocation of shared memory and L1 cache by permitting a 32KB / 32KB split between shared
memory and L1 cache. To support the increased throughput of each SMX unit, the shared memory
bandwidth for 64b and larger load operations is also doubled compared to the Fermi SM, to 256B per
core clock.
48KB Read‐Only Data Cache
In addition to the L1 cache, Kepler introduces a 48KB cache for data that is known to be read‐only for
the duration of the function. In the Fermi generation, this cache was accessible only by the Texture unit.
Expert programmers often found it advantageous to load data through this path explicitly by mapping
their data as textures, but this approach had many limitations.
Figure 4.7: Kepler Memory Hierarchy.
4.3 GPU programming languages by the example of
CUDA C
CUDA (an acronym for Compute Unified Device Architecture) is a general purpose par-
allel computing architecture developed by NVIDIA that leverages the parallel compute
engine in NVIDIA GPUs to solve many complex computational problems in a more
efficient way than on a CPU. Programmers can use C language with NVIDIA exten-
sions (C for CUDA or CUDA C) to develop programs executable on the GPU. CUDA
architecture also allows using other programming languages, such as CUDA Fortran,
OpenCL, DirectCompute and OpenACC. CUDA, OpenCL, and DirectCompute share
similar paradigm with special kernel functions written for execution on GPU while Ope-
nACC uses special directives to parallelize certain parts of the code similar to OpenMP
API.
94
4.3.1 Thread organization
CUDA provides a scalable programming model through three key abstractions: a hierar-
chy of thread groups, shared memories, and barrier synchronization. CUDA C extends C
by allowing the programmer to define C functions, called kernels, that, when called, are
executed N times in parallel by an array of N threads. Threads form blocks which can
be executed independently in parallel (Fig. 4.811). The maximum number of threads per
block is 102411. Blocks are executed independently in a random order and on a random
streaming multiprocessor (SM) concurrently or sequentially. This allows thread blocks
to be scheduled in any order across any number of cores and provide the scalability
of the code. Thus no assumption about data integrity in SM shared memory between
different block executions can be made. On the contrary, threads within one block are
guaranteed to be executed on the same SM. Thus threads within a block can cooperate
by sharing data through the shared memory and by synchronizing their execution.
Blocks form a grid that performs the kernel execution. The max-
imum number of blocks per kernel is 232-1. The number of CUDA
blocks in a grid and the number of threads per block are specified using
<<< NumberO f Blocks,NumberO f T Hreads >>> execution configuration syntax at
the kernel invocation. For example, MatMult <<< 3,32 >>> will execute the kernel
with the name MatMult by three blocks of 32 threads each.
4.3.2 Memory organization
There are three six memory scopes in CUDA: register, local, shared, global, constant
and texture. Register memory is the fastest form of memory on the multiprocessor and
is only accessible by the thread. However, it has very limited size and when the data
does not fit into register part of the variables will be placed in the local memory. Local
95
Figure 4.8: Grid structure. Thread blocks form a grid that correspond to onekernel.
memory is located in global memory DRAM, which makes it very slow compared to
the register. Local memory is a private memory of the thread. Shared memory is an on
chip memory and is almost as fast as a register one. Shared memory is accessible by
all threads of the block and has the same lifetime as the block. Global memory resides
in GPU DRAM and accessible by all threads of all blocks and kernels. Global memory
is potentially 100-150 times slower than register or global memory; however, on new
GPUs (Fermi and Kepler architectures) it is cashed. Constant memory is a read-only
GPU DRAM memory, which can be written only from the host (CPU). Constant mem-
ory cashed on all GPUs. Texture memory is also resides in the GPU DRAM memory
and is used mostly by graphical applications.
96
Large latency and size difference between different types of memory makes the
appropriate memory management very important. Inefficient memory use is one of the
main bottlenecks of the GP GPU programs.
4.4 Review of existing quantum chemistry methods
accelerated with GPU.
GPUs are emerging as a very promising architecture for computational chemistry and
for quantum chemistry in particular. There were several examples of implementation of
quantum chemical methods on GPU, such as quantum Monte Carlo15, 16, density func-
tional theory (DFT)5, 7, Hartree-Fock self-consistent field (HF SCF)6–8, 17, second-order
Moller-Plesset (MP2)18, 19 and coupled-cluster (CCD, CCSD, CCSD(T))20, 21 quantum
chemistry methods. These implementations are briefly discussed below.
One of the first quantum chemical methods implemented on GPU was Quantum
Monte Carlo method15. The nature of this method is well suited for parallelization,
which allowed efficient implementation of this method on GPU with reported speedup
factors up to 350 on an NVIDIA Tesla C1060 GPU compared to a 2.66 GHz Intel Xeon
E5430 CPU16.
