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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.

A detailed description of calculations using thermodynamic integration within VASP is given in reference [1] (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


Here and 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 . The SCALEE sets the value for the coupling constant. The notation denotes an ensemble average of a system driven by the following classical Hamiltonian


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 SCALEE1, 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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