ML_RCUT2

ML_RCUT2 = [real]
Default: ML_RCUT2 = 5.0

Description: This flag sets the cutoff radius $R_{cut}$ for the angular descriptor $ρ_{i}^{(3)} (r)$ in the machine learning force field method. The unit of the cut-off radius is $Å$ .

The angular descriptor is constructed from

$ρ_{i}^{(3)} (r, s, θ) = \iint d \hat{𝐫} d \hat{𝐬} δ (\hat{𝐫} \cdot \hat{𝐬} - c o s θ) \sum_{j = 1}^{N_{a}} \sum_{k \neq j}^{N_{a}} ρ_{i k} (r \hat{𝐫}) ρ_{i j} (s \hat{𝐬}), where ρ_{i j} (𝐫) = f_{c u t} (r_{i j}) g (𝐫 - 𝐫_{i j})$

and $g (𝐫)$ is an approximation of the delta function. A basis set expansion of $ρ_{i}^{(3)} (r)$ yields the expansion coefficients $p_{n ν l}^{i}$ which are used in practice to describe the atomic environment (see this section for details). The tag ML_RCUT2 sets the cutoff radius $R_{cut}$ at which the cutoff function $f_{c u t} (r_{i j})$ decays to zero.

Mind: The cutoff radius determines how many neighbor atoms

N_{a}

are taken into account to describe each central atom's environment. Hence, important features may be missed if the cutoff radius is set to a too small value. On the other hand, a large cutoff radius increases the computational cost as the cutoff sphere contains more neighbor atoms. A larger cutoff can also significantly degrade the learning efficiency. A good compromise is system-dependent, therefore different values should be tested to achieve satisfactory accuracy and speed.

For materials containing only H, B, C, O, N, and F (i.e. organic molecules, polymers), the learning efficiency might increase when ML_RCUT2 is set to values around 4 $Å$ (that is, less training data are required to achieve a specific accuracy), wheres for materials with very long bonds, a larger value around 6 $Å$ can improve the accuracy,

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