Metallic bonding

[[File:Metallic Bonding Example.svg|thumb|An example showing metallic bonding. + represents [[cation]]s, - represents the free floating electrons.]]'''Metallic bonding''' is a type of [[chemical bond]]ing that arises from the electrostatic attractive force between [[conduction electrons]] (in the form of an electron cloud of [[delocalized electron]]s) and positively charged metal [[ion]]s. Metal atoms lose their [[Valence electron|valence electrons]] to a large, delocalized orbital, which leaves the nucleus, and other electrons that are closer to the nucleus, as positively charged cations. The ions form a [[Crystal structure|crystal lattice]] as they are held together by the negative charge of the delocalized orbital.<ref name=":0">{{Cite web |title=IB Colourful Solutions in Chemistry |url=https://ibchem.com/IB25/s2.31.php |access-date=2026-05-14 |website=ibchem.com}}</ref> It may be described as the sharing of ''free'' electrons among a structure of positively charged ions, and as a more delocalized version of [[Covalent bond|covalent bonding]]. Metallic bonding accounts for many [[physical property|physical properties]] of metals, such as [[Strength of materials|strength]], [[ductility]], [[thermal conductivity|thermal]] and [[electrical resistivity and conductivity]], [[Opacity (optics)|opacity]], and [[lustre (mineralogy)|lustre]].<ref>[http://www.chemguide.co.uk/atoms/bonding/metallic.html Metallic bonding]. chemguide.co.uk</ref><ref>[http://www.chemguide.co.uk/atoms/structures/metals.html Metal structures]. chemguide.co.uk</ref><ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html Chemical Bonds]. chemguide.co.uk</ref><ref>[https://web.archive.org/web/19991018204506/http://www.physics.ohio-state.edu/%7Eaubrecht/physics133.html "Physics 133 Lecture Notes" Spring, 2004. Marion Campus]. physics.ohio-state.edu</ref>

Metallic bonding is not the only type of chemical bonding a metal can exhibit as a pure substance.<ref name=":1">{{Cite web |title=What is a Metallic Bond? |url=https://byjus.com/chemistry/metallic-bonds/ |access-date=2026-04-28 |website=BYJUS |language=en}}</ref> For example, elemental [[gallium]] consists of covalently-bound pairs of atoms in both liquid and solid-state—these pairs form a crystal structure with metallic bonding between them. Another example of a metal–metal covalent bond is the [[mercurous ion]] ({{chem|Hg|2|2+}}).<ref>{{Cite web |last=PubChem |title=Mercury(I) ion |url=https://pubchem.ncbi.nlm.nih.gov/compound/6914533 |access-date=2026-04-28 |website=pubchem.ncbi.nlm.nih.gov |language=en}}</ref>

==History== As chemistry developed into a science, it became clear that metals formed the majority of the [[periodic table]] of the elements, and great progress was made in the description of the salts that can be formed in reactions with [[acids]]. With the advent of [[electrochemistry]], it became clear that metals generally go into solution as positively charged ions, and the oxidation reactions of the metals became well understood in their electrochemical series. A picture emerged of metals as positive ions held together by an ocean of negative electrons.<ref>{{Cite web |title=Metallic bonding – GKToday |url=https://www.gktoday.in/metallic-bonding/#:~:text=The%20development%20of%20electrochemistry%20helped%20clarify%20the,immersed%20in%20an%20ocean%20of%20mobile%20electrons. |access-date=2026-04-29 |website=www.gktoday.in}}</ref><ref>{{Cite web |title=Forming ionic compounds - Metals, non-metals and compounds - GCSE Chemistry (Single Science) Revision - OCR 21st Century |url=https://www.bbc.co.uk/bitesize/guides/z2mbjty/revision/5 |access-date=2026-04-29 |website=BBC Bitesize |language=en-GB}}</ref>

