Controlling the system

  In a molecular dynamics simulation a system could be in a state characterized by a certain density, temperature, pressure (the calculation of these quantities is described below): the phase diagram of the simulated material can be investigated. However, how can we bring the system in the desired region? In other words, how can we control the system?

In a standard calculation, the density is controlled by the choice of the box volume V. Programs usually have provisions for rescaling the volume upon request at the beginning of the calculation. Volume changes should be modest, of the order of at most a few percent. The pressure will be measured during the run, following the method described in §3.5.7. In other, more advanced simulation schemes, the user chooses the pressure, and the volume of the box is a variable to be measured (see §3.11).

Temperature changes are usually achieved by enabling a device in the code which brings the system to a desired temperature by rescaling the velocities. In the velocity Verlet algorithm discussed at the end of §2.3.1, this may be accomplished by replacing the equation

$${\bf v} (t + \Delta t/2) = {\bf v} (t) + (1/2) {\bf a} (t) \Delta t$$

with

$${\bf v} (t + \Delta t/2) = \sqrt{\frac{T_\circ}{T(t)}} {\bf v} (t) + (1/2) {\bf a} (t) \Delta t$$

where $T_\circ$ is the desired temperature, and T(t) the ``instantaneous temperature''. Such a modification means that we are no longer following Newton's equations, and the total energy is no longer conserved. Important data should not be collected in this stage: these ``controlled temperature'' simulations should be used only to bring the system from one state to another. One should always wait for the system to reach equilibrium under clean constant energy conditions before collecting data.