ML MRB2
ML_MRB2 = [integer]
Default: ML_MRB2 = ML_MRB1
Description: This tag sets the number 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_\text{R}^l} (for all 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/":): l ) of radial basis functions used to expand the angular descriptor within the machine learning force field method.
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. In practice, the continuous function above is transformed into a discrete set of numbers 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}} by expanding it into a set of radial basis functions 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 \chi_{nl}(r)} and Legendre polynomials 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 P_{l}\left(\mathrm{cos}\theta\right)} (see this section for more details):
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) = \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 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_\text{R}^l} of radial basis functions to use in this expansion. The same number is used for all 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/":): l .
| Mind: The number of angular descriptor 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}} scales quadratically with 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_\text{R}^l} set by this tag. It also depends on ML_LMAX2 and the number of elements. |
Related Tags and Sections
ML_LMLFF, ML_LMAX2, ML_MRB1, ML_W1, ML_RCUT2, ML_SION2