ML_MRB1

ML_MRB1 = [integer]
Default: ML_MRB1 = 12

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

The radial descriptor is constructed from

${\displaystyle \rho_{i}^{(2)}\left(r\right) = \frac{1}{4\pi} \int \rho_{i}\left(r\hat{\mathbf{r}}\right) d\hat{\mathbf{r}}, \quad \text{where} \quad \rho_{i}\left(\mathbf{r}\right) = \sum\limits_{j=1}^{N_{\mathrm{a}}} f_{\mathrm{cut}}\left(r_{ij}\right) g\left(\mathbf{r}-\mathbf{r}_{ij}\right) }$

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 by expanding it into a set of radial basis functions $\chi_{n0}(r)$ (see this section for more details):

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

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

Related tags and articles