Atomic Shell Approximation: Electron Density Fitting Algorithm Restricting Coefficients to Positive Values

Expressing molecular electron densities as linear combinations of Guassian 1S spherical functions extends accurate computations of ab initio quantum molecular similarity measures to large systems. These approximate least squares fitted functions lose the density of probability statistical meaning since some coefficients might be negative. A new algorithm using positive coefficients only and thus providing an electron density picture as a superposition of atomic shells is presented.