Sextuple bond

Roos et al argue that no stable element can form bonds of higher order than a sextuple bond, because the latter corresponds to a hybrid of the s orbital and all five d orbitals, and f orbitals contract too close to the nucleus to bond in the lanthan­ides.{{cite journal |last1=Roos |first1=Björn O. |last2=Borin |first2=Antonio C. |author3=Laura Gagliardi |year=2007 |title=Reaching the Maximum Multiplicity of the Covalent Chemical Bond |url=https://www.academia.edu/13598187 |journal=Angewandte Chemie International Edition|volume=46 |issue=9 |pages=1469–72 |doi=10.1002/anie.200603600 |pmid=17225237}} Indeed, quantum mechanical calculations have revealed that the di­molybdenum bond is formed by a combination of two σ bonds, two π bonds and two δ bonds. (Also, the σ and π bonds contribute much more significantly to the sextuple bond than the δ bonds.){{Cite journal |last1=Bursten |first1=Bruce E. |last2=Cotton |first2=F. Albert |last3=Hall |first3=Michael B. |date=September 1980 |title=Dimolybdenum: nature of the sextuple bond |journal=Journal of the American Chemical Society |volume=102 |issue=20 |pages=6348–6349 |doi=10.1021/ja00540a034 |issn=0002-7863}}

Although no φ bonding has been reported for transition metal dimers, it is predicted that if any sextuply-bonded actinides were to exist, at least one of the bonds would likely be a φ bond as in quintuply-bonded diuranium and di­neptunium.{{Cite journal |last1=Bursten |first1=Bruce E. |last2=Ozin |first2=Geoffrey A. |date=August 1984 |title=X.alpha.-SW calculations for naked actinide dimers: existence of .vphi. bonds between metal atoms |journal=Inorganic Chemistry |volume=23 |issue=18 |pages=2910–2911 |doi=10.1021/ic00186a039 |issn=0020-1669}} No sextuple bond has been observed in lanthanides or actinides.

For the majority of elements, even the possibility of a sextuple bond is foreclosed, because the d electrons ferromagnetically couple, instead of bonding. The only known exceptions are dimolybdenum and ditungsten.

The formal bond order (FBO) of a molecule is half the number of bonding electrons surplus to antibonding electrons; for a typical molecule, it attains exclusively integer values. A full quantum treatment requires a more nuanced picture, in which electrons may exist in a superposition, contributing fractionally to both bonding and antibonding orbitals. In a formal sextuple bond, there would be {{math|P {{=}} 6}} different electron pairs; an effective sextuple bond would then have all six contributing almost entirely to bonding orbitals.

In Roos et al's calculations, the effective bond order (EBO) could be determined by the formula$$EBO\; =\; \backslash left\; (\; \backslash frac\{1\}\{2\}\; \backslash right\; )\backslash sum\_\{p=1\}^P(\backslash eta\_\{b,p\}-\backslash eta\_\{ab,p\})-c$$ where {{math|η_b}} is the proportion of formal bonding orbital occupation for an electron pair {{mvar|p}}, {{math|η_ab}} is the proportion of the formal antibonding orbital occupation, and {{mvar|c}} is a correction factor account­ing for deviations from equilibrium geometry. Several metal-metal bonds' EBOs are given in the table at right, compared to their formal bond orders.

Dimolybdenum and ditungsten are the only mole­cules with effective bond orders above 5, with a quintuple bond and a partially formed sixth covalent bond. Dichromium, while formally described as having a sextuple bond, is best described as a pair of chromium atoms with all electron spins exchange-coupled to each other.{{Cite journal |last1=Goodgame |first1=Marvin M. |last2=Goddard |first2=William A. |date=February 1981 |title=The "sextuple" bond of chromium dimer |journal=The Journal of Physical Chemistry |volume=85 |issue=3 |pages=215–217 |doi=10.1021/j150603a001 |issn=0022-3654}}

While diuranium is also formally described as having a sextuple bond, relativistic quantum mechanical calculations have determined it to be a quadruple bond with four electrons ferro­magnetically coupled to each other rather than in two formal bonds. Previous calcu­lations on diuranium did not treat the electronic molecular Hamiltonian relativistically and produced higher bond orders of 4.2 with two ferromagnetically coupled electrons.{{Cite journal |last1=Gagliardi |first1=Laura |last2=Roos |first2=Björn O. |date=2005-05-17 |title=Quantum Chemical Calculations Show that the Uranium Molecule U2 Has a Quintuple Bond. |url=https://archive-ouverte.unige.ch/unige:3652 |journal=ChemInform |volume=36 |issue=20 |pages=848 |bibcode=2005Natur.433..848G |doi=10.1002/chin.200520001 |issn=0931-7597|url-access=subscription }}

