Molecular Dynamics at Constant Temperature and Pressure

Molecular dynamics is traditionally performed in the constant NVE (or NVEP) ensemble. Although thermodynamic results can be transformed between ensembles, this is strictly only possible in the limit of infirate system size ( the thermodjmamic limit ). It may therefore be desired to perform the simulation in a different ensemble. The two most common alternative ensembles are the constant NVT and the constant NPT ensembles. In this section we will therefore consider how molecular dynamics simulations can be performed under conditions of constant temperature and/ or constant pressure. 

There are several reasons why we might want to maintain or otherwise control the temperature during a molecular dynamics simulation. Even in a constant NVE simulation it is common practice to adjust the temperature to the desired value during the equilibration phase. A constant temperature simulation may be required if we wish to determine how 

1 he temperature of the system is related to the time average of the kinetic energy, which for an unconstrained system is given by 

An obvious way to alter the temperature of the system is thus to scale the velocities [Woodcock 1971]. If the temperature at time t is T(t) and the velocities are multiplied by a factor A, then the associated temperature change can be calculated as follows  

The simplest way to control the temperature is thus to multiply the velocities at each time step by the factor A = VT) 7 cu / where T arr is the current temperature as calculated from the kinetic energy and T q is the desired temperature. 

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