A parameterization of the Abell-Tersoff potential is presented for all pairwise interactions of silicon atoms with each of the elemental components comprising InGaAs. That is, Tersoff models are provided for Si-In, Si-Ga and Si-As. Data obtained using ab initio pseudopotential calculations (DFT+GGA) were used as the reference information against which the Tersoff parameters were fitted, since experimental data are unavailable for the Si-X systems considered here. These sets of Tersoff parameters are optimized to describe the structural and elastic properties of the mostly theoretical alloys Si-As, Si-Ga and SI-In. We demonstrate the transferability of these parameters by partially predicting the defect formation energies of extrinsic point defects of Si across ternary InGaAs alloys with different local configurations. Comparison is made to a newly created DFT/GGA database of defect formation energies, showing that correct trends can be reproduced by the Tersoff models, given sensitive adjustments to a Tersoff model parameter, .