Convergence of exchange lattice summations in direct-space polymer calculations

We studied various stereoregular polymers [monoatomic (beryllium chains), diatomic (hydrogen fluoride chains and polyyne) and polyatomic (polyethylene and polymethineimine)] and monitored the effective convergence of the lattice summations, especially the one corresponding to the exchange contribution. The relations to geometry (bond length alternation), pseudo-linear-dependencies, basis set, and band gap are addressed. In all cases, including for extremely conjugated systems, the exchange is found to present an exponentially decreasing, rather than 1/J̄², behavior, although convergence, in some cases, can be very slow.