Order N non-orthogonal tight-binding molecular dynamics and its application to the study of glass transition in germanium

Order N non-orthogonal tight-binding molecular dynamics based on the Fermi operator expansion method is implemented and tested, where N is the number of atoms. The method is described in detail, with several notes on the actual implementation. We find that the potential energy and forces consistent with it are calculated in an O(N) fashion almost as easily as in the cases of orthogonal tight-binding models. Our method thus implemented is applied to the study of glass transition in germanium (Ge). We quench liquid Ge well above melting temperature by an NVT ensemble molecular dynamics simulation, with N = 512. We investigate the pair correlation function, the static structure factor, and the bond-angle distribution function for liquid, super-cooled liquid, and amorphous Ge. From the analyses of these properties, we find that substantial structural changes occur when the temperature of liquid Ge is decreased. In particular, we find that with the decrease of temperature, covalent bonds in liquid Ge become more significant, and transform from a highly distorted tetrahedral-like bonding to a diamondlike tetrahedral bonding.