Enhancing structure relaxations for first-principles codes: An approximate Hessian approach

James M. Rondinelli; Bin Deng; Laurence D. Marks

doi:10.1016/j.commatsci.2007.01.004

Enhancing structure relaxations for first-principles codes: An approximate Hessian approach

James M. Rondinelli, Bin Deng, Laurence D. Marks^*

^*Corresponding author for this work

Materials Science and Engineering

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We present a method for improving the speed of geometry relaxation by using a harmonic approximation for the interaction potential between nearest neighbor atoms to construct an initial Hessian estimate. The model is quite robust, and yields approximately a 30% or better reduction in the number of calculations compared to an optimized diagonal initialization. Convergence with this initializer approaches the speed of a converged BFGS Hessian, therefore it is close to the best that can be achieved. Hessian preconditioning is discussed, and it is found that a compromise between an average condition number and a narrow distribution in eigenvalues produces the best optimization.

Original language	English (US)
Pages (from-to)	345-353
Number of pages	9
Journal	Computational Materials Science
Volume	40
Issue number	3
DOIs	https://doi.org/10.1016/j.commatsci.2007.01.004
State	Published - Sep 2007

Keywords

BFGS optimization
DFT
Hessian
Structure relaxation

ASJC Scopus subject areas

Computer Science(all)
Chemistry(all)
Materials Science(all)
Mechanics of Materials
Physics and Astronomy(all)
Computational Mathematics

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10.1016/j.commatsci.2007.01.004

Cite this

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title = "Enhancing structure relaxations for first-principles codes: An approximate Hessian approach",

abstract = "We present a method for improving the speed of geometry relaxation by using a harmonic approximation for the interaction potential between nearest neighbor atoms to construct an initial Hessian estimate. The model is quite robust, and yields approximately a 30% or better reduction in the number of calculations compared to an optimized diagonal initialization. Convergence with this initializer approaches the speed of a converged BFGS Hessian, therefore it is close to the best that can be achieved. Hessian preconditioning is discussed, and it is found that a compromise between an average condition number and a narrow distribution in eigenvalues produces the best optimization.",

keywords = "BFGS optimization, DFT, Hessian, Structure relaxation",

author = "Rondinelli, {James M.} and Bin Deng and Marks, {Laurence D.}",

note = "Funding Information: We wish to acknowledge D. Russell Luke for helpful discussions on optimization methods and scaling techniques. Peter Blaha also provided the Bi 4 Ti 3 O 12 structure and assisted in the beta-testing of the pairhess program. This work was funded by the NSF under Grant # DMR-0455371.",

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T1 - Enhancing structure relaxations for first-principles codes

T2 - An approximate Hessian approach

AU - Rondinelli, James M.

AU - Deng, Bin

AU - Marks, Laurence D.

N1 - Funding Information: We wish to acknowledge D. Russell Luke for helpful discussions on optimization methods and scaling techniques. Peter Blaha also provided the Bi 4 Ti 3 O 12 structure and assisted in the beta-testing of the pairhess program. This work was funded by the NSF under Grant # DMR-0455371.

PY - 2007/9

Y1 - 2007/9

N2 - We present a method for improving the speed of geometry relaxation by using a harmonic approximation for the interaction potential between nearest neighbor atoms to construct an initial Hessian estimate. The model is quite robust, and yields approximately a 30% or better reduction in the number of calculations compared to an optimized diagonal initialization. Convergence with this initializer approaches the speed of a converged BFGS Hessian, therefore it is close to the best that can be achieved. Hessian preconditioning is discussed, and it is found that a compromise between an average condition number and a narrow distribution in eigenvalues produces the best optimization.

AB - We present a method for improving the speed of geometry relaxation by using a harmonic approximation for the interaction potential between nearest neighbor atoms to construct an initial Hessian estimate. The model is quite robust, and yields approximately a 30% or better reduction in the number of calculations compared to an optimized diagonal initialization. Convergence with this initializer approaches the speed of a converged BFGS Hessian, therefore it is close to the best that can be achieved. Hessian preconditioning is discussed, and it is found that a compromise between an average condition number and a narrow distribution in eigenvalues produces the best optimization.

KW - BFGS optimization

KW - DFT

KW - Hessian

KW - Structure relaxation

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DO - 10.1016/j.commatsci.2007.01.004

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SN - 0927-0256

VL - 40

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JO - Computational Materials Science

JF - Computational Materials Science

IS - 3

ER -

Enhancing structure relaxations for first-principles codes: An approximate Hessian approach

Abstract

Keywords

ASJC Scopus subject areas

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