I'm not sure if this question would be more appropriate for Chemistry or Physics SE, but if so please forgive me.
I have drawn the following picture; the spheres represent atoms and the lines connecting them represent chemical bonds.
Another view:
I would like to determine two dihedral angles:
- the dihedral angle comprised of the vertices C-G-O-A. (Or maybe, although I am not sure, I should state this as the dihedral angle between the bonds C-G and O-A.)
- the dihedral angle comprised of the vertices D-A-O-G. (Or perhaps this should be the dihedral angle between D-A and O-G.
O is the origin. The Cartesian coordinates of the vertices are:
- O = {0, 0, 0}
- A = {-1.2211, -0.705, 0}
- B = {1.2211, -0.705, 0}
- C = {0, 1.41, 0}
- D = {-1.2211, -2.115, 0}
- E = {1.2211, -2.115, 0}
- G = {0, 0.705, 1.2211}
One problem that I am encountering is that it is not clear to me how a bond between two atoms can define a plane, since I think that a plane is only uniquely defined by three noncollinear points. Wikipedia says that the dihedral angle $\varphi_{AB}$ between two planes $A$ and $B$ is simply $\cos \varphi_{AB} = \textbf{n}_A \cdot \textbf{n}_B$ where $\textbf{n}_A$ and $\textbf{n}_B$ are the unit vectors normal to planes $A$ and $B$. But it is not clear to me how to actually define $A$ and $B$ given only two vertices (i.e., two atoms) defining each plane.
Do you have any suggestions?