Understanding Metal Bonding

Our insights follow from Friedel's 1960s rigorous quantum approach of 'bonding paths' radiating from one or more atoms. See V.Heine & S.Chen, J. Phys.: Condens. Matter 36 (2024) 353002. (Also author index references to Friedel in Solid State Phys. vols 24 & 35) These insights include the energy driving surface catalysis and special sites, vacancy energies, surface reconstructions, easy phase transitions and more. To first approximation, the total energy varies only as the *square root* of the total number of nearest neighbours to an atom, in a *cluster bond* to them as a whole. It comes from the quantum mixing ("resonance") of all possible electron distributions among bonds between neighbours, giving (a) strong cohesion. But (b) metals are malleable with little energy change or energy barrier in shuffling and holding the 12 or 14 close neighbours around in deformation, (c) even with only one electron per atom in the monovalent alkali metals. (d) Similarly a pinch of sugar, sand or salt crushes into a powder when hit with a hammer, but a bit of metal just flattens.