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

$\Delta F = \int\limits_{0}^{1} d\lambda \langle U_{1}(\lambda) - U_{0}(\lambda) \rangle_{\lambda}$.

Here $U_{1}(\lambda)$ and $U_{0}(\lambda)$ 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 $\lambda$. The SCALEE sets the value for the coupling constant. The notation $\langle \ldots \rangle_{\lambda}$ denotes an ensemble average of a system driven by the following classical Hamiltonian

$H_{\lambda}= \lambda H_{1} + (1-\lambda) H_{0}$.

By default SCALEE=1 and scaling of the energies and forces via the coupling constant is carried out. To enable the scaling SCALEE<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 (from a previous calculation using PHON_NSTRUCT=-1) and SCALEE$\ne$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

$H_{\lambda} = (1-\lambda) H_{\mathrm{harmonic}} + \lambda H_{\mathrm{ab initio}}.$

Related Tags and Sections

VCAIMAGES, IMAGES, NCORE IN IMAGE1, PHON_NSTRUCT

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