ML RCUT2

ML_RCUT2 = [real]
Default: ML_RCUT2 = ML_RCUT1 

Description: This flag sets the cutoff radius [math]\displaystyle{ R_\text{cut} }[/math] for the angular descriptor [math]\displaystyle{ \rho^{(3)}_i(r) }[/math] in the machine learning force field method.

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The angular descriptor is constructed from

[math]\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 \ne 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) }[/math]

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

Mind: The cutoff radius determines how many neighbor atoms [math]\displaystyle{ N_\mathrm{a} }[/math] 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 [math]\displaystyle{ \AA }[/math].

Related Tags and Sections

ML_LMLFF, ML_RCUT1, ML_W1, ML_SION1, ML_SION2

Examples that use this tag

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