The implementation of the DFT and HF SCF methods on GPU started from the two-
electron integral evaluation algorithms5, 6. The speedups of more than 130x in the single
precision were achieved using an NVIDIA GeForce 8800 GTX GPU in comparison
to an Opteron 175 CPU6. Later the complete SCF procedure was implemented using
CUBLAS library for matrix operations7. In this implementation specially designed
97
memory management was used which allowed to preload required data from CPU mem-
ory to GPU memory and then further to SM shared memory to overcome memory band-
width and latency limitations. This code demonstrated the speedup of up to 650x in
the single precision for molecules with as many as 453 atoms (2131 basis functions)
on an NVIDIA GeForce 280GTX compared to an Intel Pentium D 3 GHz. In the same
work7 the 2.0-2.8x speedups over a single GPU was obtained on a 3-GPU (280 GTX)
system. Further development of the analytical energy gradients calculations on GPU
made possible to run geometry optimization and first principles molecular dynamics on
GPU with a 180x speedup for such systems as a hydronium ion solvated by 30 waters
(94 atoms, 405 basis functions) and an aspartic acid molecule solvated by 147 waters
(457 atoms, 2014 basis functions)8. The implementation of the direct SCF calcula-
tion with Hartree-Fock method on a high-performance computer cluster with GPUs has
demonstrated impressive 2,452x speedup for Olestra molecule (453 atoms, 2131 basis
functions) when using eight cluster nodes with two NVIDIA Tesla C1060 GPUs each17.
Hybrid parallel model with CUDA for GPU and message passing interface (MPI) and
POSIX threads for multi-node multi-GPU configuration was used in this implementa-
tion. However, despite such impressive speedups there was a severe disadvantage in
all these calculations. GPUs used in the described calculations were either not able to
perform 64-bit double-precision (DP) operations at all or such operations were very inef-
ficient. The absolute energy error generated by 32-bit single-precision (SP) arithmetic
as compared to DP calculations can be as big as 36 millihartree (20 kcal/mol) which is
an order of magnitude worse than required “chemical accuracy” (typically 1 kcal/mol)7.
To improve the accuracy DP capability of newer GPU (NVIDIA 280GTX) was used to
implement summation of integrals while the integrals themselves were still calculated
in SP. The use of DP accumulation made the error to be less than 1 kcal/mol7. Further
98
improvement of this code and use of modern GPUs allowed to achieve impressive 114x
speedup in RHF/6-31G* calculation of large Olestra molecule using TeraChem on an
singe GeForce GTX580 GPU, as compared to GAMESS on the state-of-the-art Intel
Westmere 3.33 GHz CPU core22.
The first reported implementation of correlated quantum chemistry method on GPU
was resolution-of-the-identity MP2 method. One of the most time consuming routine in
MP2 calculations is matrix-matrix multiplications, which can be efficiently performed
on GPU using CUBLAS23 functions. In the paper18 it was shown that in SP matrix-
matrix multiplication for matrices larger than 750 elements per side the GPU (NVIDIA
Quadro FX 5600 GPU) significantly outperforms CPU (Opteron 170) with up to 13x
speedup. However, for smaller matrices the CPU was more efficient. Therefore, the
hybrid model where matrices with a size above the certain threshold were calculated
on GPU while the rest were calculated on CPU was proposed. Speedups of 1.5x to
4.3x were achieved with this algorithm for a series of linear alkanes using the cc-pVDZ
basis set. Described algorithm gives reasonable average error 0.3 millihartree due to
use of SP operations on GPU. To improve the accuracy of matrix-matrix multiplica-
tion more advanced heterogeneous computing model was proposed19. This model splits
each matrix element-wise into ‘large’ and ‘small’ components and calculates only small
components on GPU. With this model applied for the 168-atom valinomycin molecule
in a cc-pVDZ basis set the speedup of 10.1 times was observed on an NVIDIA Tesla
C1060 GPU compared to AMD Athlon 5600+. While for calculations with pure GPU
matrix operations speedups of 13.8 and 7.8 times for single-precision (SGEMM) and
double-precision (DGEMM) were observed. The errors in the correlation energy were
-10.0 and -1.2 kcal mol-1 for SP and heterogeneous calculations, respectively. Consider-
ing drastically improved DP performance of the modern GPU, which is only three times
99
smaller than SP for the latest NVIDIA Tesla K20x, the advantages of the proposed het-
erogeneous model are questionable. Speedups for various matrix-matrix multiplications
using different *GEMM calls from CUDA library can be seen on Fig.4.919.
to a full *GEMM implementation, which includes thepossibility of transposes being taken, is tedious butstraightforward.
We have implemented this approach for the GPU, as acomplete replacement for *GEMM. The pi and qj values arechosen such that each submultiplication fits within thecurrently available GPU memory. Each multiplication isstaged through the GPU, and the results assembled on theCPU. This process is hidden from the user code, whichsimply sees a standard *GEMM call.
