Two-photon absorption in the relativistic four-component Hartree–Fock approximation

Abstract

A first implementation of the single residue of the quadratic response function in the four-component Hartree-Fock approximation is presented. The implementation is based on a Kramers paired molecular orbital basis and takes full advantage of time and spatial symmetry reductions in a quaternion formulation-in analogy with the previous work on the quadratic response function [J. Chem. Phys. 121, 6145 (2004)]. Sample calculations are given in terms of the monochromatic and coherent two-photon absorption cross sections in the noble gases. The relativistic two-photon selection rule DeltaJ = {0,+/-2} allows for nonrelativistically spin-forbidden transitions, and, even in neon, strong two-photon absorption is shown to occur for the X (1)S(0)-->2 (3)P(2) transition. It is argued that relevant comparisons between nonrelativistic and relativistic calculations must be performed at the level of integrated absorption cross sections.

Quadratic response functions in the relativistic four-component Kohn-Sham approximation

“…In the present work, we therefore develop and implement the quadratic response function in the time-dependent four-component Kohn-Sham DFT approximation. Our work should be seen as an extension of the previous mentioned work in the HF approximation 24,28,29 as well as the work on the linear response function in the DFT approximation. 30 In Sec.…”

“…The most striking example when spinorbit effects in the valence electron density are of prominent importance in the calculation of a quadratic response function is given by the two-photon absorption spectra ͑which relate to a first-order residue of the quadratic response func-tion͒. It was demonstrated by Henriksson et al 24 that even for a light element such as neon, the inclusion of spin-orbit interactions is necessary to obtain a qualitatively correct twophoton absorption spectrum.…”

“…21 Full inclusion of scalar relativistic and spin-orbit effects in the calculation of third-order molecular properties was accomplished with the implementation of the quadratic response function ͑and its first-and second-order residues͒ in the time-dependent four-component Hartree-Fock approximation. 24,28,29 While accurate with respect to relativistic effects, it is expected that the applicability of this method is severely limited due to the large effects of electron correlation on nonlinear response properties and since it is inappropriate to treat relativity and electron correlation separately. In the present work, we therefore develop and implement the quadratic response function in the time-dependent four-component Kohn-Sham DFT approximation.…”

A theoretical and experimental study of non-linear absorption properties of substituted 2,5-di-(phenylethynyl)thiophenes and structurally related compounds

“…This approach does not only reduce the computational effort but also increase the accuracy by providing relativistically correct potentials for the motions of the valence electrons. We have previously made a series of benchmarking calculations that show the virtues and limitations of ECP calculations for linear and nonlinear valence electron properties [34,[45][46][47]. In summary, these investigations showed that excitation energies and one-photon moments can be quite accurately determined with use of ECPs but that two-photon moments in reality break spin selection rules even for light compounds.…”

“…In summary, these investigations showed that excitation energies and one-photon moments can be quite accurately determined with use of ECPs but that two-photon moments in reality break spin selection rules even for light compounds. (The integrated TPA cross sections may, however, be of fair quality with the ECP approach) [46].…”