Constructing approximatively diabatic states from LCAO-SCF-CI calculations

We consider here two approaches which have been proposed in the literature to obtain diabatic states from ab initio calculations. First by calculating explicitely the coupling vector g which describes the nonadiabatic interaction between the adiabatic states. Second, by some extrapolation process of the wavefunctions obtained at a particular reference point. The coupling vector is a sum of three contributions. The first two represent the the change in character of the adiabatic states in the region of nonadiabatic coupling due the variation of the CI and LCAO coefficients, whereas the third results from the translation of the atomic orbitals with the moving nuclear centers. Criteria have been given to recognize when it is possible to transform a set of CI wave functions into a pair of useful diabatic states. A particularly favorable situation is obtained when the interacting electronic states are doubly excited with respect to each other. Within the two-states approximation, the first term, depending on the CI coefficients, is strictly irrotational and never gives rise to problems. One can expect situations where it is also true for the second term depending on the LCAO coefficients. However, the third term of the coupling can never be described as a rotation of two diabatic functions. Nevertheless, the latter contribution can frequently be neglected, at least when the coupling is strong. The theory of the electron transfer factors (ETF's) provides further insight into the problem and confirm our conclusions