Relativistic Effects on X-ray Structure Factors

TL;DR

This study quantifies relativistic effects on X-ray structure factors in certain metal complexes, showing they can be significant for individual reflections and are well approximated by quasi-relativistic methods like DKH2 and ZORA.

Contribution

It systematically analyzes relativistic effects on structure factors using four-component wave functions and compares different quasi-relativistic approximations.

Findings

Relativistic effects on structure factors average around 0.5% to 1.3%.

Quasi-relativistic methods reduce discrepancies by an order of magnitude.

Relativistic effects can be larger for specific reflections, impacting experimental interpretation.

Abstract

X-ray structure factors from four-component molecular wave functions have been calculated for the model systems $M$(C$_2$H$_2$) ($M$= Ni, Pd, Pt). Relativistic effects on the structure factors are investigated by the comparison to results obtained from a non-relativistic reference and in order to systematically analyse the effect of different quasi-relativistic approximations, we also included the DKH2 and the ZORA Hamiltonian in our study. We show, that the overall effects of relativity on the structure factors on average amount to 0.47, 0.80 and 1.27% for the three model systems under investigation, but that for individual reflections or reflection series the effects can be orders of magnitude larger. Employing the DKH2 or ZORA Hamiltonian takes these effects into account to a large extend, reducing the according differences by one order of magnitude. In order to determine the experimental significance of the results, the magnitude of the relativistic effects on the structure factors is compared to the according changes due to charge transfer and chemical bonding.