Category:Advanced molecular-dynamics sampling - Revision history

Liebetreu at 14:09, 22 July 2026

2026-07-22T14:09:39Z

Csheldon: /* Thermodynamic integration */

2026-07-20T08:51:15Z

Thermodynamic integration

← Older revision		Revision as of 08:51, 20 July 2026
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	In the [[Thermodynamic integration\|thermodynamic integration]] method,{{cite\|dorner:PRL:2018}}{{Cite\|kirkwood:jcp:1935}} the energy differences of a fully interacting and non-interacting system are calculated. This is achieved by making the potential energy depend on a coupling parameter and defining the free energy as a smooth integral over the potential energy along this coupling parameter. As the reference state for a non-interacting system, usually an [[SCALEE\|ideal gas]] or a [[TILAMBDA\|harmonic solid]] is chosen.		In the [[Thermodynamic integration\|thermodynamic integration]] method,{{cite\|dorner:PRL:2018}}{{Cite\|kirkwood:jcp:1935}} the energy differences of a fully interacting and non-interacting system are calculated. This is achieved by making the potential energy depend on a coupling parameter and defining the free energy as a smooth integral over the potential energy along this coupling parameter. As the reference state for a non-interacting system, usually an [[SCALEE\|ideal gas]] or a [[TILAMBDA\|harmonic solid]] is chosen.

	[[Thermodynamic integration\|Thermodynamic integration]] is usually used to compute free energy differences between [[VCAIMAGES\|different phases]].		[[Thermodynamic integration\|Thermodynamic integration]] is usually used to compute free energy differences between [[VCAIMAGES\|different phases or states]].
	*[[Thermodynamic integration]]		*[[Thermodynamic integration]]
	*[[Thermodynamic integration calculations]]		*[[Thermodynamic integration calculations]]

Csheldon at 08:46, 20 July 2026

2026-07-20T08:46:49Z

← Older revision		Revision as of 08:46, 20 July 2026
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	*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]		*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]

	Biased MD, blue moon ensemble, constrained dynamics, metadynamics, and thermodynamic integration are introduced in our {{Video\|advanced_md:tomas:2022\|advanced methods of MD}} lecture. {{Tutorial\|md:e08\|The slow-growth approach, blue-moon ensemble, and constrained MD}} are then explored in a tutorial for a simple chemical reaction. For a more advanced example of applying advanced MD to model a chemical reaction, see the {{Video\|dynamic:tomas:2025\|dynamic approach for modelling a chemical reaction}} lecture and the {{Tutorial\|transition_states:part3\|accompanying tutorials}}.		Biased MD, umbrella sampling, blue moon ensemble, constrained dynamics, metadynamics, and thermodynamic integration are introduced in our {{Video\|advanced_md:tomas:2022\|advanced methods of MD}} lecture. {{Tutorial\|md:e08\|The slow-growth approach, blue-moon ensemble, and constrained MD}} are then explored in a tutorial for a simple chemical reaction. For a more advanced example of applying advanced MD to model a chemical reaction, see the {{Video\|dynamic:tomas:2025\|dynamic approach for modelling a chemical reaction}} lecture and the {{Tutorial\|transition_states:part3\|accompanying tutorials}}.

	== Thermodynamic integration ==		== Thermodynamic integration ==

Csheldon at 08:43, 20 July 2026

2026-07-20T08:43:10Z

← Older revision		Revision as of 08:43, 20 July 2026
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	*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]		*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]

	~~Umbrella sampling~~, blue moon ensemble, constrained dynamics, metadynamics, and thermodynamic integration are introduced in our {{Video\|advanced_md:tomas:2022\|advanced methods of MD}} lecture. {{Tutorial\|md:e08\|The slow-growth approach, blue-moon ensemble, and constrained MD}} are then explored in a tutorial for a simple chemical reaction. For a more advanced example of applying advanced MD to model a chemical reaction, see the {{Video\|dynamic:tomas:2025\|dynamic approach for modelling a chemical reaction}} lecture and the {{Tutorial\|transition_states:part3\|accompanying tutorials}}.		Biased MD, blue moon ensemble, constrained dynamics, metadynamics, and thermodynamic integration are introduced in our {{Video\|advanced_md:tomas:2022\|advanced methods of MD}} lecture. {{Tutorial\|md:e08\|The slow-growth approach, blue-moon ensemble, and constrained MD}} are then explored in a tutorial for a simple chemical reaction. For a more advanced example of applying advanced MD to model a chemical reaction, see the {{Video\|dynamic:tomas:2025\|dynamic approach for modelling a chemical reaction}} lecture and the {{Tutorial\|transition_states:part3\|accompanying tutorials}}.

