Biased molecular dynamics - Revision history

Huebsch: /* How to */

2025-10-21T13:14:23Z

How to

← Older revision		Revision as of 13:14, 21 October 2025
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	* For a biased molecular dynamics run with [[Andersen thermostat]], one has to:		* For a biased molecular dynamics run with [[Andersen thermostat]], one has to:
	#Set the standard MD-related tags: {{TAG\|IBRION}}=0, {{TAG\|TEBEG}}, {{TAG\|POTIM}}, and {{TAG\|NSW}}.		#Set the standard MD-related tags: {{TAG\|IBRION}}=0, {{TAG\|TEBEG}}, {{TAG\|POTIM}}, and {{TAG\|NSW}}.
	#Set {{TAG\|MDALGO}}=1 (or {{TAG\|MDALGO}}=11 in VASP 5.x), and choose an appropriate setting for {{TAG\|ANDERSEN_PROB}}.		#Choose thermostat:
			## Set {{TAG\|MDALGO}}=1 (or {{TAG\|MDALGO}}=11 in VASP 5.x), and choose an appropriate setting for {{TAG\|ANDERSEN_PROB}}.
			## Set {{TAG\|MDALGO}}=2 (or {{TAG\|MDALGO}}=21 in VASP 5.x), and choose an appropriate setting for {{TAG\|SMASS}}.
	#In order to avoid updating of the bias potential, set {{TAG\|HILLS_BIN}}={{TAG\|NSW}}.		#In order to avoid updating of the bias potential, set {{TAG\|HILLS_BIN}}={{TAG\|NSW}}.
	#Define collective variables in the {{FILE\|ICONST}}-file, and set the <tt>STATUS</tt> parameter for the collective variables to 5.		#Define collective variables in the {{FILE\|ICONST}}-file, and set the <tt>STATUS</tt> parameter for the collective variables to 5.
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	The values of all collective variables for each MD step are listed in the {{FILE\|REPORT}} file. Check the lines after the string <tt>Metadynamics</tt>.		The values of all collective variables for each MD step are listed in the {{FILE\|REPORT}} file. Check the lines after the string <tt>Metadynamics</tt>.


	== References ==		== References ==

Huebsch at 12:53, 21 October 2025

2025-10-21T12:53:47Z

← Older revision		Revision as of 12:53, 21 October 2025
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	One of the most popular methods using bias potentials is umbrella sampling{{cite\|torrie:jcp:1977}}. This method uses a bias potential to enhance sampling of ξ in regions with low ''P''(ξ<sub>''i''</sub>), e.g., transition regions of chemical reactions. The correct distributions are recovered afterward using the equation for <math>\langle A \rangle_{H}</math> above.		One of the most popular methods using bias potentials is umbrella sampling{{cite\|torrie:jcp:1977}}. This method uses a bias potential to enhance sampling of ξ in regions with low ''P''(ξ<sub>''i''</sub>), e.g., transition regions of chemical reactions. The correct distributions are recovered afterward using the equation for <math>\langle A \rangle_{H}</math> above.

			=== How to ===

			For a description of biased molecular dynamics see {{TAG\|Biased molecular dynamics}}.

			* For a biased molecular dynamics run with [[Andersen thermostat]], one has to:
			#Set the standard MD-related tags: {{TAG\|IBRION}}=0, {{TAG\|TEBEG}}, {{TAG\|POTIM}}, and {{TAG\|NSW}}.
			#Set {{TAG\|MDALGO}}=1 (or {{TAG\|MDALGO}}=11 in VASP 5.x), and choose an appropriate setting for {{TAG\|ANDERSEN_PROB}}.
			#In order to avoid updating of the bias potential, set {{TAG\|HILLS_BIN}}={{TAG\|NSW}}.
			#Define collective variables in the {{FILE\|ICONST}}-file, and set the <tt>STATUS</tt> parameter for the collective variables to 5.
			#Define the bias potential in the {{FILE\|PENALTYPOT}} file if necessary.

			The values of all collective variables for each MD step are listed in the {{FILE\|REPORT}} file. Check the lines after the string <tt>Metadynamics</tt>.


