# Cutoff functions

enum nnp::CutoffFunction::CutoffType

List of available cutoff function types.

Most cutoff types allow the definition of an inner cutoff $$r_{ci} := \alpha \, r_c$$. Then the cutoff is equal to $$1$$ up to the inner cutoff:

$$f_c(r) = \begin{cases} 1, & \text{for } 0 \le r < r_{ci} \\ f(x), & \text{for } r_{ci} \le r < r_c \text{ where } x := \frac{r - r_{ci}}{r_c - r_{ci}} \\ 0 & \text{for } r \geq r_c \end{cases}$$

Values:

enumerator CT_HARD

$$f(x) = 1$$

enumerator CT_COS

$$f(x) = \frac{1}{2} \left[ \cos (\pi x) + 1\right]$$

enumerator CT_TANHU

$$f_c(r) = \tanh^3 \left(1 - \frac{r}{r_c} \right)$$

enumerator CT_TANH

$$f_c(r) = c \tanh^3 \left(1 - \frac{r}{r_c} \right),\, f(0) = 1$$

enumerator CT_EXP

$$f(x) = e^{1 - \frac{1}{1 - x^2}}$$

enumerator CT_POLY1

$$f(x) = (2x - 3)x^2 + 1$$

enumerator CT_POLY2

$$f(x) = ((15 - 6x)x - 10) x^3 + 1$$

enumerator CT_POLY3

$$f(x) = (x(x(20x - 70) + 84) - 35)x^4 + 1$$

enumerator CT_POLY4

$$f(x) = (x(x((315 - 70x)x - 540) + 420) - 126)x^5 + 1$$