Justin Kim, Yinghua Wu, Xin Chen and Victor S. BatistaDepartment of Chemistry, Yale University, New Haven, CT

06520-8107

Ultrafast Excited State Intramolecular Proton Transfer in HPO and HBT

Israel Science Foundation WorkshopDiffusion, Solvation and Transport of Protons in Complex and Biological Systems

Hilton Eilat Queen of Sheba Hotel, January 13-17, 2008Organizers: E. Pines, N. Agmon, M. Gutman and D. Huppert.

Funding: • NSF CHE-0345984• NSF ECCS-0725118• NIH 2R01-GM043278-14• DOE DE-FG02-07ER15909• US-Israel BSF • Sloan Fellowship• Camillie Dreyfus Teacher Scholar Award• NSF ECS-0404191 • Research Corporation Innovation Award RI0702• ACS PRF-37789-G6

Transient appearance of the C=O stretching mode of the keto*-state of HBT after excitation of the enol → enol* transition.

Ultrafast Excited State Intramolecular Proton Transfer in HBT

E. T. J. Nibbering, H. Fidder and E. Pines Annu. Rev. Phys. Chem. (2005) 56:337-67

310-350 nm

IVR~ 750 fs, 15 ps ~50 fs

Time-Sliced Simulations of Quantum Processes

Wu,Y.; Batista, V.S. J. Chem. Phys. (2003) 118, 6720Wu,Y.; Batista, V.S. J. Chem. Phys. (2003) 119, 7606Wu,Y.; Batista, V.S. J. Chem. Phys. (2004) 121, 1676Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. (2005) 122, 64102Wu,Y.; Herman, M.F.; Batista, V.S. J. Chem. Phys. (2005) 122, 114114Wu,Y.; Batista, V.S. J. Chem. Phys. (2006) 124, 224305Chen, X.; Batista, V.S. J. Chem. Phys. (2006) 125, 124313Chen, X.; Batista, V.S. J. Photochem. Photobiol. (2007) 190, 274

MP/SOFT Method

Trotter Expansion

Wu,Y.; Batista, V.S. J. Chem. Phys. 121, 1676 (2004)

Fixed Point Self-Consistent Contraction Mapping

2

Re

Re

( )Re

i ii

i

i ii

i

i i ii

i

g xx

g

g pp

g

g x x

g

1 12 2Min( ) =0; where y { , , }i i iy x p

Computation of Observables

Time dependent reactant population:

Absorption Spectrum:

Reaction Surface 69-dimensional Model

V(r1,r2,z) = V0(r1,r2) + 1/2 [z- z0(r1,r2)] F(r1,r2) [z-z0(r1,r2)]

V0 : Reaction surface

z0 : ab initio geometries

F : ab initio force constants

r1,r2 : reaction coordinatesr2

r1

Energy (kcal/mol)

Energy (kcal/mol)

OH bond length (a.u.)

S0

S1

OH bond length (a.u.)

CCC bend. angle

(degrees)

Reaction Surface V0(r1,r2)

KETO

CCC bend. angle

(degrees)

ENOL

t=0 fst=50 fst=100 fst=200 fst=300 fst=400 fst=500 fst=600 fst=700 fst=800 fst=900 fs

ESIPT or ESIHT ?

Ultrafast Charge Redistribution in HBT

PR(t), (TDSCF)PR(t), (MP/SOFT)

Tr [2(t)], (MP/SOFT)

ESIPT in HBT: 69-Dimensional MP/SOFT Wavepacket Propagation

t = 50 fs

UV-Vis Photoabsorption Spectrum of HBT

MP/SOFT spectrum

Experiments:Rini M,KummrowA, Dreyer J, Nibbering ETJ, Elsaesser T. 2003. Faraday Discuss. 122:27–40Rini M, Dreyer J, Nibbering ETJ, Elsaesser T. 2003. Chem. Phys. Lett. 374:13–19

t = 0 fs

t = 500 fs

Ultrafast Excited State Intramolecular Proton Transfer in HBT

Wavenumber [cm-1]1700 1600 1500 1400 1300 1200 1100 1000

IR - S1 (Calc.)

