Comparison of density-functional, tight-binding, and empirical methods for the simulation of amorphous carbon

Amorphous carbon networks are used to test various levels of theoretical approaches to molecular dynamics simulations. The density-functional theory as implemented in the Car-Parrinello method, nonorthogonal tight-binding method, the environment-dependent interaction potential (EDIP), and the Brenner potential are compared directly in liquid quench simulations containing 125 atoms at four densities. We find that at low densities the predictions of the Brenner potential are in agreement with those from density-functional theory, while structures produced by nonorthogonal tight-binding method compare well with density-functional theory at all densities. The tight-binding method does, however, find a slightly lower ${\mathrm{sp}}^3$ fraction at high densities and the presence of singly coordinated atoms at low densities. The frequency of three-membered rings are underpredicted by the tight-binding and EDIP methods due to an overestimate of strain energy relative to density- functional theory and experiment. Aside from the small rings, and a slight underestimate in ${\mathrm{sp}}^3$ fraction at the highest densities, the EDIP simulations are in very good agreement with density-functional theory. The EDIP method is also used to quantify the statistical variability of liquid quenching, and comparisons with film growth simulations verify that liquid quenching is a good representation of bulk amorphous carbon.