Thermodynamic integration between machine-learned force fields - Revision history

Csheldon: Attribute the supplementary figure and table; add a recommendation on what a non-linear curve means

2026-09-18T12:19:27Z

Attribute the supplementary figure and table; add a recommendation on what a non-linear curve means

Csheldon: /* Step 3: Extracting and averaging the energies */

2026-09-18T08:21:50Z

Step 3: Extracting and averaging the energies

← Older revision		Revision as of 08:21, 18 September 2026
Line 544:		Line 544:

	{{CB\|grep "free energy ML TOTEN" 01/OUTCAR {{!}} awk '{print $6}' > free_E.dat\|:}}		{{CB\|grep "free energy ML TOTEN" 01/OUTCAR {{!}} awk '{print $6}' > free_E.dat\|:}}
	{{CB\|grep "free energy ML TOTEN =" 02/OUTCAR {{!}} awk '{print $6}' >> free_E.dat\|:}}		{{CB\|grep "free energy ML TOTEN {{=}}" 02/OUTCAR {{!}} awk '{print $6}' >> free_E.dat\|:}}
	{{CB\|grep temperature 01/OUTCAR {{!}} awk '{print $6}' > T.dat\|:}}		{{CB\|grep temperature 01/OUTCAR {{!}} awk '{print $6}' > T.dat\|:}}

Csheldon: Point at the published title; hold the unpublished density-functionals link; make categories live

2026-09-18T08:07:33Z

Point at the published title; hold the unpublished density-functionals link; make categories live

← Older revision		Revision as of 08:07, 18 September 2026
Line 1:		Line 1:
	Thermodynamic integration (TI) can be performed between two machine-learned force fields (MLFFs), significantly speeding up the calculation. Here, the free energy difference <math>\Delta A</math> between Fe<sup>2+</sup>/Fe<sup>3+</sup> in an electrochemical half-cell is calculated {{Cite\|jinnouchi:ncm:2024}}. The accuracy of this MLFF:MLFF approach is confirmed later by performing another [[~~Construction:~~Thermodynamic integration between a machine-learned force field and a density functional\|TI from the MLFF to a DFT functional]].		Thermodynamic integration (TI) can be performed between two machine-learned force fields (MLFFs), significantly speeding up the calculation. Here, the free energy difference <math>\Delta A</math> between Fe<sup>2+</sup>/Fe<sup>3+</sup> in an electrochemical half-cell is calculated {{Cite\|jinnouchi:ncm:2024}}. The accuracy of this MLFF:MLFF approach is confirmed later by performing another [[Thermodynamic integration between a machine-learned force field and a density functional\|TI from the MLFF to a DFT functional]].

	== Input files ==		== Input files ==
Line 667:		Line 667:
	* [[Thermodynamic integration: redox potential]]		* [[Thermodynamic integration: redox potential]]
	* [[Vacuum reference]]		* [[Vacuum reference]]
	* [[~~Construction:~~Thermodynamic integration between a machine-learned force field and a density functional\|Thermodynamic integration between a machine-learned force field and a density functional]]		* [[Thermodynamic integration between a machine-learned force field and a density functional\|Thermodynamic integration between a machine-learned force field and a density functional]]
	* [[~~Construction:~~Thermodynamic integration between density functionals]]		<!--* [[Thermodynamic integration between density functionals]] (not yet published)-->
	;Theory		;Theory
	* [[Thermodynamic integration]]		* [[Thermodynamic integration]]

Csheldon: Point the links at the published titles; categories made live

2026-09-18T08:03:55Z

Point the links at the published titles; categories made live

← Older revision		Revision as of 08:03, 18 September 2026
Line 1:		Line 1:
	Thermodynamic integration (TI) can be performed between two machine-learned force fields (MLFFs), significantly speeding up the calculation. Here, the free energy difference <math>\Delta A</math> between Fe<sup>2+</sup>/Fe<sup>3+</sup> in an electrochemical half-cell is calculated {{Cite\|jinnouchi:ncm:2024}}. The accuracy of this MLFF:MLFF approach is confirmed later by performing another [[Construction:Thermodynamic integration between ~~MLFF~~ and ~~GGAs~~\|TI from the MLFF to a DFT functional]].		Thermodynamic integration (TI) can be performed between two machine-learned force fields (MLFFs), significantly speeding up the calculation. Here, the free energy difference <math>\Delta A</math> between Fe<sup>2+</sup>/Fe<sup>3+</sup> in an electrochemical half-cell is calculated {{Cite\|jinnouchi:ncm:2024}}. The accuracy of this MLFF:MLFF approach is confirmed later by performing another [[Construction:Thermodynamic integration between a machine-learned force field and a density functional\|TI from the MLFF to a DFT functional]].