	== References ==		== References ==

Karsai: Removed redirect to Category:Biased molecular dynamics

2024-10-16T11:40:55Z

Removed redirect to Category:Biased molecular dynamics

← Older revision		Revision as of 11:40, 16 October 2024
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	~~#REDIRECT~~ [[:Category:Biased molecular dynamics]]		''Biased molecular dynamics''' (MD) refers to advanced [[:Category:Molecular dynamics\|MD-simulation methods]] that introduce a ''bias potential''. One of the most important purposes of using bias potentials is to enhance the sampling of phase space with low probability density (e.g., transition regions of chemical reactions). Depending on the type of sampling and in combination with the corresponding statistical methods one then has access to important thermodynamic quantities like, e.g., free energies. Biased molecular dynamics comes in very different flavors such as, e.g., umbrella sampling{{cite\|torrie:jcp:1977}} and umbrella integration{{cite\|kaestner:jcp:2005}}, to name a few. For a comprehensive description (especially about umbrella sampling), we refer the interested user to Ref. {{cite\|frenkel:ap-book:2002}} written by D. Frenkel and B. Smit.

			The probability density for a geometric parameter ξ of the system driven by a Hamiltonian
			:<math>
			H(q,p) = T(p) + V(q), \;
			</math>
			with ''T''(''p''), and ''V''(''q'') being kinetic, and potential energies, respectively, can be written as
			:<math>
			P(\xi_i)=\frac{\int\delta\Big(\xi(q)-\xi_i\Big) \exp\left\{-H(q,p)/k_B\,T\right\} dq\,dp}{\int \exp\left\{-H(q,p)/k_B\,T\right\}dq\,dp} =
			\langle\delta\Big(\xi(q)-\xi_i\Big)\rangle_{H}.
			</math>
			The term <math>\langle X \rangle_H</math> stands for a thermal average of quantity ''X'' evaluated for the system driven by the Hamiltonian ''H''.

			If the system is modified by adding a bias potential <math>\tilde{V}(\xi)</math> acting on one or multiple selected internal coordinates of the system ξ=ξ(''q''), the Hamiltonian takes the form
			:<math>
			\tilde{H}(q,p) = H(q,p) + \tilde{V}(\xi),
			</math>
			and the probability density of ξ in the biased ensemble is
			:<math>
			\tilde{P}(\xi_i)= \frac{\int \delta\Big(\xi(q)-\xi_i\Big) \exp\left\{-\tilde{H}(q,p)/k_B\,T\right\} dq\,dp}{\int \exp\left\{-\tilde{H}(q,p)/k_B\,T\right\}dq\,dp} = \langle\delta\Big(\xi(q)-\xi_i\Big)\rangle_{\tilde{H}}.
			</math>
			It can be shown that the biased and unbiased averages are related via
			:<math>
			P(\xi_i)=\tilde{P}(\xi_i) \frac{\exp\left\{\tilde{V}(\xi)/k_B\,T\right\}}{\langle \exp\left\{\tilde{V}(\xi)/k_B\,T\right\} \rangle_{\tilde{H}}}.
			</math>
			More generally, an observable
			:<math>
			\langle A \rangle_{H} = \frac{\int A(q) \exp\left\{-H(q,p)/k_B\,T\right\} dq\,dp}{\int \exp\left\{-H(q,p)/k_B\,T\right\}dq\,dp}
			</math>
			can be expressed in terms of thermal averages within the biased ensemble as
			:<math>
			\langle A \rangle_{H} =\frac{\langle A(q) \,\exp\left\{\tilde{V}(\xi)/k_B\,T\right\} \rangle_{\tilde{H}}}{\langle \exp\left\{\tilde{V}(\xi)/k_B\,T\right\} \rangle_{\tilde{H}}}.
			</math>

			One of the most popular methods using bias potentials is umbrella sampling{{cite\|torrie:jcp:1977}}. This method uses a bias potential to enhance sampling of ξ in regions with low ''P''(ξ<sub>''i''</sub>), e.g., transition regions of chemical reactions. The correct distributions are recovered afterward using the equation for <math>\langle A \rangle_{H}</math> above.

