Advances in deterministic, stochastic, and semistochastic quantum chemistry
dc.contributor.author | Holmes, Adam | |
dc.contributor.chair | Umrigar, Cyrus Jehangir | |
dc.contributor.committeeMember | Mueller, Erich | |
dc.contributor.committeeMember | Franck, Carl Peter | |
dc.date.accessioned | 2017-04-04T20:27:27Z | |
dc.date.available | 2018-11-18T07:03:11Z | |
dc.date.issued | 2017-01-30 | |
dc.description.abstract | In this dissertation, I present my original research in the development of algorithms for computing ground-state properties of strongly-correlated electronic systems from first principles. I present three main algorithms. First, I present a 'semistochastic' projection algorithm, dubbed Semistochastic Quantum Monte Carlo, which combines the best qualities of deterministic and stochastic methods for projecting out a ground state wavefunction in a basis of Slater determinants. This new algorithm can treat systems as large as a fully-stochastic algorithm can, while dramatically reducing the statistical uncertainty and bias by treating the most important part of the problem deterministically. Second, I present an efficient algorithm for sampling many-particle states in Fock space with probability proportional to the Hamiltonian matrix element connecting them to a reference state, which I refer to as the heat-bath distribution. This sampling algorithm, referred to as Efficient Heat-bath Sampling in Fock Space, factors and approximates the heat-bath probabilities in such a way that they can be efficiently stored and sampled, without having to enumerate all of the possible excitations. Efficient Heat-bath Sampling dramatically improves the efficiency of stochastic Fock space methods by sampling the more relevant Slater determinants more frequently. Third, I present the deterministic analog of Efficient Heat-bath Sampling, which enables one to generate all Slater determinants that are connected to a reference by Hamiltonian matrix elements larger in magnitude than a cutoff, without wasting any time on those determinants that do not meet the cutoff. This deterministic heat-bath \sampling" algorithm is then incorporated into a highly-efficient quantum chemistry algorithm that I call Heat-bath Configuration Interaction, which rst generates a variational wavefunction and then computes the lowest-order perturbative correction. Both the variational and perturbative stages of Heat-bath Configuration Interaction make use of deterministic heat-bath "sampling" to perform highly efficient calculations using only the most important Slater determinants. | |
dc.identifier.doi | https://doi.org/10.7298/X4GH9FXP | |
dc.identifier.other | Holmes_cornellgrad_0058F_10020 | |
dc.identifier.other | http://dissertations.umi.com/cornellgrad:10020 | |
dc.identifier.other | bibid: 9906024 | |
dc.identifier.uri | https://hdl.handle.net/1813/47777 | |
dc.language.iso | en_US | |
dc.subject | Computer science | |
dc.subject | electronic structure theory | |
dc.subject | quantum Monte Carlo | |
dc.subject | strongly-correlated electrons | |
dc.subject | Quantum physics | |
dc.subject | Molecular chemistry | |
dc.title | Advances in deterministic, stochastic, and semistochastic quantum chemistry | |
dc.type | dissertation or thesis | |
dcterms.license | https://hdl.handle.net/1813/59810 | |
thesis.degree.discipline | Physics | |
thesis.degree.grantor | Cornell University | |
thesis.degree.level | Doctor of Philosophy | |
thesis.degree.name | Ph. D., Physics |
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