# Research Highlights

## Metallic Bonding Explained

Many of the properties of metallic bonding can be explained from a simple consideration of co-ordinaton number and the basic idea of resonance in quantum mechanics.

Metals are malleable, and do not shatter like sugar or quartz when hit, although their atoms are similarly bonded. Quantum mechanics shows that in a metal each electron forms a "covalent cluster bond" from its atom to all of its neighbours, stronger than a single-neighbour pair bond by a factor of the square root of the number of neighbours. This enhancement makes metals strong, graphite more stable than diamond, and gives most metals one of the three close-packed structure with twelve nearest neighbours for each atom, and often a phase transition between two of them at modest temperature and pressure.

The curvature of the square root function also explains some surface reconstructions, and the fact that the energy of a vacancy is only about half of the cohesive energy (per atom), rather than equal to the cohesive energy as a pair-wise bonding model would suggest. It also shows why just the total number of atomic neighbours is the dominant factor in models of structural damage in metals. The theory can even be applied to a benzene ring, with the oscillating reactivities at the meta, ortho and para positions being analogous to the Friedel oscillations around a substitutional impurity in a metal.

The theory demonstrates the origin of surface catalysis. If an isolated diatomic molecule of a metal dissociates, each atom reduces its neighbour count from one to zero. If it dissociates while adsorbed on the surface of the same metal, each of its atoms will retain its number of bonds to atoms of the substrate, typically around four. The dissociation then reduces the neighbour count of each of the two molecular atoms from five to four. If the bond energy is proportional to the square root of the number of neighbours, and the energy required to reduce from one neighbour to zero is one unit, then that for reducing from five neighbours to four is just √5-√4=0.23 units. Dissociation on a surface is over four times easier.

*Understanding metal bonding*, V Heine and S Chen,
J Phys Cond Matt
**36** 353002 (2024)