			== References ==
			<references/>

			[[Category:Advanced molecular-dynamics sampling]][[Category:Theory]]

Huebsch: Redirected page to Category:Biased molecular dynamics

2023-04-24T09:38:14Z

Redirected page to Category:Biased molecular dynamics

Show changes

Huebsch at 09:32, 24 April 2023

2023-04-24T09:32:12Z

Show changes

Tbucko at 08:44, 11 April 2023

2023-04-11T08:44:23Z

← Older revision		Revision as of 08:44, 11 April 2023
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	where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.		where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.
	The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.		The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.
	Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|SPRING_V0}}.		Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via the parameter {{TAG\|SPRING_V0}}.
	The number of items defined via {{TAG\|SPRING_K}}, {{TAG\|SPRING_R0}}, and {{TAG\|SPRING_V0}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.		The number of items defined via {{TAG\|SPRING_K}}, {{TAG\|SPRING_R0}}, and {{TAG\|SPRING_V0}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.
	This form of bias potential is employed in several simulation protocols, such as the umbrella sampling<ref name="Torrie77"/>, umbrella integration, or steered MD, and is useful also in cases where the <math>\xi_{\mu}</math> values need restrained.		This form of bias potential is employed in several simulation protocols, such as the umbrella sampling<ref name="Torrie77"/>, umbrella integration, or steered MD, and is useful also in cases where the <math>\xi_{\mu}</math> values need restrained.

Tbucko at 08:30, 11 April 2023

2023-04-11T08:30:03Z

← Older revision		Revision as of 08:30, 11 April 2023
Line 52:		Line 52:
	where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.		where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.
	The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.		The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.
	Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|~~SPRING_V~~}}.		Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|SPRING_V0}}.
	The number of items defined via {{TAG\|SPRING_K}}, {{TAG\|SPRING_R0}}, and {{TAG\|~~SPRING_V~~}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.		The number of items defined via {{TAG\|SPRING_K}}, {{TAG\|SPRING_R0}}, and {{TAG\|SPRING_V0}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.
	This form of bias potential is employed in several simulation protocols, such as the umbrella sampling<ref name="Torrie77"/>, umbrella integration, or steered MD, and is useful also in cases where the <math>\xi_{\mu}</math> values need restrained.		This form of bias potential is employed in several simulation protocols, such as the umbrella sampling<ref name="Torrie77"/>, umbrella integration, or steered MD, and is useful also in cases where the <math>\xi_{\mu}</math> values need restrained.

Tbucko at 08:24, 11 April 2023

2023-04-11T08:24:34Z

Tbucko at 07:54, 11 April 2023

2023-04-11T07:54:42Z

← Older revision		Revision as of 07:54, 11 April 2023
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	\tilde{V}(\xi_1,\dots,\xi_{M_8}) = \sum_{\mu=1}^{M}\frac{1}{2}\kappa_{\mu} (\xi_{\mu}(q)-\xi_{0\mu})^2 \;		\tilde{V}(\xi_1,\dots,\xi_{M_8}) = \sum_{\mu=1}^{M}\frac{1}{2}\kappa_{\mu} (\xi_{\mu}(q)-\xi_{0\mu})^2 \;
	</math>		</math>
	where the sum runs all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the status to 8.		where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the status to 8.
	The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.		The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.
	Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|SPRING_V}}.		Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|SPRING_V}}.
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	\tilde{V}(\xi_1,\dots,\xi_{M_4}) = \sum_{\mu=1}^{M_4}\frac{A_{\mu}}{1+\text{exp}\left [-D_{\mu}(\frac{\xi(q)}{\xi_{0\mu}} -1) \right ]} \;		\tilde{V}(\xi_1,\dots,\xi_{M_4}) = \sum_{\mu=1}^{M_4}\frac{A_{\mu}}{1+\text{exp}\left [-D_{\mu}(\frac{\xi(q)}{\xi_{0\mu}} -1) \right ]} \;
	</math>		</math>
	where the sum runs all (<math>M_4</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the status to 4.		where the sum runs over all (<math>M_4</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the status to 4.
	The parameters of the potential, <math>A_{\mu}</math> (the height of step), <math>D_{\mu}</math> (controlling the slope around the point <math>\xi_{0\mu}</math>), and <math>\xi_{0\mu}</math> (position of the step), are defined, respectively,		The parameters of the potential, <math>A_{\mu}</math> (the height of step), <math>D_{\mu}</math> (controlling the slope around the point <math>\xi_{0\mu}</math>), and <math>\xi_{0\mu}</math> (position of the step), are defined, respectively,
	via the keywords {{TAG\|FBIAS_A}}, {{TAG\|FBIAS_D}}, and {{TAG\|FBIAS_R0}} in {{FILE\|INCAR}}.		via the keywords {{TAG\|FBIAS_A}}, {{TAG\|FBIAS_D}}, and {{TAG\|FBIAS_R0}} in {{FILE\|INCAR}}.

