  Several methodologies are developed for large-scale atomistic simulations
with fully quantum mechanical description of electron systems. The important
methodological concepts are (i) generalized Wannier state, (ii) Krylov subspace
and (iii) hybrid scheme within quantum mechanics. Test calculations are done
with upto 10$^6$ atoms using a standard workstation. As a practical nanoscale
calculation, the dynamical fracture of nanocrystalline silicon was simulated.