3.2. Heterogeneous Computing with MGEMM. Withthe problem of limited memory solved, we will nowdemonstrate how to overcome the lack of double precisionGPU hardware. Again, consider the matrix multiplication:
C ) A·B (13)
We can split each matrix element-wise into ‘large’ and‘small’ components, giving:
C ) (Alarge + Asmall)(Blarge + Bsmall)) A·Blarge + Alarge·Bsmall + Asmall·Bsmall
The AsmallBsmall term consists entirely of ‘small’ numbersand can be run in single precision on the GPU (using thecleaving approach described above, if needed). The othertwo terms contain ‘large’ numbers and need to be run indouble precision. However, since each of the ‘large’ matricesshould be sparse, these terms each consist of a dense-sparsemultiplication. We only store the nonzero terms of the Alarge
and Blarge matrices, cutting the computational complexitysignificantly. Consider:
C′ik ) AijBjklarge (14)
Only a few Bjklarge will be nonzero, and we consider each
in turn. For a particular scalar Bjklarge, only the kth column of
C′ will be nonzero and is equal to the product of Bjklarge and
the jth column vector of A. This nonzero column vector C′ikcan be added to the final result, C, and the next Bjk
large can beconsidered. A similar process can be applied to the AlargeBsmall
term (producing row vectors of C). Again, this approach canbe generalized to a full *GEMM implementation, includingtransposes.
The remaining question is that of splitting the matrices.We have taken the simple approach of defining a cutoffvalue, δ. If |Aij| > δ, that element is considered ‘large,’otherwise it is considered to be ‘small.’
We have implemented our algorithm we have dubbedMGEMM for mixed-precision general matrix multiply. Itoperates similarly to the other *GEMM routines but takesone extra argumentsthe value of δ.
4. MGEMM Benchmarks
We will now discuss some benchmarks for MGEMM. Ouraim is to assess the speed and accuracy of MGEMM forvarious matrix structures and the choice of cutoff tolerancecompared to a DGEMM call on the CPU. In particular, it isimportant to benchmark how much computational speed isgained using the mixed-precision MGEMM with the GPUas a function of the loss in accuracy compared to DGEMM.
Throughout this section, CPU calculations were made usingan Intel Xeon E5472 (Harpertown) processor clocked at 300GHz attached to an NVIDIA Tesla C1060 (packaged into aTesla S1070). The GPU calls were limited to 256 MiB ofRAM to model a more restricted GPU in a typical BOINC(Berkeley Open Infrastructure for Network Computing)client.25,26
4.1. Using Model Matrices. In Figure 1 we show thespeedup for a variety of *GEMM calls using matrices ofincreasing (square) size. Three different types of matriceswere considered, based on the number of randomly scattered‘large’ elements. All the matrices were initialized withrandom values in the range [-1, 1], forming the ‘back-ground’ and ‘salted’ with a fraction fsalt of random largervalues in the range [90, 110]. The size of the MGEMMcutoff parameter δ was chosen such that all the saltedelements were considered ‘large’.
There are three MGEMM curves plotted, for differentvalues of fsalt ) 10-2, 10-3, and 10-4. The SGEMM(cleaver)curve corresponds to doing the full matrix multiplication onthe GPU using the GEMM(cleaver) and includes the timetaken to down convert the matrices to single precision onthe CPU. The DGEMM(cleaver) curve corresponds to a fulldouble-precision matrix multiplication on the GPU, whichis possible for modern cards, and we include it for complete-ness. Square matrices were used in all cases, with notranspositions in the *GEMM calls. All the runs wereperformed 10 times, and speedups are obtained relative tothe time taken for the corresponding DGEMM call on theCPU.
Examining the results, we see that SGEMM on the GPUgives a speedup of 17.1 times over running DGEMM onthe CPU for a matrix of size 10 048 × 10 048 and is evenfaster for larger matrices. This represents an upper boundfor the speedups we can hope to obtain with MGEMM forsuch matrices. The speedups increase significantly as thematrices become larger due to the masking of memory accesslatencies and due to other overheads when employing theGPU for more compute-intensive processes.
Figure 1. Speedup for various *GEMM calls as a function of(square) matrix size (averaged over 10 runs). Most elementswere in the range [-1, 1], with the ‘salt’ values in the range[90, 110]. Times are scaled relative to running DGEMM onthe CPU.
138 J. Chem. Theory Comput., Vol. 6, No. 1, 2010 Olivares-Amaya et al.
Figure 4.9: Speedup for various *GEMM calls as a function of square matrix size(averaged over 10 runs). MGEMM correspond to the heterogeneous model withdifferent thresholds. Times are scaled relative to running DGEMM on the CPU.
Recently some of the CC methods were also successfully implemented on GPU.
