[Messi]

Hi, I am unsure what the meaning of a quadruple moment is. Someone had mentioned it to me but I was unsure what it is. I know that the molecules N₂ and CO₂ both have a quadruple moment. But what does it mean? I know what dipole moment is... what is a quadruple moment? Picture attached below

[Corribus]

A quarupole is a charge distribution (in case of electric quadrupole) with a higher order symmetry than a dipole.  It is described mathematically by a tensor rather than a vector, so it's hard to visualize and very hard to draw out on a piece of paper. They say that two equal dipoles arranged in antiparallel fashion is the easiest description of a quadrupole, but I'd be lying if I said I could get that from the mathematical expression.  I take the mathemeticians' word for it.   The quandrupole moment is magnitude of the effect.  It is hard to measure exerimentally, which is probably why you don't see it very often.

There are spectroscopic implications of large quadrupole momen - most likely related to nonlinear optical effects - but honestly I couldn't tell you what they are off the top of my head.  I'm more used to dealing with polarizabilities and hyperpolarizabilities, and how these are exactly related to the quadrupole moment is beyond my knowledge.

[blaisem]

I have come across a couple of areas where the effects of a quadrupole moment can be significant:

-Nuclear Quadrupole Resonance spectroscopy and NMR
-IR quadrupole spectroscopy

In NMR, for example, coupling effects from a nuclei with a significant quadrupole moment (like Chlorine) will not normally be observed.  This is due to a quadrupole moment leading to more rapid relaxation times.

I also found an interesting paper on its relevance in a couple other areas:

http://scienide2.uwaterloo.ca/~rleroy/Pubn/07JCP-N2quadrupole.pdf

[Big-Daddy]

What gives rise to a quadrupole moment? (For the OP's benefit and for mine)

[Corribus]

What gives rise to a quadrupole moment? (For the OP's benefit and for mine)

A charge distribution which meets the criteria described earlier in the thread.  A simple example is a molecular pi-system.

Benzene, for example, has no permanent electronic dipole, but there ARE regions of positive and negative charge.  They just happen to balance out and give a net dipole moment of zero.  The pi electron clouds above and below the plane of the ring are negatively charged, because that's where the pi-electron density is concentrated.  To compensate, there is a slightly positive charge around the plane of the ring. 

The electronic quadrupole of benzene (and other aromatic structures) is what allows them to electrostatically interact with cations and other positively-charged metal centers.

http://en.wikipedia.org/wiki/Cation%E2%80%93pi_interaction