So far we have regarded lone pairs as equivalent to single bonds in their effect
on shape, but is that really the case? We have predicted, for instance, that the electron
arrangement of an SO3
2 ion is tetrahedral, and so we might expect OSO
angles of 109.5. However, experimental findings have shown that, although the
sulfite ion is indeed trigonal pyramidal, its bond angle is 106 (20). Such experimental
evidence tells us that the VSEPR model as we have described it is incomplete
and needs to be refined.
To account for the fact that bond angles in molecules with lone pairs are typically
smaller than expected, the VSEPR model treats lone pairs as having a more
strongly repelling effect than do electrons in bonds. That is, the lone pairs push the
atoms bonded to the central atom closer together. One possible rationalization for
this effect is that the electron cloud of a lone pair can spread over a larger volume
than a bonding pair can, because a bonding pair (or several bonding pairs in a
multiple bond) is held in place by two atoms, not one (FIG. 4.3). In summary, the
following rule leads to reasonably reliable predictions for the VSEPR model:
Rule 4 The strengths of repulsions are in the order lone pair–lone pair
lone pair–atom atom–atom.
Because of their strong mutual repulsion, the lowest energy is achieved when lone
pairs are as far from each other as possible. The energy is also lowest if the atoms
bonded to the central atom are far from lone pairs, even though that might bring
the atoms closer together.
Our improved model helps to account for the bond angle of the AX3E sulfite
ion. The atoms and the lone pair adopt a tetrahedral arrangement around the S
atom. However, the lone pair exerts a strong repulsion on the O atoms, forcing
them to move together slightly, reducing the OSO angle from the 109.5 of a regular
tetrahedron to 106. Note that, although the VSEPR model can predict the
direction of the distortion, it cannot predict its extent. We can predict that, in any
AX3E species, the XAX angle will be less than 109.5, but its actual value cannot
be predicted: we must measure it experimentally or calculate it by solving the
Schrödinger equation numerically with a computer.