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

A method of evaluating chemical shifts of x-ray emission lines for period four and heavier elements is developed. This method is based on the relativistic pseudopotential model and one-center restoration approach [Int. J. Quantum Chem. 104, 223 (2005)] to recover a proper electronic structure in heavy-atom cores after the pseudopotential simulation of chemical compounds. The approximations of instantaneous transition and frozen core are presently applied to derive an expression for chemical shift as a difference between mean values of certain effective operator. The method allows one to avoid evaluation of small quantities (chemical shifts $\sim 0.01$–1 eV) as differences of very large values (transition energies $\sim 1$–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 group-14 metal cations with respect to neutral atoms are presented. Calculations of $K{\alpha }_1$-line chemical shifts for the Pb core transitions in PbO and PbF${}_2$ with respect to those in the Pb atom are also performed and discussed. The accuracy of approximations used is estimated and the quality of the calculations is analyzed.