Riemannian three dimensional molecular spaces

A simple manipulation of the first order density function permits to define a curved 3D Riemannian coordinate set, which can substitute the usual flat 3D Cartesian space, where atoms and molecules are supposed to exist. Several simple models are discussed. Gaussian type orbitals generate a space division with positive and negative curvatures, the later one being near the centre of the functions; contrarily Slater type orbitals provide a positive curvature everywhere.