Applications of the Spectral Theory of Chemical Bonding to Simple Hydrocarbons

TL;DR

This paper surveys the spectral theory of chemical bonding, applying it to simple hydrocarbons, and demonstrates how it accurately reproduces chemical valence and angular effects while suggesting ways to extend its applicability.

Contribution

It introduces a pair formulation of spectral theory for chemical bonding, showing how to solve polyatomic Hamiltonians with antisymmetrized electron exchange and improving basis reduction methods.

Findings

Accurately reproduces chemical valence and angular effects

Demonstrates application to hydrocarbons with hydrogen and carbon

Provides methods to reduce basis size for larger molecules

Abstract

The finite-basis, pair formulation of the Spectral Theory of chemical bonding is briefly surveyed. Solutions of the Born-Oppenheimer polyatomic Hamiltonian totally antisymmetric in electron exchange are obtained from diagonalization of an aggregate matrix built up from conventional diatomic solutions to atom-localized problems. A succession of transformations of the bases of the underlying matrices and the unique character of symmetric orthogonalization in producing the archived matrices calculated "once-of-all" in the pairwise-antisymmetrized basis are described. Application is made to molecules containing hydrogens and a single carbon atom. Results in conventional orbital bases are given and compared to experimental and high-level theoretical results. Chemical valence is shown to be respected and subtle angular effects in polyatomic contexts are reproduced. Means of reducing the size of the atomic-state basis and improve the fidelity of the diatomic descriptions for fixed basis size, so as to enable application to larger polyatomic molecules, is outlined along with future initiatives and prospects.