We describe strategies to accelerate the terminal stage of molecular dynamics (MD)-based relaxation algorithms, where a large fraction of the computational resources are used. First, we analyze the qualitative and quantitative behavior of the QuickMin family of MD relaxation algorithms and explore the influence of spectral properties and dimensionality of the molecular system on the algorithm efficiency. We test two algorithms, the MinMax and Lanczos, for spectral estimation from an MD trajectory, and use this to derive a practical scheme of time step adaptation in MD relaxation algorithms to improve efficiency. We also discuss the implementation aspects. Secondly, we explore the final state refinement acceleration by a combination with the conjugate gradient technique, where the key ingredient is an implicit corrector step. Finally, we test the feasibility of passive Hessian matrix accumulation from an MD trajectory, as another route for final phase acceleration. Our suggestions may be implemented within most MD quench implementations with a few, straightforward lines of code, thus maintaining the appealing simplicity of the MD quench algorithms. In this paper, we also bridge the conceptual gap between the MD quench algorithms inspired from physics and the mathematically rooted line search algorithms.
On the Hessian matrix and Minkowski addition of quasiconvex functions