Molecular Dynamics and Monte Carlo¶
In this course, we will treat computational methods that are able to describe the properties of thermodynamic ensembles of molecules. These properties are either determined via stochastic sampling methods (Monte Carlo Simulations) or by following the time evolution of a molecular system for a sufficient amount of time (Molecular Dynamics Simulations).
The prediction of molecular properties at finite temperature - no matter whether it be a chemical reaction in solution or in an enzyme - requires more than the tools treated in the course ‘Introduction to Electronic Structure Methods’. Finite temperature effects can give rise to substantial differences between an (idealised) isolated system at a hypothetical 0 K and the physical system at \(T > 0\) K. Molecules have kinetic energy, and the system’s behaviour is not governed by its potential energy alone, but by its free energy, with the effects of entropy taken into account. Consider the basic thermodynamical concept of the free energy of a reaction, \(\Delta G = \Delta H - T\Delta S\). Although a reaction may be predicted to be endothermic based on quantum chemical calculations at 0 K, the entropic term of the transformation may still favour the reaction to be exergonic. The reaction will thus be spontaneous at finite temperature (cf. the solvation of certain salts in water, where the solute cools down due to an positive reaction enthalpy, but the process is spontaneous due to a considerable rise in entropy).
Both Molecular Dynamics (MD) and Monte Carlo (MC) simulations are techniques that allow to obtain information about the statistical distribution of a system, and thus on its thermodynamic properties at finite temperature, entropic effects included. The link between the microscopic system and the macroscopic thermodynamic observables is established in a branch of physics known as statistical mechanics. During the following exercise sessions, you will apply the techniques that have been treated in the lecture to both theoretical and practical problems; ranging from simple coding over statistical mechanics to actually performing both MD and MC simulations. Although the scope of this course is too small to give you a complete overview of the field, you should be able to gain some insight into the basic methodology and concepts.
Theses exercises are based on various textbooks and the Molecular Simulations tutorial provided by the University of Amsterdam.
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