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
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