Bending potentials¶

A bending type is defined by a triplet of atom types, a functional form and the corresponding parameters values. The order of the atom types correspond to the numerical order of the figure.

Image title — A bending angle between atoms 1, 2 and 3

Animation — The bending angle $\theta$ oscillates around its equilibrium value $\theta_0$ (here with a harmonic potential).

The bending angle $\theta$ is defined by:

\[ \theta = \arccos{\frac{\mathbf{r}_{21}\cdot \mathbf{r}_{23}}{r_{21}r_{23}}} \]

The angle is computed as $\theta = \operatorname{atan2}(\lVert \mathbf{r}_{21}\times\mathbf{r}_{23}\rVert, \mathbf{r}_{21}\cdot\mathbf{r}_{23})$, which gives the same value but stays accurate close to 0 and 180 degrees. Linear (or almost linear) angles are allowed: the force is then computed with $\sin\theta$ bounded below by $10^{-3}$.

The following types of bending potentials are defined in exastamp: