Efficient implementation of isotropic cubic response functions for two-photon absorption cross sections within the...

Within the self-consistent field approximation, computationally tractable expressions for the isotropic second-order hyperpolarizability have been derived and implemented for the calculation of two-photon absorption cross sections. The novel tensor average formulation presented in this work allows for the evaluation of isotropic damped cubic response functions using only ∼3.3% (one-photon off-resonance regions) and ∼10% (one-photon resonance regions) of the number of auxiliary Fock matrices required when explicitly calculating all the needed individual tensor components. Numerical examples of the two-photon absorption cross section in the one-photon off-resonance and resonance regions are provided for alanine-tryptophan and 2,5-dibromo-1,4-bis(2-(4-diphenylaminophenyl)vinyl)-benzene. Furthermore, a benchmark set of 22 additional small- and medium-sized organic molecules is considered. In all these calculations, a quantitative assessment is made of the reduced and approximate forms of the cubic response function in the one-photon off-resonance regions and results demonstrate a relative error of less than ∼5% when using the reduced expression as compared to the full form of the isotropic cubic response function.