The minimal deformation criterion, previously proposed for the partition of the molecular density into atomic contributions, is updated and extended. For any Gaussian basis set, these atomic contributions are expanded in a series of real spherical harmonics by radial factors. The terms with l = 0 determine the spherical parts of the atomic clouds and the remaining ones, their deformations. This detailed description is complemented with a simplified representation of the molecular density in terms of atomic charges and multipoles. Moreover, these descriptions give a simple way to calculate the electrostatic potential of the molecule as well as the electrostatic interaction between molecules.