ML_MRB2

ML_MRB2 = [integer]
Default: ML_MRB2 = 8

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

The angular descriptor is constructed from

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

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

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

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

Mind: The number of angular descriptor expansion coefficients

p_{n\nu l}^{i}

scales quadratically with

N_\text{R}^l

set by this tag. It also depends on ML_LMAX2 and the number of elements.

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