ML_LMAX2

ML_LMAX2 = [integer]

Default: ML_LMAX2	= 3	for ML_LAFILT2 = .TRUE.
	= 6	else

Description: This tag specifies the maximum angular momentum quantum number [math]\displaystyle{ L_\max }[/math] 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

[math]\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), }[/math]

where [math]\displaystyle{ g\left(\mathbf{r}\right) }[/math] is an approximation of the delta function, is expanded in terms of radial basis functions [math]\displaystyle{ \chi_{nl}(r) }[/math] and spherical harmonics [math]\displaystyle{ Y_{lm}\left(\hat{\mathbf{r}}\right) }[/math] (see this section for more details):

[math]\displaystyle{ \rho_{i} \left( \mathbf{r} \right) = \sum\limits_{l=1}^{L_{\mathrm{max}}} \sum\limits_{m=-l}^{l} \sum\limits_{n=1}^{N^{l}_{ \mathrm{R}}} c_{nlm}^{i}\chi_{nl} \left( r \right) Y_{lm} \left( \hat{\mathbf{r}} \right), }[/math]

The tag ML_LMAX2 specifies the maximum angular momentum quantum number [math]\displaystyle{ L_\max }[/math] of spherical harmonics used in this expansion.

Mind: This tag is only relevant for the angular descriptor [math]\displaystyle{ \rho^{(3)}_i(r) }[/math]. The corresponding number of expansion coefficients [math]\displaystyle{ p_{n\nu l}^{i} }[/math] scales linearly with [math]\displaystyle{ L_\max }[/math] (however the calculation of the spherical harmonics scales quadratically) 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=3 is perfectly safe for most applications. If you need to improve the accuracy, you might also try to increase it to ML_LMAX2=4. If the angular filter is switched off, we recommend to use a value of ML_LMAX2=6 (this is then the default value).

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