yinghua wu* xin chen, yinghua wu and victor s. batista department of chemistry, yale university, new...
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Yinghua Wu*
Xin Chen, Yinghua Wu and Victor S. Batista
Department of Chemistry, Yale University, New Haven, CT 06520-8107
Xin Chen*Current address: Department of Chemistry, Tulane University.
Multidimensional Quantum Dynamics: Methods and Applications
Tuesday, September 28th, 2004 - Physical Chemistry Seminar 11:00 a.m., Room 1315 Chemistry Building Department of Chemistry, University of Wisconsin-Madison
Wcrest.gif
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.; Kuhn, 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)
Computation of Observables
Time Dependent Reactant Population:
Absorption Spectrum:
Time Dependent Survival Amplitude
Reaction Surface 35-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 coordinates
Reaction Coordinates in HPO
r1: H-stretching
Reaction Coordinates in HPO
r2: internal bending
CASSCF Reaction Surface Potential V0(r1,r2)
Time-Sliced Simulations of Quantum Processes
Wu,Y.; Batista, V.S. J. Chem. Phys. 118, 6720 (2003)Wu,Y.; Batista, V.S. J. Chem. Phys. 119, 7606 (2003)Wu,Y.; Batista, V.S. J. Chem. Phys. 121, 1676 (2004)Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. submitted (2004)Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004)
MP/SOFT Method
Trotter Expansion
Time-Dependent Survival AmplitudeHK SC-IVR vs. MP/SOFT
Time-Dependent Survival Amplitude
HK SC-IVR vs. Classical Wigner
Wigner SC-IVR
Douhal et.al. JPC 100, 19789 (1997), HPMO in n-hexane
S1
S0
Comparison with experimental data
WIGNER, TD-SCF, HK SC-IVR, MP/SOFT
Time Dependent Reactant Population
Early Time Relaxation Dynamics
WIGNER, TD-SCF, HK SC-IVR, MP/SOFT
Time Dependent Reactant PopulationLonger Time Relaxation Dynamics
[1]
[2]
[2][1]Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004)Guallar, V.; Batista, V.S.; Miller, W.H. J. Chem. Phys. 113, 9510 (2000)
Time Dependent Reactant PopulationHK SC-IVR, Classical Wigner (SC/L) and WKB
Comparison with experimental data
Femtosecond fluorescent transient at 420nm for HPMO in 3-methylpentane JPC 102,1657 (1998) Zewail and co-workers
Time dependent reactant (enol) population
Decoherence 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. in prep. (2004)
Development of new methodologies for studies of Decoherence and Coherent-Control
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
Electron Tunneling in Multidimensional Systems
Wu,Y.; Batista, V.S. J. Chem. Phys. 121, 1676 (2004)
2-dimensional (Model I)
2-dimensional (Model I)
2-dimensional (Model I)
2-dimensional (model I)
5-dimensional (model I)
5-dimensional (model I)
5-dimensional (model I)
5-dimensional (model I)
5-dimensional (model I)
5-dimensional (model I)
5-dimensional (model I)
10-dimensional (model I)
Electron Tunneling in Multidimensional Systems
Model II
(2-dimension Model II)
2-dimensional (model II)
2-dimensional (model II)
2-dimensional (Model II)
20-dimensional (Model II)
20-dimensional (model II)
Benchmark calculation:
Thermal Correlation Functions
Boltzmann Ensemble Averages
Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. submitted (2004)
Bloch Equation: MP/SOFT Integration
Partition Function Boltzmann Matrix:
Calculations of Thermal Correlation Functions
Time-Dependent Position Ensemble Average
Position-Position Correlation Function:
Model System:
Classical density
Quantum density
Ground State, V0
Excited State, V1
Model System, cont’d
Position-Position Correlation Function
Time-Dependent Position Ensemble Average
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 2-(2’-hydroxyphenyl)-oxazole (HPO), as modeled by an ab initio 35-dimensional reaction surface Hamiltonian, as well as in simulations of deep-tunneling quantum dynamics for systems with up to 20 coupled degrees of freedom. •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 Career Award CHE#0345984•ACS PRF#37789-G6•NSF Nanoscale Exploratory Research (NER) Award ECS#0404191•Research Corporation, Innovation Award#RI0702•Hellman Family Fellowship•Anderson Fellowship•Yale University, Start-Up Package•NERSC Allocation of Supercomputer Time •Department of Chemistry, University of Wisconsin Madison
Thank you !
Acknowledgments