Hello, as a chemist I sometimes run into mechanisms or reactions that are explained through the use of an electric quadrapole moment. I've spent some time looking at various sources, and I'd like to summarize what I believe it is. Hopefully someone here can provide feedback on my understanding.
Any charge distribution (electric field) is completely described by its multipole expansion. The quadrapole moment is simply the third term in this expansion, after a monopole and dipole.
Basically, when we, as chemists, refer to a dipole moment in a molecule, we are really only partially describing the electric field present because we are limiting ourselves to one term. This often works--at least approximately--because the dipole moment is a relatively highly contributing term in the multipole expansion.
This leads me to some questions on under what conditions a term in the multipole expansion, like the quadrapole moment, is zero or non-zero:
1. Since all the pictures of a quadrapole moment show four point charges, I am wondering if that is a minimum requirement for a non-zero quadrapole moment. For example, if I have two unlike point charges in space, can I have both non-zero dipole and quadrapole moments?
2. If two charges are opposite and equal, what terms would I expect to be non-zero in its multipole expansion? Right now I would expect only the monopole and dipole terms to be non-zero. Although I have to admit I don't really understand how a monopole here fits in since there are two charges; I only assume it because the dipole moment is non-zero.
Thanks so much for any advice and patience :)
Any charge distribution (electric field) is completely described by its multipole expansion. The quadrapole moment is simply the third term in this expansion, after a monopole and dipole.
Basically, when we, as chemists, refer to a dipole moment in a molecule, we are really only partially describing the electric field present because we are limiting ourselves to one term. This often works--at least approximately--because the dipole moment is a relatively highly contributing term in the multipole expansion.
This leads me to some questions on under what conditions a term in the multipole expansion, like the quadrapole moment, is zero or non-zero:
1. Since all the pictures of a quadrapole moment show four point charges, I am wondering if that is a minimum requirement for a non-zero quadrapole moment. For example, if I have two unlike point charges in space, can I have both non-zero dipole and quadrapole moments?
2. If two charges are opposite and equal, what terms would I expect to be non-zero in its multipole expansion? Right now I would expect only the monopole and dipole terms to be non-zero. Although I have to admit I don't really understand how a monopole here fits in since there are two charges; I only assume it because the dipole moment is non-zero.
Thanks so much for any advice and patience :)