Category:Advanced molecular-dynamics sampling - Revision history

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 ===

Csheldon: /* Metadynamics */

2026-06-09T12:29:38Z

Metadynamics

← Older revision		Revision as of 12:29, 9 June 2026
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	*[[Metadynamics]].		*[[Metadynamics]].
	*[[Metadynamics calculations]].		*[[Metadynamics calculations]].
			*[[Using metadynamics to train a machine-learned force field]]

	<div style="clear:both;"></div>		<div style="clear:both;"></div>

Csheldon: /* How to */

2026-06-09T11:44:07Z

How to

← Older revision		Revision as of 11:44, 9 June 2026
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	**[[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]].		*[[Blue moon ensemble calculations]].
	*[[Slow-growth approach calculations]].		*[[Slow-growth approach calculations]].

Csheldon at 08:36, 9 June 2026

2026-06-09T08:36:47Z

Csheldon at 08:35, 9 June 2026

2026-06-09T08:35:08Z

← Older revision		Revision as of 08:35, 9 June 2026
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	*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]		*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]
	*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]		*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]

			== 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.]]
			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 calculations]]

			<div style="clear:both;"></div>

	== Constrained molecular dynamics ==		== Constrained molecular dynamics ==
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	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	== 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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	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	== ~~Thermodynamic integration~~ ==		=== Metadynamics ===
	[[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.

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

	~~<div style="clear:both;"></div>~~

	~~== Metadynamics~~ ==
	[[File:Metadynamics.png\|250px\|thumb\|right\|In metadynamics, a biased potential (coloured lines) is applied along selected collective variables (x), cf. potential V, to gradually fill free-energy minima and allows the system to cross barriers and explore the potential energy surface, including other minima.]]		[[File:Metadynamics.png\|250px\|thumb\|right\|In metadynamics, a biased potential (coloured lines) is applied along selected collective variables (x), cf. potential V, to gradually fill free-energy minima and allows the system to cross barriers and explore the potential energy surface, including other minima.]]
	In [[Metadynamics\|metadynamics]],{{cite\|laio:pnas:02}}{{cite\|iannuzzi:prl:03}} a [[PENALTYPOT\|biased potential]] that acts on a few selected geometric parameters (collective variables) is added to the Hamiltonian of a system. The biased potential is constantly built up during a molecular dynamics run by adding [[HILLS_H\|Gaussian hills]] at selected time increments. This way even deep potential minima can be filled and overcome.		In [[Metadynamics\|metadynamics]],{{cite\|laio:pnas:02}}{{cite\|iannuzzi:prl:03}} a [[PENALTYPOT\|biased potential]] that acts on a few selected geometric parameters (collective variables) is added to the Hamiltonian of a system. The biased potential is constantly built up during a molecular dynamics run by adding [[HILLS_H\|Gaussian hills]] at selected time increments. This way even deep potential minima can be filled and overcome.
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	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	== 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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	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	== Slow-growth approach ==		=== Slow-growth approach ===
	[[File:Slow_growth_md.png\|250px\|thumb\|right\|In the slow-growth approach, a reaction pathway can be followed linearly on a reaction coordinate (x) from the reactant state (λ = 0) to the target state (λ = 1).]]		[[File:Slow_growth_md.png\|250px\|thumb\|right\|In the slow-growth approach, a reaction pathway can be followed linearly on a reaction coordinate (x) from the reactant state (λ = 0) to the target state (λ = 1).]]
	In the [[Slow-growth approach\|slow-growth approach]],{{Cite\|woo:ziegler:1997}} the free energy profile is scanned along a reaction coordinate. The scanning is done by linearly changing the reaction coordinate from that of the reactant state to that of a transition or product state via [[Constrained molecular dynamics\|constrained molecular dynamics]] ([[Constrained molecular dynamics\|SHAKE algorithm]]{{cite\|ryckaertt:jcp:1977}}).		In the [[Slow-growth approach\|slow-growth approach]],{{Cite\|woo:ziegler:1997}} the free energy profile is scanned along a reaction coordinate. The scanning is done by linearly changing the reaction coordinate from that of the reactant state to that of a transition or product state via [[Constrained molecular dynamics\|constrained molecular dynamics]] ([[Constrained molecular dynamics\|SHAKE algorithm]]{{cite\|ryckaertt:jcp:1977}}).

