Single-Determinant Theory of Electronic Excited States and Many-Electron Integrals for Explicitly Correlated

Abstract

The aim of this thesis is twofold. Its first part, Part A, is concerned with the development and assessment of a single-determinant theory for electronic excited states. The theory is based on two simple algorithms for finding excited-state solutions to self-consistent field (SCF) equations, the Maximum Overlap Method (MOM) and the Initial Maximum Overlap Method (IMOM). The extent to which these higher SCF solutions are useful approximations to excited states is examined in diverse case studies, including challenging instances such as double excitations, conical intersections and charge-transfer states. Results indicate that single-determinant models yield, in most cases, accurate approximations to electronic excited states, even for di cult excitations where other low-cost excited-state methods either perform poorly or fail completely. In Part B, we present efficient methods for the accurate evaluation of many-electron integrals arising in the explicitly correlated electronic structure theory. In our computational schemes e cient screening techniques, which adopt newly developed upper bounds, are used to sift out the tiny fraction of integrals which are significant. Then, non-negligible integrals are evaluated via recurrence relations that represent the generalization to three and four-electron integrals of two-electron integrals contraction-e cient schemes such as the Head-Gordon-Pople and PRISM algorithms. In this way, we developed general computational schemes for integrals arising from the use of a wide class of multiplicative correlation factors of the form f12 = f(|r1 r2|) and more specific methods for many electron integrals involving Gaussian Geminals. Our results support the evidence that our Gaussian-Geminal-based schemes yield a dramatic reduction of the computational complexity of these integral

    Similar works