Multipole density formalism

Definition

The multipole density formalism is a way to improve the modelling of the electron density of crystal structures by departing from the purely spherical and independent atom model. In this formalism, the electron density of each atom is split into two parts, the core and the valence electron densities. The density of the valence electrons is again split into two parts, namely a spherical and an aspherical density. The aspherical density is based on spherical harmonic functions which are usually limited to the lowest orders. The aspherical part is thus able to improve the modelling of e.g. valence bonds in organic molecules or electron pairs around some metal atoms.

Bibliography

Coppens, P.; Hansen, N. K. (1978). "Testing aspherical atom refinements on small molecule data sets" . Acta Cryst.. A34 (6): 909–921. https://doi.org/10.1107/S0567739478001886

Genoni, A.; Macchi, P. Quantum Crystallography in the Last Decade: Developments and Outlooks. Crystals 2020, 10, 473. https://doi.org/10.3390/cryst10060473