Generating non-natural ensembles

A standard MD simulation generates an NVE ensemble, i.e. the temperature and pressure will fluctuate. The total energy is a sum of the kinetic and potential energies, and can be calculated from the positions and velocities. 

Owing to the finite precision with which the atomic forces are evaluated, and the finite time step used, the total energy is not exactly constant, but this error can be controlled by the magnitude of the time step. Indeed, preservation of the energy to within a given threshold may be used to define the maximum permissible time step. 

The temperature of the system is proportional to the average kinetic energy. 

Although the NVE is the natural ensemble generated by an MD simulation, it is possible also to generate NVT or NET ensembles by MD techniques by modifying the velocities or positions in each time step. As indicated in eq. (14.14) the instant value of the temperature is given by the average of the kinetic energy. If this is different from the desired temperature, all velocities may be scaled by a factor of in 

The pressure can similarly be held (approximately) constant by coupling to a pressure bath . Instead of changing the velocities of the particles, the volume of the system is changed by scaling aU coordinates according to eq. (14.16). 

---