# NpT ensemble

The NpT ensemble (isothermal-isobaric ensemble) is a statistical ensemble that is used to study material properties under the conditions of a constant particle number N, a pressure p fluctuating around an equilibrium value ${\displaystyle \langle p\rangle }$ and a temperature T fluctuating around an equilibrium value ${\displaystyle \langle T\rangle }$. This page describes how to sample the NpT ensemble from a molecular-dynamics run.

Instructions for setting up an NpT ensemble

The Parinello-Rahman algorithm[1][2] is the method of choice when setting up an NpT molecular-dynamics run. To use the Parinello-Rahman algorithm the Langevin thermostat has to be adjusted for an NpT simulation by setting the ISIF=3 in the INCAR file. Otherwise, the lattice is not allowed to change during the simulation, preventing VASP from keeping the pressure constant. Additionally the user can set LANGEVIN_GAMMA as when simulating a NVT ensemble, the tag LANGEVIN_GAMMA_L which is a friction coefficient for the lattice degrees of freedom and the PMASS tag to assign a fictitious mass to the lattice degrees of freedom.

NpT ensemble Langevin
MDALGO 3
ISIF 3
additional tags to set LANGEVIN_GAMMA, LANGEVIN_GAMMA_L
optional tags to set PMASS

The additional tags in the column for the thermostat have to be set because the default values are zero resulting in a different ensemble. To use the NpT ensemble VASP has to be compiled with the precompiler flag -Dtbdyn. A general guide for molecular-dynamics simulations can be found on the molecular-dynamics page.

An example INCAR file for the NpT ensemble

 #INCAR molecular-dynamics tags NpT ensemble
IBRION = 0                      # choose molecular-dynamics
MDALGO = 3                      # using Langevin thermostat
ISIF = 3                        # compute stress tensor and change box volume/shape
TEBEG = 300                     # set temperature
NSW = 10000                     # number of time steps
POTIM = 1.0                     # time step in femto seconds
LANGEVIN_GAMMA = 10.0 10.0 10.0 # Langevin friction coefficient for three atomic species
LANGEVIN_GAMMA_L = 10.0         # Langevin friction coefficient for lattice degrees of freedom
PMASS = 1000                    # the fictitious mass of the lattice degrees of freedom

 Mind: This INCAR file only contains the parameters for the molecular-dynamics part. The electronic minimization or the machine learning tags have to be added.
 Warning: Calculations of systems with limited long-range order (e.g. liquids) may lead to irreversible deformations of the cell within this ensemble. For those systems one must use an ICONST file containing constraints for the Bravais lattice.