(Hyper)polarizabilities of GaN, GaP, and GaAs clusters: An ab initio time-dependent Hartree-Fock study

The (hyper)polarizabilities of GaN, GaP, and GaAs clusters have been calculated using an ab initio time-dependent Hartree-Fock method and an even-tempered Gaussian basis set. The geometries of the clusters used in the study were optimized by ab initio Hartree-Fock calculations using the same basis set, The clusters used in this calculation are of the type GamXn (m = 1, 3, 4 and n = 1, 3, 4) where X = N, P, or As. The Ga,X, clusters are in a charge neutral (q = 0) state for m = n and in an appropriately charged state for m not equal n. All of the clusters studied are stable in a nearly tetrahedral geometry. The magnitude of the calculated (hyper)polarizabilities appears to depend on the size of the cluster. The cluster-size dependence of calculated (hyper)polarizabilities is more pronounced for the first hyperpolarizability, beta, than for the polarizability, alpha. The calculated frequency-dependent polarizability, alpha(omega), exhibits a small but finite dispersion with the frequency of the optical field. The magnitude of the calculated beta(-omega(0);omega(1),omega(2)) corresponding to various second-order effects shows the expected trend of beta(-2 omega;omega,omega) > beta(-omega;0,omega) > beta(0;0,0).