Molecular dynamics

Molecular dynamics or molecular dynamics (MD ) refers to computer simulations in molecular design, which are interactions between atoms and molecules calculated and displayed over a short period of time. When modeling complex systems with a large number of participating atoms force fields or semi-empirical methods are mainly used because of the computational effort for the application of quantum mechanical methods ( ab initio methods) would be too large in this case. Due to the ever-increasing computing power available, however, quantum chemical methods ( ab initio Molecular Dynamic ) are possible also for medium-sized systems increasingly.

The MD method has its origins in the late 1950s and early 1960s, playing a major role in the simulation of liquids, such as water or aqueous solutions, where structural and dynamic properties in experimentally difficult to access areas (eg. of pressure and temperature) can be calculated.

The term molecular dynamics is sometimes used as a synonym for the discrete element method (DEM ) because the methods are very similar. However, the particles in the molecules need not be. Generally, the term stands for the MD simulation in various fields of chemistry (inorganic, organic, physical, theoretical and biochemistry ) and adjacent areas ( materials science, biology, pharmacy, medicine).

Physical principles

Microcanonical ensemble ( NVE )

The ensemble microcanonical describes a system which is not isolated, and the particles ( N ), volume ( V ), or energy (E) communicates with the environment.

For a system with particles associated coordinates and velocities can set up the following pair of ordinary differential equations:

It describes

• The force
• The mass
• The time
• The potential energy of the interaction of atoms and molecules. is also called force field. It is defined by two parts: the mathematical form (ie, the functional approach for the individual types of interactions, most of classical mechanics borrowed )
• The atom- specific parameters. The latter is obtained from spectroscopic experiments, diffraction experiments ( XRD ) and / or quantum mechanical calculations ( quantum chemistry ) and in some force fields also from macroscopic measurements (experimental) to be satisfied by the parameterization. Therefore, there may be different sets of parameters for a force field approach.

The parametrization of a force field with a wide range of applications is a great challenge. When performing MD simulations, choosing the right force field is an important decision. Generally, force fields are always applicable only to those systems for which they are parameterized ( eg, proteins or silicates).

Canonical ensemble ( NVT)

The canonical ensemble is characterized in contrast to the microcanonical by constant temperature of. In order to realize it, in addition, a thermostat is required. For example, the Andersen thermostat, the Langevin thermostat or the Nose -Hoover thermostat can be used. In some cases (especially for equilibration ) is also still used the Berendsen or weak -coupling thermostat. However, this does not generate correct NVT ensemble. Thermostats are based on the equipartition theorem.

Isothermal - isobaric ensemble ( NPT)

To realize the NPT ensemble is required in addition to a thermostat additionally barostat. For example, the Andersen barostat, the Parrinello -Rahman barostat or the Berendsen barostat can be used. Barostate based on the Clausius virial theorem.

Methodology

The simulated volume element is filled at the start with the particles to be examined. The forces are then computed for each of the particles, which act on it due to its neighbors, and moves the particles in accordance with this force in a very small time step. After a few steps ( with a good, appropriate force model) enters the sample volume in thermal equilibrium, and the particles begin to move " makes sense ". Can now be calculated from the forces and movements of the particles and the temperature and pressure changed stepwise. The particles may be complete molecules from individual atoms, which may also undergo conformational changes. Larger molecules are often full of more atoms, inherently rigid components assembled (discrete element method ), which minimizes the computational effort, however, requires very well-adapted force fields.

MD simulations usually take place under periodic boundary conditions: each particle that leaves the simulated volume on one side, appeared on the opposite again, all interactions take place also via these boundaries instead. These identical copies of the simulated volume are placed side by side, so that the three-dimensional space forms the surface of a four-dimensional torus. Since thereby each particle in the neighboring cells ( 3x3x3 = 1) 26 copies arise interactions only to the one, the closest of these identical image particles is calculated ( "Minimum Image Convention ").