Formalismo matemático da dinâmica molecular de Car-Parrinello

Abstract

In this work we have done an introduction to the concepts of modern quantum mechanics, using mathematical tools that constitute the formalism this subject. Thus, the objective was to describe, from the perspective of mathematics ,equations governing the method of Molecular Dynamics of Car-Parrinello applied in computer simulation of the molecule 2-butene, using the software QuantumESPRESSO. The method in question was proposed in 1985 by Roberto Car and Michelle Parrinello and is based on the separability of electronic and nuclear movements. The mathematical analysis focused on two pillars essences of this research: 1- Mathematical-physics bases of molecular modeling, based on classical mechanics, quantum and molecular dynamics 2- The Car-Parrinello method, with a dynamic Ab Initio, centralized on the Car-Parrinello Lagrangean and it’s equations of motion, dynamics of Born-Oppenheimer, Verlet and the LeapFrog of Hockney algorithms and finally, on the dynamics of Car-Parrinello. For the calculation of molecular properties and the exchange and correlation energy of the molecule being studied, was invoked the Density Functional Theory [DFT]. Subsequently, were presented the chapter of results and analysis / methodology and conclusion, where we determined the importance of differential calculus / integral and variational formalism in the Car-Parrinello method.