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.

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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.

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We have developed an original program package for molecular visualizations. This program (Makiko) allows us to visualize molecular structures, molecular orbitals, normal mode vectors, spin structures and their dynamics in fine graphics. The Makiko program is written in Java language, Makiko could be used on a wide variety of different operating systems. High program extensibility of Makiko is also available. Thus the Makiko program package would be useful to develop new program tools for molecular visualizations, structure analyses, and interfaces for other computational programs, including editorial functions for their input/output files. The Makiko program package will be provided free of charge.

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The ground state of 2 fermions trapped in a 1 or 3 dimensional harmonic potential was simulated with the Basis Quantum Monte Carlo (BQMC) Method. In the general Diffusion Quantum Monte Carlo Method, a guide function must be used to obtain the information about nodes of the system. However in the BQMC method, we were able to evaluate the ground state energy of the system including the anti-symmetry problem without any guide function. Some different methods for calculating the energy were used to obtain more accurate results for both the one and the three dimensional system.

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