ML_RCUT2

ML_RCUT2 = [real]
Default: ML_RCUT2 = 5.0

Description: This flag sets the cutoff radius Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle R_\text{cut}} for the angular descriptor Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \rho^{(3)}_i(r)} in the machine learning force field method. The unit of the cut-off radius is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \AA .

The angular descriptor is constructed from

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle g\left(\mathbf{r}\right)} is an approximation of the delta function. A basis set expansion of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle \rho^{(3)}_i(r)} yields the expansion coefficients Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): p_{{n\nu l}}^{{i}} which are used in practice to describe the atomic environment (see this section for details). The tag ML_RCUT2 sets the cutoff radius Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle R_\text{cut}} at which the cutoff function Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle f_{\mathrm{cut}}\left(r_{ij}\right)} decays to zero.

Mind: The cutoff radius determines how many neighbor atoms Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): {\displaystyle N_\mathrm{a}} are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfying accuracy and speed.

For materials (i.e. organic molecules, polymers) containing only H, B, C, O, N, and F, the learning efficiency might increase when ML_RCUT2 is set to values around 4 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \AA (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): \AA might improve the accuracy,

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