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| A detailed description of calculations using thermodynamic integration within VASP is given in reference {{cite|dorner:PRL:2018}} ('''caution''': the tag ''ISPECIAL''=0 used in that reference is not valid anymore, instead the tag {{TAG|PHON_NSTRUCT}}=-1 is used).
| | The tag {{TAG|SCALEE}} sets the coupling parameter <math>\lambda</math> and hence controls the Hamiltonian of the calculation. |
| | By default {{TAG|SCALEE}}=1 and the scaling of the energies and forces via the coupling constant is internally skipped in the code. To enable the scaling {{TAG|SCALEE}}<math>\ne</math>1 has to be specified. |
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| | More information using this tag is given [[Thermodynamic integration calculations|here]]. |
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| Using thermodynamic integration the free energy difference between two systems is written as
| | == Related tags and articles == |
| | | {{TAG|VCAIMAGES}}, {{TAG|IMAGES}}, {{TAG|NCORE IN IMAGE1}}, {{TAG|PHON_NSTRUCT}}, {{TAG|IBRION}} |
| <math> \Delta F = \int\limits_{0}^{1} d\lambda \langle U_{1}(\lambda) - U_{0}(\lambda) \rangle_{\lambda} </math>.
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| Here <math>U_{1}(\lambda)</math> and <math>U_{0}(\lambda)</math> describe the potential energies of a fully-interacting and a non-interacting reference system, respectively. The coupling strength of the systems is controlled via the coupling parameter <math>\lambda</math>. The {{TAG|SCALEE}} sets the value for the coupling constant. The notation <math>\langle \ldots \rangle_{\lambda}</math> denotes an ensemble average of a system driven by the following classical Hamiltonian
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| <math> H_{\lambda}= \lambda H_{1} + (1-\lambda) H_{0} </math>.
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| By default {{TAG|SCALEE}}=1 and scaling of the energies and forces via the coupling constant is carried out. To enable the scaling {{TAG|SCALEE}}<1 has to be specified.
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| Two possible options are available for the reference system:
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| *Ideal gas:
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| Usually the thermodynamic integration is carried out from the ideal gas to the liquid state.
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| *Harmonic solid
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| If the file {{TAG|DYNMATFULL}} exists in the calculation directory (from a previous calculation using {{TAG|PHON_NSTRUCT}}=-1) and {{TAG|SCALEE}}<math>\ne</math>1, the second order Hessian matrix is added to the force and thermodynamic integration from a harmonic model to a fully interacting system is carried out. Here the Hamiltonian for a certain integration point along the thermodynamic integration pathway is given as
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| <math>H_{\lambda} = (1-\lambda) H_{\mathrm{harmonic}} + \lambda H_{\mathrm{ab initio}}. </math>
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| == Related Tags and Sections == | |
| {{TAG|VCAIMAGES}}, {{TAG|IMAGES}}, {{TAG|NCORE IN IMAGE1}}, {{TAG|PHON_NSTRUCT}} | |
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| | | [[Category:INCAR tag]][[Category:Advanced molecular-dynamics sampling]] |
| [[Category:INCAR]][[Category:Molecular Dynamics]][[Category:Thermodynamic integration]] | |
SCALEE = [real]
Default: SCALEE = 1
Description: This tag specifies the coupling parameter of the energies and forces between a fully interacting system and a reference system.
The tag SCALEE sets the coupling parameter 
and hence controls the Hamiltonian of the calculation.
By default SCALEE=1 and the scaling of the energies and forces via the coupling constant is internally skipped in the code. To enable the scaling SCALEE
1 has to be specified.
More information using this tag is given here.
Related tags and articles
VCAIMAGES, IMAGES, NCORE IN IMAGE1, PHON_NSTRUCT, IBRION
