Equation of state of nitrogen (N2) at high pressures and high temperatures: molecular dynamics simulation

Nitrogen equation of state at pressures up to 30 GPa (300 kbars) and temperatures above 800 K was studied by molecular dynamics (MD) simulations. The dynamics of the N(2) molecules is treated in hard rotor approximation, i.e., it accounts both translational and rotational degrees of freedom. The rotational motion of the N(2) molecule is treated assuming constant moment of inertia of the nitrogen molecule. The new MD program fully accounts anisotropic molecular nitrogen interaction. The N(2)-N(2) interaction potential has been derived by van der Avoird et al. J. Chem. Phys. 84, 1629 (1986)] using the results of high precision Hartree-Fock ab initio quantum mechanical calculations. The potential, fully accounts rotational symmetry of the N(2)-N(2) system, by employing 6-j Wigner symbols, i.e., preserving full rotational symmetry of the system. Various numerical algorithms were tested, in order to achieve the energy preservation during the simulation. It has been demonstrated that the standard Verlet algorithm was not preserving the energy for the standard MD time step, equal to 5x10(-16) s. Runge-Kutta fourth order method was able to preserve the energy within 10(-4) relative error, but it requires calculation of the force four times for each time step and therefore it is highly inefficient. A predictor-corrector method of the fifth order (PC5) was found to be efficient and precise and was therefore adopted for the simulation of the molecular nitrogen properties at high pressure. Singer and Fincham algorithms were tested and were found to be as precise as PC5 algorithm and they were also used in the simulation of the equation of state. Results of MD simulations are in very good agreement with the experimental data on nitrogen equation of state at pressures below 1 GPa (10 kbars). For higher pressures, up to 30 GPa (300 kbars), i.e., close to molecular nitrogen stability limit, determined by Nellis et al. Phys. Rev. Lett. 85, 1262 (1984)], the obtained numerical results provide new data of the experimentally unexplored region. These data were formulated in the analytical form of pressure-density-temperature equation of state.