Calculation of the static electron second hyperpolarizability or χ(3) tensor of three dymensional periodic compounds with a local basis set

The coupled perturbed Hartree–Fock (CPHF) method for evaluating static first (β) and second (γ) hyperpolarizability tensors of periodic systems has recently been implemented in the CRYSTAL code [ Bishop et al., J. Chem. Phys. 114, 7633 (2001) ]. We develop here an efficient and accurate computational protocol, along with the local basis sets needed for first and second row atoms. Application is made to several high symmetry three-dimensional systems including one (pyrope) with an 80 atom unit cell. CPHF second-order hyperpolarizabilities substantially undershoot experimental values, due to an overestimate of the band gap, but trends are satisfactorily reproduced for β as well as γ.