You want to solve for 3 to 10 particle systems (3D per particle)? As far as I am aware, mean field theories do not work especially well for so few particles, but it seems there has been DFT work on diatomic molecules.
Is this a system where Born-Oppenheimer is valid? If so, I might be inclined to expand the electronic wavefunction using a linear combination of Slater determinants possibly using sparse grid or spectral sparse grids This paper perhaps could help.
Another option is to try using a tight-binding approach, although the fact that you mentioned absorbing boundary conditions suggests you may be thinking of problems involving ionization/dissociation. TB would mostly be useful if you were trying to approximate low level states.
Possibly something like the multi-configurational time-dependent Hartree-Fock method could work here MCTDHF.
Finally, you could look at quantum Monte Carlo methods. These are the methods by which exchange and correlation functional models for single atoms are obtained to do DFT calculations. It looks like there are poly-atomic extensions. (I'm out of link privileges).