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.

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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.

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Basis Quantum Monte Carlo(BQMC)法でImportance Samplingを行うための定式化を行い，1次元の調和振動子内における2個のフェルミ粒子の系に対する基底状態を求めた．通常のBQMC計算で得られる粒子の平均分布から波動関数やQuantum Force，及び局所エネルギーを求め，これらを用いてImportance Sampling付きのBQMC計算を行った．Importance Samplingを行うことにより，分散が小さくより高い精度でエネルギーを求めることができた．

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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.

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