DePrince et al. implemented CCSD and TD-CISD methods in Psi3 electronic structure
package20. They developed a new code that uses CUBLAS and GotoBLAS libraries
and performs operations on both CPU and GPU simultaneously. For the large systems
where the data structures does not fit entirely in GPU memory, the tensors were tiled
and required data copied to the GPU as needed. This approach resulted in 4.3 times
faster execution on NVIDIA Tesla C2050 (Fermi) GPU compare to the corresponding
CPU-only algorithm on two Intel Xeon X5550 CPUs for the systems as large as system
100
with 70 electrons and 250 virtual orbitals. Wenjing et al. used different approach to
implement CCSD(T) method on GPU in NWChem that produce optimized CUDA code
given the specification of a tensor contraction expression. Instead of using CUBLAS
DGEMM special custom CUDA kernels for tensor contractions were developed. This
approach demonstrated speedup over a factor of 8.4 using one NVIDIA Tesla T10 GPU
as compared to one CPU core and over 2.6 when utilizing the entire system using hybrid
CPU + GPU solution with 2 GPUs and 5 cores (instead of 7 cores per node). Execution
of this code on NVIDIA Tesla T20 (Fermi architecture) demonstrated speedup of about
3.4 over T10 GPUs with this code.
4.5 Challenges of the implementation of the CCSD
method on GPU
As described in the Chapter 1 the process of solving CC equations requires calculations
of many complex tensor contractions. Consider one of the typical contractions in CCSD
method from T2 equation24
∑e f
te fi j Wabe f
where Wabe f is an intermediate, i, j represent occupied orbitals and a, b, e, f are unoc-
cupied orbitals. The computational complexity of this term using big O notation is
O(O2V4), where O is the number of occupied orbitals and V is the number of virtual
orbitals. The overall computational cost per iteration is typically O(O2V4 + O3V3 +
O4V2) operations. Considering that, for example, one DNA base molecule with the cc-
pVTZ basis set has more than 1000 basis functions one can estimate the tremendous
computational resources required to calculate DNA bases clusters. Thus it is extremely
important that tensor contraction operations implemented as efficiently as possible. The
101
described contraction as well as most tensor contractions in CCSD method can be rep-
resented as matrix operations, in particularly as matrix-matrix multiplications. The effi-
ciency of the matrix operations has been studied for a long time and there are several
efficient algorithms and programming libraries, such as different Basic Linear Algebra
Subprograms (BLAS) implementations. Because of the nature of matrix operations and
the layout of matrices in memory, parallelization of the matrix operations can give a
substantial speedup, which is implemented in many BLAS libraries, such as ATLAS,
Intel Math Kernel Library (MKL), AMD Core Math Library (ACML) and NVIDIA
CUBLAS. Therefore CCSD method computational time can be significantly reduced
through parallelization.
In addition to the contraction operations efficient implementation of the permutation
operation is needed especially for CCSD(T) method. In CCSD(T) method up to 50% of
time could be spent for permutation operations. There is no permutation operations for
tensors in standard libraries for GPU. Thus special kernels for permutation operations
has to be written.
CCSD(T) method requires one specific operation that comes from the following
expression for CCSD(T) energy correction:
E = ∑i jkabc
t(a)i jkabct(b)i jkabc
∆ia +∆ jb +∆kc
It is similar to dot-product matrix operation but requires the division by elements of ∆
matrices. Thus it cannot be implemented through the BLAS functions and has to be
developed as a special CUDA kernel.
102
4.6 Implementation details
4.6.1 Overview of the code structure and libraries design
Our GPU implementation of CC methods is a part of ccman2 library25 of Q-Chem 4
electronic structure package13.
Fig. 4.10 gives an overview of different components of CC/EOM-CC codes and
libraries. ccman2 drives the execution, libcc contains codes for specific CC equations
(such as CC amplitudes update codes, etc) implemented using tensor objects, libsolve
contains code for DIIS and Davidson procedures, libctx stores the context of calcula-
tions. The two interface components that link ccman2 to a host electronic structure plat-
form are: (i) liblegacy that provides the information about orbital spaces, integrals, MO
coefficients; and (ii) virtual memory manager (livmm) that handles the IO and mem-
ory. Only vertical dependencies (e.g., ccman2 knows about libcc, but libcc does not
depend on ccman2) are present (no circular or horizontal dependencies). The two weak
dependencies (ccman2 to libvmm and libtensor) are used for initialization only. Initially
ccman2 code was developed for CPU calculations only. However, the libraries were
specifically designed to allow an extension to different computer architectures. Using
modular and layered architecture of the ccman2 package we we able to implement GPU
version of the ccman2 with changes only in libtensor, libcc and libvmm libraries. The
short description of this libraries are given below.
Libtensor library is an open-source object-oriented C++ library of classes and rou-
tines designed to perform general-purpose tensor algebra. The primary purpose of the
library is to enable post-Hartree Fock electronic structure methods, such as coupled-
cluster methods. The library supports tensors of arbitrary order (number of dimensions),
size, and symmetry.
103
Libraries and dependencies
� Only vertical dependencies, no circular dependencies.
� Encapsulation: one gateway to the rest of Q-Chem.
� Weak dependencies (ccman2 to libvmm, libtensor) for initializationonly.
Figure 4.10: Overview of CC/EOM-CC code architecture.