With the advent of quantum mechanics, this picture was given a more formal interpretation in the form of the [[free electron model]] and its further extension, the [[nearly free electron model]].<ref>{{Cite journal |last=Jensen |first=William |date=1992 |title=The Historical Development of the van Arkel Bond-Type Diagram* |url=https://homepages.uc.edu/~jensenwb/reprints/060.%20History%20Bond%20Triangle.pdf |journal=Department of Chemistry, University of Cincinnati |pages=1-5 |via=University of Cincinnati}}</ref> In both models, the electrons are seen as a gas traveling through the structure of the solid with an energy that is essentially isotropic, in that it depends on the square of the [[magnitude (vector)|magnitude]], ''not'' the direction of the momentum vector '''[[wave vector|k]]'''. In three-dimensional k-space, the set of points of the highest filled levels (the [[Fermi surface]]) should therefore be a sphere. In the nearly-free model, box-like [[Brillouin zone]]s are added to k-space by the periodic potential experienced from the (ionic) structure, thus mildly breaking the isotropy.

The advent of [[X-ray diffraction]] and [[thermal analysis]] made it possible to study the structure of crystalline solids, including metals and their alloys; and [[phase diagram]]s were developed. Despite all this progress, the nature of [[Intermetallic|intermetallic compounds]] and [[Alloy|alloys]] largely remained a mystery, and their study was often merely empirical. Chemists generally steered away from anything that did not seem to follow Dalton's [[Law of multiple proportions#Law 3: Law of Multiple Proportions|laws of multiple proportions]]; and the problem was considered the domain of a different science, metallurgy.<ref>{{Cite web |last=Gill |first=Charles |date=April 10, 2026 |title=metallurgy |url=https://www.britannica.com/science/metallurgy |url-status=live |archive-url=https://web.archive.org/web/20260326151615/https://www.britannica.com/science/metallurgy |archive-date=March 26, 2026 |access-date=May 20, 2026 |website=Encyclopedia Britannica}}</ref>

The nearly-free electron model was eagerly taken up by some researchers in metallurgy, notably [[William Hume-Rothery|Hume-Rothery]], in an attempt to explain why intermetallic alloys with certain compositions would form and others would not. Initially, Hume-Rothery's attempts were quite successful.<ref>{{Cite news |title=William Hume-Rothery {{!}} British Scientist, Metallurgist, Chemist {{!}} Britannica |url=https://www.britannica.com/biography/William-Hume-Rothery |archive-url=http://web.archive.org/web/20250710020617/https://www.britannica.com/biography/William-Hume-Rothery |archive-date=2025-07-10 |access-date=2026-05-12 |work=Encyclopedia Britannica |language=en}}</ref> His idea was to add electrons to inflate the spherical Fermi-balloon inside the series of Brillouin-boxes and determine when a certain box would be full. This predicted a fairly large number of alloy compositions that were later observed. As soon as [[Electron cyclotron resonance|cyclotron resonance]] became available and the shape of the balloon could be determined, it was found that the balloon was not spherical as the Hume-Rothery believed, except perhaps in the case of [[caesium]]. This revealed how a model can sometimes give a whole series of correct predictions, yet still be wrong in its basic assumptions. The nearly-free electron debacle compelled researchers to modify the assumpition that ions flowed in a sea of free electrons. A number of quantum mechanical models were developed, such as band structure calculations based on molecular orbitals, and the [[density functional theory]]. These models either depart from the atomic orbitals of neutral atoms that share their electrons, or (in the case of density functional theory) departs from the total electron density. The free-electron picture has, nevertheless, remained a dominant one in introductory courses on metallurgy.<ref>{{Cite journal |last=Jones |first=R. O. |date=25 August 2015 |title=Density functional theory: Its origins, rise to prominence, and future |url=https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.87.897 |journal=Rev. Mod. Phys. |volume=87 |issue=897 |via=APS Journals}}</ref>

The electronic band structure model became a major focus for the study of metals and even more of [[semiconductor]]s. Together with the electronic states, the vibrational states were also shown to form bands. [[Rudolf Peierls]] showed that, in the case of a one-dimensional row of metallic atoms, an inevitable instability would break such a chain into individual molecules.<ref>Peierls, Rudolf (1985). ''Bird of Passage: Recollections of a Physicist''. p. 229. Princeton, New Jersey: Princeton University Press. [[ISBN (identifier)|ISBN]] [[Special:BookSources/0-691-08390-8|<bdi>0-691-08390-8</bdi>]]. [[OCLC (identifier)|OCLC]] [https://search.worldcat.org/title/925040112 925040112].</ref> This sparked an interest as to when collective metallic bonding is stable, and when localized bonding will take its place. Further research went into the study of clustering of metal atoms.

