The vibrational Stark shifts of sulfate internal modes in SO42- doped potassium, rubidium and cesium selenates. A quantum model for measurement of crystalline fields

A quantum theoretical basis for the experimentally observed vibrational Sta rk shifts of the sulfate internal modes in SO42- doped K2SeO4, Rb2SeO4 and Cs2SeO4 is presented. Analytical first order perturbation theoretical expre ssions are derived for the field-dependent wavenumbers of the 1<--0 and 2<- -0 transitions, harmonic wavenumbers, as well as for the Stark tuning rate and the electrostatic field strength at the C-s sites of the host lattices. It is shown that the local field differences are the factor dominating ove r the differences in the anharmonicities of the guest anions in various hos t lattices, and are thus responsible for the experimentally observed trends . The proposed method allows calculation of the local crystalline field str ength if the anharmonic potential energy parameters of the dopant anions ar e known. The calculated values for the studied series of matrices range fro m 229 to 259 V nm-1, which are approximately 3 times larger than those repo rted for water molecule sites in several clathrate hydrates and for the N2O adsorbed in the NaA zeolite cavities. The model also successfully explains the greater bond length distortions than the angular ones of the dopant an ions observed in all studied cases.