Total-energy tight-binding modelisations of silicon

We present a systematic comparison of several tight-binding total-energy modelisations of silicon. These modelisations include the tight-binding electronic cohesive energy and a phenomenological description of a repulsive term. We examine both the electronic band gap and various structural properties such as structural stability, bulk modulus, elastic constants, four typical vibrational modes and their Grüneisen constants. We then apply these models to the calculations of the minimised energies of some multivariant grain boundaries. We discuss the influence of the choice of cut radii.