As powerful as the band structure model proved to be in describing metallic bonding, it remains a one-electron approximation of a many-body problem: the energy states of an individual electron are described as if all the other electrons form a homogeneous background. Researchers such as Mott and Hubbard realized that the one-electron treatment was perhaps appropriate for strongly delocalized [[azimuthal quantum number|'''s'''- and '''p'''-electrons]]; but for '''d'''-electrons,<ref>{{Cite web |title=Nobel Prize in Physics 1977 |url=https://www.nobelprize.org/prizes/physics/1977/mott/lecture/ |access-date=2026-05-20 |website=NobelPrize.org |language=en-US}}</ref> and even more for '''f'''-electrons, the interaction with nearby individual electrons (and atomic displacements) may become stronger than the delocalized interaction that leads to broad bands. This gave a better explanation for the transition from localized [[unpaired electron]]s to itinerant ones partaking in metallic bonding.

==The nature of metallic bonding== The combination of two phenomena gives rise to metallic bonding: [[delocalized electron|delocalization of electrons]] and the availability of a far larger number of delocalized energy states than of delocalized electrons.<ref>{{Cite web |date=2018-07-15 |title=9.5: Metallic Bonding |url=https://chem.libretexts.org/Courses/Bellarmine_University/BU%3A_Chem_103_(Christianson)/Phase_3%3A_Atoms_and_Molecules_-_the_Underlying_Reality/9%3A_Chemical_Bonding/9.5%3A_Metallic_Bonding |access-date=2026-04-22 |website=Chemistry LibreTexts |language=en}}</ref> The latter could be called [[electron deficiency]].

===In 2D=== [[Graphene]] is an example of two-dimensional metallic bonding. Its metallic bonds are similar to [[aromaticity|aromatic bonding]] in [[benzene]], [[naphthalene]], [[anthracene]], [[ovalene]], etc.<ref>{{Cite web |date=2018-04-23 |title=A Guide to Graphene |url=https://www.azonano.com/article.aspx?ArticleID=4841 |access-date=2026-05-12 |website=AZoNano |language=en}}</ref>

===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. Metallic bonding is mostly non-polar, because there is little to no difference, even in [[alloys]], among the [[Electronegativity|electronegativities]] of the [[atom]]s participating in the bonding interaction. Thus, metallic bonding is an extremely delocalized communal form of covalent bonding. Metallic bonding may be described as not a unique type of bond at all, as it describes the bonding only as present in a portion of condensed matter, be it crystalline solid or liquid. Metallic vapors, in contrast, are often atomic ([[mercury (element)|Hg]]) or at times contain molecules, such as [[sodium|Na2]], held together by a more conventional covalent bond. This is why it is not correct to speak of a single 'metallic bond'.<ref>{{Cite news |title=Metallic bond {{!}} Properties, Examples, & Explanation {{!}} Britannica |url=https://www.britannica.com/science/metallic-bond |archive-url=http://web.archive.org/web/20250831015533/https://www.britannica.com/science/metallic-bond |archive-date=2025-08-31 |access-date=2026-04-22 |work=Encyclopedia Britannica |language=en}}</ref>

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+ 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.<ref>{{Cite web |date=2016-11-28 |title=Delocalization of Electrons |url=https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Chemical_Bonding/Valence_Bond_Theory/Delocalization_of_Electrons |access-date=2026-05-25 |website=Chemistry LibreTexts |language=en}}</ref>

===Electron deficiency and mobility=== Metal [[atoms]] contain few [[electron]]s in their [[Electron shell#Valence shells|valence shells]] relative to their periods or [[energy level]]s. They are [[Electron deficiency|electron-deficient]] elements and the communal sharing does not change that. There remain far more available energy states than there are shared electrons. Both requirements for conductivity are therefore fulfilled: strong delocalization and partly filled energy bands. Such electrons can therefore easily change from one energy state to a slightly different one. Thus, not only do they become delocalized, forming a sea of electrons permeating the structure, but they are also able to migrate through the structure when an external electrical field is applied, leading to electrical conductivity.<ref name=":1" /> Without the field, there are electrons moving equally in all directions. Within such a field, some electrons will adjust their state slightly, adopting a different [[wave vector]]. Consequently, there will be more moving one way than another and a net current will result.

