CSVR thermostat - Revision history

Singraber at 21:18, 17 October 2025

2025-10-17T21:18:41Z

← Older revision		Revision as of 21:18, 17 October 2025
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	==Related tags and articles==		==Related tags and articles==
	[[Molecular dynamics calculations\|Molecular-dynamics calculations]], [[Andersen thermostat]], [[~~Nose~~-Hoover thermostat]], [[Langevin thermostat]], [[~~Nose~~-Hoover-chain thermostat]], {{TAG\|ISIF}}, {{TAG\|MDALGO}}, {{TAG\|CSVR_PERIOD}}		[[Molecular dynamics calculations\|Molecular-dynamics calculations]], [[Andersen thermostat]], [[Nosé-Hoover thermostat]], [[Langevin thermostat]], [[Nosé-Hoover chain thermostat]], {{TAG\|ISIF}}, {{TAG\|MDALGO}}, {{TAG\|CSVR_PERIOD}}

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Liebetreu at 14:14, 14 October 2025

2025-10-14T14:14:08Z

← Older revision		Revision as of 14:14, 14 October 2025
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	<references />		<references />
	One popular strategy to control the temperature in NVT MD is based on rescaling atomic velocities (<math>\~~bold~~{v}_{i}</math>) at a certain predefined frequency by a factor <math>\alpha = \sqrt{\bar{K}/K}</math> in such a way that the total kinetic energy of the system		One popular strategy to control the temperature in NVT MD is based on rescaling atomic velocities (<math>\mathbf{v}_{i}</math>) at a certain predefined frequency by a factor <math>\alpha = \sqrt{\bar{K}/K}</math> in such a way that the total kinetic energy of the system

	::<math>		::<math>
	K= \frac{1}{2} \sum\limits_{i=1}^{N} m_i \|\~~bold~~{v}_{i}\|^2,		K= \frac{1}{2} \sum\limits_{i=1}^{N} m_i \|\mathbf{v}_{i}\|^2,
	</math>		</math>

Jona at 10:32, 24 February 2025

2025-02-24T10:32:18Z

← Older revision		Revision as of 10:32, 24 February 2025
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	As shown by Bussi et al.<ref name=":0" />, the CSVR thermostat does not significantly affect the evaluation of dynamical properties, such as the velocity autocorrelation functions or diffusion coefficients.		As shown by Bussi et al.<ref name=":0" />, the CSVR thermostat does not significantly affect the evaluation of dynamical properties, such as the velocity autocorrelation functions or diffusion coefficients.

			==Related tags and articles==
			[[Molecular dynamics calculations\|Molecular-dynamics calculations]], [[Andersen thermostat]], [[Nose-Hoover thermostat]], [[Langevin thermostat]], [[Nose-Hoover-chain thermostat]], {{TAG\|ISIF}}, {{TAG\|MDALGO}}, {{TAG\|CSVR_PERIOD}}

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Huebsch at 06:53, 19 March 2024

2024-03-19T06:53:30Z

← Older revision		Revision as of 06:53, 19 March 2024
Line 1:		Line 1:
	<references />		<references />
	One popular strategy to control temperature in NVT MD is based on rescaling atomic velocities (<math>\bold{v}_{i}</math>) at a certain predefined frequency by a factor <math>\alpha = \sqrt{\bar{K}/K}</math> in such a way that the total kinetic energy of the system		One popular strategy to control the temperature in NVT MD is based on rescaling atomic velocities (<math>\bold{v}_{i}</math>) at a certain predefined frequency by a factor <math>\alpha = \sqrt{\bar{K}/K}</math> in such a way that the total kinetic energy of the system

	::<math>		::<math>
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	</math>		</math>