	== Thermodynamic integration ==		== Thermodynamic integration ==

Csheldon: /* Additional resources */

2026-07-20T08:41:33Z

Additional resources

← Older revision		Revision as of 08:41, 20 July 2026
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	*''Statistical Mechanics: Theory and Molecular Simulation'' by M. Tuckerman {{Cite\|tuckerman:book:2023}}.		*''Statistical Mechanics: Theory and Molecular Simulation'' by M. Tuckerman {{Cite\|tuckerman:book:2023}}.
	*''Understanding Molecular Simulation - From Algorithms to Applications'' by D. Frenkel and B. Smit {{Cite\|frenkel:smit:2023}}.		*''Understanding Molecular Simulation - From Algorithms to Applications'' by D. Frenkel and B. Smit {{Cite\|frenkel:smit:2023}}.

	~~=== Tutorials ===~~
	*Tutorial for chloromethane-chloride inversion {{Tutorial\|md:e08\|using the slow-growth approach, blue-moon ensemble, and constrained MD}}.
	*Tutorial for a chemical reaction in a zeolite {{Tutorial\|transition_states:part3\|using the slow-growth approach, blue-moon ensemble, and constrained MD}}.

	~~=== Lectures ===~~
	*Lecture on {{Video\|advanced_md:tomas:2022\|advanced methods of MD}}.
	*Lecture on {{Video\|dynamic:tomas:2025\|advanced methods of MD applied to a chemical reaction}}.

	== References ==		== References ==

	[[Category:VASP]][[Category:Molecular dynamics]]		[[Category:VASP]][[Category:Molecular dynamics]]

Csheldon at 08:40, 20 July 2026

2026-07-20T08:40:25Z

← Older revision		Revision as of 08:40, 20 July 2026
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	*[[:Category:Advanced molecular-dynamics sampling#Slow-growth approach\|Slow-growth approach]]		*[[:Category:Advanced molecular-dynamics sampling#Slow-growth approach\|Slow-growth approach]]
	*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]		*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]

			Umbrella sampling, blue moon ensemble, constrained dynamics, metadynamics, and thermodynamic integration are introduced in our {{Video\|advanced_md:tomas:2022\|advanced methods of MD}} lecture. {{Tutorial\|md:e08\|The slow-growth approach, blue-moon ensemble, and constrained MD}} are then explored in a tutorial for a simple chemical reaction. For a more advanced example of applying advanced MD to model a chemical reaction, see the {{Video\|dynamic:tomas:2025\|dynamic approach for modelling a chemical reaction}} lecture and the {{Tutorial\|transition_states:part3\|accompanying tutorials}}.

	== Thermodynamic integration ==		== Thermodynamic integration ==

Liebetreu at 12:39, 26 June 2026

2026-06-26T12:39:48Z

← Older revision		Revision as of 12:39, 26 June 2026
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	== References ==		== References ==

	[[Category:VASP~~\|Advanced molecular-dynamics sampling~~]][[Category:~~Molecular dynamics\|~~Molecular dynamics]]		[[Category:VASP]][[Category:Molecular dynamics]]

Csheldon: /* How to */

2026-06-17T10:18:34Z

How to

← Older revision		Revision as of 10:18, 17 June 2026
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	*''Statistical Mechanics: Theory and Molecular Simulation'' by M. Tuckerman {{Cite\|tuckerman:book:2023}}.		*''Statistical Mechanics: Theory and Molecular Simulation'' by M. Tuckerman {{Cite\|tuckerman:book:2023}}.
	*''Understanding Molecular Simulation - From Algorithms to Applications'' by D. Frenkel and B. Smit {{Cite\|frenkel:smit:2023}}.		*''Understanding Molecular Simulation - From Algorithms to Applications'' by D. Frenkel and B. Smit {{Cite\|frenkel:smit:2023}}.

