Molecular Dynamics Simulation

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Molecular dynamics or molecular dynamics (MD) refers to computer simulations in molecular modeling , in which interactions between atoms and molecules and their resulting spatial movements are iteratively calculated and represented. When modeling complex systems with a large number of atoms involved, mainly force fields or semi-empirical methods are used, since the computational effort for the application of quantum mechanical processes (ab initio methods) would be too great. Due to the steadily increasing available computing power , however, quantum chemical methods (ab initio Molecular Dynamics) are also increasingly possible for medium-sized systems.

The term molecular dynamics is sometimes used as a synonym for the Discrete Element Method (DEM) because the methods are very similar. The particles in DEM do not have to be molecules.

history

The MD method has its origins in the late 1950s and early 1960s and plays a major role in the simulation of liquids such as B. water or aqueous solutions , where structural and dynamic properties can be calculated in areas that are difficult to access experimentally (e.g. pressure and temperature). Pioneers were Bernie Alder and Thomas E. Wainwright (model of hard balls) in the late 1950s and Aneesur Rahman , Loup Verlet and Bruce J. Berne (with his student George Harp) in the 1960s .

Physical principles

From the point of view of statistical physics , an MD simulation generates configurations that correspond to certain thermodynamic ensembles . Some of these ensembles are listed below. Monte Carlo simulations generate comparable configurations using the sum of states of these ensembles.

Micro-canonical ensemble (NVE)

The micro-canonical ensemble describes a system that is isolated and does not exchange any particles (N), volume (V) or energy (E) with the environment.

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

It describes

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

The parameterization of a force field with a large area of ​​application is a great challenge. When performing MD simulations, choosing the right force field is an important decision. In general, force fields can only be applied to systems for which they are parameterized (e.g. proteins or silicates ).

Canonical Ensemble (NVT)

In contrast to the micro-canonical ensemble, the canonical ensemble is characterized by constant temperature. A thermostat is also required to implement it . For example, the Andersen thermostat , the Langevin thermostat, or the Nose-Hoover thermostat can be used. In some cases (especially for equilibration) the Berendsen thermostat or weak coupling thermostat is also used. However, this does not produce a correct NVT ensemble. Thermostats are based on the equipartition theorem .

Isothermal-Isobaric Ensemble (NPT)

In order to implement the NPT ensemble, a barostat is required in addition to a thermostat . For example, the Andersen barostat , the Parrinello Rahman barostat or the Berendsen barostat can be used. Barostats are based on Clausius' virial theorem .

methodology

Algorithm of a molecular dynamics simulation

The simulated volume element is initially filled with the particles to be examined. This is followed by the equilibration : For each particle the forces that act on it due to its neighbors are calculated and the particles are moved in very small time steps according to these forces. After a few steps (with a good, suitable force model) the sample volume reaches a thermal equilibrium and the particles begin to move “meaningfully”. Now pressure and temperature can be calculated from the forces and movements of the particles and changed step by step. The particles can be complete molecules made up of individual atoms, which can also undergo conformational changes . Larger molecules are often composed of rigid components comprising several atoms ( discrete element method ), which minimizes the computational effort, but requires very well-adapted force fields.

MD simulations usually take place under periodic boundary conditions : every particle that leaves the simulated volume on one side reappears on the opposite side, and all interactions take place directly beyond these limits. To do this, identical copies of the simulated volume are placed side by side so that the three-dimensional space forms the surface of a flat, four-dimensional torus . Since there are 26 copies of each particle in the neighboring cells (3 × 3 × 3 - 1 =) , short-range interactions are only calculated with the one closest of these identical image particles (“Minimum Image Convention”).

Non-equilibrium molecular dynamics

The molecular dynamics method can also be used to simulate systems that are not in thermodynamic equilibrium . For example, a particle can be pulled through a solution with a constant external force.

literature

  • BJ Alder, TE Wainwright (1959): Studies in Molecular Dynamics. I. General Method. J. Chem. Phys. 31 (2): 459.
  • MP Allen, DJ Tildesley (1989): Computer simulation of liquids. Oxford University Press. ISBN 0-19-855645-4 .
  • D. Frenkel, B. Smit (2002): Understanding Molecular Simulation. From algorithms to applications. Academic Press. ISBN 0-12-267351-4 .
  • DC Rapaport (1996): The Art of Molecular Dynamics Simulation. ISBN 0-521-44561-2 .
  • M. Griebel, A. Caglar, S. Knapek, A. Caglar (2004): Numerical Simulation in Molecular Dynamics. Numerics, algorithms, parallelization, applications. Jumper. ISBN 978-3-540-41856-6 .
  • JM Haile (2001): Molecular Dynamics Simulation. Elementary Methods. ISBN 0-471-18439-X .
  • RJ Sadus: Molecular Simulation of Fluids. Theory, Algorithms and Object Orientation. 2002, ISBN 0-444-51082-6 .
  • Tamar Schlick (2002): Molecular Modeling and Simulation. Jumper. ISBN 0-387-95404-X .
  • Andrew Leach (2001): Molecular Modeling. Principles and Applications. 2nd Edition, Prentice Hall. ISBN 978-0-582-38210-7 .

Web links