Perturbative second-order optical susceptibility of bulk materials: a symmetry-enforced return to non-orthogonal localized basis sets

Abstract The second-order optical susceptibility of semiconductors χ i j k ( 2 ) ( − 2 ω ; ω , ω ) finds application in metrology, spectroscopy, telecommunications, material characterization, and quantum information. Pioneering calculations of χ i j k ( 2 ) ( − 2 ω ; ω , ω ) utilized non-orthogonal Gaussian orbitals centered at atoms. That formulation transitioned into plane-wave-based algorithms as time went by. As of late, nevertheless, multiple tools for calculating optical susceptibilities have recast the problem using Wannier (i.e. localized ) orbitals, making a comeback onto frameworks based on localized basis sets. Here, we present an approach for calculating χ i j k ( 2 ) ( − 2 ω ; ω , ω ) reliant on numerical pseudo-atomic orbitals (PAOs) within perturbation theory in the velocity gauge. Its salient feature is a calculation of ‘Slater–Koster-like’ two-center integrals of the momentum operator in between PAOs identified by symmetry. The approach was successfully tested on paradigmatic cubic silicon carbide (3C-SiC) and gallium arsenide, for which linear responses are contributed as well.