Bonding and Antibonding Molecular Orbitals?

What does it mean that when the energy difference between the atomic orbitals of two atoms is quite large, one atom's orbitals contribute almost entirely to the bonding orbitals, and the others atom's orbitals contribute almost entirely to the antibonding orbitals?

• Answer:

  The phenomenon of differing molecular orbital distributions in bonds arises from differences in electron affinity.  Electron affinity is the tendency of an atom to pull electrons inwardly towards its center, and atoms with strong electron affinity tend to dominate the occupied molecular orbitals.  Those with weak electron affinity tend to dominate the unoccupied molecular orbitals.  Arvi Rauk's Orbital Interaction Theory of Organic Chemistry has an excellent discussion of this phenomenon. Let us demonstrate this with a wide range of simple bonds: Nitrogen, N2, has equal contributions from the two nitrogen atoms when they interact with each other to form the molecular orbitals.  Its HOMO and LUMO both have equal amounts on the two atoms, shown below: As you can see from these diagrams, the two sides are the same for both HOMO and LUMO.  This occurs because the two atoms are at the same energy before the bond is formed between them. ClF, or chlorine fluoride, has a slight imbalance in the way energy used to influence the atomic orbitals of chlorine and fluorine.  This occurs because the two atoms have differing electron affinity, and one atom will dominate over the other in terms of energy contributions for the HOMO.  The other atom will dominate over the LUMO energy contributions, since the effects are the same.  With an electronegativity value of 3.98, fluorine is expected to dominate the HOMO, while chlorine, with an electronegativity value of 3.16, should make up most of the electron density in the LUMO.  The difference of electronegativity between atoms generally influences how strongly each atom dominates the HOMO or LUMO respectively.  In ClF, the difference is less than 1.00, so the bond is fairly polar.  The dominance effect is best illustrated using the same orbitals to form sigma bonding and sigma anti-bonding orbitals, since the anti-bonding orbital is likely to be dominant in the less-electronegative atom, while the bonding orbital is more prominent in the more-electronegative atom.  The HOMO of ClF is shown here, where the dominance by F is clearly seen. The green atom is the fluorine atom, which has taken up most of the electron density of the HOMO when the ClF molecule was formed.  It lies lower in relative energy compared to chlorine, and the sigma bond tends to lie closer to that of fluorine.  This causes the majority of the electron density to be concentrated on the fluorine atom.  For the empty orbital that also forms upon formation of ClF, it lies closer to the chlorine atom in terms of energy, since chlorine started at a higher energy level.  This diagram, originally made for an online class, shows the effects of polarization on simple s-orbital bonds.  Other orbitals work in the same way. Red and green are the phase colors in the picture, and the blue lines represent the new sigma bonds formed from the atomic orbitals used to produce the X-Y molecule.  If X=Y, then both atoms contribute equally to the two new orbitals.  If X is not the same as Y, the more electronegative atom lies lower in energy prior to forming X-Y.  It is actually possible for sigma bonds to be so lopsided that electron density exists on only one atom of the X-Y bond!  This occurs with large electronegativity differences between the two atoms.  It is the reason why we have a rule of thumb for deciding whether a bond is ionic or covalent.  In the previous examples, all of the bonds were covalent.  In ionic bonds, the two atoms lie so far apart in terms of energy, that when they form new orbitals, the occupied orbital lies with the electronegative atom only.  As we saw with NaCl, this is what really happens.  The difference in electronegativity for NaCl is 3.16-0.93 or 2.23, greater than the 'cutoff value' of 1.7.  Even the computed HOMO for a NaCl molecule shows the strong dominance of chlorine over sodium. There is virtually no electron density on sodium in this picture.  This is a tell-tale sign of ionic bonding.  However, bonds are always partial ionic and partial covalent.  The electronegativity difference between atoms in a bond decides how much of a bond is ionic, and how much of it is equal sharing (covalent) between the atoms.