PARSIMONIOUS ALGORITHMS AND IMPLEMENTATION IN QUANTUM CHEMISTRY

Abstract

The fundamental crux affecting the performance of quantum chemistry calculations is the need to cover a large number of terms in a way that may entail managing a large amount of data. The costs in time and storage associated with these methods can be mitigated in numerous ways: judiciously exclude insignificant terms, reformulate terms in ways that avoid computing some intermediates, and avoid full formulation of intermediaries. This thesis explores such efforts by examining a direct Density Fitted Coulomb and Exchange (JK) formation algorithm, application of numerous advances in JK construction to Hybrid DFT calculations, reformulation of Coulomb terms to avoid ERI calculations, and parsimonious formation of Coulomb and exchange matrices with different row and column bases under the density fitting approximation.