ML_SION2

ML_SION2 = [real]
Default: ML_SION2 = ML_SION1

Description: This tag specifies the width [math]\displaystyle{ \sigma_\text{atom} }[/math] of the Gaussian functions used for broadening the atomic distributions of the angular descriptor [math]\displaystyle{ \rho^{(3)}_i(r) }[/math] 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 the following approximation of the delta function:

[math]\displaystyle{ g\left(\mathbf{r}\right)=\frac{1}{\sqrt{2\sigma_{\mathrm{atom}}\pi}}\mathrm{exp}\left(-\frac{|\mathbf{r}|^{2}}{2\sigma_{\mathrm{atom}}^{2}}\right). }[/math]

The tag ML_SION2 sets the width [math]\displaystyle{ \sigma_\text{atom} }[/math] of the above Gaussian function (see this section for more details).

Tip: Our test calculations indicate that ML_SION1 = ML_SION2 results in an optimal training performance. Furthermore, a value of 0.5 was found to be a good default value for both. However, the best choice is system-dependent, careful testing may improve machine learning results.

The unit of ML_SION2 is [math]\displaystyle{ \AA }[/math].

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