Wavenumber [cm-1]1700 1600 1500 1400 1300 1200 1100 1000

IR - S0 (Calc.)

IR I

nten

sity

IR I

nten

sity

IR I

nten

sity

Wavenumber [cm-1]

Wavenumber [cm-1]

Wavenumber [cm-1]

1700 1600 1500 1400 1300 1200 1100 1000

1700 1600 1500 1400 1300 1200 1100 1000

1700 1600 1500 1400 1300 1200 1100 1000

IR - S0 (Exp.)

IR - S0 (Calc.)

IR - S1 (Calc.)

Infrared spectra of HBT

Wavenumber [cm-1]

Wavenumber [cm-1]

TheoreticalExperimental

Transient infrared spectra of HBT

Experiments:Rini M,KummrowA, Dreyer J, Nibbering ETJ, Elsaesser T. 2003. Faraday Discuss. 122:27–40Rini M, Dreyer J, Nibbering ETJ, Elsaesser T. 2003. Chem. Phys. Lett. 374:13–19

ESIPT in the keto-enolic tautomerization of 2-(2’-hydroxyphenyl)-oxazole (HPO).

Changes in hybridization and connectivityClassical Dynamics (HPMO)

Vendrell, O.; Moreno, M.; Lluch J.M.; Hammes-Schiffer, S. J. Phys. Chem. B 108, 6745 (2004)

Quantum Dynamics (7-d simulation, related ESIPT system)

Petkovic, M.; Kühn, O. J. Phys. Chem. A 107, 8458 (2003)

SC-IVR (HPO)

Guallar, V.; Batista, V.S.; Miller, W.H. J. Chem. Phys. 113, 9510 (2000)Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002) Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 249903 (2002)

Wu,Y.; Batista, V.S. J. Chem. Phys. (2006) 124, 224305

CASSCF Reaction Surface Potential V0(r1,r2)

UV-Vis Absorption Spectrum of 2-2’-(hydroxyphenyl)-oxazole (HPO)

35-dimensional wave-packet propagation

Wu,Y.; Batista, V.S. J. Chem. Phys. (2006) 124, 224305

HPMO in n-hexane

Douhal et.al. JPC 100, 19789 (1997)

Time-Dependent Reactant (enol) Population

Wu,Y.; Batista, V.S. J. Chem. Phys. (2006) 124, 224305Guallar, V.; Batista, V.S.; Miller, W.H. J. Chem. Phys. 113, 9510 (2000)Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002) Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 249903 (2002)

Femtosecond fluorescent transient at 420nm for HPMO in 3-methylpentane

JPC 102,1657 (1998) Zewail, Fiebig and co-workers

Decoherence and Recoherence DynamicsHK SC-IVR vs. MP/SOFT

Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002)

[2]

[2]

[1]

[1]Wu,Y.; Batista, V.S. J. Chem. Phys. (2006) 124, 224305

Contour plot of the percentage product yield for bichromatic coherent-control at 100 fs after photoexcitation of the system, as a function of the laser controllable parameters.

Coherent-Control of the keto-enolic isomerization in HPO

Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002)

Nonadiabatic Propagation

Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. (2005) 122, 64102

Chen, X.; Batista, V.S. J. Chem. Phys. (2006) 125, 124313

MP/SOFT Nonadiabatic Propagation

Chen,X.; Batista, V.S. J. Chem. Phys. (2006) in prep.Nonadiabatic Dynamics of Pyrazine

S1/S2 Conical Intersection

Chen,X.; Batista, V.S. J. Chem. Phys. (2006) 125, 124313

Benchmark Calcs.: 4-mode model

Nonadiabatic Dynamics of PyrazineS1/S2 Conical Intersection

Chen,X.; Batista, V.S. J. Chem. Phys. (2006) 125, 124313

Benchmark Calcs.: 24-mode model

Benchmark Calcs.: 24-mode model

Flores SC and Batista VS, J. Phys. Chem. B (2004) 108: 6745-6749.Gascon JA, Batista VS, Biophys. J. (2004) 87:2931-29411.Gascon JA, Sproviero EM, Batista VS, J. Chem. Theor. Comput. (2005) 1:674-685.Gascon JA, Sproviero EM, Batista VS, Acc. Chem. Res. (2006) 39, 184-193.Chen X and Batista VB, J. Photochem. Photobiol. (2007) 190, 274-282.

