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.

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In thermodynamic integration a coupling parameter $\lambda$ 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

$\delta \mu =\underset{0}{\overset{1}{\int }}⟨\frac{dH(\lambda )}{d\lambda }{⟩}_{\lambda }d\lambda .$

Using machine learning force fields the Hamiltonian can be written as

$H(\lambda )=\sum _{i=1}^{N_a}\frac{|{\mathbf{𝐩}}_i{|}^2}{2m_i}+\sum _{i\notin M}{U}_i(\lambda )+\lambda \sum _{i\in M}{U}_i(\lambda )+\sum _i^{N_a}{U}_{i,\mathbf{𝐚}\mathbf{𝐭}\mathbf{𝐨}\mathbf{𝐦}}.$

where $N_a$ denotes the number of atoms and $U_{i,\mathbf{𝐚}\mathbf{𝐭}\mathbf{𝐨}\mathbf{𝐦}}$ 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 $i$. The index $M$ denotes the atoms whose interaction is controlled by a coupling parameter. Further details on the implementation can be found in reference .

Related Tags and Sections

ML_FF_LMLFF, ML_FF_NATOM_COUPLED_MB, ML_FF_ICOUPLE_MB, ML_FF_RCOUPLE_MB

Examples that use this tag

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