	~~=== How to ===~~
	*[[Nuclephile_Substitution_CH3Cl_-_mMD1 \| Chemical reaction using metadynamics - part 1]]
	*[[Nuclephile_Substitution_CH3Cl_-_mMD2 \| Chemical reaction using metadynamics - part 2]]
	*[[Nuclephile_Substitution_CH3Cl_-_mMD3 \| Chemical reaction using metadynamics - part 3]]
	*How to for [[Using_metadynamics_to_train_a_machine-learned_force_field \| training a machine-learned force field (MLFF) using metadynamics for chloromethane-chloride inversion]].

	=== Tutorials ===		=== Tutorials ===

Csheldon: /* How to */

2026-06-17T10:18:07Z

How to

← Older revision		Revision as of 10:18, 17 June 2026
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	=== How to ===		=== How to ===
	**[[Nuclephile_Substitution_CH3Cl_-_mMD1 \| Chemical reaction using metadynamics - part 1]]		*[[Nuclephile_Substitution_CH3Cl_-_mMD1 \| Chemical reaction using metadynamics - part 1]]
	**[[Nuclephile_Substitution_CH3Cl_-_mMD2 \| Chemical reaction using metadynamics - part 2]]		*[[Nuclephile_Substitution_CH3Cl_-_mMD2 \| Chemical reaction using metadynamics - part 2]]
	**[[Nuclephile_Substitution_CH3Cl_-_mMD3 \| Chemical reaction using metadynamics - part 3]]		*[[Nuclephile_Substitution_CH3Cl_-_mMD3 \| Chemical reaction using metadynamics - part 3]]
	**How to for [[Using_metadynamics_to_train_a_machine-learned_force_field \| training a machine-learned force field (MLFF) using metadynamics for chloromethane-chloride inversion]].		*How to for [[Using_metadynamics_to_train_a_machine-learned_force_field \| training a machine-learned force field (MLFF) using metadynamics for chloromethane-chloride inversion]].

	=== Tutorials ===		=== Tutorials ===

Csheldon at 10:10, 17 June 2026

2026-06-17T10:10:47Z

← Older revision		Revision as of 10:10, 17 June 2026
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	=== How to ===		=== How to ===
	*[[Constrained molecular dynamics calculations]].
	*[[Biased molecular dynamics calculations]]
	*[[Interface pinning calculations]].
	*[[Metadynamics calculations]].
	**[[Nuclephile_Substitution_CH3Cl_-_mMD1 \| Chemical reaction using metadynamics - part 1]]		**[[Nuclephile_Substitution_CH3Cl_-_mMD1 \| Chemical reaction using metadynamics - part 1]]
	**[[Nuclephile_Substitution_CH3Cl_-_mMD2 \| Chemical reaction using metadynamics - part 2]]		**[[Nuclephile_Substitution_CH3Cl_-_mMD2 \| Chemical reaction using metadynamics - part 2]]
	**[[Nuclephile_Substitution_CH3Cl_-_mMD3 \| Chemical reaction using metadynamics - part 3]]		**[[Nuclephile_Substitution_CH3Cl_-_mMD3 \| Chemical reaction using metadynamics - part 3]]
	**How to for [[Using_metadynamics_to_train_a_machine-learned_force_field \| training a machine-learned force field (MLFF) using metadynamics for chloromethane-chloride inversion]].		**How to for [[Using_metadynamics_to_train_a_machine-learned_force_field \| training a machine-learned force field (MLFF) using metadynamics for chloromethane-chloride inversion]].
	*[[Blue moon ensemble calculations]].
	*[[Slow-growth approach calculations]].
	*[[Thermodynamic integration calculations]].

	=== Tutorials ===		=== Tutorials ===

← Older revision		Revision as of 10:18, 17 June 2026
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	*''Statistical Mechanics: Theory and Molecular Simulation'' by M. Tuckerman {{Cite\|tuckerman:book:2023}}.		*''Statistical Mechanics: Theory and Molecular Simulation'' by M. Tuckerman {{Cite\|tuckerman:book:2023}}.
	*''Understanding Molecular Simulation - From Algorithms to Applications'' by D. Frenkel and B. Smit {{Cite\|frenkel:smit:2023}}.		*''Understanding Molecular Simulation - From Algorithms to Applications'' by D. Frenkel and B. Smit {{Cite\|frenkel:smit:2023}}.

