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