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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageEnglish (US)
Pages (from-to)345-353
Number of pages9
JournalComputational Materials Science
Issue number3
StatePublished - Sep 2007


  • 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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