Cold Magnetically trapped \u3csup\u3e2\u3c/sup\u3eD\u3csub\u3eg\u3c/sub\u3e scandium atoms. I. Interaction potential

We present a first principles description of the interaction of two ground-state scandium atoms. Scandium has a 2Dg ground state. Thirty molecular states correlate to the lowest dissociation limit of the dimer. In the short range, potential energy curves are calculated using second-order n-electron valence state perturbation theory. The first-order long-range interaction is calculated at the complete active space self-consistent field level. We determine the second-order long-range dispersion interaction from atomic dynamic polarizabilities at imaginary frequencies. These polarizabilities are calculated using time-dependent density functional theory. We merge the short-range approach with the long-range model to obtain a physical description of the 30 potential energy curves correlating to the 2Dg + 2Dg limit. Diabatic potentials are presented that can be used in quantum scattering calculations, in order to study Zeeman relaxation of ultracold scandium atoms