ML_MRB1

ML_MRB1 = [integer]
Default: ML_MRB1 = 12

Description: This tag sets the number [math]\displaystyle{ N_\text{R}^0 }[/math] of radial basis functions used to expand the radial descriptor [math]\displaystyle{ \rho^{(2)}_i(r) }[/math] within the machine learning force field method.

The radial descriptor is constructed from

[math]\displaystyle{ \rho_{i}^{(2)}\left(r\right) = \frac{1}{4\pi} \int \rho_{i}\left(r\hat{\mathbf{r}}\right) d\hat{\mathbf{r}}, \quad \text{where} \quad \rho_{i}\left(\mathbf{r}\right) = \sum\limits_{j=1}^{N_{\mathrm{a}}} 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. In practice, the continuous function above is transformed into a discrete set of numbers by expanding it into a set of radial basis functions [math]\displaystyle{ \chi_{n0}(r) }[/math] (see this section for more details):

[math]\displaystyle{ \rho_{i}^{(2)}\left(r\right) = \frac{1}{\sqrt{4\pi}} \sum\limits_{n=1}^{N^{0}_{\mathrm{R}}} c_{n00}^{i} \chi_{n0}\left(r\right). }[/math]

The tag ML_MRB1 sets the number [math]\displaystyle{ N_\text{R}^0 }[/math] of radial basis functions to use in this expansion.

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