Dissertation/Thesis Abstract

Novel Thawed Gaussian Methods for Solving Time-Dependent Schrödinger Equation
by Kong, Xiangmeng, Ph.D., Yale University, 2017, 74; 10633253
Abstract (Summary)

The development of exact methods for quantum dynamics simulations of multidimensional systems has been a challenging field due the high dimensionalities of integrals required. Although various approximate methods have been developed to simulate complex molecular systems, rigorous simulation is still required to capture chemical processes with strong quantum effects, such as tunneling and zero-point energy.

Proposed here are two methods for simulation of rigorous quantum dynamics. Both of them are based on the thawed Gaussian representation for which the short time evolution can be solved exactly on a harmonic potential. The Matching-Pursuit/Gauss (MP/Gauss) method incorporates the Matching-Pursuit algorithm and Fast Gaussian Wavepacket Transform (FGWT) to represent a target wavefunction as local Gaussians and solves the evolution of the wavefunction by propagating each thawed Gaussian locally. The Time-Sliced Thawed Gaussian (TSTG) method uses a closely packed basis set of local Gaussians derived from FGWT and obtains coefficients of the expansion analytically. Then the basis functions are propagated in the same fashion as in MP/Gauss method. Both methods are tested on a one-dimensional system with a double-well potential energy surface and on a two dimensional system where a double-well is coupled with a harmonic bath, and compared to the exact results obtained from the Split Operator Fourier Transform (SOFT) method. While PM/Gauss demonstrates satisfactory agreement with SOFT in one dimensional systems, it does not preserve the norm of the wavefunction for the two dimensional system in long time propagation. On the other hand, the TSTG scheme agrees very well with SOFT for both systems and reproduced tunneling effect with expected tunneling rate.

Although the TSTG method can easily be generalized to higher dimensionality systems, the size of the basis set scales exponentially. Further studies are attempted to either reduce the storage required for basis sets by various tensor tools or reduce the size of the basis set by tracking the trajectories of the basis functions to limit the expansion only to neighbouring Gaussians.

Indexing (document details)
Advisor: Batista, Victor Salvador
School: Yale University
School Location: United States -- Connecticut
Source: DAI-B 78/11(E), Dissertation Abstracts International
Subjects: Physical chemistry, Quantum physics, Theoretical physics
Keywords: Gaussian Wavepacket, Semi-Classical Dynamics, Simulation, Time-Dependent Schrodinger Equation
Publication Number: 10633253
ISBN: 978-0-355-10545-2
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