Different orbitals for different spins for solids: Fully variationalab initiostudies on hydrogen and carbon atomic chains, polyene, and poly(sulphur nitride)

The spin unrestricted-Hartree-Fock (UHF) method (the fully variational version of the different-orbitals-for-different-spins crystal-orbital method) is applied to four infinite one-dimensional model-system linear chains of hydrogen and carbon atoms, polyene [i.e., ${\left(\mathrm{CH}\right)}_x$] and poly(sulphurnitride). The calculations were performed by using the linear-combination-of-atomic-orbitals (LCAO) approximation evaluating exactly all the integrals over atomic orbitals within a given interaction radius. The part of the correlation energy which is taken into account by the method as well as the width of the forbidden energy gap are studied as function of the geometry parameters of H and C chains. It is concluded that the electrons lying around the Fermi level are strongly correlated by this method, while the other electrons are practically not correlated at all. No metal-insulator transition can be described by the method for the H and C chains. The very large gap obtained with the equidistant model of polyene chains supports the assumption that the model with alternating bond lengths should be preferred. In contrast to what is a common assumption, the UHF stabilization energy per unit cell is much smaller than the forbidden bandwidth owing to self-consistent rearrangement of electrons.