Bethe logarithm ln(k0) is one of the leading quantum-electrodynamics energy corrections of the order of α^3. A method for calculating this correction, which is an alternative to the method of Schwartz et al. , is presented. An effective algorithm for selecting a basis set to be used in the ln k 0 calculation is also shown. This work is based on the previous paper by Stanke et al. . The approach proposed by Stanke et al. in that paper is extended for calculating multi-electron atoms and two-center molecules. The proposed algorithm employs a spectral representation of a function of an operator and its spectral decomposition. The calculations are done within the Born-Oppenheimer approximation using explicitly correlated Gaussian functions with shifted centers.
In both cases, the atomic and the molecular, one of the main problems is the choice of appropriate basis sets.