Determination of Effective Atomic Charges from the Chemical Shifts of X-Ray Emission Lines

Abstract

The x-ray line shifts obtainable as differences of level shifts from various quantum mechanical calculations using the free-ion model provided values which were in good agreement with each other at least for the Kα shifts. This justifies the determination of effective atomic charges from experimental x-ray line shifts. The formation of inner holes can be taken into account by using the values of Z + 1 for the charge determination of compounds of the element Z. With the 3d elements the Kβ shift must be considered besides the Kα one due to the opposite effects of missing 3d and 4s electrons. The charges determined for the first time only x-ray spectroscopically—generally between 0.8 and 1.5—as well as the 3d and 4s orbital populations change in the same manner as the values obtained from MO calculations. In contrast to the situation with the main group elements where the effective charge increases with increasing formal charge, the former decreases for formal charges above 2 with the 3d elements.