Heat bath system relaxation dynamics

In a molecular dynamics calculation, you can add a term to adjust the velocities, keeping the molecular system near a desired temperature. During a constant temperature simulation, velocities are scaled at each time step. This couples the system to a simulated heat bath at Tq, with a temperature relaxation time of "r. The velocities arc scaled bv a factor X. where... 

The simplest method that keeps the temperature of a system constant during an MD simulation is to rescale the velocities at each time step by a factor of (To/T) -, where T is the current instantaneous temperature [defined in Eq. (24)] and Tq is the desired temperamre. This method is commonly used in the equilibration phase of many MD simulations and has also been suggested as a means of performing constant temperature molecular dynamics [22]. A further refinement of the velocity-rescaling approach was proposed by Berendsen et al. [24], who used velocity rescaling to couple the system to a heat bath at a temperature Tq. Since heat coupling has a characteristic relaxation time, each velocity V is scaled by a factor X, defined as... 

It can be seen from the discussion in later sections that vibrational relaxation in dense media plays a very important role in ultrafast phenomena. The dynamics of vibrational relaxation can be described as follows. Let Q be the normal coordinate of the system mode and assume that the system oscillator is linearly coupled to the heat bath [8,11-16], i.e.,... 

Molecular dynamics with periodic boundary conditions is presently the most widely used approach for studying the equilibrium and dynamic properties of pure bulk solvent,97 as well as solvated systems. However, periodic boundary conditions have their limitations. They introduce errors in the time development of equilibrium properties for times greater than that required for a sound wave to traverse the central cell. This is because the periodicity of information flow across the boundaries interferes with the time development of other processes. The velocity of sound through water at a density of 1 g/cm3 and 300 K is 15 A/ps for a cubic cell with a dimension of 45 A, the cycle time is only 3 ps and the time development of all properties beyond this time may be affected. Also, conventional periodic boundary methods are of less use for studies of chemical reactions involving enzyme and substrate molecules because there is no means for such a system to relax back to thermal equilibrium. This is not the case when alternative ensembles of the constant-temperature variety are employed. However, in these models it is not clear that the somewhat arbitrary coupling to a constant temperature heat bath does not influence the rate of reequilibration from a thermally perturbed... 

The term f. plays a role similar to a friction term in Brownian dynamics except that it can also serve to speed up the molecules if takes on negative values. The parameter is a generalized mass. Its precise value is not crucial, but for efficient coupling between the system and the heat bath, it should be selected so that the thermostat relaxation time corresponds roughly to a typical oscillation period for the molecules in the system.The integration of In s in Eq. [46] is redundant in the equations of motion. However, it appears in the expression,... 

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