Molecular Dynamics with Constant Energy

To understand the main ideas that define ab initio MD, it is useful to first review some concepts from classical mechanics. Classical MD is a well-developed approach that is widely used in many types of computational chemistry and 

Density Functional Theory A Practical Introduction. By David S. Sholl and Janice A. Steckel Copyright 2009 John Wiley Sons, Inc. 

We will consider a situation where we have N atoms inside a volume V, and we are interested in understanding the dynamics of these atoms. To specify the configuration of the atoms at any moment in time, we need to specify 3N positions, ri. r3JV, and 3N velocities,. .., r3/v. Two quantities that are useful for describing the overall state of our system are the total kinetic energy, 

Newton s laws of motion apply to these atoms since we are treating their motion within the framework of classical mechanics. That is, 

These relationships define the equations of motion of the atoms, which can be written as a system of 6N first-order ordinary differential equations  

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To investigate the effect of a protein on electron transfer and the energy conversion, the dual probes (R ) were incorporated to the hydrophobic pocket obovin serum albumin (Rubtsova et al., 1993 Vogel et al., 1994 Likhtenshtein, 1996 Lozinsky et al., 2001). Experimental temperature dependence on the rate constant of photoreduction kpr was found to be similar to that in the above-mentioned solvent. Values estimated from experiments of parameters of local molecular dynamics with the correlation frequency at... 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

The pressure often fluctuates much more than quantities such as the total energy in constant NVE molecular dynamics simulation. This is as expected because the pressure related to the virial, which is obtained as the product of the positions and the derivativ of the potential energy function. This product, rijdf rij)/drij, changes more quickly with than does the internal energy, hence the greater fluctuation in the pressure. 

For constant temperature dynamics where the constant temperature check box in the Molecular Dynamics Options dialog box is checked, the energy will not remain constant but will fluctuate as energy is exchanged with the bath. The temperature, depending on the value set for the relaxation constant, will approach con-stan cy. 

A review is given of the application of Molecular Dynamics (MD) computer simulation to complex molecular systems. Three topics are treated in particular the computation of free energy from simulations, applied to the prediction of the binding constant of an inhibitor to the enzyme dihydrofolate reductase the use of MD simulations in structural refinements based on two-dimensional high-resolution nuclear magnetic resonance data, applied to the lac repressor headpiece the simulation of a hydrated lipid bilayer in atomic detail. The latter shows a rather diffuse structure of the hydrophilic head group layer with considerable local compensation of charge density. 

The second step is the molecular dynamics (MD) calculation that is based on the solution of the Newtonian equations of motion. An arbitrary starting conformation is chosen and the atoms in the molecule can move under the restriction of a certain force field using the thermal energy, distributed via Boltzmann functions to the atoms in the molecule in a stochastic manner. The aim is to find the conformation with minimal energy when the experimental distances and sometimes simultaneously the bond angles as derived from vicinal or direct coupling constants are used as constraints. 

Perhaps the most common computer simulation method for nonequilibrium systems is the nonequilibrium molecular dynamics (NEMD) method [53, 88]. This typically consists of Hamilton s equations of motion augmented with an artificial force designed to mimic particular nonequilibrium fluxes, and a constraint force or thermostat designed to keep the kinetic energy or temperature constant. Here is given a brief derivation and critique of the main elements of that method. 

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