Large scale electronic structure calculations using the Lanczos method
نویسندگان
چکیده
The orthogonality requirement in either iterative diagonalization or conjugate gradient approaches to the single particle Schr6dinger equation/~/~u = E~u leads to an overall N 3 scaling of the effort with the number N of atoms. We show that the Lanczos method circumvents this problem even when applied to all occupied states. Our implementation shows that the method is stable, exact, scales as N 2 for N around a few hundreds, and is thus optimally suited for such mid-size (100 1000 atoms) quantum systems. The analogy between the basic Lanczos equations and Anderson's localization in a disordered one-dimensional tight-binding chain is pointed out and used to gain some insights into improved convergence and stability of the method. For a 900-atom Si cluster tested here using pseudopotentials and a plane wave basis, the Lanczos method is about an order of magnitude faster than the state-of-the-art preconditioned conjugate gradient method using the same pseudopotentials and basis set.
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