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Using the recently developed state-of-the-art empirical bond-order potential (LCBOPII), presented in the companion paper [Los et al., Phys. Rev. B 72, 214102 (2005)], we study liquid carbon by Monte Carlo simulation. We determined the equation-of-state and local structure over a wide range of temperatures $(4000--15\phantom{\rule{0.2em}{0ex}}000\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ and pressures (up to $300\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$). Comparison of the equation-of-state and local structure along the $6000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ isotherm with benchmark ab initio molecular dynamics data shows that LCBOPII provides accurate predictions. The local coordination varies gradually from mixed two- and three-fold, via dominantly threefold, to mainly fourfold with increasing temperature and pressure. This provides evidence that there is no liquid-liquid phase separation as confirmed by the regular behavior of the pressure-density relations along the isotherms in the range of $5000--15\phantom{\rule{0.2em}{0ex}}000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We provide an accurate fit of the pressure-temperature-density equation-of-state that may serve as a reference for future studies of liquid carbon.

Improved long-range reactive bond-order potential for carbon. II. Molecular simulation of liquid carbon