Convergence of non-linear optical calculations for infinite polymers: Second hyperpolarizabilities of polymers with cyclic π-conjugated elementary cells

We have selected several polymers with small elementary cells, poly-HF, poly-H2O, poly-C2H2 and poly-CNH in order to study the convergence of static and dynamic (hyper) polarizabilities at the Coupled Perturbed Hartree–Fock crystal orbital (CO) level. The parameters determining the convergence are the number of k-points over the half Brillouin zone, the number of neighbouring cells treated exactly with the complete Hamiltonian, and the effect of long-range Coulomb interactions. We also present for the first time calculations of the static and dynamic second hyperpolarizabilities γ on polymers with middle-sized cells, the five-membered heterocyclic π-conjugated systems, at this level of theory taking into account the results of the convergence study.