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

	::<math>		::<math>
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	</math>		</math>

	where <math>N_f</math> is the number of degrees of freedom (e.g., <math>N_f = 3N -3 </math> in the case of 3D periodic systems) and <math>N </math> is the number of atoms per the simulation cell. Such a method, however, suffers from several problems. First, the ensemble generated is not strictly canonical. Second, rescaling velocities creates discontinuities in trajectories. As a consequence, the method has no conserved quantity that could be used to guide the choice of simulation parameters, such as the size of the integration step. Also, the rescaling introduces artificial fast fluctuations to velocities, making the evaluation of time correlations is problematic. Finally, the trajectories generated via a naïve rescaling method often suffer from ergodicity issues, such as the flying ice-cube problem, in which kinetic energy of a part of the vibrational degrees of freedom is transferred into translations and/or rotations, violating ~~thus~~ equipartition principle.		where <math>N_f</math> is the number of degrees of freedom (e.g., <math>N_f = 3N -3 </math> in the case of 3D periodic systems) and <math>N </math> is the number of atoms per the simulation cell. Such a method, however, suffers from several problems. First, the ensemble generated is not strictly canonical. Second, rescaling velocities creates discontinuities in trajectories. As a consequence, the method has no conserved quantity that could be used to guide the choice of simulation parameters, such as the size of the integration step. Also, the rescaling introduces artificial fast fluctuations to velocities, making the evaluation of time correlations problematic. Finally, the trajectories generated via a naïve rescaling method often suffer from ergodicity issues, such as the flying ice-cube problem, in which kinetic energy of a part of the vibrational degrees of freedom is transferred into translations and/or rotations, violating the equipartition principle.

	The canonical sampling through velocity rescaling (CSVR) proposed by Bussi et al.<ref name=":0">[https://pubs.aip.org/aip/jcp/article-abstract/126/1/014101/186581/Canonical-sampling-through-velocity-rescaling?redirected G. Bussi, D. Donadio, and M. Parrinello, ''J. Chem. Phys.'' 126, 014101 (2007)]</ref> removes most of the difficulties of the naïve rescaling approach. Here, the term <math> \bar{K} </math> is replaced by <math>K_{t} </math> obtained for each time step by propagating in time via auxiliary dynamics		The canonical sampling through velocity rescaling (CSVR) proposed by Bussi et al.<ref name=":0">[https://pubs.aip.org/aip/jcp/article-abstract/126/1/014101/186581/Canonical-sampling-through-velocity-rescaling?redirected G. Bussi, D. Donadio, and M. Parrinello, ''J. Chem. Phys.'' 126, 014101 (2007)]</ref> removes most of the difficulties of the naïve rescaling approach. Here, the term <math> \bar{K} </math> is replaced by <math>K_{t} </math> obtained for each time step by propagating in time via auxiliary dynamics
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	</math>		</math>

	As shown by Bussi et al.<ref name=":0" />, the CSVR thermostat does not significantly affect evaluation of dynamical properties, such as the velocity ~~autocorreletion~~ functions or diffusion coefficients.		As shown by Bussi et al.<ref name=":0" />, the CSVR thermostat does not significantly affect the evaluation of dynamical properties, such as the velocity autocorrelation functions or diffusion coefficients.

Huebsch at 06:50, 19 March 2024

2024-03-19T06:50:55Z

← Older revision		Revision as of 06:50, 19 March 2024
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	==References==		==References==
	<references/>		<references/>

			[[Category:Molecular dynamics]][[Category:Thermostats]][[Category:Theory]]

Tbucko at 08:00, 10 September 2023

2023-09-10T08:00:01Z

← Older revision		Revision as of 08:00, 10 September 2023
Line 32:		Line 32:
	</math>		</math>

	As shown by Bussi et al., the CSVR thermostat does not significantly affect evaluation of dynamical properties, such as the velocity autocorreletion functions or diffusion coefficients.		As shown by Bussi et al.<ref name=":0" />, the CSVR thermostat does not significantly affect evaluation of dynamical properties, such as the velocity autocorreletion functions or diffusion coefficients.

Tbucko at 07:57, 10 September 2023

2023-09-10T07:57:43Z

← Older revision		Revision as of 07:57, 10 September 2023
Line 32:		Line 32:
	</math>		</math>

	As shown by Bussi et al.~~<ref name=":0" />~~		As shown by Bussi et al., the CSVR thermostat does not significantly affect evaluation of dynamical properties, such as the velocity autocorreletion functions or diffusion coefficients.

