Study of Metropolis Monte Carlo Optimization Methods and Gradient Methods in the Determination of Atomic and Electronic Structures

Abstract

Optimization methods are a set of numerical methods widely used in the scientific field, whose application allows the resolution of a wide variety of problems. In this project, two applications of optimization methods of the Metropolis Monte Carlo type and the gradient type have been studied in the field of chemistry and computational physics. Firstly, the calculation of energy values of small atomic systems has been carried out through the optimization of parameters in a variational model. Secondly, the determination of Lennard-Jones cluster structures has been carried out. Finally, in order to address higher dimensionality systems, the parallelization of the algorithms has been used through the multi-start strategy.