Metals are typically also good conductors of heat. Thermal conductivity in metals is primarily due to free electrons, and is generally tied to the electrical conductivity of the same substance, due to the [[Wiedemann–Franz law]]. Many factors can also influence thermal conductivity, such as temperature.<ref>Hahn, David W.; Özişik, M. Necati (2012). ''Heat conduction'' (3rd ed.). Hoboken, N.J.: Wiley. p. 5. [[ISBN (identifier)|ISBN]] [[Special:BookSources/978-0-470-90293-6|<bdi>978-0-470-90293-6</bdi>]].</ref>

The freedom of electrons to migrate also gives metal atoms, or layers of them, the capacity to slide past each other. Locally, bonds can easily be broken and replaced by new ones after a deformation. This process does not affect the communal metallic bonding very much, which gives rise to metals' characteristic [[malleability]] and [[ductility]].<ref name=":0" /> This is particularly true for pure elements. In the presence of dissolved impurities, the normally easily formed cleavages may be blocked and the material becomes harder. Gold, for example, is very soft in pure form (24-[[Carat (purity)|karat]]), which is why alloys are preferred in jewelry.

Electron deficiency is important in distinguishing metallic from more conventional covalent bonding. Thus, to amend the expression given above: ''Metallic bonding is an extremely delocalized communal form of electron-deficient{{efn|Electron deficiency is a relative term: it means fewer than half of the electrons needed to complete the ''next'' noble gas configuration. For example, lithium is electron deficient with respect to [[neon]], but electron-''rich'' with respect to the previous noble gas, [[helium]]. <ref>{{cite book |last1=Housecroft |first1=Catherine E. |last2=Sharpe |first2=Alan G. |title=Inorganic Chemistry |date=2005 |publisher=Pearson Prentice-Hall |isbn=0130-39913-2 |page=326 |edition=2nd |quote=An electron-deficient species possesses fewer valence electrons than are required for a localized bonding scheme.}}</ref>}} covalent bonding''.<ref>{{Cite web |date=24 Dec 2025 |title=Introduction and Extension of the Unified Theory of Multicenter Bonding: The Role of the Charge-Shift Bonding |url=https://pmc.ncbi.nlm.nih.gov/articles/PMC12786652/ |url-status=dead |archive-url=https://web.archive.org/web/20260525140233/https://pmc.ncbi.nlm.nih.gov/articles/PMC12786652/ |archive-date=25 May 2026 |access-date=25 May 2026 |website=National Library of Medicine}}</ref>

==Metallic radius== The metallic radius is defined as one-half of the distance between the two adjacent metal ions in the metallic structure.<ref>{{Cite web |date=2015-04-22 |title=6.5: Metallic Radii |url=https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Map%3A_Inorganic_Chemistry_(Housecroft)/06%3A_Structures_and_Energetics_of_Metallic_and_Ionic_solids/6.05%3A_Metallic_Radii |access-date=2026-05-20 |website=Chemistry LibreTexts |language=en}}</ref> This radius depends on the nature of the atom as well as its environment—specifically, on the [[coordination number]] (CN), which in turn depends on the temperature and applied pressure.

When comparing periodic trends in the size of atoms it is often desirable to apply the so-called Goldschmidt correction, which converts atomic radii to the values the atoms would have if they were 12-coordinated. Since metallic radii are largest for the highest coordination number, correction for less dense coordinations involves multiplying by {{mvar|x}}, where 0 < {{mvar|x}} < 1. Specifically, for CN = 4, {{mvar|x}} = 0.88; for CN = 6, {{mvar|x}} = 0.96, and for CN = 8, {{mvar|x}} = 0.97. The correction is named after [[Victor Goldschmidt]] who obtained the numerical values quoted above.<ref>{{cite book|title=Shriver and Atkins' Inorganic Chemistry|url=https://books.google.com/books?id=tUmcAQAAQBAJ&pg=PA74|year=2010|publisher=Oxford University Press|isbn=978-0-19-923617-6|pages=74–}}</ref>

