Nose-Hoover thermostat: Difference between revisions
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In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}} an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for | In the approach by Nosé and Hoover{{cite|nose:jcp:1984}}{{cite|nose:ptp:1991}}{{cite|hoover:pra:1985}}{{cite|frenkel:book:1996}}, an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate <math>s</math> which is introduced into the Lagrangian of the system. This Lagrangian for a <math>N</math> particle system is written as | ||
<math> | ::<math> | ||
\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} + | \mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} - U(\bold{r}) + \frac{Q}{2} \dot{s}^{2}-g k_{B} T \mathrm{ln} \, s | ||
</math> | </math> | ||
where <math>m_{i}</math> and <math>k_{B}</math> are the mass of ion <math>i</math> and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate <math>s</math>. These terms also ensure the energy conservation of the Nose-Hoover thermostat. The parameter <math>g</math> is usually equal to the number of degrees of freedom of the system <math>g=3N - N_{\mathrm{constraint}}</math>, where <math>N_{\mathrm{constraint}}</math> is equal to the number of constraint set (fixed coordinates in the {{TAG|POSCAR}} file). The parameter <math>Q</math> is an effective "mass" of <math>s</math>, which controls the coupling of the system to the heat bath. It is set by the {{TAG|INCAR}} tag {{TAG|SMASS}}. | |||
The Nose-Hoover thermostat is selected by {{TAG|MDALGO}}=2. | |||
== References == | == References == | ||
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[[Category:Molecular dynamics]][[Category:Thermostats]][[Category:Theory]][[Category:Howto]] | |||
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Latest revision as of 09:34, 13 July 2023
In the approach by Nosé and Hoover[1][2][3][4], an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate which is introduced into the Lagrangian of the system. This Lagrangian for a particle system is written as
where and are the mass of ion and the Boltzmann constant, respectively. The first two terms are the kinetic and potential energy of the system. The third and fourth term represent the kinetic and potential energy of the fictitious coordinate . These terms also ensure the energy conservation of the Nose-Hoover thermostat. The parameter is usually equal to the number of degrees of freedom of the system , where is equal to the number of constraint set (fixed coordinates in the POSCAR file). The parameter is an effective "mass" of , which controls the coupling of the system to the heat bath. It is set by the INCAR tag SMASS.
The Nose-Hoover thermostat is selected by MDALGO=2.
References