Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Orbital minimization with localization

Pages: 249 - 264, Volume 23, Issue 1/2, January/February 2009      doi:10.3934/dcds.2009.23.249

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Weiguo Gao - School of Mathematical Sciences, Fudan University, Shanghai 200433, China (email)
Weinan E - Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, United States (email)

Abstract: Orbital minimization is among the most promising linear scaling algorithms for electronic structure calculation. However, to achieve linear scaling, one has to truncate the support of the orbitals and this introduces many problems, the most important of which is the occurrence of numerous local minima. In this paper, we introduce a simple modification of the orbital minimization method, by adding a localization step into the algorithm. This localization step selects the most localized representation of the subspace spanned by the orbitals obtained during the intermediate stages of the iteration process. We show that the addition of the localization step substantially reduces the chances that the iterations get trapped at local minima.

Keywords:  Orbital minimization, localization, conjugate gradient
Mathematics Subject Classification:  Primary: 46N40; Secondary: 35Q40

Received: December 2007;      Revised: April 2008;      Available Online: September 2008.