The radii follow general [[periodic trends]]: they decrease across the period due to the increase in the [[effective nuclear charge]], which is not offset by the increased number of [[valence electrons]]; but the radii increase down the group due to an increase in the [[principal quantum number]]. Between the 4'''d''' and 5'''d''' elements, the [[lanthanide contraction]] is observed<ref>Chistyakov, V. M. (1968). "Biron's Secondary Periodicity of the Side d-subgroups of Mendeleev's Short Table". ''Journal of General Chemistry of the USSR''. '''38''' (2): 213–214. Retrieved 6 January 2024.</ref>—there is very little increase of the radius down the group due to the presence of poorly [[electron shielding|shielding]] [[atomic orbitals|'''f''' orbitals]].

==Strength of the bond== The atoms in metals are held together by [[Coulomb's law|electrostatic]] attractions between the positively charged cations and the delocalized negatively charged electron cloud around them. The attraction between the cations and electron cloud is strong, and the attraction gets stronger the more valence electrons the metal atoms provide for the electron cloud. For example, [[magnesium]] has a higher melting and boiling point than [[sodium]] because magnesium has two valence electrons compared to sodium's one valence electron. A magnesium atom provides two electrons for the electron cloud (twice the amount a sodium atom can) and becomes a +2 ion. The denser electron cloud and more positively charged ions result in a much stronger attractive force between them, which increases the melting point of magnesium.<ref name=":2" />

Besides other types of chemical bonding, boiling is the only way a pure metal can have no metallic bonding; molten metals are still affected by metallic bonding. This takes a lot of energy, due to the strength of the attractive forces holding the delocalized electron cloud and the cations together. Therefore, metals often have high boiling points, with the transition metal [[tungsten]] having the highest melting and boiling points among all elements. An exception is the elements of the [[Group 12 element|zinc group]]: Zn, Cd, and Hg. Their electron configurations end in ...n'''s'''2, which resembles a noble gas configuration, like that of [[helium]]. The melting and boiling points decrease more and more when going down the zinc group, because the energy differential to the empty n'''p''' orbitals becomes larger. These metals are therefore relatively volatile, and are avoided in [[ultra-high vacuum]] systems.<ref>{{Cite journal |last=Lee |first=G. |date=August 15, 1989 |title=Materials for Ultra-High Vacuum |url=https://digital.library.unt.edu/ark:/67531/metadc1185924/m1/1/ |journal=Fermi National Accelerator Laboratory |pages=2-3 |via=UNT Digital Library}}</ref>

The strong bonding of metals in liquid form demonstrates that the energy of a metallic bond is not highly dependent on the direction of the bond; this lack of bond directionality is a direct consequence of electron delocalization, and is best understood in contrast to the directional bonding of covalent bonds. The energy of a metallic bond is thus mostly a function of the number of electrons which surround the metallic atom, as exemplified by the [[embedded atom model]].<ref>{{cite journal|title=The embedded-atom method: a review of theory and applications|journal=Materials Science Reports|date=1993|volume=9|issue=7–8|pages=251–310|doi=10.1016/0920-2307(93)90001-U|author1-link=Murray S. Daw|author3-link=Michael Baskes|last1=Daw|first1=Murray S.|last2=Foiles|first2=Stephen M.|last3=Baskes|first3=Michael I.|url=https://zenodo.org/record/1258631|doi-access=free}}</ref> This typically results in metals assuming relatively simple, [[Atomic packing factor|close-packed]] crystal structures, such as FCC, BCC, and HCP.

Given high enough cooling rates and appropriate alloy composition, metallic bonding can occur even in [[metallic glass|glasses]], which have amorphous structures.<ref>{{Cite journal |last=Jafary-Zadeh |first=Mehdi |last2=Kumar |first2=Gideon |last3=Branicio |first3=Paulo |last4=Seifi |first4=Mohsen |last5=Lewandowski |first5=John |last6=Cui |first6=Fangsen |date=27 Feb 2018 |title=A Critical Review on Metallic Glasses as Structural Materials for Cardiovascular Stent Applications |url=https://pmc.ncbi.nlm.nih.gov/articles/PMC5872105/ |journal=Journal of Functional Biomaterials |volume=9 |issue=1 |pages=2 |via=National Library of Medicine}}</ref>

Many things in biochemistry are mediated by the weak interaction of metal ions and biomolecules. Such interactions, and their associated [[conformational change]]s, have been measured using [[dual polarisation interferometry]].

