  We derive interatomic potentials for zinc blende InAs, InP, GaAs and GaP
semiconductors with possible applications in the realm of nanostructures. The
potentials include bond stretching interaction between the nearest and
next-nearest neighbors, a three body term and a long-range Coulomb interaction.
The optimized potential parameters are obtained by (i) fitting to bulk phonon
dispersions and elastic properties and (ii) constraining the parameter space to
deliver well behaved potentials for the structural relaxation and vibrational
properties of nanostructure clusters. The targets are thereby calculated by
density functional theory for clusters of up to 633 atoms. We illustrate the
new capability by the calculation Kleinman and Gr\"uneisen parameters and of
the vibrational properties of nanostructures with 3 to 5.5 nm diameter.