The library features a straightforward programming interface, full tensor symmetry
(point group including non-Abelian subgroups, permutational, spin), flexible memory
management via a separate virtual memory component, and shared-memory parallel
algorithms. Modular layered architecture of the library (Fig. 4.11) provides multiple
points of extension making it possible to add support for new tensor structures and sym-
metries, algorithms and computer architectures. In layered architecture modules depend
only on modules immediately below their level. In such architecture the replacement or
addition of a certain module in the layer will require only changes in the current layer
and immediately above. For example, we can replace BLAS module with different ven-
dor implementation and we will have to change only Simple Tensor Operations level
without changing Block Tensor Operations and library interface.
Described layered architecture of libtensor library is very important for the code
development in the emerging epoch of heterogeneous computing. Currently there are a
104
Block tensor operations
Pthreads, OpenMP and MPI
Simple Tensor Operations
BLAS/CUBLAS
LAPACK
Low-level routines,
CUDA kernels
Library interface
Serial, but parallel-aware
Figure 4.11: Overview of the libtensor library structure. A multi-layer designallows for various extensions in terms of new algorithms and data types as well asnew hardware architectures. The layers interact through well-defined interfaces;any layer can be substituted by an alternative implementation without the need tomodify the code in the layers above or below.
number of computational architectures: NVIDIA and ATI GPUs, Intel Xeon Phi copro-
cessor, etc. The development of the separate code for every architecture would be very
time-consuming. Thus, it is crucial to develop a code that can be easily extended to a
different computer architecture by addition of new modules rather than by rewriting the
entire code.
Implemented data structures and algorithms operate on large tensors by splitting
them into smaller blocks, storing them both in memory and files on disk, and apply-
ing divide-and-conquer-type parallel algorithms to perform tensor algebra. The library
offers a set of general tensor symmetry algorithms and a full implementation of ten-
sor symmetries typically found in electronic structure theory: permutational, spin and
molecular point group symmetry. The Q-Chem electronic structure software uses this
105
library to drive coupled-cluster, equation-of-motion, and algebraic-diagrammatic con-
struction methods.
Figure 4.12: Diagram of classes in libtensor. For each type of tensors there arespecialized tensor operations. General block tensors and operations on them aregeneric implementations. Concrete block tensors use the generic structures andalgorithms within, but provide a simplified interface. The template argumentin gen block tensor allows to use different types of tensors, e.g., real, complexor CUDA dense tensors, sparse tensors, or tensors with special properties. Anysuch implementation of tensor have to provide tensor operation classes (tod add,tod contract2, etc.).
Fig. 4.12 shows libtensor class diagram. External programs should work with the
library through the btensor i or tensor i interfaces. They are guaranteed to be unchanged
even though the underlying code can be significantly changed. These interfaces are
implemented by different classes, such as btensor and direct btensor. In order to adopt
106
a library to a new computer architecture the set of operations classes, such as tod add,
tod contract2, tod copy, etc., has to be provided. Then a new block tensor that is based
on these operations can be created. The example will be give below in the description
of CUDA C implementation for GPU.
A virtual memory management tool in libvmm library implements necessary func-
tions for storing large tensors on disk. This component provides a memory allocator
and an interface to advise on the memory use pattern. Inside it maintains a schedule for
reading blocks from disk to RAM and writing the results back to disk if needed.
4.6.2 Description of the GPU-enabled code
In order to enable GPU computations in ccman2 new codes were added mostly in libten-
sor library. The CPU version of the library left intact and can be using along with GPU
version. The foundation of the new implementation consists of the math kernels that
use CUBLAS matrix operations and custom CUDA C kernels for such simple opera-
tions as tod copy, tod set and tod add. In addition, a simple class cuda utils is created
to simplify copy operation between the host and device memory and to handle CUDA
errors. On top of this foundation new classes cuda dense tensor and cuda block tensor
are created. This classes follow the same design pattern as regular dense tensor and
block tensor classes but use CUDA operations.
As mentioned before non-iterative triple energy correction in the CCSD(T) method
E = ∑i jkabc
t(a)i jkabct(b)i jkabc
∆ia +∆ jb +∆kc
cannot be implemented through the CUBLAS function. A new kernel was written in
libcc library in order to calculate it. Then a class that calculates triple correction to
107
CCSD energy entirely on GPU using this kernel and cuda btod tensor class of libtensor
was created in libcc.
In addition, a new class cuda ccsd pt had to be created in ccman2. All operations,
required for the calculation of triples correction were programmed in this class using
cuda block tensor and cuda btod contractions. It was required because currently default
btod operations do not work with cuda block tensor. After the creation of special VMM
for GPU the calculation of triple correction on GPU can be done with regular ccman2
code and the separate CUDA version of ccsd pt class will be removed.
