NVT ensemble: Difference between revisions

Latest revision as of 08:00, 24 October 2025

The NVT ensemble (canonical ensemble) is a statistical ensemble that is used to study material properties under the conditions of a constant particle number N, constant volume V and a temperature fluctuating around an equilibrium value [math]\displaystyle{ \langle T \rangle }[/math]. This page describes how to sample the NVT ensemble from a molecular-dynamics run.

Instructions for setting up an NVT ensemble

There are multiple choices of thermostats to control the temperature for the NVT ensemble: The stochastic Andersen thermostat, Langevin thermostat and CSVR thermostat, as well as the deterministic Nosé-Hoover thermostat, Nosé-Hoover chain thermostat and Multiple Andersen thermostats can be used. See table for the corresponding MDALGO setting and related tags.

NVT ensemble	Nosé-Hoover^[1]	Andersen	Nosé-Hoover	Langevin	Nosé-Hoover chain	CSVR	Multiple Andersen
MDALGO	0	1	2	3	4	5	13
additional tags to set	SMASS	ANDERSEN_PROB	SMASS	LANGEVIN_GAMMA	NHC_NCHAINS, NHC_PERIOD, NHC_NRESPA, NHC_NS	CSVR_PERIOD	NSUBSYS, TSUBSYS, PSUBSYS

The additional tags in the column for every thermostat have to be set. For example, the Nosé-Hoover thermostat needs the additional SMASS tag. To enforce constant volume throughout the calculation, set ISIF < 3. In NVT MD runs there is no control over pressure because the volume is fixed. The average value will therefore depend on the initial lattice given in the POSCAR file. It is often desirable to equilibrate the lattice degrees of freedom, for example, by running an NpT simulation or by performing structure and volume optimization with IBRION = 1 or 2 and setting ISIF > 2. A general guide for molecular-dynamics simulations can be found on the molecular-dynamics page.

Example INCAR file for the Nosé-Hoover thermostat

 #INCAR molecular-dynamics tags NVT ensemble 
 IBRION = 0                   # choose molecular dynamics 
 MDALGO = 2                   # use Nosé-Hoover thermostat 
 ISIF = 2                     # compute stress tensor but do not change box volume/shape 
 TEBEG = 300                  # set temperature 
 NSW = 10000                  # number of time steps 
 POTIM = 1.0                  # time step in femto seconds 
 SMASS = 1.0                  # setting the virtual mass for the Nosé-Hoover thermostat

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.

Footnotes and references

↑ If possible, use another Nosé–Hoover thermostat implementation, e.g. MDALGO = 2, see also comments here.

[legacy-nh-1] If possible, use another Nosé–Hoover thermostat implementation, e.g. MDALGO = 2, see also comments here.

[1]