	~~=== How to ===~~
	*[[Nuclephile_Substitution_CH3Cl_-_mMD1 \| Chemical reaction using metadynamics - part 1]]
	*[[Nuclephile_Substitution_CH3Cl_-_mMD2 \| Chemical reaction using metadynamics - part 2]]
	*[[Nuclephile_Substitution_CH3Cl_-_mMD3 \| Chemical reaction using metadynamics - part 3]]
	*How to for [[Using_metadynamics_to_train_a_machine-learned_force_field \| training a machine-learned force field (MLFF) using metadynamics for chloromethane-chloride inversion]].

	=== Tutorials ===		=== Tutorials ===

← Older revision		Revision as of 14:09, 22 July 2026
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	== Thermodynamic integration ==		== Thermodynamic integration ==
	[[File:~~thermodynamic_integration~~.png\|250px\|thumb\|right\|Thermodynamic integration allows integration from a non-interacting system (λ = 0) to an interacting system (λ = 1). E.g., between a harmonic and an anharmonic system.]]		[[File:Thermodynamic_integration.png\|250px\|thumb\|right\|Thermodynamic integration allows integration from a non-interacting system (λ = 0) to an interacting system (λ = 1). E.g., between a harmonic and an anharmonic system.]]
	In the [[Thermodynamic integration\|thermodynamic integration]] method,{{cite\|dorner:PRL:2018}}{{Cite\|kirkwood:jcp:1935}} the energy differences of a fully interacting and non-interacting system are calculated. This is achieved by making the potential energy depend on a coupling parameter and defining the free energy as a smooth integral over the potential energy along this coupling parameter. As the reference state for a non-interacting system, usually an [[SCALEE\|ideal gas]] or a [[TILAMBDA\|harmonic solid]] is chosen.		In the [[Thermodynamic integration\|thermodynamic integration]] method,{{cite\|dorner:PRL:2018}}{{Cite\|kirkwood:jcp:1935}} the energy differences of a fully interacting and non-interacting system are calculated. This is achieved by making the potential energy depend on a coupling parameter and defining the free energy as a smooth integral over the potential energy along this coupling parameter. As the reference state for a non-interacting system, usually an [[SCALEE\|ideal gas]] or a [[TILAMBDA\|harmonic solid]] is chosen.

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	== Constrained molecular dynamics ==		== Constrained molecular dynamics ==
	[[File:~~constrained_MD~~.png\|250px\|thumb\|right\|Selected geometric parameters in this hydrogen cyanide isomerization to hydrogen isocyanide reaction are constrained to model the transition state. R<sub>1</sub> is the C-H bond, R<sub>2</sub> is the C-N bond, and R<sub>3</sub> is the N-H bond.]]		[[File:Constrained_MD.png\|250px\|thumb\|right\|Selected geometric parameters in this hydrogen cyanide isomerization to hydrogen isocyanide reaction are constrained to model the transition state. R<sub>1</sub> is the C-H bond, R<sub>2</sub> is the C-N bond, and R<sub>3</sub> is the N-H bond.]]
	In [[Constrained molecular dynamics\|constrained molecular dynamics]] selected geometric parameters are constrained during the calculations using the {{FILE\|ICONST}} file. This is achieved by extending the Lagrangian with a term incorporating the desired constraints ([[Constrained molecular dynamics\|SHAKE algorithm]]{{cite\|ryckaertt:jcp:1977}}) directly. This method can be used on its own to support molecular dynamics calculations but some of the methods on this page also incorporate constraints via the same methodology.		In [[Constrained molecular dynamics\|constrained molecular dynamics]] selected geometric parameters are constrained during the calculations using the {{FILE\|ICONST}} file. This is achieved by extending the Lagrangian with a term incorporating the desired constraints ([[Constrained molecular dynamics\|SHAKE algorithm]]{{cite\|ryckaertt:jcp:1977}}) directly. This method can be used on its own to support molecular dynamics calculations but some of the methods on this page also incorporate constraints via the same methodology.
	*[[Constrained molecular dynamics]].		*[[Constrained molecular dynamics]].
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	== Biased molecular dynamics ==		== Biased molecular dynamics ==
	[[File:~~umbrella_sampling~~.png\|250px\|thumb\|right\|In biased MD, a biased potential can be used to pin the system to given configuration (i.e., uncommon configurations), e.g., in umbrella sampling.]]		[[File:Umbrella_sampling.png\|250px\|thumb\|right\|In biased MD, a biased potential can be used to pin the system to given configuration (i.e., uncommon configurations), e.g., in umbrella sampling.]]
	[[Biased molecular dynamics]] refers to methods introducing a biased potential {{cite\|frenkel:ap-book:2002}}. In one of this method's most popular representatives, the umbrella sampling or umbrella integration, the biased potential is used to pin the system to given configurations. This way the sampling of a system is greatly enhanced and thermodynamic methods with proper statistics become accessible. Although some of the methods on this page also use biased potentials they have differences in the usage of the potential and hence belong in their categories.		[[Biased molecular dynamics]] refers to methods introducing a biased potential {{cite\|frenkel:ap-book:2002}}. In one of this method's most popular representatives, the umbrella sampling or umbrella integration, the biased potential is used to pin the system to given configurations. This way the sampling of a system is greatly enhanced and thermodynamic methods with proper statistics become accessible. Although some of the methods on this page also use biased potentials they have differences in the usage of the potential and hence belong in their categories.

