The Use of Trust Regions in Kohn-Sham Total EnergyMinimization

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The Self Consistent Field (SCF) iteration, widely used forcomputing the ground state energy and the corresponding single particlewave functions associated with a many-electronatomistic system, is viewedin this paper as an optimization procedure that minimizes the Kohn-Shamtotal energy indirectly by minimizing a sequence of quadratic surrogatefunctions. We point out the similarity and difference between the totalenergy and the surrogate, and show how the SCF iteration can fail whenthe minimizer of the surrogate produces an increase in the KS totalenergy. A trust region technique is introduced as a way to restrict theupdate of the wave functions within a small neighborhood of anapproximate ... continued below

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Yang, Chao; Meza, Juan C. & Wang, Lin-wang May 30, 2006.

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The Self Consistent Field (SCF) iteration, widely used forcomputing the ground state energy and the corresponding single particlewave functions associated with a many-electronatomistic system, is viewedin this paper as an optimization procedure that minimizes the Kohn-Shamtotal energy indirectly by minimizing a sequence of quadratic surrogatefunctions. We point out the similarity and difference between the totalenergy and the surrogate, and show how the SCF iteration can fail whenthe minimizer of the surrogate produces an increase in the KS totalenergy. A trust region technique is introduced as a way to restrict theupdate of the wave functions within a small neighborhood of anapproximate solution at which the gradient of the total energy agreeswith that of the surrogate. The use of trust region in SCF is not new.However, it has been observed that directly applying a trust region basedSCF(TRSCF) to the Kohn-Sham total energy often leads to slowconvergence.We propose to use TRSCF within a direct constrainedminimization(DCM) algorithm we developed in \cite dcm. The keyingredients of theDCM algorithm involve projecting the total energyfunction into a sequence of subspaces of small dimensions and seeking theminimizerof the total energy function within each subspace. Theminimizer of a subspace energy function, which is computed by TRSCF, notonly provides a search direction along which the KS total energy functiondecreases but also gives an optimal "step-length" that yields asufficient decrease in total energy. A numerical example is provided todemonstrate that the combination of TRSCF and DCM is more efficient thanSCF.

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  • Journal Name: SIAM Journal on Scientific Computing; Journal Volume: 29; Journal Issue: 5; Related Information: Journal Publication Date: 2007

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  • Report No.: LBNL--59841
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 919759
  • Archival Resource Key: ark:/67531/metadc899013

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  • May 30, 2006

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  • Sept. 27, 2016, 1:39 a.m.

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  • Sept. 30, 2016, 12:58 p.m.

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Yang, Chao; Meza, Juan C. & Wang, Lin-wang. The Use of Trust Regions in Kohn-Sham Total EnergyMinimization, article, May 30, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc899013/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.