Three-phase equilibrium in argon was obtained based on the thermodynamics of a perfect solid and a perfect liquid (v2). The equation of state (EOS) for a perfect solid was obtained from our previous study of a pure substance using spherical molecules. The EOS for a perfect liquid is a van der Waals EOS with the Carnahan-Starling repulsion term to explain 3-phase equilibrium. The Lennard-Jones parameters for argon are applied to these EOSs. The pressure-volume-temperature relations on the equilibrium lines are comparable with experimental and molecular simulation results. The thermodynamic properties under low pressures have reasonable temperature dependences.
Equations of state (EOS) for a perfect solid and a perfect liquid are proposed, where the system includes only single spherical molecules. A Lennard-Jones interaction is assumed in the system. Molecular dynamics simulations are performed to obtain the temperature and density dependency of the internal energy and pressure. The internal energy in the EOS is the sum of the average kinetic energy and potential energy at 0 K, and the temperature dependent potential energy. The pressure is expressed in a similar way, where the pressure satisfies the thermodynamic EOS. The equilibrium condition is solved numerically for the phase equilibrium of argon. The Gibbs energy gives a reasonable transition pressure for 3-phase equilibrium in argon. The thermodynamic properties under low pressures have reasonable temperature dependences.
Importance sampling was applied to the Basis Quantum Monte Carlo (BQMC) method to improve the calculation accuracy. The ground state of 2 fermions trapped in a 1 dimensional harmonic potential was simulated with the importance sampling BQMC method. At first, the wave function, quantum force and local energy were obtained from the distribution evaluated by the normal BQMC calculation. Then the ground state energy was calculated with the importance sampling BQMC. By applying importance sampling, the ground state energy could be evaluated with higher accuracy.
DV-Xα method uses natural and high grade numerical AOs, which generate very precise MOs for a wide variety of molecules within the restriction of LCAO approximation. But Monte-Carlo integration used here causes serious numerical errors for total energy and energy gradient calculation. The author improved their calculation procedure, where the numerical error in physical quantity of a molecule is canceled by the corresponding errors in those of atoms imaginarily isolated from each other. With 2000–4000 sample points per atom, total energy of the molecule including up to period 5 atoms could be calculated precisely. But for energy gradient calculation, far more sample points were necessary and the procedure could be applied only for the molecule including up to period 3 atoms at present. Structure optimization was tried for series of molecules to evaluate its accuracy and performance and then the strategy of further improvement was discussed.