ON THE CONVERGENCE OF THE EXCHANGE-LIKE SUMS IN THE RANDOM-PHASE-APPROXIMATION APPLIED TO STEREOREGULAR POLYMERS

In the Random Phase Approximation procedure applied to evaluate the lo ngitudinal polarizability per unit cell of stereoregular polymers, all the direct lattice sums which enter in the evaluation of the two-elec tron integrals between crystalline orbitals converge. Proofs are given in this work that convergence of the sums generating a logarithmicall y divergent 1/\m\ series is ensured either by the orthonormalization c ondition or by the integration procedure over the first Brillouin zone . The other sums are Fourier series which converge rapidly due to the exponentially decreasing character of the overlap terms as separation increases. (C) 1995 John Wiley & Sons, Inc.