The extension of the first-principles generalized pseudopotential theory (G
PT) to transition-metal (TM) aluminides produces pair and many-body interac
tions that allow efficient calculations of total energies. In aluminum-rich
systems treated at the pair-potential level, one practical limitation is a
transition-metal overbinding that creates an unrealistic TM-TM attraction
at short separations in the absence of balancing many-body contributions. E
ven with this limitation, the GPT pair potentials have been used effectivel
y in total-energy calculations for Al-TM systems with TM atoms at separatio
ns greater than 4 Angstrom. An additional potential term may be added for s
ystems with shorter TM atom separations, formally folding repulsive contrib
utions of the three- and higher-body interactions into the pair potentials,
resulting in structure-dependent TM-TM potentials. Towards this end, we ha
ve performed numerical ab initio total-energy calculations using the Vienna
ab initio simulation package for an Al-Co-Ni compound in a particular quas
icrystalline approximant structure. The results allow us to fit a short-ran
ged, many-body correction of the form a (r(0)/r)(b) to the GPT pair potenti
als for Co-Co, Co-Ni, and Ni-Ni interactions.