ML_LMAX2

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ML_LMAX2 = [integer]

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

Description: This tag specifies the maximum angular momentum quantum number $L_{\max }$ 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

$\rho _{i}\left(\mathbf {r} \right)=\sum \limits _{j=1}^{N_{\mathrm {a} }}f_{\mathrm {cut} }\left(r_{ij}\right)g\left(\mathbf {r} -\mathbf {r} _{ij}\right),$

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

$\rho _{i}\left(\mathbf {r} \right)=\sum \limits _{l=1}^{L_{\mathrm {max} }}\sum \limits _{m=-l}^{l}\sum \limits _{n=1}^{N_{\mathrm {R} }^{l}}c_{nlm}^{i}\chi _{nl}\left(r\right)Y_{lm}\left({\hat {\mathbf {r} }}\right),$

The tag ML_LMAX2 specifies the maximum angular momentum quantum number $L_{\max }$ of spherical harmonics used in this expansion.

Mind: This tag is only relevant for the angular descriptor

\rho _{i}^{(3)}(r)

. The corresponding number of expansion coefficients

p_{n\nu l}^{i}

scales linearly with

L_{\max }

(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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