Tbucko at 07:54, 10 September 2023

2023-09-10T07:54:42Z

← Older revision		Revision as of 07:54, 10 September 2023
Line 14:		Line 14:
	where <math>N_f</math> is the number of degrees of freedom (e.g., <math>N_f = 3N -3 </math> in the case of 3D periodic systems) and <math>N </math> is the number of atoms per the simulation cell. Such a method, however, suffers from several problems. First, the ensemble generated is not strictly canonical. Second, rescaling velocities creates discontinuities in trajectories. As a consequence, the method has no conserved quantity that could be used to guide the choice of simulation parameters, such as the size of the integration step. Also, the rescaling introduces artificial fast fluctuations to velocities, making the evaluation of time correlations is problematic. Finally, the trajectories generated via a naïve rescaling method often suffer from ergodicity issues, such as the flying ice-cube problem, in which kinetic energy of a part of the vibrational degrees of freedom is transferred into translations and/or rotations, violating thus equipartition principle.		where <math>N_f</math> is the number of degrees of freedom (e.g., <math>N_f = 3N -3 </math> in the case of 3D periodic systems) and <math>N </math> is the number of atoms per the simulation cell. Such a method, however, suffers from several problems. First, the ensemble generated is not strictly canonical. Second, rescaling velocities creates discontinuities in trajectories. As a consequence, the method has no conserved quantity that could be used to guide the choice of simulation parameters, such as the size of the integration step. Also, the rescaling introduces artificial fast fluctuations to velocities, making the evaluation of time correlations is problematic. Finally, the trajectories generated via a naïve rescaling method often suffer from ergodicity issues, such as the flying ice-cube problem, in which kinetic energy of a part of the vibrational degrees of freedom is transferred into translations and/or rotations, violating thus equipartition principle.

	The canonical sampling through velocity rescaling (CSVR) proposed by Bussi et al.<ref>[https://pubs.aip.org/aip/jcp/article-abstract/126/1/014101/186581/Canonical-sampling-through-velocity-rescaling?redirected G. Bussi, D. Donadio, and M. Parrinello, ''J. Chem. Phys.'' 126, 014101 (2007)]</ref> removes most of the difficulties of the naïve rescaling approach. Here, the term <math> \bar{K} </math> is replaced by <math>K_{t} </math> obtained for each time step by propagating in time via auxiliary dynamics		The canonical sampling through velocity rescaling (CSVR) proposed by Bussi et al.<ref name=":0">[https://pubs.aip.org/aip/jcp/article-abstract/126/1/014101/186581/Canonical-sampling-through-velocity-rescaling?redirected G. Bussi, D. Donadio, and M. Parrinello, ''J. Chem. Phys.'' 126, 014101 (2007)]</ref> removes most of the difficulties of the naïve rescaling approach. Here, the term <math> \bar{K} </math> is replaced by <math>K_{t} </math> obtained for each time step by propagating in time via auxiliary dynamics

	::<math>		::<math>
Line 32:		Line 32:
	</math>		</math>

	As shown by Bussi et al.		As shown by Bussi et al.<ref name=":0" />

Tbucko at 07:54, 10 September 2023

2023-09-10T07:54:19Z

← Older revision		Revision as of 07:54, 10 September 2023
Line 32:		Line 32:
	</math>		</math>

	As shown by Bussi et al.<ref>[https://pubs.aip.org/aip/jcp/article-abstract/126/1/014101/186581/Canonical-sampling-through-velocity-rescaling?redirected G. Bussi, D. Donadio, and M. Parrinello, ''J. Chem. Phys.'' 126, 014101 (2007)]</ref>		As shown by Bussi et al.

Tbucko at 07:53, 10 September 2023

2023-09-10T07:53:32Z

← Older revision		Revision as of 07:53, 10 September 2023
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	\tilde{H}(t) = H(t) - \int_0^{t'} (\bar{K}-K)\frac{dt'}{\tau} - 2\int_0^{t} \sqrt{\frac{K{t'}\bar{K}}{N_f}} \frac{dW(t')}{\sqrt{\tau}}		\tilde{H}(t) = H(t) - \int_0^{t'} (\bar{K}-K)\frac{dt'}{\tau} - 2\int_0^{t} \sqrt{\frac{K{t'}\bar{K}}{N_f}} \frac{dW(t')}{\sqrt{\tau}}
	</math>		</math>

			As shown by Bussi et al.<ref>[https://pubs.aip.org/aip/jcp/article-abstract/126/1/014101/186581/Canonical-sampling-through-velocity-rescaling?redirected G. Bussi, D. Donadio, and M. Parrinello, ''J. Chem. Phys.'' 126, 014101 (2007)]</ref>


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	==References==		==References==
	<references/>		<references/>