Israel Science Foundation Workshop Diffusion Solvation and Transport

Israel Science Foundation Workshop Diffusion, Solvation and Transport of Protons in Complex and Biological Systems Hilton Eilat Queen of Sheba Hotel, January 13 -17, 2008 Organizers: E. Pines, N. Agmon, M. Gutman and D. Huppert. Ultrafast Excited State Intramolecular Proton Transfer in HPO and HBT Justin Kim, Yinghua Wu, Xin Chen and Victor S. Batista Department of Chemistry, Yale University, New Haven, CT 06520 -8107 Funding: • • • NSF CHE-0345984 NSF ECCS-0725118 NIH 2 R 01 -GM 043278 -14 DOE DE-FG 02 -07 ER 15909 US-Israel BSF Sloan Fellowship Camillie Dreyfus Teacher Scholar Award NSF ECS-0404191 Research Corporation Innovation Award RI 0702 ACS PRF-37789 -G 6

E. T. J. Nibbering, H. Fidder and E. Pines Annu. Rev. Phys. Chem. (2005) 56: 337 -67 Ultrafast Excited State Intramolecular Proton Transfer in HBT Transient appearance of the C=O stretching mode of the keto*-state of HBT after excitation of the enol → enol* transition. IVR~ 750 fs, 15 ps 310 -350 nm ~50 fs

Time-Sliced Simulations of Quantum Processes

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

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

Fixed Point Self-Consistent Contraction Mapping

Computation of Observables Absorption Spectrum: Time dependent reactant population:

Reaction Surface 69 -dimensional Model V(r 1, r 2, z) = V 0(r 1, r 2) + 1/2 [z- z 0(r 1, r 2)] F(r 1, r 2) [z-z 0(r 1, r 2)] V 0 : Reaction surface r 1, r 2 : reaction coordinates z 0 : ab initio geometries F : ab initio force constants r 1 r 2

Reaction Surface V 0(r 1, r 2) Energy (kcal/mol) ENOL KETO OH bond length (a. u. ) S 1 gle an d. en ees) b r CC (deg C Energy (kcal/mol) S 0 le OH bond length (a. u. ) ng. a ) nd be rees C g CC (de

ESIPT or ESIHT ? Ultrafast Charge Redistribution in HBT t=800 t=900 t=50 fs t=700 t=500 t=400 t=200 t=100 t=600 t=300 t=0 fsfs

ESIPT in HBT: 69 -Dimensional MP/SOFT Wavepacket Propagation PR(t), (MP/SOFT) PR(t), (TDSCF) Tr [ 2(t)], (MP/SOFT) t = 50 fs

UV-Vis Photoabsorption Spectrum of HBT MP/SOFT spectrum Experiments: Rini M, Kummrow. A, Dreyer J, Nibbering ETJ, Elsaesser T. 2003. Faraday Discuss. 122: 27– 40 Rini M, Dreyer J, Nibbering ETJ, Elsaesser T. 2003. Chem. Phys. Lett. 374: 13– 19

Ultrafast Excited State Intramolecular Proton Transfer in HBT t = 0 fs IR - S 0 (Calc. ) 1700 1600 1500 1400 1300 1200 1100 1000 Wavenumber [cm-1] t = 500 fs IR - S 1 (Calc. ) 1700 1600 1500 1400 1300 Wavenumber 1200 [cm-1] 1100 1000

Infrared spectra of HBT IR Intensity IR - S 1 (Calc. ) 1600 1500 1400 1300 1700 1100 1000 IR - S 0 (Calc. ) 1600 1500 1400 1300 1200 Wavenumber [cm-1] 1100 1000 IR - S 0 (Exp. ) IR Intensity 1700 1200 Wavenumber [cm-1] IR Intensity 1700 1600 1500 1400 1300 Wavenumber 1200 [cm-1] 1100 1000

Transient infrared spectra of HBT Experimental Theoretical Wavenumber [cm-1] Experiments: Rini M, Kummrow. A, Dreyer J, Nibbering ETJ, Elsaesser T. 2003. Faraday Discuss. 122: 27– 40 Rini 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). Wu, Y. ; Batista, V. S. J. Chem. Phys. (2006) 124, 224305 Changes in hybridization and connectivity Classical 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)

