ML LCOUPLE
ML_FF_LCOUPLE_MB = [logical]
Default: ML_FF_LCOUPLE_MB = .FALSE.
Description: This tag specifies whether coupling parameters are used for the calculation of chemical potentials is used or not within the machine learning force field method.
In thermodynamic integration a coupling parameter [math]\displaystyle{ \lambda }[/math] 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
[math]\displaystyle{ \delta \mu = \int\limits_{0}^{1} \langle \frac{dH(\lambda)}{d\lambda} \rangle_{\lambda} d\lambda. }[/math]
Using machine learning force fields the Hamiltonian can be written as
[math]\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}}. }[/math]
where [math]\displaystyle{ N_{a} }[/math] denotes the number of atoms and [math]\displaystyle{ U_{i,\mathbf{atom}} }[/math] 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 [math]\displaystyle{ i }[/math]. The index [math]\displaystyle{ M }[/math] denotes the atoms whose interaction is controlled by a coupling parameter. Further details on the implementation can be found in reference [1].
References
Related Tags and Sections
ML_FF_LMLFF, ML_FF_NATOM_COUPLED_MB, ML_FF_ICOUPLE_MB, ML_FF_RCOUPLE_MB