THE QUADRATIC RESPONSE FUNCTION IN THE TDHF APPROXIMATION AND ITS APPLICATION TO FREQUENCY-DEPENDENT HYPERPOLARIZABILITIES OF THE FH MOLECULE

Frequency-dependent hyperpolarizabilities of the FH molecule are calculated in the TDHF quadratic response function formalism. Various first hyperpolarizabilities beta(-omega(sigma); omega1, omega2) which depend on two different frequencies are calculated, as well as the case of a monochromatic optical oscillating field. The validity of Shelton's approximation is discussed. Second hyperpolarizabilities gamma(-omega(sigma); omega1, omega2, omega3) for the dc-induced second-harmonic generation and the dc-induced optical rectification, as well as for the static case, are calculated using a finite-difference technique to differentiate the analytical beta(-omega(sigma); omega1, omega2). A new type of basis set (the ''smooth-tempered'' basis set) is implemented, as a modification of the even-tempered basis set. The method is applied to the largest basis set P2([14s10p6d4f/9s8p3d]) in this work. Basis P2 almost solves the unsaturation problem of basis sets in practice, and results for dipole moment, polarizability, and first and second hyperpolarizability with P2 are near the Hartree-Fock limit.