ML_RCUT2

ML_RCUT2 = [real]
Default: ML_RCUT2 = 5.0

Description: This flag sets the cutoff radius $R_{\text{cut}}$ for the angular descriptor $\rho _{i}^{(3)}(r)$ in the machine learning force field method. The unit of the cut-off radius is $\mathrm {\AA}$ .

The angular descriptor is constructed from

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

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

Mind: The cutoff radius determines how many neighbor atoms

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 as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfactory accuracy and speed.

For materials containing only H, B, C, O, N, and F (i.e. organic molecules, polymers), the learning efficiency might increase when ML_RCUT2 is set to values around 4 $\mathrm {\AA}$ (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 $\mathrm {\AA}$ can improve the accuracy,

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