	== Input files ==		== Input files ==
Line 5:		Line 5:

	=== {{FILE\|POSCAR}}s ===		=== {{FILE\|POSCAR}}s ===
	The {{FILE\|POSCAR}} files are described on more detail in the [[~~Construction:~~Thermodynamic integration: redox potential\|redox potential overview page]].		The {{FILE\|POSCAR}} files are described on more detail in the [[Thermodynamic integration: redox potential\|redox potential overview page]].
	<div class="toccolours mw-customtoggle-poscar-fe3p-64h2o">'''Click to reveal the <math>[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+}</math> POSCAR'''</div>		<div class="toccolours mw-customtoggle-poscar-fe3p-64h2o">'''Click to reveal the <math>[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+}</math> POSCAR'''</div>
	<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-poscar-fe3p-64h2o">		<div class="mw-collapsible mw-collapsed" id="mw-customcollapsible-poscar-fe3p-64h2o">
Line 651:		Line 651:
	</syntaxhighlight>		</syntaxhighlight>

	This gave a value of: -1.272 eV, almost identical to the literature -1.260 eV obtained for Std. {{FILE\|POTCAR}}s provided by R. Jinnouchi (Ref. {{Cite\|jinnouchi:ncm:2024}} uses GW {{FILE\|POTCAR}}s). Combining this with <math>e \Delta \bar{\phi} </math> from the [[~~Construction:~~Vacuum reference\|previous step]] gives <math>\Delta A = -4.98 \: \mathrm{ eV}</math>. Considering that the redox potential <math>U_\mathrm{redox} = -\Delta A /e</math>, <math>U_\mathrm{redox}</math> can be calculated as:		This gave a value of: -1.272 eV, almost identical to the literature -1.260 eV obtained for Std. {{FILE\|POTCAR}}s provided by R. Jinnouchi (Ref. {{Cite\|jinnouchi:ncm:2024}} uses GW {{FILE\|POTCAR}}s). Combining this with <math>e \Delta \bar{\phi} </math> from the [[Vacuum reference\|previous step]] gives <math>\Delta A = -4.98 \: \mathrm{ eV}</math>. Considering that the redox potential <math>U_\mathrm{redox} = -\Delta A /e</math>, <math>U_\mathrm{redox}</math> can be calculated as:

	:<math>\Delta A^{\mathrm{ML}} = \int_0^1 \langle U_1 - U_0 \rangle_{\lambda}\,\mathrm{d}\lambda - n e \Delta \bar{\phi}</math>		:<math>\Delta A^{\mathrm{ML}} = \int_0^1 \langle U_1 - U_0 \rangle_{\lambda}\,\mathrm{d}\lambda - n e \Delta \bar{\phi}</math>
Line 665:		Line 665:
	== Related tags and articles ==		== Related tags and articles ==
	;How-tos		;How-tos
	* [[~~Construction:~~Thermodynamic integration: redox potential]]		* [[Thermodynamic integration: redox potential]]
	* [[~~Construction:~~Vacuum reference]]		* [[Vacuum reference]]
	* [[Construction:Thermodynamic integration between ~~MLFF~~ and ~~GGAs~~]]		* [[Construction:Thermodynamic integration between a machine-learned force field and a density functional\|Thermodynamic integration between a machine-learned force field and a density functional]]
	* [[Construction:Thermodynamic integration between density functionals]]		* [[Construction:Thermodynamic integration between density functionals]]
	;Theory		;Theory
Line 679:		Line 679:
	<references/>		<references/>

	~~<!--~~[[Category:Howto]][[Category:Advanced molecular-dynamics sampling]][[Category:Machine-learned force fields]][[Category:Electrochemistry]]-->		[[Category:Howto]][[Category:Advanced molecular-dynamics sampling]][[Category:Machine-learned force fields]]
			<!--[[Category:Electrochemistry]]-->

Csheldon: Csheldon moved page Construction:Thermodynamic integration between machine-learned force fields to Thermodynamic integration between machine-learned force fields

2026-09-18T07:59:24Z

Csheldon moved page Construction:Thermodynamic integration between machine-learned force fields to Thermodynamic integration between machine-learned force fields

