In order to improve the performance of the current parallelized direct multi-configuration
self-consistent field (MCSCF) implementations of the program package Gaussian [42],
consisting of the complete active space (CAS) SCF method [43] and the restricted active
space (RAS) SCF method [44], this thesis introduces a matrix multiplication scheme as part
of the CI eigenvalue evaluation of these methods. Thus highly optimized linear algebra
routines, which are able to use data in a sequential and predictable way, can be used in our
method, resulting in a much better performance overall than the current methods. The side
effect of this matrix multiplication scheme is that it requires some extra memory to store the
additional intermediate matrices. Several chemical systems are used to demonstrate that the
new CAS and RAS methods are faster than the current CAS and RAS methods respectively.
This thesis is structured into four chapters. Chapter One is the general introduction, which
describes the background of the CASSCF/RASSCF methods. Then the efficiency of the
current CASSCF/RASSCF code is discussed, which serves as the motivation for this thesis,
followed by a brief introduction to our method. Chapter Two describes applying the matrix
multiplication scheme to accelerate the current direct CASSCF method, by reorganizing the
summation order in the equation that generates non-zero Hamiltonian matrix elements. It is
demonstrated that the new method can perform much faster than the current CASSCF method
by carrying out single point energy calculations on pyracylene and pyrene molecules, and
geometry optimization calculations on anthracene+ / phenanthrene+ molecules. However, in
the RASSCF method, because an arbitrary number of doubly-occupied or unoccupied orbitals
are introduced into the CASSCF reference space, many new orbital integral cases arise. Some
cases are suitable for the matrix multiplication scheme, while others are not. Chapter Three
applies the scheme to those suitable integral cases that are also the most time-consuming
cases for the RASSCF calculation. The coronene molecule - with different sizes of orbital
active space - has been used to demonstrate that the new RASSCF method can perform
significantly faster than the current Gaussian method. Chapter Four describes an attempt to
modify the other integral cases, based on a review of the method developed by Saunders and
Van Lenthe [95]. Calculations on coronene molecule are used again to test whether this
implementation can further improve the performance of the RASSCF method developed in
Chapter Three.