The focus of this thesis is the techniques used in constructing a library of improved parameters for the Tersoff bond-order potential energy model which is used in atomistic modelling applications. The parameters presented here are for the elemental type-IV diamond structure semiconductors and the binary III-As, III-P, III-Sb and the cubic III-N compound semiconductors. The parameters are fitted to a number of experimental and DFT predicted properties of the materials including the lattice parameter, the cohesive energy, the elastic constants and the lattice dynamical properties, including phonon frequency and mode-Griineisen parameters, for three pertinent locations in the Brillouin zone. The conclusions of this work demonstrate that the elastic and dynamical properties of a material cannot be simultaneously predicted with the Tersoff potential due to a lack of flexibility in the current functional form. The balance between the radial and angular force contributions available in the bond-order term cannot replicate the delicate nature of the equilibrium in a real system and so two modifications to the Tersoff potential energy model have been proposed. The modifications include the addition of a second parameter and a linear contribution to the crystal anti-symmetry modelling term and the addition of a fourth parameter to the angular bonding term, which has been re-designed to be a more flexible summation of cosine terms. Also included in this work is: 1) a re-modelling of Keyes' relation which relates the dimensionless elastic properties of the cubic III-V semiconductors to the lattice parameter of the material to include a second-order term for the modelling of the III-N materials, 2) a simple method for the prediction of the effective ionic charge q* of the cubic III-V semiconductor materials based upon the X-point phonon energies and 3) the first Tersoff parameterisation of the materials GaP, InP, GaSb and InSb available in the literature.