Editing Metallic bonding (section)

===In 3D===
[[Metal aromaticity]] in [[metal cluster]]s is another example of delocalization, this time often in three-dimensional arrangements. Metals take the delocalization principle to its extreme, and one could say that a crystal of a metal represents a single molecule over which all conduction electrons are delocalized in all three dimensions. This means that inside the metal one can generally not distinguish molecules, so that the metallic bonding is neither intra- nor inter-molecular. 'Nonmolecular' would perhaps be a better term. Metallic bonding is mostly non-polar, because even in [[alloys]] there is little difference among the [[Electronegativity|electronegativities]] of the [[atom]]s participating in the bonding interaction (and, in pure elemental metals, none at all). Thus, metallic bonding is an extremely delocalized communal form of covalent bonding. In a sense, metallic bonding is not a 'new' type of bonding at all. It describes the bonding only as present in a ''chunk'' of condensed matter: be it crystalline solid, liquid, or even glass. Metallic vapors, in contrast, are often atomic ([[mercury (element)|Hg]]) or at times contain molecules, such as [[sodium|Na<sub>2</sub>]], held together by a more conventional covalent bond. This is why it is not correct to speak of a single 'metallic bond'.{{clarify|date=January 2014}}

Delocalization is most pronounced for '''s'''- and '''p'''-electrons. Delocalization in [[caesium]] is so strong that the electrons are virtually freed from the caesium atoms to form a gas constrained only by the surface of the metal. For caesium, therefore, the picture of Cs<sup>+</sup> ions held together by a negatively charged [[nearly-free electron model|electron gas]] is very close to accurate (though not perfectly so).{{efn|If the electrons were truly ''free'', their energy would only depend on the magnitude of their [[wave vector]] '''k''', not its direction. That is, in [[momentum space|'''k'''-space]], the Fermi level should form a perfect [[sphere]]. The [[Fermi surface|shape of the Fermi level]] can be measured by [[Electron cyclotron resonance|cyclotron resonance]] and is never a sphere, not even for caesium.<ref>{{cite journal|title=The Fermi Surface of Caesium|author1=Okumura, K.  |author2=Templeton, I. M.  |name-list-style=amp |journal=Proceedings of the Royal Society of London A|issue=1408 |year=1965|pages=89–104|jstor=2415064|doi=10.1098/rspa.1965.0170|volume=287|bibcode = 1965RSPSA.287...89O|s2cid=123127614 }}</ref>}} For other elements the electrons are less free, in that they still experience the potential of the metal atoms, sometimes quite strongly. They require a more intricate quantum mechanical treatment (e.g., [[tight binding]]) in which the atoms are viewed as neutral, much like the carbon atoms in benzene. For '''d'''- and especially '''f'''-electrons the delocalization is not strong at all and this explains why these electrons are able to continue behaving as [[unpaired electron]]s that retain their spin, adding interesting [[magnetism|magnetic properties]] to these metals.