In atomic systems, electron density has a simple finite expansion in spherical harmonics times radial factors. The difficulties in the calculation of some radial factors are illustrated in the low-lying states of the carbon atom.
Single-particle methods such as Hartree–Fock and approximate density functional theory cannot ensure the correct expansion of the density in spherical harmonics. Wave-function methods are appropriate but, as some expansion terms are entirely due to correlation, these methods only will give correct results for high-quality variational functions. Using full-configuration integration (CI), all the terms predicted by the theory appear and are not negligible but the convergence of the term due to correlation toward its correct value is uncertain even for very large CI spaces. © 2012 Wiley Periodicals, Inc.