# How can I determine the vector parallel to the long molecular axis?

I have a molecule in a system (the molecule is not in the center) with determined coordinates of all atoms. One of my molecule is on the picture below What I need is to determine the vector that is parallel to the long axis of the molecule. As I think I should find the inertia tensor of the molecule. I calculated $I_x$, $I_y$ and $I_z$. Then I tried to normalize the vector and compare it with the vector between two blue nitrogen atoms. It showed that I had done something wrong because vectors was not even close.

• Compute the geometric center at the leftmost and rightmost points of your molecule and use those two points to define your vector? I'm not sure this is really a physics question on-topic here... Nov 17, 2015 at 23:47

Second, use the body frame coordinates to calculate the inertia matrix in the body frame. The inertia matrix must look like this: $$\begin{pmatrix}I_{xx} & -I_{xy} & -I_{xz} \\ -I_{yx} & I_{yy} & -I_{yz} \\ -I_{zx} & -I_{zy} & I_{zz} \end{pmatrix}$$
I put the minus signs on the products of inertia because they can be easily forgotten. Sometimes the minus signs are included in the definition of $I_{jk}$, in which case they should not appear again in the inertia matrix.