Molecular (hyper)polarizabilities computed by pseudospectral methods

Abstract

We have developed algorithms based on pseudospectral (PS) ab initio electronic structure methods for solving the first- and second-order Hartree-Fock/Kohn-Sham equations and evaluating molecular polarizabilities and first- and second-order hyperpolarizabilities in the spin-restricted and spin-unrestricted formalisms at the Hartree-Fock (HF) and density functional theory (DFT) levels. We carry out calculations on 50 small molecules to test the accuracy of the PS approach. Our results demonstrate that the molecular polarizability alpha computed by the PS method is essentially identical to the value obtained from conventional methods for both HF and DFT calculations, while the first-order hyperpolarizability beta and second-order hyperpolarizability gamma have mean unsigned percentage differences of 1.26% and 0.62% (HF) and 0.78% and 0.65% (DFT), respectively. We also present CPU timing comparisons between the PS and conventional methods at the 6-31 G(**) level for 14 molecules having 185 to 1185 basis functions. The timing results show that the PS method is 25 (PS-HF) and 13 (PS-DFT) times faster than the conventional method for a system with 500 basis functions. The PS methods are found scale as N(2.70) (PS-HF) and N(2.40) (PS-DFT), while the conventional methods scale as N(2.93) (PRISM-HF) and N(2.87) (PRISM-DFT), where N is the number of basis functions.