Cutoffs

class Cut_Base

Base class to be inherited by all cutoffs

Subclassed by Cut_Cos, Cut_Dummy, Cut_Poly2, Cut_Tanh

class Cut_Dummy : public Cut_Base

Dummy cutoff function.

\[\begin{split} f_c(r) = \begin{equation} \begin{cases} 1 & \text{if } r \leq r_c\\ 0 & \text{otherwise}\\ \end{cases} \end{equation} \end{split}\]

class Cut_Cos : public Cut_Base

Cos cutoff function.

\[\begin{split} f_c(r) = \begin{equation} \begin{cases} \frac{1}{2}\big[ \cos\big( \frac{\pi r}{r_c} \big)+1 \big] & \text{if } r \leq r_c\\ 0 & \text{otherwise}\\ \end{cases} \end{equation} \end{split}\]

Behler, J., Parrinello, M. (2007). Generalized neural-network representation of high-dimensional potential-energy surfaces. Physical Review Letters, 98(14), 146401. https://doi.org/10.1103/PhysRevLett.98.146401

class Cut_Tanh : public Cut_Base

Tanh cutoff function.

\[\begin{split} f_c(r) = \begin{equation} \begin{cases} \tanh^3\big( 1 -\frac{r}{r_c} \big) & \text{if } r \leq r_c\\ 0 & \text{otherwise}\\ \end{cases} \end{equation} \end{split}\]

Behler, J. (2011). Atom-centered symmetry functions for constructing high-dimensional neural network potentials. J. Chem. Phys., 134(7), 074106. https://doi.org/10.1063/1.3553717

class Cut_Poly2 : public Cut_Base

Polynomial-2 cutoff function.

\[\begin{split} f_c(r) = \begin{equation} \begin{cases} 1 & \text{if } r \leq (r_c-1)\\ r^3(r(15-6r)-10)+1 & \text{if } (r_c-1) < r \leq r_c\\ 0 & \text{otherwise}\\ \end{cases} \end{equation} \end{split}\]

Singraber, A., Rg Behler, J., Dellago, C. (2019). Library-Based LAMMPS Implementation of High-Dimensional Neural Network Potentials. https://doi.org/10.1021/acs.jctc.8b00770