Molecular Geometry & Bonding
what the shape decides
Index

Figures

Every kind of figure in the essays, grouped by subject, with how many essays draw each one.

Each entry below is one kind of picture — an orbital contour at a stated enclosed fraction, a Hückel level diagram, a basis reduced in a character table, a band built from a finite chain. Its page shows one example and then what each essay that draws it uses it to show. The same kind of figure appears in many essays at the numbers each argument needs, so a 2s contour at ninety per cent and at ninety-nine per cent are one entry rather than two.

There are 131 kinds of figure here, drawn 754 times across 430 essays. The number beside each is how many essays draw it. Orbital pictures are also listed one by one, with the fraction each encloses, on the orbital index.

Orbitals and their contours

Isosurfaces solved for at a stated enclosed fraction, their nodes, and the shells a radial node cuts them into.

Radial functions

The one-dimensional half of a wavefunction: where the density is, what screening does to it, and how far out an orbital reaches.

Overlap

Two functions on two centres, integrated — including the integrals symmetry requires to vanish, which come out at arithmetic noise.

Where the atoms go

Repulsion minimised on a sphere, the angles that fall out of it, and the arrangements that are not all alike.

Point groups from coordinates

A molecule turned in space with its group recovered from the turned coordinates, and what the group settles on its own.

Bonding models

Valence bond, molecular orbital and hybrids, drawn as descriptions of one thing rather than as competing pictures.

Hückel systems

Adjacency matrices diagonalised: levels, coefficients, bond orders, and the shell closures that decide which rings are stable.

Representations

Character tables generated from a molecule's own operations, bases reduced in them, and what a descent in symmetry does to a level.

A basis is not a thing

The same electrons written two ways with the density unchanged, and four electronegativity scales that disagree.

Spectra

How many bands there can be, where they sit, and what an absent one proves.

Rotation and vibration

Moments of inertia, normal modes, isotope shifts, and the frequencies a force field does and does not fix.

Extended structures

Chains and rings taken far enough to behave like solids — bands, gaps, fillings, defects and ends — every one of them a finite matrix diagonalised, with no lattice anywhere in the argument.

A d shell in a field

What a set of ligands does to five degenerate orbitals — computed twice, from an integrated point-charge potential and from an angular overlap matrix, which agree on every ratio.

What a measurement can fix

The other half of every model: which of its parameters a measurement can recover, which combinations no measurement of that kind can see, and how much a second number of a different shape is worth.

When repulsion is in the model

Hubbard systems small enough to diagonalise exactly: the singlet a one-electron model cannot find, the coupling between two spins, and a gap where band theory says there is none.

All essays · The fields · The orbital index