UC Irvine

Theoretical calculations of molecular properties can assist experimental design of molecules

with interesting optical, electronic and structural properties which would help accelerate materials

discovery. Density functional theory (DFT) within the Kohn–Sham (KS) framework

has been the most widely used method for molecular properties calculations in the last three

decades because of its advantageous computational cost-to-accuracy ratio. However,

commonly used density functional approximations (DFAs) have been shown to be inadequate

for calculations involving transition metal compounds, metal clusters, conjugated molecules

and for describing noncovalent interactions. Random phase approximation is a post-KS

DFA that is accurate for describing noncovalent interactions without the need for empirical

parameters, does not diverge for small-, or even zero-gap systems and incorporates

Hartree–Fock (HF) exchange. The first part of this thesis aims at answering the question: can a

self-consistent generalized KS scheme be developed for the RPA energy functional which

also gives access to single particle energies within a variational Lagrangian formalism? To

this end, an orbital self-consistent scheme called the generalized KS semicanonical projected

RPA (GKS-spRPA) is developed, implemented and benchmarked for ground state as well

as single particle energies. The ionization energies and band-gaps that are calculated

using the GKS-spRPA suggest that it is better than the commonly used G0W0 method. The

second part of the thesis is concerned with the implementation and testing of static

polarizabilities within the GKS-spRPA method. The GKS-spRPA successfully solves the

overpolarization problem observed with the use of semilocal/hybrid DFAs for calculations

of static polarizabilities of pi-conjugated molecules. Calculations involving metallocenes, metal clusters and

a small molecule testset are used to show that the static polarizability calculated using the GKS-spRPA

method is more accurate than DFAs such as PBE, PBE0, CAM-B3LYP and wave function

based methods such as HF and the second-order Møller–Plesset perturbation theory (MP2).

Thus, this thesis conclusively shows that the GKS-spRPA within a Lagrangian framework,

is a method that provides not only accurate ground state energies but also a wide range of

molecular properties such as geometries, ionization potentials, electron affinities, dipoles and

polarizabilities with a reasonable computational cost of O(N 4 log(N )).