Csheldon at 08:34, 9 June 2026

2026-06-09T08:34:05Z

← Older revision		Revision as of 08:34, 9 June 2026
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	*[[:Category:Advanced molecular-dynamics sampling#Biased molecular dynamics\|Biased molecular dynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Biased molecular dynamics\|Biased molecular dynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Thermodynamic integration\|Thermodynamic integration]]		*[[:Category:Advanced molecular-dynamics sampling#Thermodynamic integration\|Thermodynamic integration]]
	*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]
	*[[:Category:Advanced molecular-dynamics sampling#Metadynamics\|Metadynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Metadynamics\|Metadynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]		*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]
			*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]

	== Constrained molecular dynamics ==		== Constrained molecular dynamics ==
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	*[[Thermodynamic integration calculations]]		*[[Thermodynamic integration calculations]]

	~~<div style="clear:both;"></div>~~

	~~== 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.]]~~
	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.

	~~[[Interface pinning\|Interface pinning]] is usually used to determine melting points (solid-liquid interface).~~
	*[[Interface pinning]].
	*[[Interface pinning calculations]].
	<div style="clear:both;"></div>		<div style="clear:both;"></div>

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	*[[Slow-growth approach calculations]].		*[[Slow-growth approach calculations]].

			<div style="clear:both;"></div>

			== 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.]]
			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.

			[[Interface pinning\|Interface pinning]] is usually used to determine melting points (solid-liquid interface).
			*[[Interface pinning]].
			*[[Interface pinning calculations]].
	<div style="clear:both;"></div>		<div style="clear:both;"></div>

Csheldon at 08:33, 9 June 2026

2026-06-09T08:33:35Z

← Older revision		Revision as of 08:33, 9 June 2026
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	*[[:Category:Advanced molecular-dynamics sampling#Constrained molecular dynamics\|Constrained molecular dynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Constrained molecular dynamics\|Constrained molecular dynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Biased molecular dynamics\|Biased molecular dynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Biased molecular dynamics\|Biased molecular dynamics]]
			*[[:Category:Advanced molecular-dynamics sampling#Thermodynamic integration\|Thermodynamic integration]]
	*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]		*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]
	*[[:Category:Advanced molecular-dynamics sampling#Metadynamics\|Metadynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Metadynamics\|Metadynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]		*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]
	*[[:Category:Advanced molecular-dynamics sampling#Thermodynamic integration\|Thermodynamic integration]]

	== Constrained molecular dynamics ==		== Constrained molecular dynamics ==

← 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 08:33, 9 June 2026
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	*[[:Category:Advanced molecular-dynamics sampling#Constrained molecular dynamics\|Constrained molecular dynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Constrained molecular dynamics\|Constrained molecular dynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Biased molecular dynamics\|Biased molecular dynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Biased molecular dynamics\|Biased molecular dynamics]]
			*[[:Category:Advanced molecular-dynamics sampling#Thermodynamic integration\|Thermodynamic integration]]
	*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]		*[[:Category:Advanced molecular-dynamics sampling#Interface pinning\|Interface pinning]]
	*[[:Category:Advanced molecular-dynamics sampling#Metadynamics\|Metadynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Metadynamics\|Metadynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]		*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]
	*[[:Category:Advanced molecular-dynamics sampling#Thermodynamic integration\|Thermodynamic integration]]

