Date of Award

2021-05-01

Degree Name

Master of Science

Department

Physics

Advisor(s)

Rajendra Zope

Abstract

Density functional theory (DFT) has long been the workhorse of quantum chemists and materials scientists. As the ability of modern DFT codes to address larger and more complex molecular systems has grown, so too has the computational cost, with cutting edge simulations requiring thousands of hours of wall time on the worldâ??s fastest supercomputers.For this reason, efficiency in both memory and time is critical at every step of the process. In fact, the increasing scope of physical systems that can be modeled is as much a function of computational elegance as of the physical fidelity of the simulation. The continuing desire for the latter motivates the pursuit of the former. This work presents two new developments for physically accurate, computationally efficient evaluation of two critical steps of density functional calculations. These efforts were undertaken in pursuit of improving a new self-interaction correction method, but also have general relevance to DFT. First is an algorithm for analytically calculating derivatives of Cartesian Gaussian orbitals that supports up to f and g functions. The method described here reduces the number of operations compared to an already efficient implementation, and will also enable simulation of the entire periodic table. The second is a strategy for numerically calculating Coulomb potential that builds upon and synthesizes previous strategies. This method will enable a newly developed self-interaction correction method to be made fully variational. We show that our implementation has better asymptotic scaling than an analytical calculation, while remaining accurate. Furthermore, our algorithm is basis-set independent, widening its applicability and further extending its performance advantage over an analytical calculation.

Language

en

Provenance

Recieved from ProQuest

File Size

89 p.

File Format

application/pdf

Rights Holder

Zachary John Buschmann

Included in

Physics Commons

Share

COinS