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Title: Methods of multidimensional quantum mechanics and their applications
Author: Ronto, Miklos
Awarding Body: University of Leeds
Current Institution: University of Leeds
Date of Award: 2012
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Gaussian-based numerical methods become more and more important for dealing with problems in high dimensional molecular dynamics. In the past few decades the development of semiclassical descriptions along with trajectory guided strategies, gained considerable success in the field of computational chemistry. With the introduction of importance sampling, the problem of numerical scaling of multidimensional systems can be addressed effectively. In this thesis two of these methods are compared in the same theoretical framework, on equal numerical settings. The already existing Coupled Coherent States (CCS) method is compared with a novel numerical implementation of the modified variational Multiconfiguration Gaussians (vMCG) equations. Applying the Time-Dependent Variational Principle (TDVP) to coherent state parameters enables the description of the time-dependence of an arbitrary state vector in a coherent state basis and provides a framework, where CCS and vMCG can be expressed in equal formal footing. By introducing a smoothing factor to the variational equations, numerical stability and robustness can be greatly improved. In its original formulation vMCG required the regularisation of its working matrix and needed inversion. With the modified equations vMCG can be solved as a system of linear equations. These equations are presented in multidimensional form, and implemented numerically. For the numerical tests and comparisons, a broad range of potential energy surfaces and model problems were studied. Simple oscillator systems (harmonic and Morse), Henon-Heiles model (up to 10-dimensions), high dimensional symmetric and asymmetric tunnelling problems are investigated, and compared with results from benchmark simulations from split-operator method, MCTDH and MP/SOFT. The main conclusion of this work is, that with the modified equations, vMCG can be further improved. Numerical accuracy, robustness and properties of this new implementation are lying very close to the characteristics of the CCS method.
Supervisor: Shalashilin, D. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available