Concept

Excitation — where it appears

The promotion of a system from its ground state to a higher one. Its energy is a difference between two states of the whole system, which is not an orbital energy difference except in a model that has no relaxation in it.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A half-filled ring's cheapest excitation goes to zero. The energy of the smallest available excitation of a half-filled ring, against the number of atoms, on log axes. Every doubling at least halves it, so in the limit there is no smallest excitation — which is what a metal is, before any band picture is drawn.

What a metal actually is

Not shiny, not a good conductor, not an element on the left of the table. A metal is a system with excitations of arbitrarily small energy, and that definition can be checked on a sequence of finite rings without drawing a band diagram or mentioning conduction at all.

solids · Metal

The gap against size: uniform against δ = 0.15. The HOMO–LUMO gap of a half-filled chain plotted against the number of sites, on log axes, for a uniform chain and for one whose bonds alternate. The uniform sequence falls without limit; the alternating one settles at four times the alternation.

A band gap is not a bond energy

Silicon's gap is 1.1 electronvolts and its Si–Si bond is 2.3. Both are quoted in the same units, both describe the same material, and neither is convertible into the other — one is the cost of promoting an electron and the other is the cost of taking two atoms apart.

wrong · Bands in a solid

Named alongside it

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

Bands in a solid Approximation Bond energy Conductivity Density of states Dissociation Eigenvalue Electron affinity Fermi level Filling HOMO–LUMO gap Insulator

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