==Solubility and compound formation== Metals are [[insoluble]] in water or organic solvents, unless they undergo a reaction with them. Typically, this is an [[Redox|oxidation reaction]] that robs the metal atoms of their valence electrons, destroying the metallic bonding. However, metals are often readily soluble in each other while retaining the metallic character of their bonding. Gold, for example, dissolves easily in mercury, even at room temperature. Even in solid metals, the solubility can be extensive. If the structures of the two metals are the same, there can even be complete solid solubility, as in the case of [[electrum]], an alloy of silver and gold.

At times, however, two metals will form alloys with different structures than either of the two parents, such as in [[Intermetallic|intermetallic compounds]]. But, because materials with metallic bonding are typically not molecular, Dalton's [[Law of definite proportions|law of integral proportions]] is not valid; and often a range of stoichiometric ratios can be achieved.<ref>{{Cite web |date=2013-10-02 |title=Dalton's Law (Law of Partial Pressures) |url=https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/States_of_Matter/Properties_of_Gases/Gas_Laws/Dalton's_Law_(Law_of_Partial_Pressures) |access-date=2026-05-22 |website=Chemistry LibreTexts |language=en}}</ref> It is thus better to describe [[phase (matter)|phase]]s instead of solutes or pure substances. The study of such phases has traditionally been more the domain of [[metallurgy]] than of [[chemistry]], although the two fields overlap considerably.

==Localization and clustering== The metallic bonding in complex compounds does not necessarily involve all constituent elements equally. It is quite possible to have one or more elements that do not partake at all. One could picture the conduction electrons flowing around them like a river around an island or a big rock. It is possible to observe which elements do partake: e.g., by looking at the core levels in an [[X-ray photoelectron spectroscopy]] (XPS) spectrum. If an element partakes, its peaks tend to be skewed.

Some intermetallic materials do exhibit [[metal cluster]]s reminiscent of molecules; these compounds are more a topic of chemistry than of metallurgy. The formation of the clusters could be seen as a way to localize the electron-deficient bonding into bonds of a more condensed nature. [[Hydrogen]] is an extreme example of this form of condensation, where at high pressures [[Metallic hydrogen|it is metallic]].<ref>{{Cite journal |last=Wang |first=Lin |last2=Wu |first2=Zhongyan |last3=Gao |first3=Guoying |last4=Tian |first4=Yongjun |date=9 October 2024 |title=Metallization of Hydrogen Under High Pressure: Challenges and Experimental Progress |url=https://advanced.onlinelibrary.wiley.com/doi/10.1002/adfm.202411463 |journal=Advanced Functional Materials |volume=34 |issue=18 |via=Advanced Online Library}}</ref> The core of the planet [[Jupiter]] is held together by a combination of metallic bonding and high pressure induced by gravity. At lower pressures, however, the bonding becomes entirely localized into a regular covalent bond. The localization is so complete that H2 gas results. A similar argument holds for an element such as boron. Though it is electron-deficient compared to carbon, it does not form a metal. Instead it has a number of complex structures in which [[icosahedron|icosahedral]] B12 clusters dominate. [[Charge density wave]]s are a related phenomenon.

As these phenomena involve the movement of the atoms toward or away from each other, they can be interpreted as the coupling between the electronic and the vibrational states (i.e. the phonons) of the material. A different such electron-phonon interaction is thought to lead to a very different result at low temperatures, that of [[superconductivity]]. Rather than blocking the mobility of the charge carriers by forming [[electron pair]]s in localized bonds, [[Cooper pairs]] are formed that no longer experience any resistance to their mobility.

