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January & February  2009, 23(1&2): 249-264. doi: 10.3934/dcds.2009.23.249

Orbital minimization with localization

Weinan E 2, and  Weiguo Gao 1,

1. 

School of Mathematical Sciences, Fudan University, Shanghai 200433, China
2. 

Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, United States

Received  December 2007 Revised  April 2008 Published  September 2008

Orbital minimization is among the most promising linear scalingalgorithms for electronic structure calculation. However, to achievelinear scaling, one has to truncate the support of the orbitals and thisintroduces many problems, the most important of which is theoccurrence of numerous local minima. In this paper, we introduce a simplemodification of the orbital minimization method, by adding a localizationstep into the algorithm. This localization step selects the most localizedrepresentation of the subspace spanned by the orbitals obtained during theintermediate stages of the iteration process.We show that the addition of the localization step substantially reduces thechances that the iterations get trapped at local minima.
Keywords: Orbital minimization, conjugate gradient, localization.
Mathematics Subject Classification: Primary: 46N40; Secondary: 35Q40.
Citation: Weinan E, Weiguo Gao. Orbital minimization with localization. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 249-264. doi: 10.3934/dcds.2009.23.249
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