ML_MRB2

ML_MRB2 = [integer]
Default: ML_MRB2 = 8

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

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. In practice, the continuous function above is transformed into a discrete set of numbers [math]\displaystyle{ p_{n\nu l}^{i} }[/math] by expanding it into a set of radial basis functions [math]\displaystyle{ \chi_{nl}(r) }[/math] and Legendre polynomials [math]\displaystyle{ P_{l}\left(\mathrm{cos}\theta\right) }[/math] (see this section for more details):

[math]\displaystyle{ \rho_{i}^{(3)}\left(r,s,\theta\right) = \sum\limits_{l=1}^{L_{\mathrm{max}}} \sum\limits_{n=1}^{N^{l}_{\mathrm{R}}}\sum\limits_{\nu=1}^{N^{l}_{\mathrm{R}}} \sqrt{\frac{2l+1}{2}} p_{n\nu l}^{i}\chi_{nl}\left(r\right)\chi_{\nu l}\left(s\right)P_{l}\left(\mathrm{cos}\theta\right). }[/math]

The tag ML_MRB2 sets the number [math]\displaystyle{ N_\text{R}^l }[/math] of radial basis functions to use in this expansion. The same number is used for all [math]\displaystyle{ l }[/math].

Mind: The number of angular descriptor expansion coefficients [math]\displaystyle{ p_{n\nu l}^{i} }[/math] scales quadratically with [math]\displaystyle{ N_\text{R}^l }[/math] set by this tag. It also depends on ML_LMAX2 and the number of elements.

Related tags and articles