The quality of transition current densities derived from Gaussian basis sets

Area of Science:

• Quantum Mechanics
• Computational Chemistry
• Quantum Electrodynamics

Background:

• Traditional quantum-mechanical models for luminescence and energy transfer rely on transition dipoles, which fail to capture retardation and polariton effects for larger systems.
• The transition-current-density (TCD) approach, based on macroscopic quantum electrodynamics, addresses these limitations by including retardation and polariton effects.
• The accuracy of TCD derived from ab initio calculations has not been thoroughly investigated.

Purpose of the Study:

• To assess the numerical equivalence between transition dipoles and TCDs in 1- and 2-electron systems.
• To evaluate the validity of the continuity equation (∇·Jnm = -iωnmρnm) for TCD calculations.
• To develop methods for improving the physical consistency of TCD calculations.

Main Methods:

• Calculated transition dipoles from transition charge densities and TCDs for H2+, HeH+, and H2.
• Examined the continuity equation by comparing transition charge density (ρnm) and the divergence of TCD (Jnm).
• Implemented a reciprocal-space filtering technique to mitigate spurious oscillations in TCD calculations.

Main Results:

• Transition dipole moments showed close agreement between the two methods.
• Substantial violations of the continuity equation were observed, attributed to artifacts in Gaussian-type orbitals.
• Reciprocal-space filtering effectively suppressed non-physical oscillations, enhancing the physical consistency of TCD.

Conclusions:

• While transition dipoles and TCDs are numerically similar for small systems, the continuity equation highlights discrepancies.
• Gaussian-type orbital artifacts can lead to unphysical results in TCD calculations.
• The developed reciprocal-space filtering technique offers a practical solution for improving the reliability of transition current calculations.