Further Properties of Molecular Orbitals
There is another convention in the labeling of molecular orbitals that we need to be aware of. This concerns the parity of the orbital.
The parity of an orbital is its behaviour under inversion. An orbital of even parity appears the same when inverted through its centre, while one of odd parity changes sign. In the diagrams, the lighter ares represent ares of positive amplitude in the wavefunction, the darker areas are negative in amplitude (i.e. of opposite sign to the light areas). The dark spots are the centres through which the orbital should be inverted.
A bonding σ orbital is the same sign throughout, so does not change under inversion. It is thus of even parity, and labeled with a subscript g.
An antibonding s orbital is of opposite signs at its two ends, so does change sign under inversion. It is thus of odd parity, and is labeled with a subscript u.
A bonding π orbital consists of two lobes each of a different sign. It is thus of odd parity, so is labeled with a subscript u.
An antibonding π orbital also has two lobes, however unlike the bonding orbital a lobe is not of the same sign throughout. Rather the two ends of each lobe are of the opposite sign. An antibonding π orbital is thus of even parity, so is labeled with a subscript g:
We need also to consider some of the properties of heteronuclear diatomics. The electrons in the bond will not be equally shared between the two atoms. It will be more favourable for them to be found closer to whichever of the two atoms attracts electrons more strongly.
For example, in hydrogen fluoride, HF, the fluorine attracts electrons much more strongly than the hydrogen does. This results in an unequal charge distribution, with the result that there is a partial negative charge, δ-, associated with the fluorine end of the molecule and a partial positive charge, d+, (equal in magnitude to the partial negative charge to ensure that overall the molecule has no charge) associated with the hydrogen end.
The molecule possesses a permanent dipole.
The ability of an atom to attract electrons to itself is measured by its electronegativity.
There are various different scales on which this quantity can be measured (the most common being the Pauling scale), but they all share the feature that the higher the electronegativity, the greater the ability of the atom to attract electrons to itself.
As a rule of thumb, electronegativities increase from left to right across the Periodic Table, and decrease as you go down a group. The most electronegative elements are thus F, Cl, and O.
We can rewrite our earlier statements in terms of this quantity by saying that any heteronuclear diatomic molecule will possess a permanent dipole, and the larger the difference in the electronegativities of the two elements, the larger this dipole will be. (Note there is zero dipole in a homonuclear diatomic where the atoms are identical and thus have the same electronegativity.) The negative end of the dipole will be on the atom of higher electronegativity.
|Electronegativity differences have some consequences for the molecular orbital diagrams of these species. Orbitals of more electronegative species tend to be lower in energy, as the electrons in them are more tightly bound. For example, in the MO diagram of HF the F orbitals lie much lower in energy than those of the H atom:|
From this diagram, we can clearly see that the two electrons are in a bonding orbital, which is much closer in energy to the 2p orbitals on fluorine than to the 1s orbitals on hydrogen. This indicates that the character of this bonding orbital is more like that of the 2p than the 1s – the molecular orbitals no longer contain equal contributions from the atomic orbitals that form them.
Consequently, the electrons in the bond are more likely to be found near the F atom than the H atom (the greater degree of F orbital character in the bonding orbital means that the distribution of electrons within it is no longer uniform, but biased towards the F atom).
This points to another interpretation of the electronegativity – the greater the electronegativity of an atom, the greater the contribution it makes to the bonding molecular orbitals in a diatomic molecule.