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Molecular Dynamics


Molecular dynamics (MD) simulations represent the computer approach to statistical mechanics. The primary aim of molecular dynamics is to numerically solve the problem of classical mechanics. Molecular dynamics assigns numerical values to states, thereby making states observable at least for model substance.

Molecular simulations are used to estimate equilibrium and dynamic properties of complex systems that cannot be calculated analytically. Representing the exciting interface between theory and experiment, MD simulations occupy a venerable position at the crossroads of mathematics, biology, chemistry, physics and computer science.

Introduction to Molecular Dynamics

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Molecular dynamics methods are used for simulating molecular scale models of matter in order to relate collective dynamics to single particle dynamics. Typical situations for its application are self assembly of structures such as micelles and vesicles.

Molecular dynamics simulations are used to describe the patterns, strength and properties of drug-receptor interactions, the solvation of molecules, the conformational changes that a molecule may undergo various conditions and other events that require the systematic evaluation of molecular properties in dynamic molecular systems.

Molecular Dynamics Simulation

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Molecular simulation refers to computational methods in which molecular structure is explicitly taken into account. Molecular dynamics simulations (MD) is a principal tool in the theoretical study of biological molecules. Dynamical simulations monitor time dependent processes in a molecular system, providing detailed information about the fluctuations and conformational changes of proteins.

Molecular dynamics simulation method is routinely used to investigate the structure, dynamics and thermodynamics of biological molecules and dynamic processes such as protein stability, conformational changes, protein folding, molecular recognition of proteins and ion transport.
  1. The first molecular dynamics was performed by Alder and Wainwright in 1957 to study the interactions of hard spheres and provided insight into the microscopic nature of liquids.
  2. Simulation of a realistic system, liquid water was published in 1971 and the first protein simulations appeared in 1977 with the simulation of the bovine pancreatic trypsin inhibitor. (BPTI)

Today molecular dynamics simulations of solvated proteins and their complexes are frequently found.

Non equilibrium Molecular Dynamics

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Non-equilibrium molecular dynamics (NEMD) simulation of transport processes can be done in two ways.

The phenomenological coefficients describing the heat transfer and other properties can be expressed in terms of time correlation functions by using Kubo formalism. The main advantage of this approach is the generality of the resulting formulas, which can be applied in any density regime. The computation times require longer time than the characteristic relaxation time of the correlation itself, which makes them computationally expensive.

Using NEMD it is possible to create stationary non-equilibrium states using temperature gradients produced by placing the material between two heat reservoirs at fixed temperatures. It is used to determine the thermal conductivity of the material. The method is computationally less expensive and more accurate than linear response. It deals with the signal itself instead of its average fluctuations in the equilibrium state.

Molecular Reaction Dynamics

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Molecular reaction dynamics studies what happens at the molecular level during an elementary chemical reaction. Molecular reaction dynamics also called microscopic kinetics has gained importance due to the pioneer work of D.R.Herschbach, Y.T.Lee and J.C.Polanvi.

The development of molecular reaction dynamics began in the 1930s but it wasn't until the 1960s that new experimental techniques and the availability of electronic computers for theoretical calculations allowed reliable information to be obtained. With these developments, chemists are beginning to understand what happens in an elementary chemical reaction.

Molecular reactions dynamics deals with the intermolecular and intramolecular motions that take place in the elementary act of chemical change and with the quantum states of the reactant and product molecules. It is to be remembered that molecular reaction dynamics does not supersede macroscopic kinetics.

Born Oppenheimer Molecular Dynamics

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In this technique at each step the electronic structure is computed according to the static coordinates of the nuclei, in other words solving for each new positions the time independent Schrodinger equation. Between two steps the nuclei are moved following rules of classical mechanics.

The Born Oppenheimer dynamics can be realized with any ab initio method. Each step brings the new positions of the nuclei; the minimum energy is computed following the chosen method and then the forces which are used in the determination of the displacements of the atoms. In this way the system is kept on the BO hyper surface all along the simulation.

Accelerated Molecular Dynamics

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Accelerated molecular dynamics method is the fast multipole expansion method to an antiferroelectric liquid crystalline molecule to understand the origin of bent structure formation and the molecular packing property in crystalline phase.

Another interesting development is temperature-accelerated molecular dynamics. Here for simplicity we will focus on the over damped-dynamics case. The extension to molecular dynamics is quite straightforward.

The main idea is again a simple equation given below.

$\gamma$ x = - $\bigtriangledown$ V (x) + $\mu$ (X - q(x)) $\bigtriangledown$ q(x) + $\sqrt{2\gamma \beta ^{-1}}w$

X = - $\mu$ (X-q(x)) + $\sqrt{2\beta ^{-1}}W$

When $\mu$ is large the effective dynamics for the coarse grained variables is a gradient flow for the free energy of the coarse grained variables.