SCALEE

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.

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A detailed description of calculations using thermodynamic integration within VASP is given in reference (caution: the tag ISPECIAL=0 used in that reference is not valid anymore, instead the tag PHON_NSTRUCT=-1 is used).

Using thermodynamic integration the free energy difference between two systems is written as

[math]\displaystyle{ \Delta F = \int\limits_{0}^{1} d\lambda \langle U_{1}(\lambda) - U_{0}(\lambda) \rangle_{\lambda} }[/math].

Here [math]\displaystyle{ U_{1}(\lambda) }[/math] and [math]\displaystyle{ 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]\displaystyle{ \lambda }[/math]. The tag SCALEE sets the value for the coupling constant. The notation [math]\displaystyle{ \langle \ldots \rangle_{\lambda} }[/math] denotes an ensemble average of a system driven by the following classical Hamiltonian

[math]\displaystyle{ H_{\lambda}= \lambda H_{1} + (1-\lambda) H_{0} }[/math].

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.

Two possible options are available for the reference system:

• Ideal gas:

Usually the thermodynamic integration is carried out from the ideal gas to the liquid state.

• Harmonic solid:

If the file DYNMATFULL exists in the calculation directory and SCALEE[math]\displaystyle{ \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. The DYNMATFULL file stores the eigenmodes and eigenvalues from diagonalizing the dynamic matrix. This file is written by a previous calculation using the INCAR tags IBRION=6 and PHON_NSTRUCT=-1.

Related Tags and Sections

VCAIMAGES, IMAGES, NCORE IN IMAGE1, PHON_NSTRUCT, IBRION

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