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# ML MRB1

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ML_MRB1 = [integer]
Default: ML_MRB1 = 8

Description: This tag sets the number ${\displaystyle N_{\text{R}}^{0}}$ of radial basis functions used to expand the radial descriptor ${\displaystyle \rho _{i}^{(2)}(r)}$ within the machine learning force field method.

The radial descriptor is constructed from

${\displaystyle \rho _{i}^{(2)}\left(r\right)={\frac {1}{4\pi }}\int \rho _{i}\left(r{\hat {\mathbf {r} }}\right)d{\hat {\mathbf {r} }},\quad {\text{where}}\quad \rho _{i}\left(\mathbf {r} \right)=\sum \limits _{j=1}^{N_{\mathrm {a} }}f_{\mathrm {cut} }\left(r_{ij}\right)g\left(\mathbf {r} -\mathbf {r} _{ij}\right)}$

and ${\displaystyle g\left(\mathbf {r} \right)}$ is an approximation of the delta function. In practice, the continuous function above is transformed into a discrete set of numbers by expanding it into a set of radial basis functions ${\displaystyle \chi _{n0}(r)}$ (see this section for more details):

${\displaystyle \rho _{i}^{(2)}\left(r\right)={\frac {1}{\sqrt {4\pi }}}\sum \limits _{n=1}^{N_{\mathrm {R} }^{0}}c_{n00}^{i}\chi _{n0}\left(r\right).}$

The tag ML_MRB1 sets the number ${\displaystyle N_{\text{R}}^{0}}$ of radial basis functions to use in this expansion. The value of ML_MRB1 is the default value for ML_MRB2.