Requests for technical support from the VASP group should be posted in the VASP-forum.

# 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 ${\displaystyle L_{\max }}$ 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

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

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

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

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

 Mind: This tag is only relevant for the angular descriptor ${\displaystyle \rho _{i}^{(3)}(r)}$. The corresponding number of expansion coefficients ${\displaystyle p_{n\nu l}^{i}}$ scales linearly with ${\displaystyle L_{\max }}$ 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).