Multiple-precision Hartree–Fock equations are solved for the ground states of the He, Li, and Be atoms and highly accurate wave functions are determined. The numbers of significant figures of the total energies are 66 for He, 43 for Li, and 43 for Be. The Lambda function, which is a Laguerre-type basis and can be used to construct a complete orthonormal system, acts as the basis function. Using the resulting Hartree–Fock wave functions, nucleus-electron cusp conditions are also calculated. Their significant figures are 30 for He, 19 for Li, and 19 for Be, in close proportion to the numbers of significant figures for the total energies. In fact, the ratios are 0.45, 0.44, and 0.44, respectively. The radial expectation values, < rⁱ > (i = −2, −1, 1, ... 9), are also investigated. It is verified that the computational accuracy varies depending on the physical property.

To elucidate the micro-scale wear mechanisms of concentrated polymer brushes (CPB), we developed a coarse-grained molecular dynamics (CGMD) model of CPB-against-slider sliding simulation with an explicit solvent. Under good solvent conditions, the CPB swelled. The thickness of the swollen CPB reached approximately 77% of the fully stretched length, which is in close agreement with the experimentally determined range for swollen film thicknesses of CPB. The validity of the developed model was evaluated through a sliding simulation. The simulation analysis showed that the wear of the CPB can involve multiple factors, such as contact with the slider, solvent flow, and interactions between polymer chains. This indicates that the simulation model allows us to analyze not only the wear caused by direct contact with the slider but also the wear caused by solvent flow.