    ## VSEPR and bond angles

The VSEPR model does a remarkably good job of predicting molecular geometries in a general way, based on symmetry arguments and the all-important idea of electron pair repulsions. We have stated (see page 82 in the text) that lone pairs "tend to occupy more space" than bonding pairs, but with one more idea, we can be quantitative about the effect of lone pairs on the final geometry.

We will discuss this idea—called "ligand close-packing"—in the context of simple triatomics with a central O atom bonded to two other atoms, either H, F, or Cl. We start with the symmetric possibilities, H2O, OF2, and OCl2. The bond angles and bond lengths of these three molecules are shown below: Note that the bond lengths increase in a way we can understand easily: H is smaller than F, which is smaller than Cl. But look at the bond angles. We have claimed that the two lone pairs on the O atom (not shown) should push the bonding pairs of electrons down, lowering the bond angle from the perfect tetrahedral angle of 109.47°. Indeed, the first two molecules have smaller bond angles, as expected, but the bond angle in OCl2 is 110.9°, more than a degree larger than the tetrahedral angle. What's going on?

The ligand close-packing concept says that the atoms bonded to the central atom (i.e., the ligands) have a fixed radius, and the bond angle adjusts until these ligands are just touching ("close-packed," in other words). The bond length is determined by parameters such as atomic radius, but the angle is determined by lone pair electrons repelling the bonding pairs until the ligands just "touch."

It is easy, given the bond angles and lengths shown above, to use a little trigonometry to calculate how far apart the ligands themselves are. This distance should equal the diameter of the ligand, or half that distance is the ligand radius. This calculation is shown below in pictures that represent the H, F, and Cl ligands as spheres that just touch. From this figure, we see that the radius of H bound to O should be about (1.514 Å)/2 = 0.757 Å, the F radius should be about (2.201 Å)/2 = 1.10 Å, and the Cl radius should be about (2.793 Å)/2 = 1.40 Å. Armed with these values, we can make a prediction about the structures of the HOF and HOCl molecules. For HOF, we would predict the H and F atoms to be about 0.757 Å + 1.10 Å = 1.86 Å apart, and for HOCl, we predict a HCl distance of 0.757 Å + 1.40 Å = 2.16 Å. Moreover, we can accurately locate the O atom if we assume the H–O bond length is always close to what it is in water, the F–O bond length is always close to what it is in OF2, and the Cl–O bond length is always close to what it is in OCl2.

The figure below shows how well we do. The experimental ligand-to-ligand distances are both quite close to our predictions (shown in parentheses) based on these radii: Moreover, the experimental bond lengths to the O atom are quite close to our expectations from the original three molecular structures.

What have we learned? First, the VSEPR idea that lone pairs repel bonding pairs, distorting bond angles away from (usually to values smaller than) the ideal angles is valid. But second, when we add the concept of ligand close-packing, we can predict these angles with remarkable accuracy. We can see why apparent violations of the "bond angle is less than ideal" rule occur, as in the OCl2 case: sometimes the ligands are so big that, at their ideal bond length, they have to form a bond angle larger than ideal because the ligand repulsion is greater than the lone pair–bonding pair repulsion and ligand repulsion determines the final geometry.

You can now take the various bond lengths and ligand radii quoted above and, with a little trigonometry, predict the structure of the final triatomic of this family, FOCl. Give it a try!   