The quality of transition current densities derived from Gaussian basis sets

Quantum-mechanical descriptions of luminescence, excitation energy transfer, and resonant dipole-dipole interactions are usually formulated in terms of transition dipoles from the 1-particle density matrix. However, transition dipoles cannot adequately capture the retardation and polariton effects for large entities. A previous study [M.-W. Lee and L.-Y. Hsu, Phys. Rev. A, 107, 053709 (2023)] showed that based on macroscopic quantum electrodynamics, the transition-current-density (TCD) approach not only enables the description of retardation effects but also accounts for the polariton effects arising from material structures and vacuum electromagnetic fields. Nevertheless, the quality of transition currents derived from ab initio calculations remains largely unexplored. In this study, we examine the numerical equivalence between transition dipoles derived from transition charge densities and those from TCDs for 1- and 2-electron systems, including H2+, HeH+, and H2. We further examine the continuity equation ∇ · Jnm = -iωnmρnm by comparing the transition charge density (ρnm) and the divergence of TCD (Jnm), for a transition between states n and m. Despite close agreement of transition dipole moments, we find substantial violations of the continuity equation. The deviations manifest as spurious oscillations in ∇ · Jnm due to the artifacts from the second-derivative features of the underlying Gaussian-type orbitals. To overcome this issue, we implement a reciprocal-space filtering technique that suppresses these non-physical oscillations, improving physical consistency for the TCD. Our study provides practical considerations for future calculations that require reliable transition currents.