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# ML_RCUT2

ML_RCUT2 = [real]
Default: ML_RCUT2 = ML_RCUT1

Description: This flag sets the cutoff radius ${\displaystyle R_{\text{cut}}}$ for the angular descriptor ${\displaystyle \rho _{i}^{(3)}(r)}$ in the machine learning force field method.

The angular descriptor is constructed from

${\displaystyle \rho _{i}^{(3)}\left(r,s,\theta \right)=\iint d{\hat {\mathbf {r} }}d{\hat {\mathbf {s} }}\delta \left({\hat {\mathbf {r} }}\cdot {\hat {\mathbf {s} }}-\mathrm {cos} \theta \right)\sum \limits _{j=1}^{N_{a}}\sum \limits _{k\neq j}^{N_{a}}\rho _{ik}\left(r{\hat {\mathbf {r} }}\right)\rho _{ij}\left(s{\hat {\mathbf {s} }}\right),\quad {\text{where}}\quad \rho _{ij}\left(\mathbf {r} \right)=f_{\mathrm {cut} }\left(r_{ij}\right)g\left(\mathbf {r} -\mathbf {r} _{ij}\right)}$

and ${\displaystyle g\left(\mathbf {r} \right)}$ is an approximation of the delta function. A basis set expansion of ${\displaystyle \rho _{i}^{(3)}(r)}$ yields the expansion coefficients ${\displaystyle p_{n\nu l}^{i}}$ which are used in practice to describe the atomic environment (see this section for details). The tag ML_RCUT2 sets the cutoff radius ${\displaystyle R_{\text{cut}}}$ at which the cutoff function ${\displaystyle f_{\mathrm {cut} }\left(r_{ij}\right)}$ decays to zero.

 Mind: The cutoff radius determines how many neighbor atoms ${\displaystyle N_{\mathrm {a} }}$ are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost of the descriptor as the cutoff sphere contains more neighbor atoms. A good compromise is always system-dependent, therefore different values should be tested to achieve satisfying accuracy and speed.

The unit of the cut-off radius is ${\displaystyle \mathrm {\AA} }$.