@@ Line 1: / Line 1: @@
-The NVT ensemble is a statistical ensemble that is used to study material properties under the conditions of a
+The [[NVT ensemble]] (canonical ensemble) is a [[:Category:Ensembles|statistical ensemble]] that is used to study material properties under the conditions of a
-constant particle number N, constant volume V and a temperature fluctuating around an equilibrium value T.
+constant particle number N, constant volume V and a temperature fluctuating around an equilibrium value <math>\langle T \rangle</math>.
-This page describes how to sample the NVT ensemble from a [[Molecular dynamics calculations|molecular dynamics]] run.
+This page describes how to sample the NVT ensemble from a [[Molecular dynamics calculations|molecular-dynamics]] run.
-''' Instructions for setting up a NVT ensemble '''
+''' Instructions for setting up an NVT ensemble '''
-There are four choices of thermostats which can either be stochastic or deterministic to simulate the NVT ensemble.
+There are multiple choices of thermostats to control the temperature for the NVT ensemble:
-The stochastic [[Andersen thermostat]] or [[Langevin thermostat]],
+The stochastic [[Andersen thermostat]], [[Langevin thermostat]] and [[CSVR thermostat]], as well as
-the deterministic [[Nose-Hoover thermostat]] or [[MDALGO#MDALGO.3D13:_Multiple_Anderson_thermostats|Multiple Andersen thermostats]] can be used.
+the deterministic [[Nosé-Hoover thermostat]], [[Nosé-Hoover chain thermostat]] and [[MDALGO#MDALGO.3D13:_Multiple_Anderson_thermostats|Multiple Andersen thermostats]] can be used.
-See table for the corresponding {{TAG|MDALGO}} tags.
+See table for the corresponding {{TAG|MDALGO}} setting and related tags.
 {|class="wikitable" style="margin:aut
-! NVT ensemble !! Andersen !! Langevin !! Nose-Hoover !! Multiple Andersen
+! NVT ensemble !! Nosé-Hoover<ref name="legacy-nh"/> !! Andersen !! Nosé-Hoover !! Langevin  !! Nosé-Hoover chain !! CSVR !! Multiple Andersen
 |-
-|{{TAG|MDALGO}}          ||     1        ||     3            ||      2      ||        13
+|{{TAG|MDALGO}}        ||  style="text-align:center;"|   0          ||  style="text-align:center;"|   1        ||   style="text-align:center;"|   2            ||   style="text-align:center;"|   3      ||   style="text-align:center;"|   4      ||   style="text-align:center;"|   5      ||   style="text-align:center;"|      13
 |- {{TAG|PSUBSYS}}
-| additional tags || {{TAG|ANDERSEN_PROB}} ||   {{TAG|LANGEVIN_GAMMA}} ||  {{TAG|SMASS}}      || {{TAG|NSUBSYS}}, {{TAG|TSUBSYS}}, {{TAG|PSUBSYS}}
+| additional tags to set || style="text-align:center;"| {{TAG|SMASS}}  || style="text-align:center;"| {{TAG|ANDERSEN_PROB}} || style="text-align:center;"| {{TAG|SMASS}} || style="text-align:center;"|   {{TAG|LANGEVIN_GAMMA}}      || style="text-align:center;"|   {{TAG|NHC_NCHAINS}}, {{TAG|NHC_PERIOD}}, {{TAG|NHC_NRESPA}}, {{TAG|NHC_NS}}      || style="text-align:center;"|   {{TAG|CSVR_PERIOD}}      || style="text-align:center;"|  {{TAG|NSUBSYS}}, {{TAG|TSUBSYS}}, {{TAG|PSUBSYS}}
 |}
-The additional tags in the column of every thermostat have to be set. For example the Nose-Hover thermostat needs the additional {{TAG|SMASS}} tag. To enforce constant volume throughout the calculation, {{TAG|ISIF}} has to be set to less than 3. The cell shape and volume have
+The additional tags in the column for every thermostat have to be set. For example, the [[Nosé-Hoover thermostat]] needs the additional {{TAG|SMASS}} tag. To enforce constant volume throughout the calculation, set {{TAG|ISIF|3|op=<}}. In NVT MD runs there is no control over pressure because the volume is fixed. The average value will therefore depend on the initial lattice given in the {{FILE|POSCAR}} file. It is often desirable to equilibrate the lattice degrees of freedom, for example, by running an [[NpT_ensemble|NpT simulation]] or by performing structure and volume optimization with {{TAG|IBRION|1 or 2}} and setting {{TAG|ISIF|2|op=>}}. A general guide for molecular-dynamics simulations can be found on the [[Molecular dynamics calculations|molecular-dynamics]] page.
-to be preoptimized when doing NVT simulations. This can either be done with a [[NpT_ensemble|NPT]] molecular-dynamics run or by doing static optimization calculations with {{TAG|IBRION}} one or two and setting {{TAG|ISIF}} larger than 2.
-Other tags related to molecular dynamics simulations can be found [[Molecular dynamics calculations|here]].
+''Example {{FILE|INCAR}} file for the [[Nosé-Hoover thermostat]]''
-''An example INCAR file for the [[Langevin thermostat]] could look like'''
+   #INCAR molecular-dynamics tags NVT ensemble
+   {{TAGBL|IBRION}} = 0                   # choose molecular dynamics
-   #INCAR molecular dynamics tags NVT ensemble
+   {{TAGBL|MDALGO}} = 2                   # use Nosé-Hoover thermostat
-   IBRION = 0                   # choose molecular dynamics
+   {{TAGBL|ISIF}} = 2                     # compute stress tensor but do not change box volume/shape
-   MDALGO = 3                   # using Langevin thermostat
+   {{TAGBL|TEBEG}} = 300                  # set temperature
-   ISIF = 2                     # compute stress tensor but do not change box volume/shape
+   {{TAGBL|NSW}} = 10000                  # number of time steps
-   TEBEG = 300                  # set temperature
+   {{TAGBL|POTIM}} = 1.0                  # time step in femto seconds
-   NSW = 10000                  # number of time steps
+   {{TAGBL|SMASS}} = 1.0                  # setting the virtual mass for the Nosé-Hoover thermostat
-   POTIM = 1.0                  # time step in femto seconds
+{{NB|mind| This {{FILE|INCAR}} file only contains the parameters for the molecular-dynamics part. The [[Electronic minimization|electronic minimization]] or the [[Machine-learned force fields|machine learning]] tags have to be added.}}
-   LANGEVIN_GAMMA = 10.0   10.0 # setting friction coefficient in inverse time units for two atom types
-{{NB|mind| This {{FILE|INCAR}} file only contains the parameters for the molecular dynamics part. The [[Electronic minimization|electronic minimization]] or the [[Machine-learned force fields|machine learning]] tags have to be added.}}
+==Related tags and articles==
+[[Molecular dynamics calculations|Molecular-dynamics calculations]], {{TAG|ISIF}}, {{TAG|MDALGO}}, {{TAG|LANGEVIN_GAMMA}}, {{TAG|SMASS}},{{TAG|ANDERSEN_PROB}}, {{TAG|NSUBSYS}}, {{TAG|TSUBSYS}}, {{TAG|PSUBSYS}}
-==Related tags and articles==
+== Footnotes and references ==
-{{FILE|REPORT}}, [[Molecular dynamics calculations]]
+<references>
+<ref name="legacy-nh">If possible, use another Nosé–Hoover thermostat implementation, e.g. {{TAG|MDALGO|2}}, see also comments [[MDALGO#MDALGO=0:_Standard_molecular_dynamics|here]].</ref>
+</references>
 [[Category:Molecular dynamics]][[Category:Ensembles]][[Category:Thermostats]]