Saller, Maximilian A. C. (2017) Sampling minimal, adaptive basis sets for multidimensional, nuclear quantum dynamics using simple, semi-classical trajectories. PhD thesis, University of Warwick.

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Abstract

Methods for the study of nuclear quantum dynamics can be categorised by the nature of the basis set expansion they employ. The wavefunction can be expanded in a static set of time-independent basis functions, the time evolution being described solely via the expansion coefficients. Alternatively, basis functions can be propagated in time, along with the coefficients, via equations of motion for their parameters. Time-independent basis sets are plagued by exponential scaling, while the equations of motion for time-dependent basis functions are challenging to integrate and, if not derived variationally, can violate energy conservation laws. This work presents a novel basis set sampling method which represents a compromise between these two categories. A set of sampling trajectories, evolving on the potential energy surface of the system, are used to place basis functions in regions of phase space, relevant to wavefunction propagation. These functions then act as a time-independent basis set, the wavefunction being evolved via exact, variational equations of motion for the expansion coefficients. This approach is applied to a challenging quantum dynamics benchmark, namely the relaxation dynamics of photoexcited pyrazine, and yields highly encouraging results. In order to address divergence from exact dynamics at longer timescales, which is attributed to the classical sampling trajectories being a sound approximation to quantum propagation of the wavefunction only in the short-time limit, a modification of this method is proposed. Shorter iterations of trajectory sampling and wavefunction propagation are used, linked by a minimisation algorithm that continuously optimises the basis set, preventing unfavourable scaling. This adaptive sampling approach is again applied to the pyrazine benchmark with a significant increase in performance and accuracy. Highly encouraging results are also obtained for a quantum tunnelling benchmark system, which are improved upon even further, and at little extra cost, by the use of path integral sampling trajectories.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QD Chemistry
Library of Congress Subject Headings (LCSH):	Quantum theory, Photochemistry, Basis sets (Quantum mechanics), Molecular dynamics
Official Date:	July 2017
Dates:	Date Event July 2017 Submitted
Institution:	University of Warwick
Theses Department:	Department of Chemistry
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Habershon, Scott
Sponsors:	Engineering and Physical Sciences Research Council
Format of File:	pdf
Extent:	xix, 159 pages : illustrations, charts
Language:	eng

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