Calculation of first and second static hyperpolarizabilities of one- to three-dimensional periodic compounds. Implementation in the CRYSTAL code.

Abstract

A computational scheme for the evaluation of the static first (β) and second (γ) hyperpolarizability tensors of systems periodic in 1D (polymers), 2D (slabs), 3D (crystals), and, as a limiting case, 0D (molecules) has been implemented, within the coupled perturbed Hartree–Fock framework (CPHF), in the CRYSTAL code, which uses a Gaussian type basis set. This generalizes to 2D and 3D the work by Bishop et al. (J. Chem. Phys. 114, 7633 (2001)). CPHF is applied for β and γ (the polarizability tensor α is also reported for completeness) of LiF in different aggregation states: finite and infinite chains, slabs, and cubic crystal. Correctness of the computational scheme and its numerical efficiency are documented by the trend of β and γ for increasing dimensionality: for a finite linear chain containing N LiF units, the hyperpolarizability tends to the infinite chain value at large N, N parallel chains give the slab value when N is sufficiently large, and N superimposed slabs tend to the bulk value. High numerical accuracy can be achieved at relatively low cost, with a dependence on the computational parameters similar to that observed for field-free self-consistent field (SCF) calculations.