Characterization of an Exact Electron Correlation Symmetry in AHCs Using MO Theory at the Single CI Level of Approximation
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 (AHCs) – specifically, butadiene and hexatriene. Data was generated using the semiempirical Pariser-Parr-Pople Method, which combines molecular orbital (MO) theory approximation techniques and configuration interaction (CI) calculations. Slater determinants are used to derive configurational wavefunctions that account for all possible single-electron excitations. Each electronic state �� can then be expressed as a linear combination of the singly-excited configurations, with coefficients and corresponding transition energies calculated using the CI method. 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 (��+ > 0 → alternancy heap) and correlated minus states (��– = 0 → 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 AHCs.
Primary Advisor's Department
Stander Symposium, College of Arts and Sciences
"Characterization of an Exact Electron Correlation Symmetry in AHCs Using MO Theory at the Single CI Level of Approximation" (2023). Stander Symposium Projects. 3111.