  Using the effective mass theory and the multi-valley envelope function
representation, we have developed a theoretical framework for computing the
single-electron electronic structure of several phosphorus donors interacting
in an arbitrary geometrical configuration in silicon taking into account the
valley-orbit coupling. The methodology is applied to three coupled phosphorus
donors, arranged in a linear chain and in a triangle, and to six donors
arranged in a regular hexagon. The results of the simulations evidence that the
valley composition of the single-electron states strongly depends on the
geometry of the dopant molecule and its orientation relative to the
crystallographic axes of silicon. The electron binding energy of the triatomic
linear molecules is larger than that of the diatomic molecule oriented along
the same crystallographic axis, but the energy gap between the ground state and
the first excited state is not significantly different for internuclear
distances from 1.5 to 6.6 nm. Three donor atoms arranged in a triangle geometry
have larger binding energies than a triatomic linear chain of dopants with the
same internuclear distances. The planar donor molecules are characterized by a
strong polarization in favor of the valleys oriented perpendicular to the plane
of the molecule. The polarization increases with number of atoms forming the
planar molecule.