CCSD(T) has a high computational cost that scales as N7 and relatively low require-
ments for memory (N4). These facts allowed us to store all the tensors required for cal-
culation of triples’ correction in the GPU memory. We copy all tensors to GPU memory,
compute triples’ correction and copy back only a minor amount of data, that we sum up
on CPU to get triples’ correction to energy. Low memory requirements of CCSD(T)
allows us to compute the energy of the system with more than 300 basis functions on
a typical Tesla GPUs with 6 Gb of memory. This can be further improved if batching
of contraction operation is implemented. In this approach only part of the tensors are
copied to the GPU and a partial result is calculated at a time. During the execution of
tensor operations on GPU, the next batch of data can be copied to the GPU memory and
then the new batch is executed as soon as the calculation of the previous batch is done.
In order to use other CC methods, such as CCSD that has higher memory require-
ments, an implementation of a new virtual memory manager in libvmm is required.
Current implementation of VMM in libvmm library manages data storage between the
hard disk and RAM. When tensors are too large to fit in the RAM, VMM stores ten-
sors that are currently not in use on disk. When a tensor is required it is automatically
loaded by VMM from disk to RAM. In order to use such VMM with GPU a new layer
108
of GPU memory has to be added (Fig. 4.13). In this version of VMM tensor can be
stored in up to three locations: on disk, in host (CPU) RAM or in device (GPU) RAM.
In order to minimize the data transfer it should be allowed to store a copy of the ten-
sor in multiple memory layers. Thus VMM has to keep track where the “latest” (most
recently changed) version is stored and update the “older” version when the program
tries to access them. In addition VMM distinguish two types of tensor copies: read-only
and read-write. Read-only copies are never changed thus they can never become the
“latest” copies and never have to be copied back, for example from GPU memory to
host memory. The GPU-enabled version of VMM is currently under development.
Virtual memory
management GPU memory
CPU memory
Hard Disk Drive
PC
I E
xp
ress
S
AS
Figure 4.13: Memory layers of GPU implementation of VMM. Multiple copies ofthe tensor can be stored in all three layers. VMM keeps track of the latest copy ofthe tensor and updates older version as needed.
109
4.6.3 Results and conclusions
The GPU-enabled version of the CCSD(T) method was implemented. Preliminary
benchmarks on previous generation NVIDIA Tesla M2070 based on Fermi architecture
(448 cores) showed the performance close to the performance of Intel Xeon CPU of the
same generation. According to Tesla K20X (Kepler architecture) DGEMM benchmarks
we can expect three times speed up on the latest NVIDIA GPU. GPU load analysis
shows that our code utilizes about 50% of the GPU. The reason for underutilization of
the GPU could be because one tensor is not big enough to load the whole GPU and we
use only one host stream to launch kernels. Thus other kernels are not able to use idle
cores. The use of several streams can significantly improve performance, especially on
Kepler GPUs. Analysis of time spent for different operations shows that about half of
the time is spent in DGEMM calls and the other half is permutation operations. The
time spent in permutations operations can be significantly reduced by optimization of
the permutation kernel. In particular the big performance gain can be achieved by use of
shared memory and coalesced memory access. However, while non-coalesced memory
access can result in a significant performance lost in Fermi architecture GPUs it is less
important in Kepler GPUs.
All tod operations required for other CC and EOM-CC methods are implemented
and tested on GPU. A new efficient GPU-enabled VMM is required in order to use this
methods with real-sized systems. When such VMM is implemented cuda block tensor
can be directly plugged in to existing ccman2 code and all available CC methods will
work on GPU.
The purpose of this research was not only to develop a CUDA C implementation
of CC methods but to design an architecture that allows a relatively easy development
of new versions for difference computer architecture. Our implementation demonstrates
110
how the version for CPU and for heterogeneous computing on GPU can be implemented
within the same library, design and interfaces. A new modules for computing on AMD
GPUs (with OpenCL) and Intel Xeon Phi coprocessor can be added to the library with
reasonable efforts using the same approach.
111
4.7 Chapter 4 references
[1] S. Saebo and P. Pulay. The local correlation treatment. ii. implementation and tests.J. Chem. Phys., 88:1884–1890, 1988.
[2] Moore’s law. http://www.singularity.com/charts/page67.html,2009.
[3] http://www.spiral.net/problem.html, 2009.
[4] J.P. Shen and M.H Lipasti. Mcgraw-Hill, 2004.
[5] K. Yasuda. Two-electron integral evaluation on the graphics processor unit. Jour-nal of Computational Chemistry, 29(3):334–342, 2008.
[6] I.S. Ufimtsev and T.J. Martinez. Quantum chemistry on graphical processing units.1. strategies for two-electron integral evaluation. Journal of Chemical Theory andComputation, 4(2):222–231, 2008.
[7] I.S. Ufimtsev and T.J. Martinez. Quantum chemistry on graphical processing units.2. direct self-consistent-field implementation. Journal of Chemical Theory andComputation, 5(4):1004–1015, 2009.
[8] I.S. Ufimtsev and T.J. Martinez. Quantum chemistry on graphical processing units.3. analytical energy gradients, geometry optimization, and first principles molec-ular dynamics. Journal of Chemical Theory and Computation, 5(10):2619–2628,2009.
