Stabilized Quasi-Newton Optimization of Noisy Potential Energy Surfaces

Abstract

Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient, but also very reliable. Unfortunately computational noise in forces and energies is inherent to electronic structure codes. This computational noise poses a sever problem to the stability of efficient optimization methods like the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. We here present a technique that allows obtaining significant curvature information of noisy potential energy surfaces. We use this technique to construct both, a stabilized quasi-Newton minimization method and a stabilized quasi-Newton saddle finding approach. We demonstrate with the help of benchmarks that both the minimizer and the saddle finding approach are superior to comparable existing methods.

References in corpus (8)

• Daubechies wavelets as a basis set for density functional pseudopotential calculations
• Acceleration Schemes for Ab-Initio Molecular Dynamics and Electronic Structure Calculations
• Daubechies Wavelets for Linear Scaling Density Functional Theory
• Global minimum determination of the Born-Oppenheimer surface within density functional theory
• Metrics for measuring distances in configuration spaces
• Minima Hopping Guided Path Search: An Efficient Method for Finding Complex Chemical Reaction Pathways
• Linear scaling relaxation of the atomic positions in nano structures
• Optimization and Parallelization of a force field for silicon using OpenMP

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