Module 7 : MC Simulation in various ensembles

Lecture 33 : NVE and NPT ensemble

In the particle displacement, we decide maximum displacement, . Similarly for volume change move maximum volume change () need to be decided before the simulation run. For volume change, choose a volume randomly from the range - to + (similar to - to + ). Final volume, , from which calculate the modified box size, L f and then recalculate the coordinates of all particles based on box size, L f . Final energy needs to be calculated based on this new coordinates.

We have seen in NVT ensemble, the probability from initial to final state is , where, In the NPT ensemble, since there is change in volume is involved, the probability takes the following form:

(1)

Second and third terms are due to the volume change move. Hence one MC step refers to the on average one attempt to particle displacement and volume change. Thus, we need to randomly choose one number from, (N + 1). The ‘+1' is to accommodate volume change.