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A conjugate gradient method for electronic structure calculations. (English) Zbl 1378.65120

Summary: In this paper, we study a conjugate gradient method for electronic structure calculations. We propose a Hessian based step size strategy, which together with three orthogonality approaches yields three algorithms for computing the ground state energy of atomic and molecular systems. Under some mild assumptions, we prove that our algorithms converge locally. It is shown by our numerical experiments that the conjugate gradient method is efficient.

MSC:

65K05 Numerical mathematical programming methods
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
90C30 Nonlinear programming
81V55 Molecular physics

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