The Primary Step in Vision cis/trans isomerization in visual rhodopsin

Empirical model (G. Stock)

Time dependent wavepacket undergoing nonadiabatic dynamics at the conical intersection of S1/S0 potential energy surfaces

Xin Chen and Victor S. Batista. J. Photochem. Photobiol. (2007) 190, 274

Time dependent reactant population

Ptrans(S0)

Pcis(S1)

‡Chen X, Batista VS; J. Photochem. Photobiol. (2007) 190, 274 *Flores SC and Batista VS, J. Phys. Chem. B (2004) 108: 6745-6749

MP/SOFT‡

TDSCF*

Time, fs

0.67

| k >

| j >

Isomerization coordinate, )cc( 1211

Quantum interference of molecular wavepackets associated with indistinguishable pathways to the same

target stateFlores SC; Batista VS, J. Phys. Chem. B 108: 6745-6749 (2004) Batista VS; Brumer P, Phys. Rev. Lett. 89, 143201 (2002)

CR =

CR=

Bichirped Coherent Control ScenarioFlores SC; Batista VS, J. Phys. Chem. B (2004) 108: 6745-6749

Chirped Pump Pulses (Wigner transformation forms)

Energy

Reaction coordinate (Stretch. Coord.)

S1

NC:

Impulsive Stimulated Raman Scattering

S0

Excited State S1

Ground State S0

cis trans

Exact Quantum Dynamics Simulations (t=218 fs, CR=212 fs2)

)fs35FWHM(nm500

Excited State S1

Ground State S0

cis trans

Exact Quantum Dynamics Simulations (t=218 fs, CR=-146 fs2)

)fs35FWHM(nm500

Bichirped Coherent Control Maps (1.2 ps)

Pulse Relative Intensities

Pul

se R

elat

ive

Pha

ses

Thermal Correlation Functions

Time-Dependent Boltzmann Ensemble Averages

Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. 122, 64102 (2005)

Bloch Equation: MP/SOFT Integration

Partition Function Boltzmann Matrix:

Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. 122, 64102 (2005)

Position-Position Correlation Function

Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. 122, 64102 (2005)

Conclusions

• We have introduced the MP/SOFT method for time-sliced simulations of quantum processes in systems with many degrees of freedom. The MP/SOFT method generalizes the grid-based SOFT approach to non-orthogonal and dynamically adaptive coherent-state representations generated according to the matching-pursuit algorithm. • The accuracy and efficiency of the resulting method were demonstrated in simulations of excited-state intramolecular proton transfer in HPO and HBT, as modeled by multidimensional ab initio reaction surface Hamiltonians, as well as in benchmark simulations of nonadiabatic quantum dynamics in pyrazine.• Further, we have extended the MP/SOFT method for computations of thermal equilibrium density matrices (equilibrium properties of quantum systems), finite temperature time-dependent expectation values and time-correlation functions. The extension involves solving the Bloch equation via imaginary-time propagation of the density matrix in dynamically adaptive coherent-state representations, and the evaluation of the Heisenberg time-evolution operators through real-time propagation.

• NSF CHE-0345984• NSF ECCS-0725118• NIH 2R01-GM043278-14• DOE DE-FG02-07ER15909• US-Israel BSF • Sloan Fellowship• Camillie Dreyfus Teacher Scholar Award• NSF ECS-0404191 • Research Corporation Innovation Award RI0702• ACS PRF-37789-G6 • DOE NERSC Allocation of Supercomputer Time

Workshop Organizers: E. Pines, N. Agmon, M. Gutman and D. Huppert.

Thank you !

Acknowledgments