Molecular Geometry & Bonding
what the shape decides
Figure

Which site a long bond takes, and it is not the one the rule says

The energy of the axial placement minus the energy of the equatorial one, against the odd bond's length. Above the line the equatorial placement wins and below it the axial one does. The textbook sentence is that a bulkier group goes equatorial where there is more room; given a longer bond and nothing else, the repulsion model puts it AXIAL, at every length, by a margin that grows. A site pushed further out interacts with everything less, so what is left to decide is the arrangement of the four sites left behind — and three equatorial with one axial is the better set of four.
Which site a long bond takes, and it is not the one the rule says. The energy of the axial placement minus the energy of the equatorial one, against the odd bond's length. Above the line the equatorial placement wins and below it the axial one does. The textbook sentence is that a bulkier group goes equatorial where there is more room; given a longer bond and nothing else, the repulsion model puts it AXIAL, at every length, by a margin that grows. A site pushed further out interacts with everything less, so what is left to decide is the arrangement of the four sites left behind — and three equatorial with one axial is the better set of four.

One of the figures on where the atoms go: Repulsion minimised on a sphere, the angles that fall out of it, and the arrangements that are not all alike.

Two essays draw this figure, each at the values its own argument needs rather than at the setting shown above. What each one uses it to show is below, in the words of its own caption.

In the essays

The sites are not the same size

Where each placement wins, in the plane of the two knobs, at a larger site weight than the map above uses. The boundary moves and the shape of the region does not — so which site a long bond takes is decided by the ratio of the two effects rather than by either of them, and no single number settles it.

The energy of the axial placement minus the energy of the equatorial one, against the odd bond’s length. At equal lengths the two are one structure and the difference is exactly zero. As the bond lengthens, the axial placement wins, and the margin grows monotonically.

For each electron demand, the range of bond lengths over which the equatorial placement wins. It is a window rather than a threshold, and below a demand of 0.933 it closes altogether — the axial placement then wins at every length.

The long bond goes to the crowded site

The energy of the odd bond placed axially minus placed equatorially, against its length relative to the others, at five and at seven sites.

The angles from each kind of site to its neighbours, with the sums of 1/r and 1/r¹² over them, at five and at seven sites.

The axial and equatorial bond lengths of phosphorus pentafluoride and iodine heptafluoride, from gas-phase electron diffraction.

Every figure · Every orbital, by what it encloses · All essays