Quadratic response functions in the time-dependent four-component Hartree-Fock approximation

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Relativistic Effects

Background:

• The accurate calculation of molecular properties is crucial in chemistry.
• Relativistic effects become significant for heavy elements, influencing electronic structure and properties.
• Time-dependent Hartree-Fock (TDHF) methods are used to study molecular responses to electromagnetic fields.

Purpose of the Study:

• To implement and apply a second-order response function within the time-dependent four-component Hartree-Fock (TDHF) approximation.
• To investigate the relativistic corrections to electric dipole first-order hyperpolarizabilities (beta) for CsAg and CsAu in the second-harmonic generation (SHG) process.
• To analyze the impact of resonances and excited states on the calculated hyperpolarizabilities.

Main Methods:

• Implementation of a direct, atomic orbital-based, second-order response function in the four-component TDHF framework.
• Utilization of a quaternion symmetry scheme for computational efficiency, considering time-reversal and spatial symmetries.
• Calculation of beta(-2omega;omega,omega) for CsAg and CsAu, including static limit beta(0;0,0).

Main Results:

• Relativistic corrections were found to be substantial for CsAg and CsAu.
• Nonrelativistic calculations overestimated the static hyperpolarizability by 18% for CsAg and 66% for CsAu.
• Anomalous dispersion was observed in the band gap region due to resonances with nonrelativistically spin-forbidden states.

Conclusions:

• Relativistic effects are essential for accurate hyperpolarizability calculations of heavy-element compounds.
• The presence of weakly absorbing states can lead to divergences in the quadratic response function due to the infinite excited-state lifetime approximation.
• Caution is advised when applying these methods if the exact positioning of all excited states is unknown.