Molecular Geometry & Bonding
what the shape decides
Figure

The surface-honest curve and the page-honest curve

The 2pz orbital in its xz plane, drawn twice. The outer curve is the contour whose SURFACE encloses 90.0 per cent of the density in space — the claim every orbital figure here makes — and in this plane it encloses 96.7 per cent. The inner curve is the one that encloses 90 per cent in the plane, which is what a reader looking at a flat picture would take the caption to mean. The two levels differ by a factor of 1.87 and the curves differ visibly; the caption does not. Contours drawn: 2pz at 90% of its density, |ψ| = 9.48e-3.
The surface-honest curve and the page-honest curve. The 2pz orbital in its xz plane, drawn twice. The outer curve is the contour whose SURFACE encloses 90.0 per cent of the density in space — the claim every orbital figure here makes — and in this plane it encloses 96.7 per cent. The inner curve is the one that encloses 90 per cent in the plane, which is what a reader looking at a flat picture would take the caption to mean. The two levels differ by a factor of 1.87 and the curves differ visibly; the caption does not. Contours drawn: 2pz at 90% of its density, |ψ| = 9.48e-3.

One of the figures on orbitals and their contours: Isosurfaces solved for at a stated enclosed fraction, their nodes, and the shells a radial node cuts them into.

One essay draws 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

A slice is not the surface

A 1s orbital in a plane through its nucleus, drawn twice. The outer curve is the contour whose surface encloses 90 per cent of the density in space; in this plane the same curve encloses 96.9 per cent. The inner curve is the one that encloses 90 per cent in the plane, at a level 2.05 times as high. Both are ninety per cent pictures and they are visibly different sizes.

Seven hydrogenic orbitals, each at a contour solved for so that it encloses ninety per cent in space, and what the same contour encloses in the plane it would be printed in. Every one of them is between 95.4 and 96.9 per cent, so every ninety per cent picture in this collection, printed flat, is a ninety-six per cent picture on the page.

Every contour level of a 1s, from far inside the density to far outside it, and what each encloses in the two senses. The two curves never cross: a picture is always more complete than a surface at the same level. The two marks are where each claim is honestly ninety per cent.

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