Cutoffs

class Cut_Base

Base class to be inherited by all cutoffs

Subclassed by Cut_Cos, Cut_CosS, Cut_Dummy, Cut_PT, Cut_Poly, Cut_PolyS, Cut_Tanh

class Cut_Dummy : public Cut_Base

Represents a basic cutoff function with a sharp transition at the cutoff radius.

The Cut_Dummy class implements a simple cutoff function defined by:

\[\begin{split} f_c(r) = \begin{cases} 1, & \text{if } r \leq r_{\text{cut}} \\ 0, & \text{if } r > r_{\text{cut}} \end{cases} \end{split}\]

and its derivative:

\[ f_c'(r) = 0 \]

where:

  • \( r \) is the radial distance.

  • \( r_{\text{cut}} \) is the cutoff radius.

Characteristics:

  • The function value is constant (1) within the cutoff radius and zero beyond it.

  • The derivative of the function is zero everywhere except at \( r = r_{\text{cut}} \) where it is undefined due to the discontinuity.

Note: Since the function is discontinuous at \( r = r_{\text{cut}} \) its derivative is not defined at that point. In practical computations, the derivative function calc_prime returns 0.0 for all \( r \)

class Cut_Cos : public Cut_Base

Cosine cutoff function.

The Cut_Cos class implements a smooth cosine cutoff function defined by:

\[\begin{split} f_c(r) = \begin{cases} \dfrac{1}{2}\left[ \cos\left( \dfrac{\pi r}{r_c} \right) + 1 \right], & \text{if } r \leq r_c \\ 0, & \text{if } r > r_c \end{cases} \end{split}\]

This function smoothly transitions from 1 to 0 over the interval \( 0 \leq r \leq r_c \). It is commonly used in molecular simulations to smoothly truncate interactions without introducing discontinuities in the potential energy or its derivatives.

Reference:

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

class Cut_Tanh : public Cut_Base

Hyperbolic tangent cutoff function.

The Cut_Tanh class implements a smooth cutoff function using the hyperbolic tangent, defined by:

\[\begin{split} f_c(r) = \begin{cases} \tanh^3\left( 1 - \dfrac{r}{r_c} \right), & \text{if } r \leq r_c \\ 0, & \text{if } r > r_c \end{cases} \end{split}\]

This function smoothly transitions from 1 to 0 over the interval \( 0 \leq r \leq r_c \), with the transition shape controlled by the cubic power of the hyperbolic tangent.

Reference:

Behler, J. (2011). Atom-centered symmetry functions for constructing high-dimensional neural network potentials. Journal of Chemical Physics, 134(7), 074106. DOI:10.1063/1.3553717

Warning

doxygenclass: Cannot find class “Cut_Poly2” in doxygen xml output for project “Tadah!” from directory: ../../build/docs/xml