In Density Functional Theory, representing and approximating the electronic charge and spin density to a required level of precision is a basic computational problem. Methods of expansion in localized highly tailored basis sets are in a continuing state of development. For a recent example see:
Radial-template approach for accurate density representation in computational quantum theory
Lj. Miljacic and D. E. Ellis, J Comput. Chem. 31, 1486-1494 (2010)
A method for improved representation of electronic charge and spin densities for molecular and solid state systems is presented, based upon extensions of least squares fits to quantum mechanical
true densities using basis functions of limited support. Attention is given to optimization of radial degrees of fit freedom, and the design of fit functions permitting rapid analytic manipulation and calculation of properties, such as Coulomb potentials. The method is demonstrated for covalent CO and for a large metal-organic crystalline structure.