Angle Functions
Functional forms for angle interactions
Below are listed the interaction forms available for angles within molecules, with energy and force equations provided in full. Parameters are listed in the input order expected by Dissolve.
Angle interaction between atoms $i$, $j$ and $k$, where the bond angle is $\theta_{ijk}$.
Note that within input files any equilibrium angles $\theta_{eq}$ should be provided in degrees, but the equations as written below work internally in radians.
Force equations are derived by applying the chain rule, and where
$$ \frac{d\theta}{d\cos\theta} = -\frac{1}{\sin\theta} $$
| Keyword | Parameters | Description |
|---|---|---|
Harmonic |
k$\theta_{eq}$ |
Simple harmonic angle bend $$ E_{ijk} = \frac{1}{2} k (\theta_{ijk} - \theta_{eq})^2 $$ $$ F_{ijk} = \frac{d\theta}{d\cos\theta} k (\theta_{ijk} - \theta_{eq}) $$ |
Cosine |
kn$\theta_{eq}$s |
Cosine angle bend with periodicity $n$ $$ E_{ijk} = k \left( 1 + s \cos(n \theta_{ijk} - \theta_{eq}\right)) $$ $$ F_{ijk} = \frac{d\theta}{d\cos\theta} k n s \sin(n \theta_{ijk} - \theta_{eq}) $$ |
Cos2 |
k$C_0$$C_1$$C_2$ |
Double cosine angle potential $$ E_{ijk} = k (C_0 + C_1 \cos(\theta_{ijk}) + C_2 \cos(2 \theta_{ijk}) ) $$ $$ F_{ijk} = \frac{d\theta}{d\cos\theta} k (C_1 \sin(\theta_{ijk}) + 2 C_2 \sin(2 \theta_{ijk}) ) $$ |