Velocity rescaling

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... 

Fig. 9.4. Pa (e) and (e) as a function of the binding energy. The simulations treated 216 water molecules, utilizing the SPC/E water model, and the Lennard-Jones parameters for methane were from [63]. The number density for both the systems is fixed at 0.03333 A 3, and T = 298 K established by velocity rescaling. These calculations used the NAMD program (www.ks.uiuc.edu/namd). After equilibration, the production run comprised 200 ps in the case of the pure water simulation and 500 ps in the case of the methane-water system. Configurations were saved every 0.5 ps for analysis...

Harvey SC, Tan RK-Z, Cheatham TE III (1998) The flying ice cube velocity rescaling in molecular dynamics leads to violation of energy equipartition. J Comput Chem 19 726-740 Lundberg M, Nishimoto Y, Irle S (2012) Delocalization errors in a Hubbard-like model consequences for density-functional tight-binding calculations of molecular systems. Int J Quant Chem 112 1701-1711... 

In contrast, a system in contact with a thermal bath (constant-temperature, constant-volume ensemble) can be in a state of all energies, from zero to arbitrary large energies however, the state probability is different. The distribution of the probabilities is obtained under the assumption that the system plus the bath constimte a closed system. The imposed temperature varies linearly from start-temp to end-temp. The main techniques used to keep the system at a given temperature are velocity rescaling. Nose, and Nos Hoover-based thermostats. In general, the Nose-Hoover-based thermostat is known to perform better than other temperature control schemes and produces accurate canonical distributions. The Nose-Hoover chain thermostat has been found to perform better than the single thermostat, since the former provides a more flexible and broader frequency domain for the thermostat [29]. The canonical ensemble is the appropriate choice when conformational searches of molecules are carried out in vacuum without periodic boundary conditions. 

The molecular dynamics simulation was conducted at constant volume and constant temperature. Periodic boundary conditions, whereby a particle exiting the cell on one side is reintroduced on the opposing side with the same velocity were imposed. Constant temperature conditions were implemented through simple velocity rescaling. The probability to rescale atom velocities was chosen to be 0.1 per time step. A dynamic time-step of 0.5 fs was used, and snapshots at 2.5 fs steps were collected. 

Bussi, G., Donadio, D., Pairinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 126, 014101(1-7) (2007)... 

An alternative stochastic-dynamical method for thermostatting molecular dynamics is the stochastic velocity rescaling method proposed by Bussi and collaborators [60, 63] and somewhat generalized in [225]. The equations are (for the case Af = /, considered for simplicity) ... 

To understand the reason for this fundamental, qualitative difference between Nos6-Hoover-Langevin and Langevin dynamics, and to compare it with Velocity Rescaling, one may study a quantity that relates the rate of convergence to equilibrium to the rate of growth of the error in the autocorrelation function. In [225], this precise quantity is introduced and termed the efficiency of the thermostat ... 

Integrators and Thermostatting. - Control of temperature in a MD simulation is a desirable feature in many applications, particularly away from equilibrium. Woodcock was the first to devise a thermostatting procedure, by velocity rescaling. Since then, many thermostatting procedures have been devised. One of the most popular has been due to Berendsen, encapsulated in the following equations of motion. 

With this said we see that, when using any one of the thermostats described by Eqs. (80), (81), and (82), the time constant chosen should not be too small to allow the energy to redistribute equally between the different degrees of freedom after it is artificially pumped into the system or taken from it by velocity rescaling. 

Our dynamics are strictly microcanonical (NVE ensemble), once thermalization has been achieved (through NVE and velocity rescaling periods of time). Our gas phase simulations use the decoupling technique of Martyna and Tuckerman [97] to eliminate the effect of the periodic images of the charge density, relevant to charged gas phase systems. 

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