Molecular Geometry & Bonding
what the shape decides
Concept

Ionic bonding — where it appears

Bonding in which charge is transferred rather than shared. How much is transferred is not fixed by an electronegativity difference: the repulsion between the electrons can suppress it by two orders of magnitude at the same difference.

Named by 5 essays across 4 fields — each of them below, with the objects they name alongside it.

What holds matter together, per pair. Four kinds of interaction between two units of matter, each computed from the model named beside it, on a logarithmic energy scale. The range from top to bottom is a factor of several hundred, which is the number behind why a molecular solid melts hundreds of degrees below a covalent one.

What holds a solid together

Four kinds of interaction between two units of matter, each computed from a stated model and put on one logarithmic scale. The ordering is not the one usually taught — an ion pair at contact beats a shared pair, which is a fact about the comparison rather than about the numbers.

solids · Cohesion What holds matter together, per pair. Four kinds of interaction between two units of matter, each computed from the model named beside it, on a logarithmic energy scale. The range from top to bottom is a factor of several hundred, which is the number behind why a molecular solid melts hundreds of degrees below a covalent one.

The lattice sum that depends on the order of adding

An ionic solid's binding is the sum of every pair of charges in it, and the series does not converge absolutely — rearranged, it gives a different answer. That is a genuine mathematical difficulty rather than a technicality, and it is the clearest example of something a real-space, neighbour-by-neighbour method cannot compute at all.

solids · Cohesion The fraction a table encloses is not one number. For each ion, the fraction of its own electron density that lies inside its tabulated radius. Along each isoelectronic series the answer runs over eight percentage points, where three neutral atoms at their contact distances spanned three tenths of one. And it peaks at the neutral rather than falling through it, because a van der Waals radius is fitted to the distance between two atoms that are not bonded and an ionic radius is one term of a sum fitted to the distance between two that are.

The surface a table draws

Three noble gases stop at a surface enclosing between 99.38 and 99.75 per cent of their density — a near-constant, and an argument that a contour is a real boundary. Charge the atoms and it collapses. Across ten electrons the tabulated radius encloses anything from 94.4 to 99.98 per cent, it peaks at the neutral rather than trending through it, and radii built at a fixed enclosure do not add up to a single measured separation.

orbitals · Contour Twelve hydrogen bonds, four tables. The bond dipole of hydrogen against each partner, in debye, on each of the four tables after all four are anchored to the same hydrogen–fluorine separation. Positive is hydrogen at the positive end. A bond whose marks straddle the axis is one the tables disagree about the direction of, and there are 3 of them.

Four tables and one molecule to disagree about

A molecule of two elements is provably safe from the choice of electronegativity table, and a series down a group should land where the tables do disagree. It does. All four agree that hydrogen iodide is the exception — and they disagree about what its dipole is by 1.245 debye, which is two and a half times the 0.448 that was measured.

shape · Dipole The covalent arrangement the inversion finds is Pauling's mean — except for hydrogen fluoride. For eight bonds, the covalent arrangement's binding found by solving the two-state problem exactly against the measured dipole and bond energy, against Pauling's covalent mean — the geometric mean of the two homonuclear bond energies — which the inversion never sees. The line is equality. HCl 0.97, HBr 0.98, HI 1.03, ClF 1.09 of the mean; HF 1.68. Open circles are the alkali halides, where the ionic weight is near 0.8 and the result is mostly the assumed repulsion.

Two measurements leave nothing to fit

A bond pictured as a mixture of its ionic and covalent arrangements has two unknowns — the coupling between them and the covalent arrangement's own energy — and a dipole fixes only one. Add the bond energy and the two-state problem inverts exactly, with no parameter left. The covalent arrangement it returns can then be held against something it never saw: Pauling's mean of the two homonuclear bond energies. For hydrogen chloride, bromide and iodide it lands on that mean to within three and a half per cent, and chlorine monofluoride within nine. Hydrogen fluoride lands 68 per cent above it. And the couplings rise and fall with length rather than falling — hydrogen fluoride's, on the shortest bond, is the smallest.

wrong · Electronegativity

Named alongside it

The objects these essays reach for when they reach for this one.

Intermolecular forceLattice energyModel limitPartial chargeApproximationCohesionConventionCoordination numberDipole momentElectronegativityPauling scaleBond dipole

All concepts