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Computation 2017, 5(4), 42; doi:10.3390/computation5040042

A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation

Department of Chemistry & Chemical Biology; McMaster University, Hamilton, ON L8S 4L8, Canada
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Received: 31 August 2017 / Revised: 22 September 2017 / Accepted: 23 September 2017 / Published: 26 September 2017
(This article belongs to the Special Issue In Memory of Walter Kohn—Advances in Density Functional Theory)
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Abstract

We propose a limited-memory quasi-Newton method using the bad Broyden update and apply it to the nonlinear equations that must be solved to determine the effective Fermi momentum in the weighted density approximation for the exchange energy density functional. This algorithm has advantages for nonlinear systems of equations with diagonally dominant Jacobians, because it is easy to generalize the method to allow for periodic updates of the diagonal of the Jacobian. Systematic tests of the method for atoms show that one can determine the effective Fermi momentum at thousands of points in less than fifteen iterations. View Full-Text
Keywords: weighted density approximation; limited memory quasi-Newton method; nonlinear systems of equations; bad Broyden method; density functional theory; exchange energy density functional weighted density approximation; limited memory quasi-Newton method; nonlinear systems of equations; bad Broyden method; density functional theory; exchange energy density functional
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chan, M.; Cuevas-Saavedra, R.; Chakraborty, D.; Ayers, P.W. A Diagonally Updated Limited-Memory Quasi-Newton Method for the Weighted Density Approximation. Computation 2017, 5, 42.

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