Marius WankoBCCMS
Excited State Photodynamics on Semiempirical and QM/MM Grounds
Marius Wanko
Bremen Center for Computational Material Science
Electron Dynamics in Complex Systems
Marius WankoBCCMS
Scientific Interest
• Focus: large chromophores embedded in a complex environment
• Optical properties (control by environment)
• Excited state dynamics FluorescenceFluorescenceproperties of GFP
Ultrafast/efficientPhotoisomerization of Retinal
Marius WankoBCCMS
Understanding the Photochemistry
1. Explore ground/excited states potential energy surface (PES)
2. Excited state molecular dynamics simulation• Sampling the configuration space, dynamic effects• State coupling/transitions in nonadiabatic regions• Decay to electronic ground state, product formation
Marius WankoBCCMS
Methodological Requirements
• ONIOM or QM/MM interface (point charges)
• Efficient QM method for ground/excited state energy (MD!)
• Analytic gradient, nonadiabatic-coupling vector,time propagation of density matrix ρij(t)
• Scheme for nonadiabatic dynamics
Challenges:• Correct description of entire relevant PES (!)• Correct response to environment (mechanical, electrostatic)
Marius WankoBCCMS
Surface Hopping Approach
• Semi-classical ansatz (classical propagation of nuclei)
• Nonadiabatic electronic wave function from numerical integrationof time-dependent Schrödinger/Kohn-Sham equation:
∑=ΨΨ∂−=Ψi
iit tcttitH );()(),;(),;(),;( elelel RrRrRrRr φh
( ) )(),(nintegratio num. ttciEcc ijij
ijijiji ρδ ⎯⎯⎯⎯ →⎯⋅−=∑ dR&h&
nonadiabaticcoupling vector
jiij φφ RRd ∇=)(
Marius WankoBCCMS
Surface Hopping Approach
Forces on nuclei
Ehrenfest: Surface hopping:),;(
el
tRR HRr
FΨ
∇=);(
el)(
RrF
iHRR
i
φ∇=
“Fewest switch” criterion [Tully1990]: hop only when occ. |ρii| changes!
• Stochastic representation of nuclear wave packet (non-coherent mixed state)
• Electronic coherence maintained
Marius WankoBCCMS
TD-DFTB Surface Hopping
2001 TD-DFTB nonadiabatic (Ehrenfest) MD + linear response2004 Analytical excited-state derivatives, density matrix
based on [Furche2002] (Z-vector equation):
0,,"'
xc3
xc"',
,, ≈=≈≈ ∑∑
σσσσσσ
α
αα
α
βα
βαβ
α
δρδρδρδγ EgqMqKqqK klij
Tklijklij
Sklij
2004 Davidson algorithmformal: O(N6) -> O(N4) scalingDFTB: N3.3 scaling
TDDFT TD-DFTB
System State Basis GS ES+∇ GS ES+∇
T-stilbene 1Bu SVP 411 1114 0.22 0.22
Hexahelicene 3A SV(P) 2050 2594 0.82 1.21
DMABN 1A1 TZVPP 4386 9056 0.23 0.32
Retinal 1A SVP 2148 7521 0.93 1.92
2006 NAC vectors, surface hopping
Marius WankoBCCMS
TD-DFTB Surface Hopping
• PES: good agreement with TDDFT methods (valence π-π* excitations)
• Convergence problems near CI -> unrestricted linear response
• NAC vector: 2-center approximation of Chernyak-Mukamelagreement with CASSCF
Marius WankoBCCMS
Failure of TDDFT
• Qualitative errors in PES from TDDFT(B) – static correlation (multi-configurational ground state)– open shell ground state in nonadiabatic region (CI)– charge-transfer (failure of local X-kernel in extended π-systems)– wrong CI topology
Correct PES and response to environment requires:– explicit treatment of exchange and static correlation– balanced incorporation of dynamic/static correlation
correct TDDFT(N-2)
Marius WankoBCCMS
Semiempirical MRCI
• Idea of MRCI/MRMP2:I. Small selection of configurations “reference” to catch essential
electronic structure of relevant states (static correlation)II. Include dynamic correlation (Coulomb hole) via CISD (MP2)
• Semiempirical: (II.) included in Fock matrix by definition!
• Implicit correlation + orthogonalization reduces 2-electron integrals (2-center: short-range damped , 3- and 4-center: negligible)
=> CI matrix much more sparse
Marius WankoBCCMS
Semiempirical MRCI
• Quick convergence wrt. active-orbital window and reference!
=> correlate only π-system, use small reference
• Same effect in Grimme’s DFT/MRCI (empirical scaling of 2-e integrals to avoid double counting of dynamic correlation)
3# reference configurations
Marius WankoBCCMS
OM2/MRCI
• Conventional MNDOs (AM1, PM3) fitted to ground state/equilibrium propertiespoor single-particle spectrum (too small HOMO-LUMO gap)
• OM1/OM2: new function for resonance integral consistent with shape of 2-center 1-e integrals in Löwdin-orthogonalized basis λHµν
=> improved MRCI excitation energies
Molecule State AM1 PM3 OM2 Exp.
HBDI (anion) 1A’ 2.08 2.08 2.56 2.59
Octatetraene 1Ag1Bu
3.304.43
2.984.30
4.374.87
3.974.41
OT-retinal (gas phase) La 1.84 1.79 2.33 2.03
Naphthalene 1B2u1B3u
4.042.28
3.822.44
4.873.96
4.664.13
Azulene 1B21A11B2
1.232.672.96
1.052.412.61
1.843.383.97
1.783.524.19
Marius WankoBCCMS
OM2/MRCI: Application to Spectral Tuning
• OM2/MRCI reproduces exp./ab initio for various kinds of spectral shifts:– Polarization (counter ion, entire protein environment)– Dihedral distortion of conjugated chain and ß-ionone ring– Bond-length alternation– bR vs. sRII, various mutants
Opsin shift bR–sRIIExp.: +0.32 eVOM2/MRCI: +0.31 eV
Shift Rho–BathoExp.: -0.21 eVOM2/MRCI: -0.19 eV
• Quantitative accuracy much better than CASSCF (or CIS)• Succeeds in cases where TDDFT fails (S1 gradient, charge transfer)
3 to go…
Marius WankoBCCMS
OM2/MRCI Surface Hopping
• Nonadiabatic time propagation• Tully’s minimal switching• Semi-analytical OM2 gradient• Scaling O(N4)• QM/MM-ready (included in CHARMM)• CI optimizer, state following, MO mapping
• Bug in gradient => only preliminary examples here
2 to go…
Marius WankoBCCMS
Collaborations, Acknowledgement
• Michael Hoffmann (BCCMS Bremen)• Marcus Elstner, Jan Frähmcke, Prasad Fatak (TU Braunschweig)• Dávid Heringer (Budapest), Paul Strodel (Cambridge)
• Tom Keal, Axel Koslowski, Walter Thiel (MPI Mülheim)• Frank Neese (Universität Bonn)• Emad Tajkhorshid (Urbana-Champaign)• Peter König, Qiang Cui (Madison)
€: DFG Forschergruppe “Molecular mechanisms of Retinal protein action”