Laser evaporation of a molybdenum sheet at low temperatures (7 K) produces gaseous dimolybdenum (Mo₂). The resulting molecules can then be imaged with, for instance, near-infrared spectroscopy or UV spectroscopy.{{cite journal|title = On the dimers of the VIB group: a new NIR electronic state of Mo₂|first1= D.|last1= Kraus|first2= M. |last2=Lorenz |first3=V. E.|last3= Bondybey|journal = PhysChemComm|year = 2001|volume = 4|pages = 44–48|doi = 10.1039/b104063b|issue = 10}}

Both ditungsten and dimolybdenum have very short bond lengths compared to neighboring metal dimers. For example, sextuply-bonded dimolybdenum has an equilibrium bond length of 1.93 Å. This equi­librium internuclear distance is signi­ficantly lower than in the dimer of any neighboring 4d transition metal, and sug­gestive of higher bond orders.{{Cite journal |last1=Borin |first1=Antonio Carlos |last2=Gobbo |first2=João Paulo |last3=Roos |first3=Björn O. |date=April 2010 |title=Electronic structure and chemical bonding in W2 molecule |journal=Chemical Physics Letters |volume=490 |issue=1–3 |pages=24–28 |bibcode=2010CPL...490...24B |doi=10.1016/j.cplett.2010.03.022 |issn=0009-2614 |doi-access=free}}{{Cite journal |last1=Efremov |first1=Yu.M |last2=Samoilova |first2=A.N |last3=Kozhukhovsky |first3=V.B |last4=Gurvich |first4=L.V |date=December 1978 |title=On the electronic spectrum of the Mo2 molecule observed after flash photolysis of Mo(CO)6 |journal=Journal of Molecular Spectroscopy |volume=73 |issue=3 |pages=430–440 |bibcode=1978JMoSp..73..430E |doi=10.1016/0022-2852(78)90109-1 |issn=0022-2852}} However, the bond dissociation energies of ditungsten and dimolybdenum are rather low, because the short internuclear distance introduces geometric strain.{{Cite journal |last1=Joy |first1=Jyothish |last2=Jemmis |first2=Eluvathingal D. |date=2017 |title=A halogen bond route to shorten the ultrashort sextuple bonds in Cr2 and Mo2 |journal=Chemical Communications |volume=53 |issue=58 |pages=8168–8171 |doi=10.1039/c7cc04653g |issn=1359-7345 |pmid=28677703 |s2cid=206066221}}

One empirical technique to determine bond order is spectroscopic exami­nation of bond force constants. Linus Pauling investigated the relationships between bonding atoms{{Cite journal |last=Hardcastle |first=F. D. |date=2016-01-01 |title=A General Valence-Length Correlation for Determining Bond Orders: Application to Carbon-Carbon and Carbon-Hydrogen Chemical Bonds |url=https://scholarworks.uark.edu/jaas/vol70/iss1/17 |journal=Journal of the Arkansas Academy of Science |volume=70 |doi=10.54119/jaas.2016.7009 |issn=2326-0505|doi-access=free }} and developed a formula that predicts that bond order is roughly{{Cite journal |last1=Lombardi |first1=John R. |last2=Davis |first2=Benjamin |date=2002-06-01 |title=Periodic Properties of Force Constants of Small Transition-Metal and Lanthanide Clusters |url=https://pubs.acs.org/doi/10.1021/cr010425j |journal=Chemical Reviews |language=en |volume=102 |issue=6 |pages=2431–2460 |doi=10.1021/cr010425j |pmid=12059275 |issn=0009-2665 |quote=Pauling showed that the force constant is approximately proportional to the bond order...Note that the term 'bond order' as used here is not the same as the usual chemical definition [i.e., 1/2(no. of bonding electrons - no. of antibonding electrons) or better a function of the electron density]. This might more accurately be termed the 'vibrational bond order' since it is experimentally determined.|url-access=subscription }} proportional to the force constant; that is, $$k\_e=n\backslash cdot\; k\_e^\{(1)\}$$ where {{mvar|n}} is the bond order, {{math|k_e}} is the force constant of the interatomic inter­action and {{math|k_e⁽¹⁾}} is the force constant of a single bond between the atoms.{{Cite book |last=Johnston |first=Harold S. |url=https://books.google.com/books?id=Zj4wAAAAIAAJ |title=Gas Phase Reaction Rate Theory |date=1966 |publisher=Ronald Press Company |isbn=978-0-608-30060-3 |language=en}}

The table at right shows some select force constants for metal-metal dimers com­pared to their EBOs; consistent with a sextuple bond, molybdenum's summed force constant is substantially more than quintuple the single-bond force constant.

