An inverse iteration method using multigrid for quantum chemistry

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We present a method to compute the lowest eigenpairs of a generalized eigenvalue problem resulting from the discretization of a stationary Schrödinger equation by a fourth order finite difference scheme of Numerov type. We propose to use an inverse iteration method combined with a Rayleigh-Ritz procedure to correct several eigenvectors at the same time. The linear systems in the inverse iteration scheme are regularized by projections on lower dimensional spaces and approximately solved by a multigrid algorithm.We apply the method to the electronic structure calculation in quantum chemistry.