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.

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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

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

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. The interaction of the atoms are controlled by scaling the contributions to the atom density via the coupling parameter

$\rho (\mathbf{𝐫},\lambda )=\sum _{j\notin M}{f}_{\mathrm{c}\mathrm{u}\mathrm{t}}\left(|{\mathbf{𝐫}}_j-{\mathbf{𝐫}}_i|\right)g[\mathbf{𝐫}-({\mathbf{𝐫}}_j-{\mathbf{𝐫}}_i)]+\lambda \sum _{j\in M}{f}_{\mathrm{c}\mathrm{u}\mathrm{t}}\left(|{\mathbf{𝐫}}_j-{\mathbf{𝐫}}_i|\right)g[\mathbf{𝐫}-({\mathbf{𝐫}}_j-{\mathbf{𝐫}}_i)].$

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 ($i\in M$): 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 $\lambda$ between 0 and 1: ML_RCOUPLE.

The derivative of the hamiltonian with respect to the coupling constant $dH/d\lambda$ 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

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