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	== Blue moon ensemble ==		== Blue moon ensemble ==
	[[File:~~blue_moon~~.png\|250px\|thumb\|right\|In the Blue moon ensemble method, the free energy profile along a chosen reaction coordiante (x) can be calculated by calculating the unbiased free-energy derivative.]]		[[File:Blue_moon.png\|250px\|thumb\|right\|In the Blue moon ensemble method, the free energy profile along a chosen reaction coordiante (x) can be calculated by calculating the unbiased free-energy derivative.]]
	The [[Blue moon ensemble\|blue moon ensemble]] method{{Cite\|carter:kapral:1989}} is designed to calculate the free energy profile along the path of selected reaction coordinates. It also employs constraining of the atoms during molecular dynamics ([[Constrained molecular dynamics\|SHAKE algorithm]]{{cite\|ryckaertt:jcp:1977}}). The term "[[LBLUEOUT\|blue moon]]" refers to rare events such as the "moon turning blue".		The [[Blue moon ensemble\|blue moon ensemble]] method{{Cite\|carter:kapral:1989}} is designed to calculate the free energy profile along the path of selected reaction coordinates. It also employs constraining of the atoms during molecular dynamics ([[Constrained molecular dynamics\|SHAKE algorithm]]{{cite\|ryckaertt:jcp:1977}}). The term "[[LBLUEOUT\|blue moon]]" refers to rare events such as the "moon turning blue".

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	== Interface pinning ==		== Interface pinning ==
	[[File:~~water_ice_interface~~.png\|250px\|thumb\|right\|Interface pinning is used to model two different phases on the same system in the same cell, e.g., the water-ice interface.]]		[[File:Water_ice_interface.png\|250px\|thumb\|right\|Interface pinning is used to model two different phases on the same system in the same cell, e.g., the water-ice interface.]]
	In [[Interface pinning\|interface pinning]],{{cite\|pedersen:prb:13}} two different phases of the same system are simulated in a single simulation box. The goal of this method is to look for the right conditions where both phases would coexist, which corresponds to a phase transition point. Above a transition point, the whole system would quickly turn into one phase and below the point into the other phase. With this, the transition point could be searched via bi-sectioning, but this would involve a huge effort. To accelerate the search for a phase transition point the order parameters are used to control the composition of the box and the force that would drive the system towards equilibrium is used to estimate the phase transition point.		In [[Interface pinning\|interface pinning]],{{cite\|pedersen:prb:13}} two different phases of the same system are simulated in a single simulation box. The goal of this method is to look for the right conditions where both phases would coexist, which corresponds to a phase transition point. Above a transition point, the whole system would quickly turn into one phase and below the point into the other phase. With this, the transition point could be searched via bi-sectioning, but this would involve a huge effort. To accelerate the search for a phase transition point the order parameters are used to control the composition of the box and the force that would drive the system towards equilibrium is used to estimate the phase transition point.