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.

---

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).

In thermodynamic integration the free energy difference between two systems is defined as

[math]\displaystyle{ \Delta F = \int\limits_{0}^{1} d\lambda \langle U_{1}(\lambda) - U_{0}(\lambda) \rangle }[/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 interaction of the constituents within the system is controlled via the coupling parameter [math]\displaystyle{ \lambda }[/math]. The SCALEE sets the value for the coupling constant.

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[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. Here the Hamiltonian for a certain integration point along the thermodynamic integration pathway is given as

[math]\displaystyle{ H_{\lambda} = (1-\lambda) H_{\mathrm{harmonic}} + \lambda H_{\mathrm{ab initio}}. }[/math]

Related Tags and Sections

VCAIMAGES, IMAGES, NCORE IN IMAGE1, PHON_NSTRUCT

---