Analytical expressions for the Coulomb interaction between an s-orbital electron and the surroundings, infinite ionic crystal lattice are derived. The s-orbital wave functions are presented in the form of a Gaussian expansion. As a test, Madelung constants and interaction energy for NaCl, KMgF₃, CaF₂ are calculated using a single Gaussian exponent. The calculated values are coincided with known literature data with a high degree of accuracy.

The tetragonal crystalline electric field parameters for Yb³⁺ and Ce³⁺ ions are expressed via ground multiplet exited doublets energies and parameters defining doublets' wave functions. The crystalline electric field parameters for Yb³⁺ ion in YbRh₂Si₂, YbIr₂Si₂ and KMgF₃ crystals extracted from excited state doublets energies and g-factors of ground state doublet are compared with parameters determined in other works.

The low temperature 4f¹³-4f¹²5d absorption and emission band shapes of the impurity Tm²⁺ ions have been simulated within adiabatic approximation on the basis of a microscopic model operating with the real phonon spectrum of the host CaF₂ lattice. Crystal field parameters and electron-phonon coupling constants were treated in the framework of the exchange charge model. Results of simulations of the spectral envelopes agree satisfactorily with the experimental data available from literature.