I report on a high statistics simulation of advection in an incompressible helical flow and the measurement of effective diffusivity. Helicity greatly enhances the large-scale diffusion constant and theoretically this is hard to explain, but a qualitative explanation is presented. With these tools one can study complicated problems such as the properties of solids and defects, while including electron correlation effects with high precision. Applications to the study of silicon self-interstitials will be highlighted. We perform quantum Monte Carlo simulations for the Hubbard model, one of the simplest repulsively interacting models, where we find that the pairing correlation function is enhanced due to the repulsive interaction, suggesting an occurrence of superconductivity of purely electronic origin.
Molecular geometry is essential to chemical investigation.
Though many spectroscopic methods such as X-ray diffraction technique are usually applied to a direct observation of molecular geometry, computational geometry optimization by quantumchemical molecular orbital calculation is more useful because of cost and time. A good initial parameter for molecular geometries is very important to reduce computation time for geometry optimization. In order to have a good initial molecular geometry simply and fast, we modified the extended Huckel method and developed a geometry optimization method using only total energy value. Cost of the extended Huckel calculation increase proportional with cubic of the number of electrons in molecule because the most time consuming step is bdiagonalization of Hamiltonian matrix. The matrix is real symmetric.