CASSCF Reaction Surface Potential V 0(r 1, r 2)

Wu, Y. ; Batista, V. S. J. Chem. Phys. (2006) 124, 224305 UV-Vis Absorption Spectrum of 2 -2’-(hydroxyphenyl)-oxazole (HPO) HPMO in n-hexane Douhal et. al. JPC 100, 19789 (1997) 35 -dimensional wave-packet propagation

Wu, Y. ; Batista, V. S. J. Chem. Phys. (2006) 124, 224305 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) Time-Dependent Reactant (enol) Population Femtosecond fluorescent transient at 420 nm for HPMO in 3 methylpentane JPC 102, 1657 (1998) Zewail, Fiebig and co-workers

Decoherence and Recoherence Dynamics HK SC-IVR vs. MP/SOFT [1] [2] [1] Wu, Y. ; Batista, V. S. J. Chem. Phys. (2006) 124, 224305 [2] Batista, V. S. ; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002)

Coherent-Control of the keto-enolic isomerization in HPO 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. Batista, V. S. ; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002)

Chen, X. , Wu, Y. ; Batista, V. S. J. Chem. Phys. (2005) 122, 64102 Chen, X. ; Batista, V. S. J. Chem. Phys. (2006) 125, 124313 Nonadiabatic Propagation

MP/SOFT Nonadiabatic Propagation

Chen, X. ; Batista, V. S. J. Chem. Phys. (2006) 125, 124313 Chen, X. ; Batista, V. S. J. Chem. Phys. (2006) in prep. Nonadiabatic Dynamics of Pyrazine S 1/S 2 Conical Intersection Benchmark Calcs. : 4 -model

Chen, X. ; Batista, V. S. J. Chem. Phys. (2006) 125, 124313 Nonadiabatic Dynamics of Pyrazine S 1/S 2 Conical Intersection Benchmark Calcs. : 24 -model

Benchmark Calcs. : 24 -model

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

Empirical model (G. Stock)

Time dependent wavepacket undergoing nonadiabatic dynamics at the conical intersection of S 1/S 0 potential energy surfaces Xin Chen and Victor S. Batista. J. Photochem. Photobiol. (2007) 190, 274

Time dependent reactant population MP/SOFT‡ TDSCF* 0. 67 Ptrans(S 0) Pcis(S 1) Time, fs ‡Chen X, Batista VS; J. Photochem. Photobiol. (2007) 190, 274 *Flores SC and Batista VS, J. Phys. Chem. B (2004) 108: 6745 -6749

Quantum interference of molecular wavepackets associated with indistinguishable pathways to the same target state Flores SC; Batista VS, J. Phys. Chem. B 108: 6745 -6749 (2004) Batista VS; Brumer P, Phys. Rev. Lett. 89, 143201 (2002) |j> |k> Isomerization coordinate,

Bichirped Coherent Control Scenario Flores SC; Batista VS, J. Phys. Chem. B (2004) 108: 6745 -6749 Chirped Pump Pulses (Wigner transformation forms) CR = CR=

Impulsive Stimulated Raman Scattering Energy S 1 S 0 Reaction coordinate (Stretch. Coord. ) NC:

Exact Quantum Dynamics Simulations (t=218 fs, CR=212 fs 2) Excited State S 1 Ground State S 0 cis trans

Exact Quantum Dynamics Simulations (t=218 fs, CR=-146 fs 2) Excited State S 1 Ground State S 0 cis trans

Pulse Relative Phases Bichirped Coherent Control Maps (1. 2 ps) Pulse Relative Intensities

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

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 timecorrelation 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 timeevolution operators through real-time propagation.

Acknowledgments • • • NSF CHE-0345984 NSF ECCS-0725118 NIH 2 R 01 -GM 043278 -14 DOE DE-FG 02 -07 ER 15909 US-Israel BSF Sloan Fellowship Camillie Dreyfus Teacher Scholar Award NSF ECS-0404191 Research Corporation Innovation Award RI 0702 ACS PRF-37789 -G 6 • DOE NERSC Allocation of Supercomputer Time Workshop Organizers: E. Pines, N. Agmon, M. Gutman and D. Huppert. Thank you !