Tbucko at 09:16, 7 April 2023

2023-04-07T09:16:44Z

← Older revision		Revision as of 09:16, 7 April 2023
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	*sum of Fermi-like step functions (see curve (b) on the plot above)		*sum of Fermi-like step functions (see curve (b) on the plot above)
	:<math>		:<math>
	\tilde{V}(\xi_1,\dots,\xi_{M_4}) = \sum_{\mu=1}^{M_4}\frac{A_{\mu}}{1+\text{exp}\left [-D_{\mu}\frac{\xi(q)}{\xi_{0\mu}} -1 \right ]} \;		\tilde{V}(\xi_1,\dots,\xi_{M_4}) = \sum_{\mu=1}^{M_4}\frac{A_{\mu}}{1+\text{exp}\left [-D_{\mu}(\frac{\xi(q)}{\xi_{0\mu}} -1) \right ]} \;
	</math>		</math>
	where the sum runs all (<math>M_4</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the status to 4.		where the sum runs all (<math>M_4</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the status to 4.
Line 93:		Line 93:
	4.32824726 8.75151396 7.80743202		4.32824726 8.75151396 7.80743202
	6.84157897 6.18713289 4.46842049		6.84157897 6.18713289 4.46842049

			* due to weak interactions between CH<math>_3</math>Cl and Cl<math>^-</math>, the complex can collapse at high temperature. This can be avoided by setting an upper bound for the length of the non-bonding Cl...C interactions, which can can conveniently be achieved by using a Fermi-shaped bias potential. To this end, we need to define the Cl...C distance (distance between the atoms 1 and 5) as a coordinate with status 4 in the {{FILE\|ICONST}}-file:

			R 1 5 4

			Next, we need to specify the bias potential parameters {{TAG\|FBIAS_A}}, {{TAG\|FBIAS_D}}, and {{TAG\|FBIAS_R0}} in the {{FILE\|ICONST}}-file. Since the bias potential acts only on one internal coordinate, we need to provide only one single number for each of these flags. As shown in Fig.3, the setting

			FBIAS_A = 1
			FBIAS_D = 50
			FBIAS_R0 = 3.5

			ensures that repulsive bias forces steeply increase when the C...Cl distance is increased beyond about 3.2 A, which would in effect cause shortening of the distance in next MD step. Notice that the bias force is essentially negligible for distances below 3 A.
			A careful adjustment of <math>A</math> and <math>D</math> is needed to ensure that (i) the bias force is large enough to effectively limit the value of <math>\xi</math>, and (ii) the interval of <math>\xi</math> values for which the bias forces are significant is broad enough to avoid its overcoming via random fluctuations.
			A suitable setting can be found by inspecting the analytical expression for the potential from which it is obvious that the maximal bias force of <math>\frac{D\,A}{4\xi_0}</math> is exerted on the system at the point <math>\xi = \xi_{0}</math>.

