ML LCOUPLE
ML_LCOUPLE = [logical]
Default: ML_LCOUPLE = .FALSE.
Description: This tag specifies whether coupling parameters are used for the calculation of chemical potentials or not within the machine learning force field method.
In thermodynamic integration a coupling parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \lambda } is introduced to the Hamiltonian to smoothly switch between a "non-interacting" reference state and a "fully-interacting" state. The change of the free energy along this path is written as
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \Delta \mu = \int\limits_{0}^{1} \langle \frac{dH(\lambda)}{d\lambda} \rangle_{\lambda} d\lambda. }
Using machine learning force fields the Hamiltonian can be written as
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle H (\lambda) = \sum\limits_{i=1}^{N_{a}} \frac{|\mathbf{p}_{i}|^2}{2m_{i}} + \sum\limits_{i \notin M} U_{i}(\lambda) + \lambda \sum\limits_{i \in M} U_{i}(\lambda) + \sum\limits_{i}^{N_{a}} U_{i,\mathbf{atom}}. }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): N_{{a}} denotes the number of atoms and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle U_{i,\mathbf{atom}}} is an atomic reference energy for a single non interacting atom. The first term in the equation describes the potential energy and the second and third term describe the potential energy of an atom Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): i . The index Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): M denotes the atoms whose interaction is controlled by a coupling parameter. The interaction of the atoms are controlled by scaling the contributions to the atom density via the coupling parameter
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \rho (\mathbf{r},\lambda) = \sum\limits_{j\notin M} f_{\mathrm{cut}} \left( \left| \mathbf{r}_{j} - \mathbf{r}_{i} \right| \right) g \left[ \mathbf{r} - \left( \mathbf{r}_{j} - \mathbf{r}_{i} \right) \right] + \lambda \sum\limits_{j\in M} f_{\mathrm{cut}} \left( \left| \mathbf{r}_{j} - \mathbf{r}_{i} \right| \right) g \left[ \mathbf{r} - \left( \mathbf{r}_{j} - \mathbf{r}_{i} \right) \right]. }
Further details on the implementation can be found in reference [1].
For thermodynamic integration the following parameters have to be set:
- ML_ISTART=2.
- ML_LCOUPLE=.TRUE..
- The number of atoms for which a coupling parameter is introduced (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle i \notin M } ): ML_NATOM_COUPLED.
- The list of atom indices that for that the coupling parameter is applied in the interaction: ML_ICOUPLE.
- The strength of the coupling parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle lambda} between 0 and 1: ML_RCOUPLE.
The derivative of the hamiltonian with respect to the coupling constant Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle dH/d\lambda} is written out at every MD step to the ML_LOGFILE. A sample output should look like the following
dH/dRCOUPLE (eV): 0.893558
References
Related Tags and Sections
ML_LMLFF, ML_NATOM_COUPLED, ML_ICOUPLE, ML_RCOUPLE