Nonlinear multigrid eigenvalue solver utilizing nonorthogonal localized orbitals

A nonlinear multigrid eigenvalue solver utilizing nonorthogonal localized orbitals is formulated and implemented on a real-space grid. The localization of orbitals is necessary to achieve linear scaling in the computational effort. Numerical tests are performed on the benzene molecule, C₂₀, and C₆₀. The localization centers for the orbitals are allowed to move so as to lower the total energy. The convergence rate depends on the radius of the confined regions. Also, the convergence rate slows when the number of atoms in the system increases, and/or when unoccupied orbitals are included. The slowed convergence is due to ill-conditioning, which is related to the kinetic contribution to the total energy. Work is in progress to alleviate the ill-conditioning.