Finite nuclear charge density distributions in electronic structure calculations for atoms and molecules

The present review provides comprehensive information on finite nuclear charge density distribution models, not only for the purpose of quantum chemical electronic structure calculations for atoms and molecules, but also for other fields of atomic and molecular physics. A general discussion of the electrostatic behaviour of nuclear charge density distributions, spherical ones and non-spherical ones, is given. A large and reasonably complete set of spherical finite nucleus models, covering all models widely used in atomic and nuclear physics, is discussed in detail. Analytic expressions are given for charge density distributions, for important radial expectation values, and for their corresponding electrostatic potentials; these include new material not found in the literature. Thus, the necessary prerequisites for the use of finite nucleus models which are more realistic than the simple, frequently considered models (e.g., the ‘homogeneous’, ‘Gaussian’, and Fermi models) are fulfilled. The use of finite nucleus models in standard quantum chemical electronic structure programs is briefly reviewed. In order to detect differences between physical properties obtained with various finite nucleus models, six standardized models were selected to study and compare energy shifts (non-relativistic and relativistic) in hydrogen-like atoms. It is shown that within this set a clear differentiation of models can be made, not only from the point of view of total energy shifts but also from the point of view of energy differences and in fact even for rather low nuclear charge numbers. This could be important for future experimental as well as theoretical work on hydrogen-like atoms.