TDHF evaluation of the dipole-quadrupole polarizability and its geometrical derivatives

Analytical procedures based on the time-dependent Hartree-Fock (TDHF) scheme are elaborated to evaluate the frequency-dependent electric dipole-electric quadrupole polarizability and its derivatives with respect to atomic Cartesian coordinates. On one hand, the mixed second-order TDHF equations are solved iteratively to obtain the second-order derivatives of the linear combination of atomic orbitals coefficients, once with respect to atomic Cartesian coordinates and once with respect to external dynamic electric fields or electric field gradients. On the other hand, taking advantage of the 2n + 1 rule, the first-order derivatives of A are expressed with respect to atomic Cartesian coordinates in terms of lower-order derivatives. These procedures have been implemented in the GAMESS quantum chemistry package and have been illustrated in the case of several small molecules as well as adamantane.