	== Andersen thermostat ==		== Andersen thermostat ==
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	#In order to avoid updating of the bias potential, set {{TAG\|HILLS_BIN}}={{TAG\|NSW}}		#In order to avoid updating of the bias potential, set {{TAG\|HILLS_BIN}}={{TAG\|NSW}}
	#Define collective variables in the {{FILE\|ICONST}}-file, and set the <tt>STATUS</tt> parameter for the collective variables to 5		#Define collective variables in the {{FILE\|ICONST}}-file, and set the <tt>STATUS</tt> parameter for the collective variables to 5
	#Define the bias potential in the {{FILE\|PENALTYPOT}}-file		#Define the bias potential in the {{FILE\|PENALTYPOT}}-file

	== Nose-Hoover thermostat ==		== Nose-Hoover thermostat ==

← Older revision		Revision as of 12:53, 21 October 2025
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	One of the most popular methods using bias potentials is umbrella sampling{{cite\|torrie:jcp:1977}}. This method uses a bias potential to enhance sampling of ξ in regions with low ''P''(ξ<sub>''i''</sub>), e.g., transition regions of chemical reactions. The correct distributions are recovered afterward using the equation for <math>\langle A \rangle_{H}</math> above.		One of the most popular methods using bias potentials is umbrella sampling{{cite\|torrie:jcp:1977}}. This method uses a bias potential to enhance sampling of ξ in regions with low ''P''(ξ<sub>''i''</sub>), e.g., transition regions of chemical reactions. The correct distributions are recovered afterward using the equation for <math>\langle A \rangle_{H}</math> above.

			=== How to ===

			For a description of biased molecular dynamics see {{TAG\|Biased molecular dynamics}}.

			* For a biased molecular dynamics run with [[Andersen thermostat]], one has to:
			#Set the standard MD-related tags: {{TAG\|IBRION}}=0, {{TAG\|TEBEG}}, {{TAG\|POTIM}}, and {{TAG\|NSW}}.
			#Set {{TAG\|MDALGO}}=1 (or {{TAG\|MDALGO}}=11 in VASP 5.x), and choose an appropriate setting for {{TAG\|ANDERSEN_PROB}}.
			#In order to avoid updating of the bias potential, set {{TAG\|HILLS_BIN}}={{TAG\|NSW}}.
			#Define collective variables in the {{FILE\|ICONST}}-file, and set the <tt>STATUS</tt> parameter for the collective variables to 5.
			#Define the bias potential in the {{FILE\|PENALTYPOT}} file if necessary.

			The values of all collective variables for each MD step are listed in the {{FILE\|REPORT}} file. Check the lines after the string <tt>Metadynamics</tt>.


	== References ==		== References ==

← Older revision		Revision as of 08:44, 11 April 2023
Line 52:		Line 52:
	where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.		where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.
	The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.		The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.
	Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|SPRING_V0}}.		Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via the parameter {{TAG\|SPRING_V0}}.
	The number of items defined via {{TAG\|SPRING_K}}, {{TAG\|SPRING_R0}}, and {{TAG\|SPRING_V0}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.		The number of items defined via {{TAG\|SPRING_K}}, {{TAG\|SPRING_R0}}, and {{TAG\|SPRING_V0}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.
	This form of bias potential is employed in several simulation protocols, such as the umbrella sampling<ref name="Torrie77"/>, umbrella integration, or steered MD, and is useful also in cases where the <math>\xi_{\mu}</math> values need restrained.		This form of bias potential is employed in several simulation protocols, such as the umbrella sampling<ref name="Torrie77"/>, umbrella integration, or steered MD, and is useful also in cases where the <math>\xi_{\mu}</math> values need restrained.

← Older revision		Revision as of 08:30, 11 April 2023
Line 52:		Line 52:
	where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.		where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.
	The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.		The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.
	Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|~~SPRING_V~~}}.		Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|SPRING_V0}}.
	The number of items defined via {{TAG\|SPRING_K}}, {{TAG\|SPRING_R0}}, and {{TAG\|~~SPRING_V~~}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.		The number of items defined via {{TAG\|SPRING_K}}, {{TAG\|SPRING_R0}}, and {{TAG\|SPRING_V0}} must be equal to <math>M_8</math>, otherwise the calculation terminates with an error message.
	This form of bias potential is employed in several simulation protocols, such as the umbrella sampling<ref name="Torrie77"/>, umbrella integration, or steered MD, and is useful also in cases where the <math>\xi_{\mu}</math> values need restrained.		This form of bias potential is employed in several simulation protocols, such as the umbrella sampling<ref name="Torrie77"/>, umbrella integration, or steered MD, and is useful also in cases where the <math>\xi_{\mu}</math> values need restrained.

