At 1 atmosphere (atm), sodium assumes a body-centered-cubic (bcc) structure, and it appears as a silvery metal that is easy to cut with a knife and is highly reactive with air, due to its very low ionization energy. Squeezing sodium to ∼120 GPa (about 1.2 million atm) decreases its melting point by a dramatic 700 K 2 -in sharp contrast to the melting point increase expected for bonds that strength under pressure. Seven different crystalline phases, some with extremely complex structures, have been observed at pressure and temperature conditions near sodium's melting point minimum, highlighting sodium's rich structural diversity and complicated potential energy landscape. Even more striking is sodium's behavior near 200 GPa, when it becomes transparent to visible light. Transparency in materials indicates the opening of a band-gap, meaning the valence electrons in the highest occupied crystalline orbital can no longer move freely in the conduction bands as they do in a metal, and indeed this high-pressure phase of sodium is an insulator with a band-gap calculated to exceed 1.3 eV. As will be described in detail below, this behavior stems from the way in which pressure affects the electronic structure of atoms. While at 1 atm sodium possesses a 3s 1 valence configuration, under high-pressure the energies associated with its s, p and d electronic states are reorganized (Figure ), so that projecting sodium's valence bands onto atomic orbitals reveals a high degree of p and d mixing with the broad s-based bands. It is this energetic reordering of the orbitals that changes the chemical bonding, crystalline structure, and properties of this prototypical 1 atm nearly-free-electron metal. Sodium's behavior is not unique; all elements undergo some modification of their electronic structure under pressure. Hydrogen, stable as a diatomic molecule at ambient condi-Figure : (a) Schematic illustration of the reorganization of orbital energies of an alkali metal or alkaline earth metal atom in the third, or higher, row under pressure. (b) Calculated density of states (DOS in units of states per atom) of Na-hP 4 at 190 GPa, projected onto atomic orbitals. tions, dissociates and metallizes at pressures and temperatures similar to those in Jupiter's interior. Nitrogen, another diatomic gas at ambient conditions, breaks its strong triple bond in favor of new intermolecular σ-bonds at 110 GPa and temperatures near 2000 K, forming a stable polymeric allotrope. Similarly, the transition from graphite to diamond involves a change in carbon's valence hybridization from sp 2 to sp 3 . While the stability of 3D diamond over 2D graphite under pressure is well known, many students find it remarkable that metallic superconducting iodine and oxygen, transparent and insulating sodium, and many other exotic phases, can be made under pressure! If the bonding within the elemental phases changes with increasing density, it should not be surprising that the structures, phase diagrams and properties of elements in combination with one another are also dramatically affected via pressure. Since the entropy of a solid is much lower than that of a liquid or a gas 1 , the solid's Free Energy, under pressure and at low temperature, is often well approximated by the enthalpy, which is a sum of the internal energy and the pressure-volume terms (H = E + P V ).