The Time Dimension Molecular Dynamics

So far, our discussion has focussed on stationary quantum chemical methods, which yield results for fixed atomic nuclei, i.e. for frozen molecular structures like minimum structures on the Born-Oppenheimer potential energy surface. Processes in supramolecular assemblies usually feature prominent dynamical effects, which can only be captured through explicit molecular dynamics or Monte Carlo simulations [95-98]. Molecular dynamics simulations proved to be a useful tool for studying the detailed microscopic dynamic behavior of many-particle systems as present in physics, chemistry and biology. The aim of molecular dynamics is to study a system by recreating it on the computer as close to nature as possible, i.e. by simulating the dynamics of a system in all microscopic detail over a physical length of time relevant to properties of interest. 

For large molecular aggregates only classical mechanics can be applied to describe the nuclear motion of the particles through Newtonian-type equations of motion. This is an approximation, which may only fail if the motion of light particles such as protons needs to be accurately described. If the latter is the case, explicit nuclear quantum dynamics is required. Such extensions that include quantum effects [99, 100] or that incorporate full quantum dynamics have been explored [101], 

The equations of motion may be written in various ways. We assume that a sys- 

In practice an analytical function like for example the Lennard-Jones potential is used for the potential, such that the derivative with respect to Rj can be easily calculated. The equations of motion according to Hamilton s formulation of classical mechanics read [102] 

From this Newton s second law is obtained by taking the time derivative of the first and equating it to the second part of Hamilton s equations, 

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