On the nature of the π -> π* ionic excited states: The V state of ethene as a prototype

This article addresses an analysis of the physical effects required for the correct description of the ionic π -> π* excited states in the frame of ab initio quantum chemistry, using the ionic V state of the ethene molecule as an example. The importance of the dynamic sigma polarization (absent in methods where the sigma skeleton is treated at a mean-field level) has been recognized by many authors in the past. In this article a new physical effect is described, i.e. the spatial contraction of the π and π* molecular orbitals (or of the local p atomic orbitals) originated from the reduction of the ionicity due to the dynamic sigma polarization. Such an effect is a second-order effect (it appears only as a consequence of the dynamic sigma polarization) but it cannot be ignored. Many of the difficulties found in the past in the calculation of the vertical excitation energy of the ionic states are attributed to an incomplete description of this contraction, while the few successes have been obtained when it has been fortuitously introduced by ad hoc procedures or when it is described in a brute force approach. Various strategies are proposed to allow for the spatial contraction of the p atomic orbitals. If this effect is considered at the orbital optimization step, it is shown that for the V state of ethene no Rydberg/valence mixing occurs and a simple perturbation correction (to the second order in the energy) on the π -> π* singly excited configuration gives stable results with respect to the computational parameters and in good agreement with the experimental findings and with the best theoretical calculations. Moreover, our results confirm the indication of Müller et al. (J Chem Phys 1999, 110, 7176) that the transition to the V state of ethene conforms to the Franck-Condon principle and that it is not necessary to appeal to a nonvertical transition to interpret the experimental data. The strategy reported in this article for ethene can be in principle generalized to the π -> π* ionic excited states of other molecules.