A liquid-liquid phase transition in carbon is investigated with two recent bond-order potentials. In contrary to a previous bond-order model, they show no phase change in liquid carbon, which agrees with simulations based on the nonempirical density-functional theory (DFT). Ab initio and DFT studies carried out in this work show that the observed discrepancy lies not in any inherent shortcoming in using empirical models for the bonding process, but rather in the quality of individual expressions used to represent a conjugated local environment in liquid carbon. The present work shows that the current bond-order models and a slightly modified potential proposed in this work agree with recent quantum mechanical simulations and will provide a viable tool for a large-scale study of carbon over a wide range of pressures and temperatures. (C) 2003 American Institute of Physics.