Measuring orbitals and bonding in atoms, molecules, and solids

The cloud of negative charge that determines the relative positions of the nuclei in a molecule or solid can be understood in terms of the motion of the electrons that form the cloud. Usually one pictures the charge cloud as a distribution in coordinate space. One can equally well picture it as a distribution of velocities, i.e., in momentum space. The probability that an electron has a certain energy–momentum combination is called the energy–momentum density. It is directly measured by electron-momentum spectroscopy. The results of this technique provide the most direct experimental documentation of simple ideas of orbitals and bonding, thus opening a fresh and comprehensive perspective on electronic structure. We show how measurement of the motion of electrons in solids can help us understand the bonding of atoms in molecules and solids. We give examples of a free-electron metal and an ionic insulator.