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

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 $Kα_1$, $Kα_2$, and L transitions of the group 14 metal cations with respect to neutral atoms are presented. The calculations of chemical shift of $Kα_1$-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.