Method of evaluating chemical shifts of X-ray emission lines in molecules and solids

TL;DR

This paper introduces a computational method for accurately evaluating chemical shifts of X-ray emission lines in heavy atoms within molecules and solids, avoiding large energy difference calculations.

Contribution

The paper develops a pseudopotential and one-center restoration-based method to compute chemical shifts efficiently and accurately for heavy atoms in compounds.

Findings

Calculated chemical shifts for group 14 metal cations and neutral atoms.

Analyzed chemical shifts for Pb in PbO and PbF2.

Discussed the accuracy and limitations of the method.

Abstract

Method of evaluating chemical shifts of X-ray emission lines for sufficiently heavy atoms (beginning from period 4 elements) in chemical compounds is developed. This method is based on the pseudopotential model and one-center restoration method (to reconstruct the proper electronic structure in heavy-atom cores). The approximations of instantaneous transition and frozen inner core spinors of the atom are used for derivation of an expression for chemical shift as a difference between mean values of some effective operator. The method allows one to avoid evaluating small values (chemical shifts ~$ 0.01{-}1$ eV) as differences of very large values (transition energies ~ $1{-}100$ keV in various compounds). The results of our calculations of chemical shifts for the $K\alpha_1$, $K\alpha_2$, and L transitions of the group 14 metal cations with respect to neutral atoms are presented. The calculations of chemical shift of $K\alpha_1$-line in the Pb-core transition within PbO and PbF$_2$ with respect to the neutral Pb are also performed and discussed. The accuracy of the used approximations is discussed and quality of the performed calculations is analyzed.