One-way multigrid method in electronic-structure calculations

We propose a simple and efficient one-way multigrid method for self-consist ent electronic structure calculations based on iterative diagonalization. T otal energy calculations are performed on several different levels of grids starting from the coarsest grid, with wave functions transferred to each f iner level. The, only changes compared to a single grid calculation are int erpolation and orthonormalization steps outside the original total energy c alculation and required only for transferring between grids. This feature r esults in a minimal amount of code change, and enables us to employ a sophi sticated interpolation method and noninteger ratio of grid spacings. Calcul ations employing a preconditioned conjugate gradient method are presented f or two examples, a quantum dot and a charged molecular system. Use of three grid levels with grid spacings 2h, 1.5h, and h decreases the computer time by about a factor of 5 compared to single level calculating.