#### Date of Award

12-15-2014

#### Document Type

Open Access Thesis

#### Department

Chemistry and Biochemistry

#### First Advisor

Vitaly Rassolov

#### Abstract

Excited states of chemical systems are extremely important in understanding spectra, chemical phenomena, as well as how a particular compound behaves in reactions. Computationally, excited states are normally very expensive to calculate. The difficulty in calculating these states with wavefunction based methods can be mainly attributed to the calculation of large multi-determinant wavefunctions. One reason to use a complicated multi-determinant wavefunction is to include some of the effects of correlation energy. The quantity of correlation energy can most simply be defined as the reduction in energy caused by any two or more electrons trying to avoid each other. The most common way of avoiding these computational costs is through the use of time-dependent density functional theory (TD-DFT). TD-DFT has an exceptional ratio of accuracy to computational cost because it reduces the many-electron wavefunction to a single-electron density. A single-electron quantity, however, is an improper way to descibe an innately two-electron property like correlation energy. Within this research we seek to alleviate the large computational costs required to calculate excited states with a wavefunction-based method and reduce the costs to near Hartree-Fock theory levels. We do this by using two different inexpensive excited wavefunction methods. First we reduce our multi-determinant wavefunction to a single-determinant wavefunction. The single-determinant wavefunction used in this research comes from delta self-consistent field method that essentially creates excited Hartree-Fock states. Secondly we construct the simplest multi-configurational wavefunction using a linear combination of all singly excited states with the method known as configuration interaction singles (CIS). The reduction in wavefunction size, however, reduces nearly all correlation energy recovered by both methods. This is remedied by modeling correlation energy in a computationally inexpensive manner. A potentially accurate way to model electron correlation within the single determinant wavefunction formalism is through the expectation value of a linear two-electron operator over the Kohn-Sham single-determinant wavefunction. For practical reasons, it is desirable for such an operator to be universal, i.e. independent of the positions and types of nuclei in a molecule. We choose an operator expanded in a small number of Gaussians as a model for electron correlation. The accuracy of this method is tested by computing atomic and molecular adiabatic excited states in comparison with popular TD-DFT functionals. The correlation operator combined with SCF is found to be comparable in accuracy to TD-DFT methods for both atomic and molecular excited states. SCF is limited in its applications, however, due to its inability to guarantee orthogonal excited states which leads to unwanted spin contamination. The correlation operator combined with CIS is found to be comparable in accuracy to TD-DFT methods for atomic states but has a significant loss in accuracy for excited molecular states. This drop in accuracy is theorized to be the poor description Hartree Fock theory gives of some ground and excited state wavefunctions.. We offer some possible solutions to these problems in the form of orthogonality constraints and a potential hybrid method of SCF and CIS.

#### Recommended Citation

Nichols, B. T.(2014). *Universal Two-Electron Correlation Operator on Excited States.* (Master's thesis). Retrieved from http://scholarcommons.sc.edu/etd/2985