← Older revision	Revision as of 07:59, 18 September 2026
(No difference)

Csheldon: Csheldon moved page Construction:Thermodynamic integration between MLFFs to Construction:Thermodynamic integration between machine-learned force fields

2026-09-18T07:59:10Z

Csheldon moved page Construction:Thermodynamic integration between MLFFs to Construction:Thermodynamic integration between machine-learned force fields

← Older revision	Revision as of 07:59, 18 September 2026
(No difference)

Csheldon: Both images write the ML TOTEN line, where the value is field 6; field 5 is the equals sign

2026-09-17T16:35:29Z

Both images write the ML TOTEN line, where the value is field 6; field 5 is the equals sign

← Older revision		Revision as of 16:35, 17 September 2026
Line 543:		Line 543:
	You should take the values for the <code>01</code> and <code>02</code> directories separately, e.g., by grepping for the energies and temperatures in each of the sub-directories:		You should take the values for the <code>01</code> and <code>02</code> directories separately, e.g., by grepping for the energies and temperatures in each of the sub-directories:

	{{CB\|grep "free energy" 01/OUTCAR {{!}} awk '{print $5}' > free_E.dat\|:}}		{{CB\|grep "free energy ML TOTEN" 01/OUTCAR {{!}} awk '{print $6}' > free_E.dat\|:}}
	{{CB\|grep "free energy ML TOTEN =" 02/OUTCAR {{!}} awk '{print $6}' >> free_E.dat\|:}}		{{CB\|grep "free energy ML TOTEN =" 02/OUTCAR {{!}} awk '{print $6}' >> free_E.dat\|:}}
	{{CB\|grep temperature 01/OUTCAR {{!}} awk '{print $6}' > T.dat\|:}}		{{CB\|grep temperature 01/OUTCAR {{!}} awk '{print $6}' > T.dat\|:}}

Csheldon: Separate the bare integral from the vacuum-referenced free energy, so the alignment term is not counted twice

2026-09-17T16:35:02Z

Separate the bare integral from the vacuum-referenced free energy, so the alignment term is not counted twice

← Older revision		Revision as of 16:35, 17 September 2026
Line 644:		Line 644:
	With the free energy for each individual λ, you can integrate over them to obtain the free energy of the TI.		With the free energy for each individual λ, you can integrate over them to obtain the free energy of the TI.

	<math>~~\Delta A =~~ \int_0^1 \langle U_1 - U_0 \rangle_{\lambda} d\~~lambda - ne~~\~~Delta \bar~~{\~~phi}~~ </math>		:<math>\int_0^1 \langle U_1 - U_0 \rangle_{\lambda}\,\mathrm{d}\lambda</math>

	<syntaxhighlight lang="python">		<syntaxhighlight lang="python">
Line 651:		Line 651:
	</syntaxhighlight>		</syntaxhighlight>

	This gave a value of: -1.272 eV, almost identical to the literature -1.260 eV obtained for Std. {{FILE\|POTCAR}}s provided by R. Jinnouchi (Ref. {{Cite\|jinnouchi:ncm:2024}} uses GW {{FILE\|POTCAR}}s). ~~Adding~~ this ~~to the value of~~ <math>e \Delta \bar{\phi} </math> from the [[Construction:Vacuum reference\|previous step]] gives <math>\Delta A = -4.98 \: \mathrm{ eV}</math>. Considering that the redox potential <math>U_\mathrm{redox} = -\Delta A /e</math>, <math>U_\mathrm{redox}</math> can be calculated as:		This gave a value of: -1.272 eV, almost identical to the literature -1.260 eV obtained for Std. {{FILE\|POTCAR}}s provided by R. Jinnouchi (Ref. {{Cite\|jinnouchi:ncm:2024}} uses GW {{FILE\|POTCAR}}s). Combining this with <math>e \Delta \bar{\phi} </math> from the [[Construction:Vacuum reference\|previous step]] gives <math>\Delta A = -4.98 \: \mathrm{ eV}</math>. Considering that the redox potential <math>U_\mathrm{redox} = -\Delta A /e</math>, <math>U_\mathrm{redox}</math> can be calculated as:

			:<math>\Delta A^{\mathrm{ML}} = \int_0^1 \langle U_1 - U_0 \rangle_{\lambda}\,\mathrm{d}\lambda - n e \Delta \bar{\phi}</math>

	<math>U_\mathrm{redox} = -\Delta A/e = -(-1.27 - (3.71))/1 = 4.98 \: \mathrm{V} </math>.		<math>U_\mathrm{redox} = -\Delta A/e = -(-1.27 - (3.71))/1 = 4.98 \: \mathrm{V} </math>.

