Arthur Robert Williams

Multiple scattering method based on overlapping atomic spheres with application to the TCNQ molecule

The theoretical foundation of the self‐consistent statistical exchange (X α) multiple scattering method based on overlapping atomic spheres is presented. After discussing the principal assumptions and approximations, the theory is illustrated by a study of the electronic structure of the TCNQ molecule. Satisfactory results are obtained for the energy level structure and electronic charge distribution if the atomic sphere radii are chosen in accordance with the following guidelines: (a) the calculated first ionization energy should agree with experiment; and (b) the calculated virial coefficient should be equal to −2. The present work suggests that the overlapping sphere model can be used to obtain realistic electronic structures for large planar organic molecules as well as for arrays of such molecules.

Generalization of Slater’s transition state concept

We present a generalization of the transition state technique introduced by Slater for the calculation of many‐electron relaxation effects accompanying electronic excitations in molecules and molecular simulations of solids. By making use of ground state information (which is generally available but not used in the Slater formulation) and transition states which are computationally cheaper (due to being closer to the ground state), the generalization permits the evaluation of excitation energies to be improved in any of three ways: (1) comparable accuracy for less computation; (2) improved accuracy for comparable computation; and (3) full Δ‐SCF accuracy can be approximated with arbitrary precision with additional computation. In particular, we show that excitation energies of somewhat greater accuracy are obtained from self‐consistent calculations performed for transition states corresponding to 2/3 of the transition rather than 1/2 of the transition as in the original formulation by Slater.