	== Constrained molecular dynamics ==		== Constrained molecular dynamics ==

← Older revision		Revision as of 08:36, 9 June 2026
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	In a [[:Category:Molecular dynamics\|molecular-dynamics]] (MD) calculation, we are often interested in rare events or specific transitions. '''Advanced molecular-dynamics sampling''' helps to capture these during an MD run within a feasible simulation time. There are several different available methods:		In a [[:Category:Molecular dynamics\|molecular-dynamics]] (MD) calculation, we are often interested in rare events or specific transitions. '''Advanced molecular-dynamics sampling''' helps to capture these during an MD run within a feasible simulation time. There are several different available methods:
			*[[:Category:Advanced molecular-dynamics sampling#Thermodynamic integration\|Thermodynamic integration]]
	*[[:Category:Advanced molecular-dynamics sampling#Constrained molecular dynamics\|Constrained molecular dynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Constrained molecular dynamics\|Constrained molecular dynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Biased molecular dynamics\|Biased molecular dynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Biased molecular dynamics\|Biased molecular dynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Thermodynamic integration\|Thermodynamic integration]]
	*[[:Category:Advanced molecular-dynamics sampling#Metadynamics\|Metadynamics]]		*[[:Category:Advanced molecular-dynamics sampling#Metadynamics\|Metadynamics]]
	*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]		*[[:Category:Advanced molecular-dynamics sampling#Blue moon ensemble\|Blue moon ensemble]]
			*[[: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]]

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	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	=== 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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	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	=== Metadynamics ===		== Metadynamics ==
	[[File:Metadynamics.png\|250px\|thumb\|right\|In metadynamics, a biased potential (coloured lines) is applied along selected collective variables (x), cf. potential V, to gradually fill free-energy minima and allows the system to cross barriers and explore the potential energy surface, including other minima.]]		[[File:Metadynamics.png\|250px\|thumb\|right\|In metadynamics, a biased potential (coloured lines) is applied along selected collective variables (x), cf. potential V, to gradually fill free-energy minima and allows the system to cross barriers and explore the potential energy surface, including other minima.]]
	In [[Metadynamics\|metadynamics]],{{cite\|laio:pnas:02}}{{cite\|iannuzzi:prl:03}} a [[PENALTYPOT\|biased potential]] that acts on a few selected geometric parameters (collective variables) is added to the Hamiltonian of a system. The biased potential is constantly built up during a molecular dynamics run by adding [[HILLS_H\|Gaussian hills]] at selected time increments. This way even deep potential minima can be filled and overcome.		In [[Metadynamics\|metadynamics]],{{cite\|laio:pnas:02}}{{cite\|iannuzzi:prl:03}} a [[PENALTYPOT\|biased potential]] that acts on a few selected geometric parameters (collective variables) is added to the Hamiltonian of a system. The biased potential is constantly built up during a molecular dynamics run by adding [[HILLS_H\|Gaussian hills]] at selected time increments. This way even deep potential minima can be filled and overcome.
Line 44:		Line 45:
	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	=== 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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	<div style="clear:both;"></div>		<div style="clear:both;"></div>

	=== Slow-growth approach ===		== Slow-growth approach ==
	[[File:Slow_growth_md.png\|250px\|thumb\|right\|In the slow-growth approach, a reaction pathway can be followed linearly on a reaction coordinate (x) from the reactant state (λ = 0) to the target state (λ = 1).]]		[[File:Slow_growth_md.png\|250px\|thumb\|right\|In the slow-growth approach, a reaction pathway can be followed linearly on a reaction coordinate (x) from the reactant state (λ = 0) to the target state (λ = 1).]]
	In the [[Slow-growth approach\|slow-growth approach]],{{Cite\|woo:ziegler:1997}} the free energy profile is scanned along a reaction coordinate. The scanning is done by linearly changing the reaction coordinate from that of the reactant state to that of a transition or product state via [[Constrained molecular dynamics\|constrained molecular dynamics]] ([[Constrained molecular dynamics\|SHAKE algorithm]]{{cite\|ryckaertt:jcp:1977}}).		In the [[Slow-growth approach\|slow-growth approach]],{{Cite\|woo:ziegler:1997}} the free energy profile is scanned along a reaction coordinate. The scanning is done by linearly changing the reaction coordinate from that of the reactant state to that of a transition or product state via [[Constrained molecular dynamics\|constrained molecular dynamics]] ([[Constrained molecular dynamics\|SHAKE algorithm]]{{cite\|ryckaertt:jcp:1977}}).