Numerical application of the coupled cluster theory with localized orbitals to polymers II. Optimal localization of Wannier functions and the correlation energy in different approximations

Abstract

We present an iterative method to obtain localized Wannier functions, needed in the framework of correlation energy calculations on polymers with different size-consistent methods using a localized orbital basis. Test calculations using different possible localization schemes are performed on alternating all-trans polyacetylene (t-PA), which is an example for polymers with covalently bound unit cells. The improvement of the localization is compared with respect to the total correlation energy per unit cell at the level of second order orbital invariant Møller-Plesset perturbation theory (LMP2) to the canonical MP2 (CMP2) method, and also results of the calculation of the correlation energy with the coupled cluster doubles theory (CCD) and its linear approximation (LCCD) are shown, We found that the coupled cluster expansions failed to converge for systems containing the Wannier functions belonging to two interacting unit cells if their interactions are too large (in case of a double zeta basis set and optimally localized Wannier functions). This is probably due to linear dependences in the systems of equations for such a highly symmetric system. Such a behavior can be made plausible with the help of a very simple model. Possibilities to overcome this problem are discussed. However, since in this work we are mainly concerned with the localization properties of Wannier functions in correlation calculations, we concentrate on comparisons of the correlation energy obtained with our localized orbital approximation to the energies as computed in the corresponding canonical orbital basis. Since the latter ones are available only for MP2 we concentrate in the present paper on this method, which can be viewed as a second order approximation to the coupled cluster expansion for double excitations. A comparison of the influence of the localization approximation on the correlation energy obtained with the corresponding canonical procedure is made for Clementi's minimal and double zeta basis sets on the MP2 level and, in addition, the localized Wannier functions of larger systems and the effects of the localized orbital approximation on a potential curve for t-PA are discussed.