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Results of a numerical investigation of crystalline silicon melting line within the range of pressures from -1 to 3 GPa are presented. A two-phase molecular dynamics method is applied to obtain temperature, pressure, and densities of solid and liquid phases on the melting line. Using a special procedure we ensure the strict control of the two-phase equilibrium in the simulation cell. To describe the interaction between the atoms four classic potentials have been chosen: the Stillinger-Weber one and three modified variants of the Tersoff potential. For the Stillinger-Weber and Tersoff potentials in the modification by Kumagai-Izumi-Hara-Sakai a good coincidence with experimental data on crystalline Si melting temperature is obtained within the range of pressure from 0 to 3 GPa. Calculations of the solid and liquid phase densities on the silicon melting line for the Stillinger-Weber potential are also in close agreement with experiments.

The equation of state and the structure of liquid carbon are studied by molecular simulation. Both classical and quantum molecular dynamics (QMD) are used to calculate the equation of state and the distribution of chemical bonds at 6000 K in the pressure range 1-25 GPa. Our calculations and results of other authors show that liquid carbon has a fairly low density on the order of 1.2-1.35 g/cm at pressures about 1 GPa. Owing to the coordination number analysis, this fact can be attributed to the high content of sp-bonded atoms (more than 50% according to our ab initio computations). Six empirical potentials have been tested in order to describe the density dependence of pressure and structure at 6000 K. As a result, only one potential, ReaxFF/lg, was able to reproduce the QMD simulations for both the equation of state and the fraction of sp, sp, sp-bonded atoms.

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