CSVR thermostat: Difference between revisions

Revision as of 08:27, 9 September 2023

One popular strategy to control temperature in NVT MD is to rescale atomic velocities ( $\bold{v}_{i}$ ) at a certain predefined frequency by some factor in such a way that the total kinetic energy of the system

{\displaystyle E_{kin} = \frac{1}{2} \sum\limits_{i=1}^{N} m_i |\bold{v}_{i}|^2, }

is equal to the average kinetic energy corresponding to given temperature:

{\displaystyle \bar{E}_{kin} = \frac{1}{2}N_f k_B T }

where $N_f = 3N -3$ for 3D periodc and $N_f = 3N -3$ for non-linear molecular systems and math>N </math> is the number of atoms. Such a method, however, suffers from several issues. First of all, the ensemble generated is not strictly canonical. Also, the trajectories generated via this naive rescaling method often suffer from flying ice-cube problem where kinetic energy vibrational degrees of freedom is transferred into translations and/or rotations, violating thus equipartition principle.

An elaborated approach based on the velocity rescaling has been proposed by Bussi et al.

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-One popular strategy to control temperature in NVT MD is to rescale atomic velocities at a certain predefined frequency by some factor in such a way that the total kinetic energy of the system (<math>E_{kin}</math>) is equal to the average kinetic energy  corresponding to given temperature (<math>\bar{E}_{kin} = \frac{3}{2}(N -1)k_B T</math> where <math>N</math> is the number of atoms). Such a method, however, suffers from several issues. First of all, the ensemble generated is not strictly canonical. Also, the trajectories generated via this naive rescaling method often suffer from flying ice-cube problem where kinetic energy vibrational degrees of freedom is transferred into translations and/or rotations, violating thus equipartition principle.
+One popular strategy to control temperature in NVT MD is to rescale atomic velocities (<math>\bold{v}_{i}</math>) at a certain predefined frequency by some factor in such a way that the total kinetic energy of the system
+::<math>
+E_{kin} = \frac{1}{2} \sum\limits_{i=1}^{N} m_i |\bold{v}_{i}|^2,
+</math>
+is equal to the average kinetic energy  corresponding to given temperature:
+::<math>
+\bar{E}_{kin} = \frac{1}{2}N_f k_B T
+</math>
+where <math>N_f = 3N -3 </math> for 3D periodc and <math>N_f = 3N -3 </math> for non-linear molecular systems and math>N </math> is the number of atoms. Such a method, however, suffers from several issues. First of all, the ensemble generated is not strictly canonical. Also, the trajectories generated via this naive rescaling method often suffer from flying ice-cube problem where kinetic energy vibrational degrees of freedom is transferred into translations and/or rotations, violating thus equipartition principle.
 An elaborated approach based on the velocity rescaling has been proposed by Bussi et al.