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.