Characterization of an Exact Electron Correlation Symmetry in Alternant Hydrocarbons Using Molecular Orbital Theory
Date of Award
2023
Degree Name
M.S. in Chemistry
Department
Department of Chemistry
Advisor/Chair
Mark Masthay
Abstract
Electron-electron repulsion in a quantum system facilitates the correlated motion of electrons, or electron correlation. The extent to which the movement of an electron is influenced by surrounding electrons is proportional to the correlation energy. This project explores unique electron correlation characteristics manifested in the excited singlet states of alternant hydrocarbons --- specifically, ethylene, butadiene, and hexatriene. Data was generated using the semiempirical Pariser-Parr-Pople Method, which combines molecular orbital theory approximation techniques (the Huckel and Hartree-Fock self-consistent field methods) and configuration interaction calculations. Slater determinants are used to derive configurational wavefunctions that account for all possible single- and double-electron excitations. Each electronic state can then be expressed as a linear combination of the singly- or doubly-excited configurations, with coefficients and corresponding transition energies calculated using the single or double configuration interaction method, respectively. The results indicate that certain wavefunctions --- referred to as plus and minus states --- are solely comprised of paired configurations (in equal magnitude), and all other coefficients are zero. The identical wavefunctions of the paired configurations allow for exact electron correlation symmetries to be demonstrated, yielding uncorrelated plus states (which produce an alternancy heap) and correlated minus states (yielding an alternancy hole). Analysis of each electronic state transition energy as a function of the range of electron-electron repulsion shows that at short ranges, the plus state energy increases due to the presence of alternancy heaps, while the minus state decreases because of alternancy holes. These results are consistent with the exact symmetries derived for the excited singlet states of alternant hydrocarbons.
Keywords
electron correlation, alternant hydrocarbons, Pariser-Parr-Pople, molecular orbital theory, configuration interaction
Rights Statement
Copyright © 2023, Author
Recommended Citation
Farwick, Christina Anne, "Characterization of an Exact Electron Correlation Symmetry in Alternant Hydrocarbons Using Molecular Orbital Theory" (2023). Graduate Theses and Dissertations. 7261.
https://ecommons.udayton.edu/graduate_theses/7261
