Transition moments beyond the electric-dipole approximation: Visualization and basis set requirements

Area of Science:

• Computational chemistry
• Atomic physics
• Spectroscopy

Background:

• The electric-dipole approximation is often used in x-ray absorption spectroscopy simulations.
• Going beyond this approximation involves different schemes, but their basis set needs are unclear.

Purpose of the Study:

• To assess the basis set requirements for three schemes that go beyond the electric-dipole approximation in x-ray spectroscopy simulations.
• To compare the convergence and accuracy of these schemes.

Main Methods:

• Calculations were performed on radium atom transitions (core and valence) using four-component relativistic TD-HF theory.
• Dyall.aeXz (X = 2, 3, 4) basis sets were employed.
• Radial distributions of transition moment densities were visualized.

Main Results:

• The generalized length representation electric multipole converges most easily.
• Magnetic multipole moments show a similar trend but are harder to converge.
• The generalized velocity representation electric multipoles are most difficult to converge, showing artifacts with larger basis sets.

Conclusions:

• The full semi-classical light-matter interaction scheme is recommended for x-ray spectroscopy simulations.
• Truncated multipole expansions, particularly the velocity representation, can introduce significant errors due to basis set limitations.