# How real are bond dipoles?

In general chemistry, it is common to teach students to determine a molecular dipole by having them first determine "bond dipoles" which are just based on electronegativity. Then, by adding up these vectors, one determines the direction of the overall dipole.

In quantum mechanics, however, the molecular dipole is found by calculating the expectaion value $\langle\psi|\hat{\mu}|\psi\rangle$. This can be decomposed into $x$, $y$, and $z$ components if one so desires. Regardless, the actually quite useful idea of a bond dipole is nowhere to be found.

I assume that there is not a rigorous way of defining a bond dipole so that a sum of these bond dipoles equals the expectation value above. This is because there is not a well-defined way to partition electron density which is exact. I suppose one could do this using the theory of atoms in molecules.

Nonetheless, other ideas like local mode vibrations are approximate in the sense that a local mode is not an eigenfunction of the polyatomic vibrational Hamiltonian, yet local modes are still very useful and even more accurate in some contexts.

The same is sort of true of bond dipoles in that if one imagines a very long molecule which is polar at one end, a nearby molecule which moves along this large molecule will experience a changing electric field because the dipole of the molecule is only a true point-dipole when the molecule is very far away. So, the field experienced by nearby molecules is more akin to the sum of bond dipoles in the region nearby.

So, is there a rigorous way to determine bond dipoles from first principles? Is it as simple as projecting the total dipole onto a bond axis? What is the form of this projector? Also, in cases where the partitioning of atoms is well-defined, such as the theory of atoms in molecules, are bond dipoles well-defined and do they relate to the total dipole as we expect?

Answers to any of these questions would be welcome.

To be more clear, I am talking about the bond dipoles described on this wikipedia page. They do not provide any formal way of actually calculating the bond dipoles. They mention one can get these dipoles after calculating the total dipole, but I am not sure of the uniqueness of this under unitary transformations.

• I am assuming that you are referring to the transition dipole moment. In that case, the expression given in the wiki page (en.wikipedia.org/wiki/Transition_dipole_moment) is accurate. Here is a journal that uses it to calculate the permanent dipole: journals.aps.org/pra/abstract/10.1103/PhysRevA.68.022501 – CoffeeIsLife Oct 31 '17 at 5:16
• I believe that the dipoles are real. There is ab initio software that predicts IR spectra. I am not sure if they use another form to calculate the transition dipole moment. – CoffeeIsLife Oct 31 '17 at 5:20
• I think you misunderstand. I'm referring to the idea that one that determine the total dipole moment of a molecule by adding up small contributions due the polarity of all the individual bonds. – jheindel Oct 31 '17 at 5:58
• If you look that deep, then the bonds themselves are not really real. – Ivan Neretin Oct 31 '17 at 8:18
• @IvanNeretin I don't think this is looking that deep really. I think it makes sense that there should be a way of calculating the total dipole approximately by summing up individual small dipoles which are found based on properties of the atoms themselves. I have never heard of this, but I don't see why it shouldn't be possible even if it doesn't give a good answer. Don't you think there's some sense to the idea? – jheindel Oct 31 '17 at 17:00