Direct atomic orbital based self-consistent-field calculations of nonlinear molecular properties. Application to the frequency dependent hyperpolarizability of para-nitroaniline

We outline a method for the calculation of nonlinear properties such as dynamic hyperpolarizabilities for self-consistent-field (SCF) wave functions. In this method, two-electron integrals are only addressed in the evaluation of Fock matrices and Fock matrices with one-index transformed integrals. These matrices are determined directly in terms of integrals evaluated in the atomic orbital basis, avoiding expensive integral transformations between atomic and molecular orbital bases as well as storing and retrieving the two-electron integrals. The method is double direct-direct in the sense of constructing Fock matrices from atomic integrals, and direct in the sense of solving the response equations iteratively using direct linear transformations of a generating matrix times trial vectors. Applications can be performed on species of the same size as in direct SCF. The cost of evaluating a single nonlinear molecular property is comparable to that of optimizing the wave function. Additional properties can be obtained at little extra cost by solving all response equations simultaneously. As a demonstration, we calculate the static and dynamic hyperpolarizabilities of para-nitroaniline.