[9] H.G. Kmmel. A biography of the coupled cluster method, chapter 41, pages 334–348.
[10] V. Volkov and J.W. Demmel. Benchmarking gpus to tune dense linear algebra. InProceedings of the 2008 ACM/IEEE conference on Supercomputing, SC ’08, pages31:1–31:11, Piscataway, NJ, USA, 2008. IEEE Press.
[11] CUDA C programming guide. http://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html, 2012.
[12] NVIDIA Tesla K20-K20X GPU accelerators - benchmarks. Application perfor-mance technical brief. http://www.nvidia.com/docs/IO/122874/K20-and-K20X-application-performance-technical-brief.pdf, 2012.
112
[13] Y. Shao, L. Fusti-Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld, S. Brown,A.T.B. Gilbert, L.V. Slipchenko, S.V. Levchenko, D.P. O’Neill, R.A. Distasio Jr,R.C. Lochan, T. Wang, G.J.O. Beran, N.A. Besley, J.M. Herbert, C.Y. Lin, T. VanVoorhis, S.H. Chien, A. Sodt, R.P. Steele, V.A. Rassolov, P. Maslen, P.P. Koram-bath, R.D. Adamson, B. Austin, J. Baker, E.F.C. Bird, H. Daschel, R.J. Doerksen,A. Dreuw, B.D. Dunietz, A.D. Dutoi, T.R. Furlani, S.R. Gwaltney, A. Heyden, S.Hirata, C.-P. Hsu, G.S. Kedziora, R.Z. Khalliulin, P. Klunziger, A.M. Lee, W.Z.Liang, I. Lotan, N. Nair, B. Peters, E.I. Proynov, P.A. Pieniazek, Y.M. Rhee, J.Ritchie, E. Rosta, C.D. Sherrill, A.C. Simmonett, J.E. Subotnik, H.L. WoodcockIII, W. Zhang, A.T. Bell, A.K. Chakraborty, D.M. Chipman, F.J. Keil, A. Warshel,W.J. Hehre, H.F. Schaefer III, J. Kong, A.I. Krylov, P.M.W. Gill, M. Head-Gordon.Advances in methods and algorithms in a modern quantum chemistry programpackage. Phys. Chem. Chem. Phys., 8:3172–3191, 2006.
[14] Whitepaper. NVIDIAs next generation CUDA compute architecture: KeplerGK110. http://www.nvidia.com/content/PDF/kepler/NVIDIA-Kepler-GK110-Architecture-Whitepaper.pdf, 2012.
[15] A.G. Anderson, W.A. Goddard III, and P. Schrder. Quantum monte carlo on graph-ical processing units. Computer Physics Communications, 177(3):298 – 306, 2007.
[16] K.A. Wendt, J.E. Drut, and T.A. Lhde. Toward large-scale hybrid monte carlosimulations of the hubbard model on graphics processing units. Computer PhysicsCommunications, 182(8):1651 – 1656, 2011.
[17] S. Guochun, V. Kindratenko, I. Ufimtsev, and T. Martinez. Direct self-consistentfield computations on gpu clusters. In Parallel Distributed Processing (IPDPS),2010 IEEE International Symposium on, pages 1–8, 2010.
[18] L. Vogt, R. Olivares-Amaya, S. Kermes, Y. Shao, C. Amador-Bedolla, andA. Aspuru-Guzik. Accelerating resolution-of-the-identity second-order mollerp-lesset quantum chemistry calculations with graphical processing units. The Jour-nal of Physical Chemistry A, 112(10):2049–2057, 2008. PMID: 18229900.
[19] R. Olivares-Amaya, M.A. Watson, R.G. Edgar, L. Vogt, Y. Shao, and A. Aspuru-Guzik. Accelerating correlated quantum chemistry calculations using graphicalprocessing units and a mixed precision matrix multiplication library. Journal ofChemical Theory and Computation, 6(1):135–144, 2010.
[20] E.A. DePrince III, J.R. Hammond, and S.K. Gray. Many-body quantum chemistryon graphics processing units. In Proceedings of SciDAC, July 10-14 2011.
[21] A.A. Auer, G. Baumgartner, D. E. Bernholdt, A. Bibireata, V. Choppella,D. Cociorva, X.Y. Gao, R. Harrison, S. Krishnamoorthy, S. Krishnan, C.C. Lam,
113
Q.D. Lu, M. Nooijen, R. Pitzer, J. Ramanujam, S. Sadayapan, and A. Sibiryakov.Automatic code generation for many-body electronic structure methods: The ten-sor contraction engine. Mol. Phys., 104:211–228, 2006.
[22] A.V. Titov, I.S. Ufimtsev, N. Luehr, and T.J. Martinez. Generating efficient quan-tum chemistry codes for novel architectures. Journal of Chemical Theory andComputation, 9(1):213–221, 2013.
[23] CUBLAS library. http://docs.nvidia.com/cuda/cublas/index.html, 2012.
