Origin of geometric similarities between multipoles & AO's

[Steven Hanna]

a textbook I'm reading has pointed out geometric similarities between atomic orbitals and multipoles. do these similarities originate from a mutual dependence on the spherical harmonics? if so, how does something like a dipole or a quadrupole depend on the Ylm's? Note that my I did my undergrad in chemistry, not physics.

 

[DrClaude]

Can you give the reference of the textbook you are reading?

 

[Steven Hanna]

Can you give the reference of the textbook you are reading?

It's "modern physical organic chemistry" by anslyn and dougherty, page 19. The book states that "monopoles look like s-orbitals (spheres); dipoles look like p orbitals (a + end and a - end); quadrupoles look like d orbitals; octupoles look like f orbitals, etc. The analogy between multipoles and orbitals is just given to illustrate phasing properties; orbitals do not have polar character."

 

[DrClaude]

I think it is simply an analogy.

 

[fresh_42]

I agree on @DrClaude's opinion of an analogy.

The analogy between multipoles and orbitals is just given to illustrate phasing properties; orbitals do not have polar character."

The imagination of valence electrons as geometric poles is somehow better suited to explain chemical bonds than smooth shells would be. It almost automatically reminds on our plastic models we have for the elements and the way we write bonds.
However, would be interesting to know something about to which extend this analogy is a description of reality.

 

[Steven Hanna]

I agree on @DrClaude's opinion of an analogy.

The imagination of valence electrons as geometric poles is somehow better suited to explain chemical bonds than smooth shells would be. It almost automatically reminds on our plastic models we have for the elements and the way we write bonds.
However, would be interesting to know something about to which extend this analogy is a description of reality.

right, that's what I'm curious about. I'm pretty sure that the shapes of AO's are pretty much determined by the angular wave function. And I also know that the Ylm's show up in a lot of other applications, e.g. rigid rotor. Could they also somehow be involved in generating the shapes of electric field patterns like those arising from dipole and quadrupole moments?

 

[vanhees71]

The angular-momentum eigenstates provide a multipole expansion of the solutions of the Schrödinger equation. This is in vary close analogy to a multipole expansion of any partial differential equation, including electrodynamics. Perhaps that's what the book's author had in mind.