Transcript Document

228th ACS National Meeting, August 22-August 26, 2004 Philadelphia
Quantum/Classical Calculations in Chemistry and Biophysics
Matching-Pursuit Representations for Simulations of Quantum Processes
Xin Chen, Yinghua Wu and Victor S. Batista
Department of Chemistry, Yale University, New Haven, CT 06520-8107
Xin Chen
Yinghua Wu*
*Current address: Department of Chemistry, Tulane University.
Time-Sliced Simulations of Quantum Processes
Trotter Expansion
MP/SOFT Method
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)
ESIPT in the keto-enolic tautomerization
of 2-(2’-hydroxyphenyl)-oxazole (HPO).
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.; 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)
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
r1,r2 : reaction coordinates
z0 : ab initio geometries
F : ab initio force constants
CIS/6-31G* Reaction Surface Potential V0(r1,r2)
Computation of Observables
Time dependent reactant population:
Absorption Spectrum:
Time-Dependent Survival Amplitude
HK SC-IVR vs. Classical Wigner
Wigner
SC-IVR
Time-Dependent Survival Amplitude
HK SC-IVR vs. MP/SOFT
Time Dependent Reactant Population
HK SC-IVR, Classical Wigner (SC/L) and WKB
Early Time Relaxation Dynamics
Time Dependent Reactant Population
WIGNER, TD-SCF, HK SC-IVR, MP/SOFT
Longer Time Relaxation Dynamics
Time Dependent Reactant Population
WIGNER, TD-SCF, HK SC-IVR, MP/SOFT
[1]
[2]
[1] Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004)
[2] Guallar, V.; Batista, V.S.; Miller, W.H. J. Chem. Phys. 113, 9510 (2000)
Decoherence Dynamics
HK SC-IVR vs. MP/SOFT
[1]
[2]
[1] Wu,Y.; Batista, V.S. J. Chem. Phys. in prep. (2004)
[2] Batista, V.S.; Brumer, P. Phys. Rev. Lett. 89, 143201 (2002)
Thermal Correlation Functions
Chen, X., Wu,Y.; Batista, V.S. J. Chem. Phys. submitted (2004)
Boltzmann Ensemble Averages
Bloch Equation: MP/SOFT Integration
Partition Function
Boltzmann Matrix:
Calculations of Thermal Correlation Functions
Position-Position Correlation Function:
Time-Dependent Position Ensemble Average
Model System:
Model System, cont’d
Classical density
Quantum density
Ground State, V0
Excited State, V1
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.
•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 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
•ACS Meeting Organizing Committee (Prof. Hammes-Schiffer, Prof. Jensen)
Thank you !
Electron Tunneling in Multidimensional Systems
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)
Benchmark calculation:
20-dimensional (model II)
TS/SC-IVR Approach
The (TS) implementation avoids most of the difficulties of the standard SC-IVR,
since the propagator is applied only for short time-slices while the semiclassical
approximation is still accurate and efficient. However, the method introduces a
new challenge: the reinitialization of the time-evolved wavefunction after each
propagation time-slice.
In order to optimize the efficiency of the re-expansion procedure, the timeevolved wavefunction is represented (“compressed”) at the end of each
propagation time-slice according to a matching-pursuit coherent-state expansion.
TSHK
QM
HK
2-dimensional tunneling
TS/SC-IVR Approach
157 nm
Instantaneous Time-Dependent Wavepackets
2.42 fs
3.63 fs
2.42 fs
3.63 fs
31
40
Survivial Amplitudes
Total Photodissociation Cross Sections
Partial Photodissociation Cross Sections
31
Partial Photodissociation Cross Sections
Partial Photodissociation Cross Sections
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 deep-tunneling quantum dynamics for
systems with up to 20 coupled degrees of freedom.
•Work in progress involves simulations of excited-state intramolecular proton
transfer in 2,2’-hydroxyphenyl-oxazole as well as calculations of the equilibrium
density matrix (equilibrium properties of quantum systems).
•We have also introduced the TS/SC-IVR approach, a method that concatenates
finite-time propagators and computes real-time path integrals based on the HK
SC-IVR. We have shown that the approach significantly improves not only the
accuracy of simulations of deep-tunneling quantum dynamics based on the HK
SC-IVR but also the accuracy of computations of photo-dissociation cross
sections of vibrationally hot molecules (sensitive to subtle interference effects).
Acknowledgments
•NSF Career Award CHE-0345984
•NSF Nanoscale Exploratory Research (NER) Award ECS-0404191
•ACS PRF 37789-G6
•Research Corporation, Innovation Award
•Hellman Family Fellowship
•Anderson Fellowship
•Yale University, Start-Up Package
•NERSC Allocation of Supercomputer Time
CNLS Workshop Organizing Committee at LANL
Thank you !
Reaction Coordinates in HPO
r1: H-stretching
Reaction Coordinates in HPO
r2: internal bending