Angles

Angles describe angular bonds between three atoms. These bonds are modeled as harmonic angular springs. The energy of such a bond between atoms i, j, and k is given by

$$E_{\text{angle}} = k_{\theta}{(\theta - {\theta}_0)}^2 + k_{\text{ub}}(\vert\vec{r}_{ik}\vert-r_{\text{ub}})^2$$

where

• $k_{\theta}$ = force constant specified in the parameter file for this bond type
• $\theta$ = calculated angle between the vector that connect atoms i and j and the vector that connects atoms k and j. This angle is calculated using the formula:
  
  $$\theta = {\cos}^{-1} \left(\frac{ {{\vec{r}}_{ij}} \cdot {{\... ... }{ \vert{\vec{r}}_{ij}\vert\vert{\vec{r}}_{kj}\vert} \right)$$
  
  

• ${\theta}_0$ = rest angle for this bond specified in the parameter file for this angle type
• $k_{\text{ub}}$ = Urey-Bradley constant, which defaults to zero
• $r_{\text{ub}}$ = rest distance for the Urey-Bradley term