Molecular dynamics simulations on the Lennard-Jones system are performed to obtain the pVT and UVT relations. An extended van der Waals equation of state (EOS) is derived by statistical mechanics on the perturbation approximation. A hard sphere system is used as the reference system. The attraction energy term in the canonical ensemble partition function is extended by a cluster expansion. The new EOS includes three parameters, two of which are the interaction parameters in the Lennard-Jones interaction. The last parameter is the effective volume of the hard sphere system. The extended van der Waals EOS reproduces the pVT and UVT relations, at least qualitatively, whereas the original van der Waals EOS can explain only the pVT relation.
Endohedral metallofullerenes (EMFs) are expected to have a wide range of potential applications in nanomaterials science. Chemical modification of EMFs is very important for their applications. La@C82 possesses 24 non-equivalent carbon atoms. Regioselectivies of reactions of La@C82 is a specially important problem. We applied the Paired Interacting Obitals (PIO) analysis for addition of adamantylidene(Ad), methyl anion(CH3-), diethyl bromomalonate anion(DBEM-) and methyl radical(·CH3) to La@C82. PIO calculation, proposed by Fujimoto et al., is a method for unequivocally determining the orbitals which should play dominant roles in chemical interactions between two systems, here, La@C82 and each of the above reagents. Eigen values of PIOs, which mean the contribution of PIOs, tell us that the interaction between the reagent and the La@C82 is mainly expressed in only one PIO, PIO-1, in each addition. Considering simultaneously the overlap population(OP) of the PIO-1 and the localization ratio of the PIO-1 of each atom, the most reactive carbons are the carbon(7) in Ad addition, the carbon(23) in DBEM- addition and carbon(9) or carbon(10) in ·CH3 addition, respectively,. These results are coincident with the experimental results. A combination of OP and the localization ratio of the PIO-1 is a good reactivity index of each regioselective addition.
Basis Quantum Monte Carlo(BQMC)法を用いて1次元と3次元の調和振動子内における2個のフェルミ粒子の系の基底状態の計算を行った。従来より広く利用されている拡散量子Monte Carlo法では、用いる節面の情報を事前に与えるためのガイド関数を利用するが、BQMC法ではこのガイド関数を用いることなしに、反対称性の問題を持つ系の計算を行うことができた。また、BQMC法において、いくつか異なるエネルギー計算手法を用いて平均エネルギーを求め、BQMC法による基底状態のエネルギー計算精度を比較した。