In reading inorganic teaching materials I've noticed an opposing orbital overlap trend. In the context of covalent solid state materials in the carbon column (all diamond-like structure), as you go down the column orbital overlap is said to decrease due to larger and larger atom size, thus leading to weaker bonding interactions and smaller band gaps. (Carbon is an insulator, silicon and germanium are semiconductors, alpha-tin is a metal.)
However, fast forward a few weeks in my syllabus and we are next looking at ligand field splitting parameters (the "delta" parameter) in the context of predicting high spin and low spin complexes. The parameter is said to increase from the 1st to 2nd to 3rd row of the transition metals specifically because overlap between metal and ligand orbitals is improving down the column, leading to stronger bonds and raising the eg antibonding orbitals in energy.
When the trend is applied to the halogens, their bond energies are said to decrease down the column due to poorer overlap and longer bonds. (F-F is the notable exception to the trend due to lots of e- / e- repulsion.)
What to do? Which to believe? Is the 2nd/3rd row trend different only because it involves metal/ligand overlap and not homonuclear interactions?
Thanks for any clarification!
OK. There's several questions in there. First, the group IV elements from C to Pb. The argument made about less overlap because atoms are "getting bigger" I've always found very, very odd. If you imagine a picture of a C-C bond, orbitals happily overlapping and multiply everything by 1.5, and call it "Si-Si", nothing would change in terms of orbital overlap. If all parts of the atom changed proportionally, atom size would have no effect. So the bonds must be getting longer relative to the size of the bonding orbitals.
What (I think) is going on here, is that the s-orbital is contracting more and more relative to the p-orbtial and that the amount of p-orbtial you can bond with before you bump into the first radial node is shrinking as you go down the table.
First, the s-thing. There are four anomalous sections of the periodic table that are weird because they have an anomalously small subshell. Hydrogen's 1s is anomalously small relative to the other ns orbitals, B-F have anomalously small 2p orbitals relative to the other np orbitals, the first row transition metals have anomalously small 3d orbitals relative to the 4 and 5d, and the lanthanides (lanthanoids?) have 4f orbitals that are much smaller than the 5fs of the actinides, even when correcting for atomic size in each case.
This is due to the fact that, for example, the 2p orbital can be as small as it wants, but the 3p orbital, like the second doll in one of those nesting Russian/Ukranian dolls, has to be big enough to contain the 2p (it must have a zero overlap and be orthogonal). The 4p must be big enough to hold the 3p, etc.
The consequence of this for group IV is that carbon's 2s and 2p are the same size. The 3p of silicon is much bigger than the 3s. Bonding in silicon is mostly with the p-orbitals. The gap is most dramatic between 2p and 3p, but because of incomplete shielding, the gap in size grows going down the table (the ns is less shielded than np). By the time you get to Pb...
OK, now the node thing. I may be totally wrong on this one. We always draw p-orbitals like the 2p on carbon because those **@#$%-*@$& organic chemists scarred us for life. 3p and higher orbitals have *radial nodes*. And it's not Psi^2 that overlaps to form bonds, it's Psi! So it's no good overlapping with the stuff on the other side of the first radial node--that's an antibonding interaction! Well, by the time you get to Pb, the amount of orbital you can overlap with before you hit your first node is small, so you get very little overlap. This paragraph is pure conjecture, whereas the previous ones (especially the fact that 2p is weird, and therefore hybridizes, forms pi bonds, etc.), I feel like I can provide evidence of.
OK, now delta in transition metal complexes. Remember how the first iteration of each subshell is too small? This is why hydrogen is not like other alkali metals and why B, C, N, O, and F "hybridize", form very strong bonds, do pi bonding, and all that other stuff that, you know, makes life possible, and is responsible for all of organic chemistry and biochemistry. All that is basically a result of this orthogonality requirement. We exist because of dinky 2p orbitals, dinky 1s orbitals, and non-dinky 2s orbitals. (By the way, this is responsible for all the relativistic effects that give gold the yellow color, mercury a liquid state, the stability of Au2 in the gas phase and [Hg2]2+ in solution...relativity shrinks the 1s orbtial when you switch from Schroedinger to the Dirac equation, and all the other s-orbtials constrict because of the Ukranian Doll effect...)
