SCALEE: Difference between revisions

Revision as of 09:15, 31 March 2020

SCALEE = [real]
Default: SCALEE = 1

Description: This tag specifies the scaling constant (coupling parameter) of the energies and forces.

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

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

Here $U_{1}(\lambda)$ and $U_{0}(\lambda)$ 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 $\lambda$ . 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 $\ne$ 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

@@ Line 1: / Line 1: @@
 {{TAGDEF|SCALEE|[real]|1}}
-Description: This tag specifies the scaling constant of the energies and forces.
+Description: This tag specifies the scaling constant (coupling parameter) of the energies and forces.
 ----
 In thermodynamic integration the free energy difference between two systems is defined as
-<math> \Delta F = \int\limits_{0}^{1} d\lambda \langle U_{1} - U_{0} \rangle </math>
+<math> \Delta F = \int\limits_{0}^{1} d\lambda \langle U_{1}(\lambda) - U_{0}(\lambda) \rangle </math>.
-where
+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 interaction of the constituents within the system is controlled via the coupling parameter <math>\lambda</math>. The {{TAG|SCALEE}} sets the value for the coupling constant.
+By default {{TAG|SCALEE}}=1 and scaling of the energies and forces via the coupling constant is carried out. To enable the scaling {{TAG|SCALEE}}<1 has to be specified.
-For thermodynamic integration this parameter controls the coupling parameter <math>\lambda</math>.
+Two possible options are available for the reference system:
-This parameter is only used if {{TAG|SCALEE}}<math>\ne</math>1.
+*Ideal gas:
 Usually the thermodynamic integration is carried out from the ideal gas to the liquid state.
+*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