[ramboacid]

In class we learned that the dipole moment μ is defined as μ=qR, where q is the amount of charge transferred across a bond and R is the length of the bond. To calculate the percent ionic character (%IC), we find the fraction of the fundamental charge transferred, namely
%IC = (q)(1.602E-19 C)^-1
       = (μ*3.336E-30 C·m)(R*1.602E-19 C)^-1

I understand and agree with this interpretation for cases in which one electron is being transferred, such as in NaCl or across single covalent bonds like C-O and C-N. However, what about the cases of C=O or C≡N, which if we were to treat ionically would require the transfer of 2 or 3 electrons from the carbon atom to the O or N, respectively? Would we then divide by 2 or 3 times the fundamental charge, so as to give the percent ionic character of a bond in which we would expect 2 or 3 electrons to be transferred? The resulting formula would be along the lines of
%IC = (μ*3.336E-30 C·m)(R*n*1.602E-19 C)^-1
where n is the bond order a.k.a the number of electrons that we'd expect to be transferred in a purely ionic double or triple bond (I know that's impossible, but I mean that instead of sharing the electrons in the multiple bond we'd imagine that they just went from one atom to the other). I think this idea would have some merit because dividing by the bond order would make multiple covalent bonds less ionic as we'd expect them to be (for C-N the %IC≈0.25, but for C≡N assuming a similar dipole moment %IC≈0.8 ).

I would simply just test this out by looking up data values of dipole moments, bond lengths, and %IC, and then test out my hypothesis by performing the calculations, but I can't find published values of %IC and dipole moments for multiple bonds and thus haven't been able to try it out. The flaw in my idea would be apparent if the dipole moments of multiple bonds differed significantly from their single bond counterparts (which I believe they might because of fewer lone pairs), but as I said I haven't been able to find the data to decide one way or another.

[MrTeo]

Well, obviously adding a rescaling factor (n) equal to the number of electrons, just like you did, makes perfect sense as, for example, if we used this rough extimate of the ionic percentage for something like CaCl₂ we would get 200%. I think this correction is needed not only if we want to make the expression more accurate but even if we want it to have some sense.

Talking of the validity of this expression, I think the whole idea of ionic bonding vs covalent bonding doesn't really need to be stretched this far, as it's a coarse-grained view of the much clearer (and true) fact that every bond has an electrostatic and a covalent (coming from quantum exchange forces, as they're sometimes referred to, and other effects which find no equivalent in classical physics) component. This is why you didn't find anything about IC% or things like that, there's no need to perform such calculations as they're kind of useless and sometimes misleading if not used to pinpoint some basic ideas just like it's done in General Chem (on the other hand, if we talk about dipole moments, even though they're not one of the most measured physical quantities, I'm pretty sure that you can find a cartload of old data on most of the easiest molecules).

If you want to play some more with this kind of expressions here is another one, to predict the ionic percentage of a bond. I don't really know where this comes from and I don't have enough time right now, but I think it should be easy to explain it using basic Physics and Chemistry (χ_A and χ_B are the Pauling electronegativities of the AB molecule):

[tex]
IC\%=\frac{\left(\chi_A-\chi_B\right)^2}{3+\left(\chi_A-\chi_B\right)^2} \cdot 100
[/tex]

[ramboacid]

Thanks for the reply! My class right now is covering the classical model of bonding and such before we delve into quantum, so we still were required to learn this concept for Gen Chem. I just wanted to make sure that my thinking was correct because of the lack of internet resources.

[ptryon]

If you haven't studied valence bond theory before the following may not make sense so its worth coming back to this when you have studied bonding a little more.

A double bond is comprised of a sigma bond and a pi bond. In a sigma bond the orbitals overlap on the internuclear axis and in a pi bond two unhybridized p-orbitals (that are at 90 degrees to the inter-nuclear axis) overlap. In a pi bond the electrons interact above and below the internuclear axis (p-orbitals consist of 2 lobes).

I stand to be corrected, but I think the equation for %I.C only applies to the electrons in the sigma bond because the electrons are directly between both nuclei. I am not sure how you account for the pull of the nuclei on the electrons in the pi bond.