Nose-Hoover-chain thermostat: Difference between revisions

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::<math>
::<math>
\mathcal{H'} = \mathcal{H}(\bold{r},\bold{p}) +  \sum\limits_{j=1}^{M} \frac{p_{\eta_j}^2}{2Q_j} + 3Nk_{B} T \eta_1 + k_{B} T \sum\limits_{j=2}^{M} \eta_j
\mathcal{H'} = \mathcal{H}(\bold{r},\bold{p}) +  \sum\limits_{j=1}^{M} \frac{p_{\eta_j}^2}{2Q_j} + 3(N-N_c)k_{B} T \eta_1 + k_{B} T \sum\limits_{j=2}^{M} \eta_j
</math>
</math>


where <math>\mathcal{H}(\bold{r},\bold{p})</math> is the Hamiltonian of the physical system, <math>M</math> and <math>N</math> are the numbers of thermostats and atoms in the cell, respectively, and <math>\eta_{j}</math>, <math>p_{\eta_j}</math>, and <math>Q_{j}</math> are the position, momentum, and mass-like parameter associated with the thermostat <math>j</math>. Just like the total energy in NVE ensemble,<math>\mathcal{H'}</math> is valuable for diagnostics purposes. Indeed, a significant drift in <math>\mathcal{H'}</math> indicate that the corresponding computational setting is suboptimal. Typical reasons for this behavior involve noisy forces (e.g., because of a poor SCF convergence) and/or a too large integration step (defined via {{TAG|POTIM}}).   
where <math>\mathcal{H}(\bold{r},\bold{p})</math> is the Hamiltonian of the physical system, <math>M</math>, <math>N</math> and <math>N_c</math> are the numbers of thermostats, atoms in the cell, and geometric constraints, respectively, and <math>\eta_{j}</math>, <math>p_{\eta_j}</math>, and <math>Q_{j}</math> are the position, momentum, and mass-like parameter associated with the thermostat <math>j</math>. Just like the total energy in NVE ensemble,<math>\mathcal{H'}</math> is valuable for diagnostics purposes. Indeed, a significant drift in <math>\mathcal{H'}</math> indicate that the corresponding computational setting is suboptimal. Typical reasons for this behavior involve noisy forces (e.g., because of a poor SCF convergence) and/or a too large integration step (defined via {{TAG|POTIM}}).   


The number of thermostats is controlled by the flag  {{TAG|NHC_NCHAINS}}. Typically, this flag is set to a value between 1 and 5, the maximal allowed value is 20. In the special case of {{TAG|NHC_NCHAINS}}=0, the thermostat is switched off, leading to a MD in microcanonical ensemble. Another special case of {{TAG|NHC_NCHAINS}}=1 corresponds to the  standard {{TAG|Nose-Hoover thermostat}}.  
The number of thermostats is controlled by the flag  {{TAG|NHC_NCHAINS}}. Typically, this flag is set to a value between 1 and 5, the maximal allowed value is 20. In the special case of {{TAG|NHC_NCHAINS}}=0, the thermostat is switched off, leading to a MD in microcanonical ensemble. Another special case of {{TAG|NHC_NCHAINS}}=1 corresponds to the  standard {{TAG|Nose-Hoover thermostat}}.  
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::<math>
::<math>
Q_1 = 3 N k_{B} T \tau^2
Q_1 = 3 (N -N_c)k_{B} T \tau^2
</math>
</math>
::<math>
::<math>

Revision as of 07:29, 22 April 2023

The standard Nose Hoover suffers from well known issues, such as the ergodicity violation in the case of simple harmonic oscillator[1]. As proposed by Martyna and Klein[1], these problems can be solved by using multiple Nose Hoover thermostats connected in a chain. Although the underlining dynamics is non-Hamiltonian, the corresponding equations of motion conserve the following energy term:

where is the Hamiltonian of the physical system, , and are the numbers of thermostats, atoms in the cell, and geometric constraints, respectively, and , , and are the position, momentum, and mass-like parameter associated with the thermostat . Just like the total energy in NVE ensemble, is valuable for diagnostics purposes. Indeed, a significant drift in indicate that the corresponding computational setting is suboptimal. Typical reasons for this behavior involve noisy forces (e.g., because of a poor SCF convergence) and/or a too large integration step (defined via POTIM).

The number of thermostats is controlled by the flag NHC_NCHAINS. Typically, this flag is set to a value between 1 and 5, the maximal allowed value is 20. In the special case of NHC_NCHAINS=0, the thermostat is switched off, leading to a MD in microcanonical ensemble. Another special case of NHC_NCHAINS=1 corresponds to the standard Nose-Hoover thermostat.

The only thermostat parameter is NHC_PERIOD, corresponding to a characteristic time scale () of the system expressed in time steps. This variable is used to setup the mass-like variables via the relations:


NHC_NRESPA


NHC_NS