So what about 3d?!? Surely, if 3d is anomalously small, that means fabulously great bonding, just like the small 2p in ochem, right? No. In ochem, the shrinking 2p makes it as small as the 2s. But the 3d is already smaller than the 4s and 4p. Making it even smaller makes matters worse. Like the Grinch's heart, the 3d orbitals are two sizes too small. This means they're lousy at bonding. Which means they're lousy at backbonding. If we say that octahedral complexes are d2sp3 (and the p-orbtials are high enough in energy, especially in the early metals, that they're less than full participants), then loss of d-participation has big effects on bond strengths. The first row in characterized by weak bonds, small barriers, and fast catalysis for this reason.
But when we speak of d-orbtial splitting, it's a bigger deal than that. Because eg* is purely a d sigma* set, delta is purely a function of how strongly the d-orbtials bond (assuming t2g is non-bonding...and even when it's not, t2g is a function of d-orbital pi-bonding, also affected by the small 3d). The weak d-orbital splitting that results is why you get d-d splittings in the visible (color!), high-spin complexes sometimes, and frequent population of eg* orbitals.
The difference between the 4d and 5d is smaller. They are good bonding orbitals, and their complexes are all low spin. 5d is mostly a better bonder and back donor because of the Lanthanide(oid?) contraction and relativistic effects, which both constrict the s and p orbitals, and expand the d and f orbitals (because they are better shielded by the shrunken s and p orbitals).
As an aside, this same effect, with the 4f being three sizes too small, is why the lanthanide(oid) ions are big, dumb, ionic beasts, while the less-shrunken 5f actinide(oid) elements back donate and do pseudo-organometallic-d-block-like chemistry.
Finally, the halogens. You're dead-on with the Cl-Cl>Br-Br>I-I trend being just like the Group IV carbon-to-lead series. But F-F is interesting in its own right, and that bond is weak for the same reason N-N is weak (hello, hydrazine), O-O is weak (peroxides go 'bang'), O=O is weak (fire!), and F2 has been responsible for the loss of more fingers than probably any other compound.
Many textbooks say "lone pair-lone-pair-repulsion!", which is grand until you look at the MO diagram of F2. F2 and O2 have no lone pairs!
Ok, so that's kind of a problem with this electron repulsion thing. And it can't be repulsion in the bonds. Chemical bonds are not held together (or broken apart) by positive-negative Coulombic forces. Electron-electron repulsion, nuclear-nuclear repulsion, and electron-nuclear repulsion are largely a wash.
So what isn't a wash is that anti-bonding is more anti-bonding than bonding is bonding. If you put two electrons in a bond, and two in an antibond, this is a repulsive interaction (this is what causes sterics--a steric repulsion is a filled-filled interaction). What is in common between hydrazine, peroxide, oxygen, and fluorine is population of pi* orbitals. It turns out that the shorter the bond, the more ridiculous the gap between bonding stabilization and antibonding de-stabilization gets. If your bonds are long, bonding and antibonding are close to a wash. So when you get to Cl2, the pi-bonding is minimal, but so is the pi* antibonding. So that bond isn't weakened much by this effect.
Here's a nice example of this to mess with people's brains:
C=C, the gas phase molecule, with two pi bonds and no sigma bonds, has almost the same bond length (and strength) as the triple bonds in either acetylene or carbide. Not populating the 2p sigma means stabilizing the 2s sigma by sp mixing without paying the price in populating the high-energy 2p sigma orbtial.
Thanks, Scott! I'm still digesting, but the explanations are very very helpful in resolving some long-simmering questions. (Especially the "why does overlap decrease down the column if Si-Si is just a scaled up version of C-C?" question... and the "why can carbon, nitrogen, oxygen do so many fancy bonds leading to life on Earth?" question...)
Going over these concepts might make a good last-day-of-class review-and-wrap-up discussion.
I just found a very interesting article in the Feb 2015 issue of J Chem Ed that addresses this question in terms of the binary HX acids. It's titled, "Is There a Need to Discuss Atomic Orbital Overlap When Teaching Hydrogen−Halide Bond Strength and Acidity Trends in Organic
Chemistry?"
They use computational data (and simple diagrams, really) to argue that s/p overlap increases as you proceed from HF to HCl to HBr, etc. They provide a few alternative ways to explain the trend, including the argument that we should focus on anion stability. (Larger more diffuse valence orbitals can minimize e-e repulsion.
The ref is Devarajan et al, J. Chem. Educ. 2015, 92, 286-290.
I somehow stumbled across this thread (thanks, VIPEr search function -- what was it that I looking for again??).
Nancy, this thread and explanation is *fantastic*. Thanks for replying so clearly. Extra thanks to Anne for the original question and Chip/Adam for the follow ups!