An ab Initio Investigation of van der Waals-Rich Systems and a Machine Learning Approach to Finding Analytical Functions Describing Tabulated Data

van der Waals interactions are weak, non-specific forces arising at the atomic scale. Although they are weak---much weaker than a covalent or ionic interaction---they occur in large numbers, and in total, can make a significant contribution to the properties of a system. Several systems are herein explored whose properties are influenced strongly by van der Waals interactions. These systems are investigated largely through the non-local van der Waals density functional (vdW-DF) working within density functional theory (DFT), with accurate quantum chemistry calculations and experimental results to serve as a reference against which we compare our results. Properties calculated for (H₂O)_n with n=1--5 showed systematic improvement when van der Waals interactions were included. The low-temperature phase of Mg(BH₄)₂ is incorrectly predicted by standard local or semi-local approximations. However, the inclusion of van der Waals interactions brings theory in line with experiment. Dimers of phenalenyl and the nitrogen- and boron-substituted closed-shell analogues show an interesting collection of phenomena, including a 2-electron/multi-center bond and an anomalous barrier in a rotational total energy profile caused by electron kinetic energy. In the final part of this work, the theoretical groundwork is laid for a computational tool that uses network concepts to perform analytical calculations. These \emph{network functions} are capable of learning the mathematical connection in a set of data. A course to use network functions to improve DFT through a search for a kinetic energy functional and an improved exchange-correlation functional is discussed.

Grantor dc:publisher

Wake Forest University

Year dc:date.issued

2012

Author dc:creator

• Kolb, Brian

• chemical physics

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10339/37427

OAI identifier oai:identifier

oai:wakespace.lib.wfu.edu:10339/37427