Molecular Dynamics Sample Clauses

Molecular Dynamics. Molecular dynamics [13, 14] is a well established method to study thermodynamic properties of complex many-particle systems at finite temperature. The idea is to evolve in time the atoms in the system according to the classical equations of motion to closely match the microscopic evolution of the system. Macroscopic thermodynamic properties of the system can then be computed based on the ergodic hypothesis that the statistical ensemble averages are equal to time averages along the trajectory of the system. Similar analyses can be performed with ab-initio molecular dynamics, in which the explicit calculation of the electronic structure is used to compute potential energies and forces [15]. A significant advantage of ab-initio molecular dynamics is that no parameterization of an empirical potential is needed and that systems can be simulated when unexpected chemical events take place. In this section a brief overview of two different AIMD methods used in this thesis will be given, the Car-Xxxxxxxxxx Molecular Dynamics, used in the CPMD program [16], and the Born- Xxxxxxxxxxx Molecular Dynamics, used in the CP2K software package [17].

Molecular Dynamics. Dynamical simulations are usually performed by classical mechanics and involve the integration of Newtxx'x xxxations of motion for a suitable prepared system. Semiclassical or quantum dynamics can be introduced into the

Molecular Dynamics. 26 2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.2 Ergodicity in MD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.3 Velocity-Verlet Algorithm . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.4 Thermostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.5 Classical Force Fields . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.6 Xxxxxxx-Xxxxx Potentials . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.7 Xxxxxxxxxx-Xxxxx (SW) Potentials . . . . . . . . . . . . . . . . . . . 30 2.2.8 Xxxxxxx and Xxxxxxx Potentials . . . . . . . . . . . . . . . . . . . . 31 2.3 First-Principles Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . 32 2.4 Beyond the classical calculations . . . . . . . . . . . . . . . . . . . . . . . 33 2.4.1 QM/MM Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4.2 LOTF Molecular dynamics 35 2.4.3 Summary 38 3 Fracture Modelling 39 3.1 Introduction 39 3.2 Xxxxxxxx’x Criterion 39 3.3 Velocity of the Crack Propagation 41 3.4 Results: Xxxxxxx Xxxx Breaking 45 3.5 Summary 49 4 Background- II 50