Dipoles, Quadrupoles, Octopoles, and higher multipoles

[FaNgS]

I'm taking an advanced thermodynamics course (its a pain!) anyways, we're studying intermolecular forces and how based on these forces, we can determine thermodynamic properties of pure components or mixtures, by linking them with statistical mechanics.

my question is, how do you determine which multipole does a molecule have?

i know that CO2 for example has a quadrupole and HCl has a dipole

what about other structures, for example diisopropylether ?

how would one determine?

 

[zhermes]

In general multipoles are approximations for the actual case. I.e. if you take an interaction (e.g. electromagnetic) you can expand the force of the interaction in terms of increasing powers of the separation---poles. The 'monopole' term goes like 1/r, and generally represents something like the total charge (for E&M), next would be the dipole term ($$1/r^2$$) etc etc. In general the lowest order non-zero term will be the most important.

CO2 Has no dipole term because it is linearly symmetric: the classical dipole moment would be zero. Thus the important term is the next higher term----the quadrupole. HCl on the other hand, has a dipole moment. etc etc

For an arbitrary configuration (e.g. molecule) every multipole will exist, with the higher order terms being less and less important.
Does that help at all?

 

[FaNgS]

zhermes, thanks but not much help there :(

I understand that the force or the potential energy of the molecule is dependent on the separation distance r and it varies with r raised to a power which can be anything from 1, 2 or even 6 (depending on the type of multipole present or induced dipole etc)

but i still can't make sense of how to determine the type of multipole present in a molecule.

for instance i found out in my last class that diisopropylether has a quadrupole but how?!