← Older revision		Revision as of 08:24, 11 April 2023
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	\tilde{V}(\xi_1,\dots,\xi_{M_8}) = \sum_{\mu=1}^{M}\frac{1}{2}\kappa_{\mu} (\xi_{\mu}(q)-\xi_{0\mu})^2 \;		\tilde{V}(\xi_1,\dots,\xi_{M_8}) = \sum_{\mu=1}^{M}\frac{1}{2}\kappa_{\mu} (\xi_{\mu}(q)-\xi_{0\mu})^2 \;
	</math>		</math>
	where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the status to 8.		where the sum runs over all (<math>M_8</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 8.
	The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.		The parameters of the potential, <math>\kappa_{\mu}</math> (force constant) and <math>\xi_{0\mu}</math> (minimum of potential), are defined, respectively, via the keywords {{TAG\|SPRING_K}} and {{TAG\|SPRING_R0}} in {{FILE\|INCAR}}.
	Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|SPRING_V}}.		Optionally, it is also possible to change the value of <math>\xi_{0\mu}</math> every MD step at a constant rate defined via parameter {{TAG\|SPRING_V}}.
Line 60:		Line 60:
	\tilde{V}(\xi_1,\dots,\xi_{M_4}) = \sum_{\mu=1}^{M_4}\frac{A_{\mu}}{1+\text{exp}\left [-D_{\mu}(\frac{\xi(q)}{\xi_{0\mu}} -1) \right ]} \;		\tilde{V}(\xi_1,\dots,\xi_{M_4}) = \sum_{\mu=1}^{M_4}\frac{A_{\mu}}{1+\text{exp}\left [-D_{\mu}(\frac{\xi(q)}{\xi_{0\mu}} -1) \right ]} \;
	</math>		</math>
	where the sum runs over all (<math>M_4</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the status to 4.		where the sum runs over all (<math>M_4</math>) coordinates the potential acts upon, which are defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 4.
	The parameters of the potential, <math>A_{\mu}</math> (the height of step), <math>D_{\mu}</math> (controlling the slope around the point <math>\xi_{0\mu}</math>), and <math>\xi_{0\mu}</math> (position of the step), are defined, respectively,		The parameters of the potential, <math>A_{\mu}</math> (the height of step), <math>D_{\mu}</math> (controlling the slope around the point <math>\xi_{0\mu}</math>), and <math>\xi_{0\mu}</math> (position of the step), are defined, respectively,
	via the keywords {{TAG\|FBIAS_A}}, {{TAG\|FBIAS_D}}, and {{TAG\|FBIAS_R0}} in {{FILE\|INCAR}}.		via the keywords {{TAG\|FBIAS_A}}, {{TAG\|FBIAS_D}}, and {{TAG\|FBIAS_R0}} in {{FILE\|INCAR}}.
Line 72:		Line 72:
	where <math>N_5</math> is the number of Gaussian functions and		where <math>N_5</math> is the number of Gaussian functions and
	<math>M_5</math> is the number of coordinates the potential acts upon.		<math>M_5</math> is the number of coordinates the potential acts upon.
	The latter defined in the {{FILE\|ICONST}}-file by setting the status to 5.		The latter defined in the {{FILE\|ICONST}}-file by setting the <code>status</code> to 5.
	The parameters of the potentials, <math>h_{\nu}</math>, <math>w_{\nu}</math>, and <math>\xi_{0\nu,\mu}</math> are defined in the {{FILE\|PENALTYPOT}}-file.		The parameters of the potentials, <math>h_{\nu}</math>, <math>w_{\nu}</math>, and <math>\xi_{0\nu,\mu}</math> are defined in the {{FILE\|PENALTYPOT}}-file.
	The this type of bias potential is primarily intended for the use in metadynamics but since Gaussians can be used as basis functions for more general shapes, they can be used also to prepare various atypically-shaped bias potentials.		The this type of bias potential is primarily intended for the use in metadynamics but since Gaussians can be used as basis functions for more general shapes, they can be used also to prepare various atypically-shaped bias potentials.