Csheldon: Correct the Figure 1 caption: Fe(3+) is the lambda=0 endpoint, matching the text and Figure 2

2026-09-17T16:22:18Z

Correct the Figure 1 caption: Fe(3+) is the lambda=0 endpoint, matching the text and Figure 2

← Older revision		Revision as of 16:22, 17 September 2026
Line 635:		Line 635:
	</syntaxhighlight>		</syntaxhighlight>

	[[File:Mlff_mlff_test.png\|800px\|thumb\|center\|'''Figure 1'''. Probability vs potential energy (cf. Supplementary Figure 8), the MD step number vs the potential energy, and the MD step number vs the temperature ~~for~~ between Fe<sup>2+</sup> (λ = 0) and Fe<sup>3+</sup> (λ = 1).]]		[[File:Mlff_mlff_test.png\|800px\|thumb\|center\|'''Figure 1'''. Probability vs potential energy (cf. Supplementary Figure 8), the MD step number vs the potential energy, and the MD step number vs the temperature between Fe<sup>3+</sup> (λ = 0) and Fe<sup>2+</sup> (λ = 1).]]

	=== Step 4: Integrating to obtain the free energy ===		=== Step 4: Integrating to obtain the free energy ===

Csheldon: Use the friendly imperative where the sentence tells the reader to do something

2026-09-17T16:06:45Z

Use the friendly imperative where the sentence tells the reader to do something

← Older revision		Revision as of 16:06, 17 September 2026
Line 2:		Line 2:

	== Input files ==		== Input files ==
	~~Two~~ MD calculations ~~need to be run~~ in parallel between two different systems: Fe<sup>3+</sup> in 64 H<sub>2</sub>O (<code>Fe3P_64H2O</code>) and Fe<sup>2+</sup> in 64 H<sub>2</sub>O (<code>Fe2P_64H2O</code>), that is, <math>[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+}</math> and <math>[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+}</math>.		Run two MD calculations in parallel, between two different systems: Fe<sup>3+</sup> in 64 H<sub>2</sub>O (<code>Fe3P_64H2O</code>) and Fe<sup>2+</sup> in 64 H<sub>2</sub>O (<code>Fe2P_64H2O</code>), that is, <math>[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{3+}</math> and <math>[\mathrm{Fe}(\mathrm{H}_2\mathrm{O})_n]^{2+}</math>.

	=== {{FILE\|POSCAR}}s ===		=== {{FILE\|POSCAR}}s ===
Line 533:		Line 533:
	lambda_0p0 lambda_0p25 lambda_0p5 lambda_0p75 lambda_1p0		lambda_0p0 lambda_0p25 lambda_0p5 lambda_0p75 lambda_1p0

	for 0.0, 0.25, 0.5, 0.75, and 1.0, respectively. ~~The~~ calculation ~~should be submitted~~ from the ''parent'' directory, ~~similar to~~ for [[Nudged elastic bands\|~~NEB~~]]. These will each run two parallel MD calculations for the value of λ defined in {{TAG\|VCAIMAGES}}.		for 0.0, 0.25, 0.5, 0.75, and 1.0, respectively. Submit the calculation from the ''parent'' directory, as for a [[Nudged elastic bands\|nudged elastic band]] calculation. These will each run two parallel MD calculations for the value of λ defined in {{TAG\|VCAIMAGES}}.
	{{NB\|important\|The Nosé-Hoover thermostat is used here ({{TAG\|MDALGO\|2\|color=purple}}). The trajectories in <code>01</code> and <code>02</code> directories need to be identical, so you ''cannot'' use the Langevin thermostat as it introduces random numbers.}}		{{NB\|important\|The Nosé-Hoover thermostat is used here ({{TAG\|MDALGO\|2\|color=purple}}). The trajectories in <code>01</code> and <code>02</code> directories need to be identical, so you ''cannot'' use the Langevin thermostat as it introduces random numbers.}}

← Older revision		Revision as of 08:21, 18 September 2026
Line 544:		Line 544:

