SCALEE: Difference between revisions

Latest revision as of 14:05, 16 October 2024

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 [math]\displaystyle{ \lambda }[/math] 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[math]\displaystyle{ \ne }[/math]1 has to be specified.

More information using this tag is given here.

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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.
-Using thermodynamic integration the free energy difference between two systems is written as
-<math> \Delta F = \int\limits_{0}^{1} d\lambda \langle U_{1}(\lambda) - U_{0}(\lambda) \rangle_{\lambda} </math>.
-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 {{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
-<math> H_{\lambda}= \lambda H_{1} + (1-\lambda) H_{0} </math>.
 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.
-Two possible options are available for the reference system:
+More information using this tag is given [[Thermodynamic integration calculations|here]].
-*Ideal gas:
+== Related tags and articles ==
-Usually the thermodynamic integration is carried out from the ideal gas to the liquid state.
+{{TAG|VCAIMAGES}}, {{TAG|IMAGES}}, {{TAG|NCORE IN IMAGE1}}, {{TAG|PHON_NSTRUCT}}, {{TAG|IBRION}}
-*Harmonic solid
-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
-<math>H_{\lambda} = (1-\lambda) H_{\mathrm{harmonic}} + \lambda H_{\mathrm{ab initio}}. </math>
-== 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]]