Analysis of long‐range effects in many‐body correlation approaches for one‐dimensional periodic systems

We analyze the divergent contributions to the Hamiltonian for extended, nonmetallic systems in one dimension, to both the ground-state correlation energy and to the correlated band structure. It is shown that the contribution from the long-range divergent part of the Hamiltonian tends to zero as 1/M−2, where M is the extent of the troublesome lattice summations. Therefore, it is well justified to neglect such contributions in higher order many-body perturbation theory or coupled cluster treatments of the electronic structure for polymers.