Numerical application of the coupled-cluster theory with localized orbitals to polymers .3. Bond alternation in trans-polyacetylene

We present calculations on all-trans-polyacetylene (t-PA), using localized orbitals for the calculation of total correlation energies in an ab initio framework. We show that due to the localization properties of the localized Wannier functions, especially the virtual ones, simultaneous interactions between three unit cells of a polymer must be included. However, if a larger number of neighbours are taken into account our method is still faster than those using canonical HF orbitals. Our LO approximation is shown to be able to recover about 90% of the correlation energy obtained in the canonical orbital basis in the equilibrium geometry. Furthermore, we present a different approximation which also reproduces potential curves very well, although this variant recovers only about 80% of the total correlation energy per unit cell calculated with a canonical orbital basis. This failure, however, leads only to a shift of the potential parallel to the canonical one, even in a very subtle case like that of the bond-alternation potential in t-PA which depends strongly on the quality of the correlation calculation method used. For the equilibrium bond alternation u(0) (projected onto the polymer axis) of t-PA the coupled-cluster doubles method with localized orbitals yields values almost identical to those obtained with canonical Moller-Plesset perturbation theory of fourth order including single, double, triple and quadruple excitations, published previously in the literature (Suhai S 1995 Phys. Rev. B 51 16553). Furthermore, our results on u(0) agree fairly well with experiment, while the results of density functional calculations, also given in the above-mentioned work, are usually too small. Only one of the functionals applied yields comparable values for u(0)-surprisingly, the one which contains no correlation part.