[24] G.D. Purvis and R.J. Bartlett. A full coupled-cluster singles and doubles model:The inclusion of disconnected triples. J. Chem. Phys., 76:1910–1918, 1982.
[25] E. Epifanovsky, M. Wormit, T. Kus, A. Landau, D. Zuev, K. Khistyaev, P. Manohar,I. Kaliman, A. Dreuw, and A.I. Krylov. New implementation of high-level corre-lated methods using a general block-tensor library for high-performance electronicstructure calculations. J. Comput. Chem., 2012. to be submitted soon.
114
Chapter 5: Future work
In this work the effect of microhydration on ionization energies and proton transfer
mechanism in nucleobases was studied. During this study the focus was on a small
clusters with no more than three water molecules. This study can be extended to bigger
clusters with more water molecules. In particular, it could be interesting to consider
the effects of the complete fist and second solvation shells and compare it with the bulk
water. Partially it was done in the work of Ghosh et al.1 where the EOM-IP-CCSD
method was combined with effective fragment potential method to study the effect of
solvation on the vertical ionization energy of thymine. Using the same technique one
can try to study the proton transfer from ionized water to nucleobases through water
wires in larger clusters. However, it has to be noted that the water involved in proton
transfer can not be described as part of the EFP system and has to be included in the
pure quantum part which can result in a relatively large system.
The continuation of the development of the GPU implementation of CC meth-
ods requires the development of GPU-enabled Virtual Memory Manager (VMM) as
described in Chapter 4. The development of new VMM will remove the limit to the
system size imposed by GPU memory size and will unlock all CC methods imple-
mented in the current CPU-only version of ccman2 library. Then after minor mod-
ifications it will be possible to use RI and Cholesky decomposition methods already
implemented in ccman2 on GPU. These methods significantly reduce the amount of
115
data storage required for computations but increase the computational cost. Consider-
ing GPU architecture these methods should be especially beneficial because they will
reduce the amount of data transfer through the PCI-Express interface that could be the
bottleneck in many computations on GPU. The increased computational cost of this
methods should be resolved by the excess computational power of GPU.
The optimization of permutation kernels can increase the performance of such meth-
ods as CCSD(T) which heavily use this operation. The implementation and optimization
of the multi-streaming version of the library that will run several kernels simultaneously
along with data transfer operations will help to increase the load of the GPU and further
increase the performance, especially on the new NVIDIA Kepler architecture.
Using the same library design and patterns it should be easy to develop implemen-
tations with other languages such as OpenCL and OpenACC. It will allow to use AMD
GPUs which potentially can have better performance in the future. The development of
the library version for Intel Xeon Phi most likely will require some changes to the kernel
design because of the difference in architectures. However, the basic principles are the
same and thus there should not be any significant obstacles with this implementation.
Finally, the development of the efficient implementation of the ccman2 library for
multinode clusters with GPUs will open the possibility to use the incredible computa-
tional power of supercomputers that is expected to reach exascale performance in the
nearest future.
116
5.1 Chapter 5 references
[1] D. Ghosh, O. Isayev, L.V. Slipchenko, and A.I. Krylov. The effect of solvation onvertical ionization energy of thymine: From microhydration to bulk. J. Phys. Chem.A, 115:6028–6038, 2011.
117
Appendix: Tensor algebra library
graphical processing unit
implementation
Details of the GPU implementation of tensor algebra library
As described in Chapter 4 ccman2 and libtensor libraries have layered structure.
Fig. A.1 gives a schematic representation of tensor contraction operation execution
across different layers. At the top layer the tensor contraction operations are pro-
grammed in libcc library. This tensor contractions use btod contract2 class from libten-
sor library. btod contract2 class is a general representation of block tensor contrac-
tion operations. It call gen bto contract2 operations with specific traits as a tem-
plate parameter. For example, in order to execute contractions on GPU one should
use cuda block tensor traits. gen bto contract2 forms batches of tensors from block
tensors and execute tod contract2.perform() operation for every batch. tod contract2
maps required contraction to corresponding mathematical kernel (e.g. kern mul2) with
required linalg parameter (e.g. if cuda block tensor traits were used than linalg cublas
is used). This kernel class calls suitable linalg operation (e.g. linalg cuda::ij ip jp x)
which then calls DGEMM operation (e.g. cublasDgemm).
118
btod contract2btod_contract2
gen_btod_contract2<Traits>
for every batch:
tod_contract2_
kern_mul<Linalg>
Linalg::ij_ip_jp_x
dgemm
Figure A.1: Schematic order of execution of tensor contraction operation.
Ideally, only the lowest level linalg operations has to be different for imple-
mentations for different hardware architectures. However, in order to handle sepa-
rate GPU memory without complex virtual memory manager we had to create par-
allel cuda tod contract2 and cuda btod contract2 classes. gen bto contract2 classes
are the same for CPU and GPU implementations. when the VMM is created
cuda btod contract2 class can be replaced with regular btod contract2 class.
119
