ML LMAX2
ML_LMAX2 = [integer]
| Default: ML_LMAX2 | = 4 | for ML_LAFILT2 = .TRUE. |
| = 6 | else |
Description: This tag specifies the maximum angular momentum quantum 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 L_\max} of spherical harmonics used to expand atomic distributions within the machine learning force field method.
To construct an atomic environment descriptor the atomic probability density
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}\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), }
where 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, is expanded in terms 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 spherical harmonics 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 Y_{lm}\left(\hat{\mathbf{r}}\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/":): \rho _{{i}}\left({\mathbf {r}}\right)=\sum \limits _{{l=1}}^{{L_{{{\mathrm {max}}}}}}\sum \limits _{{m=-l}}^{{l}}\sum \limits _{{n=1}}^{{N_{{{\mathrm {R}}}}^{{l}}}}c_{{nlm}}^{{i}}\chi _{{nl}}\left(r\right)Y_{{lm}}\left({\hat {{\mathbf {r}}}}\right),
The tag ML_LMAX2 specifies the maximum angular momentum quantum 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 L_\max} of spherical harmonics used in this expansion.
| Mind: This tag is only relevant 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)} . The corresponding number of 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 linearly 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 L_\max} and is also depending on ML_MRB2 and the number of elements present. |
By default an angular filtering (see ML_LAFILT2 and ML_IAFILT2) with a filtering parameter of ML_AFILT2=0.002 is used where a value of ML_LMAX2=4 is perfectly safe for most applications. If the angular filter is switched off we recommend to use a value of ML_LMAX2=6 (this is then the default value).
Related Tags and Sections
ML_LMLFF, ML_MRB1, ML_MRB2, ML_LAFILT2, ML_IAFILT2, ML_AFILT2