	{{CB\|grep "free energy ML TOTEN" 01/OUTCAR {{!}} awk '{print $6}' > free_E.dat\|:}}		{{CB\|grep "free energy ML TOTEN" 01/OUTCAR {{!}} awk '{print $6}' > free_E.dat\|:}}
	{{CB\|grep "free energy ML TOTEN =" 02/OUTCAR {{!}} awk '{print $6}' >> free_E.dat\|:}}		{{CB\|grep "free energy ML TOTEN {{=}}" 02/OUTCAR {{!}} awk '{print $6}' >> free_E.dat\|:}}
	{{CB\|grep temperature 01/OUTCAR {{!}} awk '{print $6}' > T.dat\|:}}		{{CB\|grep temperature 01/OUTCAR {{!}} awk '{print $6}' > T.dat\|:}}

← Older revision		Revision as of 12:19, 18 September 2026
Line 635:		Line 635:
	</syntaxhighlight>		</syntaxhighlight>

	[[File:Mlff_mlff_test.png\|800px\|thumb\|center\|'''Figure 1'''. Probability vs potential energy (cf. Supplementary Figure 8), the MD step number vs the potential energy, and the MD step number vs the temperature between Fe<sup>3+</sup> (λ = 0) and Fe<sup>2+</sup> (λ = 1).]]		[[File:Mlff_mlff_test.png\|800px\|thumb\|center\|'''Figure 1'''. Probability vs potential energy (cf. Supplementary Figure 8 of Ref. {{Cite\|jinnouchi:ncm:2024}}), the MD step number vs the potential energy, and the MD step number vs the temperature between Fe<sup>3+</sup> (λ = 0) and Fe<sup>2+</sup> (λ = 1).]]

	=== Step 4: Integrating to obtain the free energy ===		=== Step 4: Integrating to obtain the free energy ===
	You can then plot the free energy against the lambda values; ideally, it should be almost linear:		You can then plot the free energy against the lambda values; ideally, it should be almost linear:

	[[File:Mlff_mlff_int.png\|600px\|thumb\|center\|'''Figure 2'''. Free energy difference ΔA for thermodynamic integration using a parameter λ between Fe<sup>3+</sup> (λ = 0) and Fe<sup>2+</sup> (λ = 1) (cf. Supplementary Figure 8).]]		[[File:Mlff_mlff_int.png\|600px\|thumb\|center\|'''Figure 2'''. Free energy difference ΔA for thermodynamic integration using a parameter λ between Fe<sup>3+</sup> (λ = 0) and Fe<sup>2+</sup> (λ = 1) (cf. Supplementary Figure 8 of Ref. {{Cite\|jinnouchi:ncm:2024}}).]]

	With the free energy for each individual λ, you can integrate over them to obtain the free energy of the TI.		With the free energy for each individual λ, you can integrate over them to obtain the free energy of the TI.
Line 657:		Line 657:
	<math>U_\mathrm{redox} = -\Delta A/e = -(-1.27 - (3.71))/1 = 4.98 \: \mathrm{V} </math>.		<math>U_\mathrm{redox} = -\Delta A/e = -(-1.27 - (3.71))/1 = 4.98 \: \mathrm{V} </math>.

	Comparing this to the literature value of 4.95 eV (for Std. {{FILE\|POTCAR}}; cf. Supplementary Table 6 for GW {{FILE\|POTCAR}}), the agreement is reasonable despite the additional approximations.		Comparing this to the literature value of 4.95 eV (for Std. {{FILE\|POTCAR}}; cf. Supplementary Table 6 of Ref. {{Cite\|jinnouchi:ncm:2024}} for GW {{FILE\|POTCAR}}), the agreement is reasonable despite the additional approximations.

	== Recommendations and advice ==		== Recommendations and advice ==
	*Make sure to carefully check that you are using the correct {{FILE\|ML_FF}} files for each directory. If you mix them up, then you can always switch λ in the post-processing.		*Make sure to carefully check that you are using the correct {{FILE\|ML_FF}} files for each directory. If you mix them up, then you can always switch λ in the post-processing.
	*If you see that during the MD simulation (in the TI), U drifts far from the average, this is an indication that a chemical change has happened. Check to see if an Fe-O bond has formed. This should not happen and is an indication that your force field is unstable.		*If you see that during the MD simulation (in the TI), U drifts far from the average, this is an indication that a chemical change has happened. Check to see if an Fe-O bond has formed. This should not happen and is an indication that your force field is unstable.
			*A visibly non-linear <math>\Delta A</math> curve against λ means the λ grid is too coarse or the sampling too short. Add intermediate λ values or extend the MD runs before integrating. A deviation of a few tens of meV in the integral is not significant.

	== Related tags and articles ==		== Related tags and articles ==