First Order Methods for Geometric Optimization of Crystals: Experimental Analysis

Abstract

AbstractThe geometric optimization of crystal structures is a procedure widely used in computational chemistry that changes the geometrical placement of the particles inside a structure. It is called structural relaxation and constitutes a local minimization problem with a non‐convex objective function whose domain complexity increases according to the number of particles involved. This work studies the performance of the two most popular gradient methods in structural relaxation, Steepest Descent and Conjugate Gradient. Although frequently employed, there is a lack of their study in this context from an algorithmic point of view. The algorithms are initially benchmarked on the basis of a constant step size. Three concepts for designing dynamic step size rules are then examined in detail and analyzed. Results show that there is a trade‐off between convergence rate and the possibility of an experiment to succeed. In order to address this, a function is proposed as a formal means for assigning utility to each method based on preference. The function is built according to a recently introduced model of preference indication concerning algorithms with deadline and their run time. It introduces the quantification of the optimization algorithms' performance according to convergence speed and success rate, thus enabling the appointment of a specific algorithmic recipe as the best choice for balanced preferences.