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WIREs Comput Mol Sci
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Molecular dynamics out of equilibrium: mechanics and measurables

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Molecular dynamics is fundamentally the integration of the equations of motion over a representation of an atomic and molecular system. The most rigorous choice for performing molecular dynamics entails the use of quantum‐mechanical equations of motion and a representation of the molecular system through all of its electrons and atoms. For most molecular problems involving at least hundreds of atoms, but generally many more, this is simply computationally prohibitive. Thus the art of molecular dynamics lies in choosing the representation and the appropriate equations of motion capable of addressing the requisite measurables. When used adroitly, it can provide both equilibrium (averaged) and time‐dependent properties of a molecular system. Many computational packages now exist that perform molecular dynamics simulations. They generally include force fields to represent the interactions between atoms and molecules (smoothing out electrons through the Born‐Oppenheimer approximation) and integrate the remaining particles classically. Despite these simplifications, all‐atom molecular dynamics remains computationally inaccessible if one includes the number of atoms required to simulate mesoscopic solvents. Here we use analytical models to demonstrate how molecular dynamics can be used to limit the solvent size in systems experiencing either equilibrium or nonequilibrium conditions. It is equally important to address the measurables (such as reaction rates) that are to be obtained prior to the generation of the data‐intensive trajectories. WIREs Comput Mol Sci 2014, 4:541–561. doi: 10.1002/wcms.1190

Schematic representation of a reaction process. The two‐well potential surface divides the state space into the reactant (left well) and product (right well) states. The transition state (TS) corresponds to the saddle region between the wells. Three parabolas with horizontal hordes depict the vibrational potentials at three states with their low energy levels. Green particles show the initial distribution of the reactants along the vibrational coordinate and energy level (vertical axis). Yellow spheres are those particles which have been able to reach the TS. Only part of them moving to the right (with red arrows) constitute the reactional flow.
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Trans‐isomer of stilbene molecule in methoxymethane. Green, red and white balls are carbon, oxygen and hydrogen atoms, correspondingly.
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Cis‐isomer of stilbene molecule in methoxymethane. Green, red and white balls are carbon, oxygen and hydrogen atoms, correspondingly.
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Stochastic potential for the problem of the escape rate constant: the height of the barrier changes randomly sometimes fully closing the well (blue and violet curves); sometimes opening it (orange and red curves). Insert: fluctuation of the barrier obeys the distribution P(Eb).
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VACF, Cw(t), taken from Figure , for various w values (in nm/ms), rescaled both vertically and horizontally in accordance with Eq. . The reference rate is taken equal to w0 = 1 nm/ms.
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Time dependencies of the function Cw(t) for a Brownian particle in a medium of nonequilibrium particles swelling at various rates w (shown in nm/ms).
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Molecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods
Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics

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