## AN AB INITIO STUDY OF THE ZERO-FIELD SPLITTING PARAMETERS OF $^{3}B_{1{u}}$ BENZENE

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### Date

1975

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Ohio State University

### Abstract

The electron spin dipole-dipole contribution to the zero-field splitting in the benzene $^{3}B_{1{u}}$ electronic state was calculated using the $D_{6{h}}$ ground state geometry. The correct microscopic Hamiltonian is used and all integrals are evaluated accurately for a set of contracted Gausstan-lobe functions of double-zeta quality. The self-consistent-field result for the splitting parameter D is 0.1133 cm$^{-1}$ which is significantly lower Chan the experimental value of D$^{*} = \sqrt{{D}^2+3{E}^2} = 0.1581$ cm$^{-1}$ obtained from the electron resonance spectra of benzene in a C$_{6}$D$_{6}$ host crystal. An extensive study of the effect of electron correlation on the splitting parameter D was undertaken. Excitation of the type $\sigma^{2}$ $\rightarrow$ $\Pi^{2}$ and $\Pi^{2}$ $\rightarrow$ $\sigma^{2}$ are observed to have little effect on D whereas excitations of the types $\Pi^{2} \rightarrow \Pi^{\prime}_{2}$ $\Pi$ $\rightarrow$ $\Pi$$^{\prime}$ and $\sigma$$\Pi$ $\rightarrow$ $\sigma^{\prime}$$\Pi$$^{\prime}$ increase D and excitations of the types $\sigma^{2}$ $\rightarrow$ $\sigma^{2}$ and $\sigma$$^{\prime}$ $\rightarrow$ $\sigma$$^{\prime}$ decrease D. The sum of the absolute values of the configuration-interaction (CI) effects for these classes of excitations is greater than the value of D itself. A CI wave function with almost 9400 symmetry adapted configurations (in D$_{2{h}}$, symmetry), including all single excitations and the most important double excitations of each class, obtained a value of D = 0.2065 cm$^{-1}$. The implication of this theoretical treatment for previous semi-empirical calculations is considered. Finally, an attempt is made to discuss the shortcomings of the calculation which could account for a calculated value for D which is larger then the experimental result.

### Description

Author Institution: Battelle Memorial Institute; Department of Chemistry, The Ohio State University; Department of Chemistry University of Washington, Seattle, Washington, 98195.