ML LCOUPLE

ML_LCOUPLE = [logical]
Default: ML_LCOUPLE = .FALSE. 

Description: This tag specifies whether thermodynamic integration is activated in order to calculate the chemical potentials 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 .

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 \in 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 this:

# DCOUPLE ################################
# DCOUPLE This line shows the derivative of the Hamiltonian with respect to coupling constant (dH/dlambda).
# DCOUPLE 
# DCOUPLE nstep .......... MD time step or input structure counter
# DCOUPLE der_H_lambda ... dH/dlambda
# DCOUPLE ################################
# DCOUPLE           nstep     der_H_lambda
# DCOUPLE               2                3
# DCOUPLE ################################
DCOUPLE                 1  -1.08332135E+01
DCOUPLE                 2  -1.08132321E+01
DCOUPLE                 3  -1.07631992E+01
DCOUPLE                 4  -1.06786675E+01
DCOUPLE                 5  -1.05493088E+01
DCOUPLE                 6  -1.03561161E+01
DCOUPLE                 7  -1.00762443E+01
DCOUPLE                 8  -9.69961878E+00
DCOUPLE                 9  -9.25531640E+00
DCOUPLE                10  -8.82525354E+00
...

Related tags and articles

ML_LMLFF, ML_NATOM_COUPLED, ML_ICOUPLE, ML_RCOUPLE

Examples that use this tag

---