Shape of the geometrically active atomic states of carbon

We have developed a computer code for {\em ab initio} the variational configuration interaction calculation of the electronic structure of atoms via variationally optimized Lagurre type orbitals, treating the orbital effective charges as variational parameters. Excited states of the same symmetry, in order to avoid the inherent restrictions of the standard method of Hylleraas--Unheim and MacDonald, are computed variationally by minimizing the recently developed minimization functionals for excited states. By computing, at the minimum, the one-electron density and the probability distribution of the two-electron angle, and the most probable two-electron angle, we investigate the atomic states of the carbon atom. We show that, without resorting to the (admittedly unproven) concept of hybridization, as an intrinsic property of the atomic wave function, the most probable value of the two-electron angle is around the known angles of carbon bonding, i.e. either 109^\circ or 120^\circ or 180^\circ, depending on each low-lying state of the bare carbon atom.