Lecture #21

 Text: Section 14.4

  CURMUDGEON GENERAL'S WARNING. These "slides" represent highlights from lecture and are neither complete nor meant to replace lecture. It is advised not to use these as a reliable means to replace missed lecture material. Do so at risk to healthy academic performance in 09-105.
Lecture Outline Quantum Theory of the Chemical Bond

Molecular Orbitals

Importance of energy match vs mismatch

Importance of net overlap

Heteronuclear diatomic molecules

In acknowledging the important factors for what leads to effective molecular orbital (MO) formation, one feature is the similarity in energy of the atomic orbitals which are combining (through interference) from different atoms. Similar energies lead to bonding molecular orbitals (and antibonding orbitals) that are highly stabilized (and destabilized), compared to their atomic orbital (AO) origins. These differences are mathematically indicated by the weighting coefficients (c's) in the linear combinations.
In heteronuclear diatomic molecules where the atomic orbitals might differ substantially in energy (such as for atoms with very different electronegativities or ionization energies), the bonding molecular orbital is only stabilized slightly compared to the atomic orbital of the more electronegative species. Its geometric shape will also closely resemble that of the atomic orbital of that same more electronegative atom. This feature will emerge in the example we discuss soon.
Another important feature of atomic orbitals in determining molecular orbital formation has to do with relative geometries of the combining orbitals, both in terms of sizes and in the symmetry with which the + and - lobes on each atomic orbital combine to give a net interference effect different than zero.
The above factors for influencing the construction of molecular orbitals are particularly important in looking a molecules where the valence electrons from two bonding atoms are in distinctly different atomic orbitals to begin with. Hydrogen fluoride is an excellent example. Where will the electrons be in the molecule? How do you describe the molecular orbitals?
The 2s atomic orbital on F is so much lower in energy than the valence 1s atomic orbital on hydrogen that no molecular orbital will form between them. In HF then, the first valence electrons go into an orbital that is indistinguishable from a 2s atomic orbital on F. In contrast, the 1s(H) and one of the 2p(F) orbitals can give rise to bonding and antibonding s orbitals as shown on the left. The contribution from the more electronegative F dominates the appearance of the constructed molecular orbital which appears (in yellow) similar to the fluorine contributing atomic orbital. (The "exact" result is from a computer calculation.)
The flip side of the previous result is that the antibonding combination is dominated mostly by the more electropositive species, hydrogen, and its appearance most closely resembles that of the originating 1s(H) as shown in yellow.
Finally, the 2p(F) atomic orbitals -- which are each perpendicular to the one previously used to construct the bonding and antibonding molecular orbitals -- do not give net interference combinations with the 1s(H) and so remain unchanged in the HF molecule. That is, they become non-bonding orbitals in the molecule.
Illustrating molecular orbitals (valence electrons only) in HF whose atoms are very different in electronegativity. The lowest molecular orbital is virtually indistinguishable from the 2s atomic orbital on F (because of the large energy difference with H's atomic orbital). The s bonding molecular orbital is close in energy and shape to that of the F 2px atomic orbital. Fluorine's 2py and 2pz atomic orbitals have the wrong symmetry with respect to H's 1s and remain as "nonbonding" orbitals -- containing lone pairs on the F.