Tersoff Potential
The particle simulation methods, such as the molecular dynamics method and the Monte Carlo method, allow studying the behavior of materials at the atomic level. The validity of results obtained from any atomistic simulation depends mostly on the adequacy of the potential function used to describe inter-atomic interactions. During recent decades an immense effort has been put into developing new potentials, and many new potentials of high quality have been proposed as a result. Among them, the Tersoff potential has turned out to be one of the most successful approaches for investigating covalently bonded structures.
The overall success of the Tersoff potential mostly originates from the fact that – unlike the traditional molecular mechanics force fields – it allows the formation and dissociation of covalent chemical bonds. This is achieved by explicitly accounting for the multibody effects, which within the Tersoff potential are captured by the bond order. This parameter depends on the local chemical environment of the bond in question and acts in such a way as to control its strength. As a consequence the Tersoff potential is able to “automatically” recognize different bonding schemes, being able to simultaneously describe single, double and triple covalent bonds. It has been recently shown that the Tersoff potential is even capable of correctly describing materials which possess mixed hybridization. Computationally, this inter-atomic potential describe with below equations:
where f_R is a two-body and repulsive term and f_A includes three-body and attraction interactions. The summations in the formula are over all neighbors j and k of atom i within a cutoff distance = R+D.
References
[1] Tersoff, J. (1988). New empirical approach for the structure and energy of covalent systems. Physical Review B, 37(12), 6991–7000.
doi:10.1103/physrevb.37.6991.
[2] Winczewski, Szymon. (2017). Central-force decomposition of the Tersoff potential. TASK Quarterly, Scientific Bulletin of the Academic Computer Centre in Gdansk. 21. 261.
doi:10.17466/tq2017/21.3/p.