==Optical properties== The presence of an ocean of mobile charge carriers has profound effects on the [[optical properties]] of metals, which can only be understood by considering the electrons as a ''collective'', rather than considering the states of individual electrons involved in more conventional covalent bonds.<ref name=":2">{{Cite web |last=Clark |first=Jim |title=Metallic Bonding |url=https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Chemical_Bonding/Fundamentals_of_Chemical_Bonding/Metallic_Bonding |archive-url=https://web.archive.org/web/20251212065106/https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Chemical_Bonding/Fundamentals_of_Chemical_Bonding/Metallic_Bonding |archive-date=December 12, 2025 |access-date=May 19, 2026 |website=LibreTexts Chemistry|date=May 19, 2026}}</ref>

[[Light]] consists of a combination of an electrical and a magnetic field. The electrical field is usually able to excite an elastic response from the electrons involved in the metallic bonding. The result is that photons cannot penetrate very far into the metal and are typically reflected, although some may also be absorbed. This holds equally for all photons in the visible spectrum, which is why metals are often silvery white or grayish with the characteristic specular reflection of metallic [[lustre (mineralogy)|lustre]]. The balance between reflection and absorption determines how white or how gray a metal is, although surface tarnish can obscure the lustre. Silver, a metal with high conductivity, is one of the whitest.<ref>{{Cite news |title=Silver {{!}} Facts, Properties, & Uses {{!}} Britannica |url=https://www.britannica.com/science/silver |archive-url=http://web.archive.org/web/20251205165837/https://www.britannica.com/science/silver |archive-date=2025-12-05 |access-date=2026-05-19 |work=Encyclopedia Britannica |language=en}}</ref>

Notable exceptions are reddish copper and yellowish gold. The reason for their color is that there is an upper limit to the frequency of the light that metallic electrons can readily respond to, which is the [[plasmon frequency]]. At the plasmon frequency, the frequency-dependent dielectric function of the [[Free electron model#Dielectric function of the electron gas|free electron gas]] goes from negative (reflecting) to positive (transmitting); higher frequency photons are not reflected at the surface, and do not contribute to the color of the metal. There are some materials, such as [[indium tin oxide]] (ITO), that are metallic conductors (actually [[degenerate semiconductor]]s) for which this threshold is in the [[infrared]],<ref>{{cite journal|doi=10.1021/jp026600x|title=Indium Tin Oxide Plasma Frequency Dependence on Sheet Resistance and Surface Adlayers Determined by Reflectance FTIR Spectroscopy|year=2002|last1=Brewer|first1=Scott H.|last2=Franzen|first2=Stefan|journal=The Journal of Physical Chemistry B|volume=106|issue=50|pages=12986–12992}}</ref> which is why they are transparent in the visible, but good reflectors in the infrared.

For [[silver]] the limiting frequency is in the far ultraviolet, but for copper and gold it is closer to the visible.<ref>{{Cite journal |last=Yang |first=Honghua |last2=D'Archangel |first2=Jeffery |last3=Sundheimer |first3=Micheal |last4=Tucker |first4=Eric |last5=Boreman |first5=Glenn |last6=Raschke |first6=Markus |date=22 June 2015 |title=Optical dielectric function of silver |url=https://nano-optics.colorado.edu/wp-content/uploads/2020/06/Yang_PhysRevB_15_MainText.pdf |journal=Physical Review B |volume=91 |pages=5 |via=Raschke Nano-Optics Group}}</ref> This explains the colors of these two metals. At the surface of a metal, resonance effects known as [[Surface plasmon resonance|surface plasmons]] can result. They are collective oscillations of the conduction electrons, like a ripple in the electronic ocean. However, even if photons have enough energy, they usually do not have enough [[momentum]] to set the ripple in motion. Therefore, plasmons are hard to excite on a bulk metal. This is why gold and copper look like lustrous metals albeit with a dash of color. However, in [[colloidal gold]] the metallic bonding is confined to a tiny metallic particle, which prevents the oscillation wave of the plasmon from 'running away'. The momentum selection rule is therefore broken, and the plasmon resonance causes an extremely intense absorption in the green, with a resulting purple-red color. Such colors are orders of magnitude more intense than ordinary absorptions seen in dyes and the like, which involve individual electrons and their energy states.

==See also== * {{annotated link|Atomic radii of the elements (data page)}} * {{annotated link|Bonding in solids}} * {{annotated link|Metal aromaticity}}

==Notes== {{notelist}}

==References== {{Reflist}}

{{DEFAULTSORT:Metallic Bond}} [[Category:Chemical bonding]] [[Category:Metals]]