Strongly localized approaches for delocalized systems. I. Ground state of linear polyenes

When approaching the theoretical description of the electronic structure of a molecule, instead of starting the construction of the electronic wave function from the self-consistent field single determinant, one may use a strongly localized determinant, corresponding to the Lewis picture of the molecule. Following this approach, the delocalization and the correlation effects are clearly identified and they can be treated simultaneously. This analysis, applied to the study of the ground state of π-conjugated systems, in particular to all-trans linear polyenes, shows the short-range character of the delocalization, essentially taking place between adjacent double bonds, and of the valence correlation energy, mainly coming from intra-double bond double excitations. This suggests that these systems can be described with a very limited model space, reduced to the corresponding excitations, the size of which scales linearly with the dimension of the system. Of course the effect of other excitations and of multiple excitations has to be taken into account at least in a perturbation scheme. The numerical studies on the first terms of the polyenes series show that the so-obtained energies are very close to those of the full π Complete Active Space Self-Consistent Field treatment. Moreover, one can correctly reproduce the dependence of the energy on the bond length alternation, thus showing the origin of the differences observed in these systems for the HF and CASSCF equilibrium geometries.