Selection Criteria of the thermodynamic ensemble in molecular dynamics simulation

MD have three different stages, minimisation, equilibrium and production run, and it all depend on the user what he want from these MD runs. During equilibration and production, one need to use thermodynamic ensemble in order to sample dynamic behaviour.

Many of textbooks on statistical mechanics claim that thermodynamical description is independent on statistical ensembles when one invoke thermodynamic limit, but this idea is wrong in presence of phase transitions, specially, discontinuous phase transitions. System with phase coexistence and nonhomogeneities can present anomalous thermodynamical behaviors, whose observation crucially depends on statistical ensemble that is considered. Any way, you have to take into consideration the experimental situation you are interested to compare your MD simulations.

Basically, it depends on what molecular property one wants to simulate/reproduce.

What is NVE, NVT and NPT?

In the microcanonical , or NVE ensemble, the system is isolated from changes in moles (N), volume (V) and energy (E). It corresponds to an adiabatic process with no heat exchange. A microcanonical molecular dynamics trajectory may be seen as an exchange of potential and kinetic energy, with total energy being conserved.

In the canonical ensemble (NVT), amount of substance (N), volume (V) and temperature (T) are conserved. It is also sometimes called constant temperature molecular dynamics (CTMD). In NVT, the energy of endothermic and exothermic processes is exchanged with a thermostat.

In the isothermal–isobaric ensemble, amount of substance (N), pressure (P) and temperature (T) are conserved. In addition to a thermostat, a barostat is needed. It corresponds most closely to laboratory conditions with a flask open to ambient temperature and pressure.

Standard MD is NVE since the total energy should be fixed there is a need to enable MD at constant temperature and constant pressure. NVE represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. Also, with NVE, it is very hard to set initial positions and velocities to give a desired T or P with any accuracy

Why NPT production run work in most cases? Why NPT is ideal for biological system ?

You can sample system via other ensemble and carry out production run by NPT that will model thermodynamic equilibrium. You can always bring you systems to the desired equilibrium conditions using NPT.

To my opinion, production run should be NPT, once you model chemical reactions, (bio)molecular conformational changes, drug-target binding etc. These usually happen under constant (atmospheric) pressure (e.g. in a test tube or in a living cell).

Another reason to choose NPT might be a comparison with experimental data (binding constants, NMR data) which were measured under constant pressure.

If you want to simulate a laboratory condition, NPT would be the most realistic choice, since pressure and temperature of a closed system tend to be constant due to atmospheric pressure and physiological/room temperature of the surroundings.

Production run with NVE can also good?

production run with NVE will avoid the bias introduced by thermostat and/or barostat. However, there are cases where NVE should not be used, chiefly when non-NVE systems are under study. The thermo-/barostat is applied to provide the right ensemble, and many of us study test-tube-like conditions, which are normally NVP.

NVE ensemble contains more thermodynamical information than any other ensemble, precisely, because of it is more close to the exact microscopic dynamics of the isolated system.

A microcanonical NVE molecular dynamics trajectory may be seen as an exchange of potential and kinetic energy, with total energy being conserved.

General rule for the selection of ensembles?

The application of the NPT or NVE ensembles strongly depends on the conditions of phenomena you want to model. However as a general rule, for more stable conditions you need to go for NVE method, but if you want to make it more real and related to experimental work you should go for NPT method instead of NVT.

In other words, if the system is not affected by metastabilities and user is simply interested in equilibrium properties, NVE simulations are equivalent to NPT at the P and T measured in the NVE MD, provided that your system is big enough so that the fluctuations of the kinetic energy and the virial are not too big with respect to T and P.

Though NPT is ideal for biological systems in mimicking experimental conditions, however, sometimes the phenomena of interest do not happen in thermodynamic equilibrium for a period of time. since the temperature is not the same across the systems. For instance, in a collision cascade event. Therefore, in such instances, both NPT and NVE both are very useful ensembles.

General rule of thumb.

If you want to calculate thermo physical properties like density, then NPT is preferred. And if you want to calculate structural property then NVT is good and if you want to calculate dynamical property, then NVE is the best.

It is not advisable to run "NVT/NPT MD" if your objective is computing nonequilibrium properties along a nonequilibrium simulations.

meaning of temperature in MD?

Temperature can be estimated from the instantaneous temperature, which is found by equating the kinetic energy of the system to nkBT/2 where n is the number of degrees of freedom of the system.

General Criteria:

In case of any explicit solvent simulation it is essential to run in constant pressure at some point to equilibrate the density. Whether you will use NVE/ NPT depends on if you believe that your system will like change its shape during simulation time. In my opinion you use the following ensembles at different stages

1) During Heating: NVT

It is necessary to use NVT as int low temperatures the

calculation of pressure is inaccurate and can cause the barostat to

overcorrect leading to instabilities.

2) Equilibrate the system using NVE/NPT

3) Production using NVT

if I don't expect the system to change shape, e.g. unfold

and fold back up etc.

Few more blogs, i will write in future on the following topics.

• NVT is more suitable for materials?

• What if my periodic box is empty?

NPT or NVT are almost same.

Anyway, the differences between NPT and NVT are usually quite small (pV, the difference between Helmholtz and Gibbs free energies, is small).

I advise you to read the following books

"The Art of Molecular Dynamics Simulation" by D. C. Rapaport

"Understanding Molecular Simulation, Second Edition: From Algorithms to Applications" by Daan Frenkel and Berend Smit

"Introduction to Practice of Molecular Simulation: Molecular Dynamics, Monte Carlo, Brownian Dynamics, Lattice Boltzmann and Dissipative Particle Dynamics" by Akira Satoh