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: \(f(x) = (x(x((315 - 70x)x - 540) + 420) - 126)x^5 + 1\)