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

• Main Authors: Matthew Chan, Rogelio Cuevas-Saavedra, Debajit Chakraborty, Paul W. Ayers
• Format: Article
• Language: English
• Published: MDPI AG 2017-09-01
• Series: Computation
• Subjects: weighted density approximation; limited memory quasi-Newton method; nonlinear systems of equations; bad Broyden method; density functional theory; exchange energy density functional
• Online Access: https://www.mdpi.com/2079-3197/5/4/42
• ISSN: 2079-3197

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.