Like dichromium, dimolybdenum and ditungsten are expected to exhibit a ¹Σ_g⁺ singlet ground state.{{cite journal |last1=Merino |first1=Gabriel |last2=Donald |first2=Kelling J. |last3=D'Acchioli |first3=Jason S. |last4=Hoffmann |first4=Roald |year=2007 |title=The Many Ways To Have a Quintuple Bond |journal=J. Am. Chem. Soc. |volume=129 |issue=49 |pages=15295–15302 |doi=10.1021/ja075454b |pmid=18004851}}{{Cite journal |last1=Borin |first1=Antonio Carlos |last2=Gobbo |first2=João Paulo |last3=Roos |first3=Björn O. |date=January 2008 |title=A theoretical study of the binding and electronic spectrum of the Mo2 molecule |journal=Chemical Physics |volume=343 |issue=2–3 |pages=210–216 |bibcode=2008CP....343..210B |doi=10.1016/j.chemphys.2007.05.028 |issn=0301-0104}} However, in tungsten, this ground state arises from a hybrid of either two ⁵D₀ ground states or two ⁷S₃ excited states. Only the latter corresponds to the formation of a stable, sextuply-bonded ditungsten dimer.

Although sextuple bonding in homodimers is rare, it remains a possibility in larger molecules.

Theoretical computations suggest that bent dimetallocenes have a higher bond order than their linear counterparts.{{Cite journal |last1=Xu |first1=Bing |last2=Li |first2=Qian-Shu |last3=Xie |first3=Yaoming |last4=King |first4=R. Bruce |last5=Schaefer |first5=Henry F. |date=2010-02-17 |title=Metal−Metal Quintuple and Sextuple Bonding in Bent Dimetallocenes of the Third Row Transition Metals |journal=Journal of Chemical Theory and Computation |volume=6 |issue=3 |pages=735–746 |doi=10.1021/ct900564p |issn=1549-9618 |pmid=26613304}} For this reason, the Schaefer lab has investi­gated dimetallocenes for natural sextuple bonds. However, such com­pounds tend to exhibit Jahn–Teller distortion, rather than a true sextuple bond.

For example, dirhenocene is bent. Calculating its frontier molecular orbitals sug­gests the existence of relatively stable singlet and triplet states, with a sextuple bond in the singlet state. But that state is the excited one; the triplet ground state should exhibit a formal quintuple bond. Similarly, for the dibenzene complexes Cr₂(C₆H₆)₂, Mo₂(C₆H₆)₂, and W₂(C₆H₆)₂, molecular bonding orbitals for the triplet states with symmetries D_6h and D_6d indicate the possibility of an intermetallic sex­tuple bond. Quantum chemistry calculations reveal, however, that the corre­sponding D_2h singlet geometry is stabler than the D_6h triplet state by {{Val|3|-|39|u=kcal/mol}}, depending on the central metal.{{Cite journal |last1=Sun |first1=Zhi |last2=Schaefer |first2=Henry F. |last3=Xie |first3=Yaoming |last4=Liu |first4=Yongdong |last5=Zhong |first5=Rugang |date=September 2013 |title=Does the metal–metal sextuple bond exist in the bimetallic sandwich compounds Cr2(C6H6)2, Mo2(C6H6)2, and W2(C6H6)2?† |journal=Molecular Physics |volume=111 |issue=16–17 |pages=2523–2535 |bibcode=2013MolPh.111.2523S |doi=10.1080/00268976.2013.798434 |issn=0026-8976 |s2cid=94537427}}

Both quantum mechanical calculations and photoelectron spectroscopy of the tungsten oxide clusters W₂O_n (n = 1–6) indicate that increased oxidation state reduces the bond order in ditungsten. At first, the weak δ bonds break to yield a quadruply-bonded W₂O; further oxidation generates the ditungsten complex W₂O₆ with two bridging oxo ligands and no direct W–W bonds.{{Cite journal |last1=Zhai |first1=Hua-Jin |last2=Huang |first2=Xin |last3=Cui |first3=Li-Feng |last4=Li |first4=Xi |last5=Li |first5=Jun |last6=Wang |first6=Lai-Sheng |date=July 2005 |title=Electronic and Structural Evolution and Chemical Bonding in Ditungsten Oxide Clusters: W2On-and W2On(n= 1−6) |journal=The Journal of Physical Chemistry A |volume=109 |issue=27 |pages=6019–6030 |bibcode=2005JPCA..109.6019Z |doi=10.1021/jp051496f |issn=1089-5639 |pmid=16833938}}

{{Reflist}}

{{refbegin|}}

• {{cite journal|doi=10.1073/pnas.0610364104|date=Feb 2007|last=Chisholm|first=M. H.|title=Metal to metal multiple bonds in ordered assemblies|volume=104|issue=8|pages=2563–70|pmid=17299047|pmc=1815223|journal=PNAS|bibcode=2007PNAS..104.2563C|doi-access=free}}
• {{cite journal|title=Metal–metal bond energies in diatomic molybdenum, octachloromolybdate ({{chem|Mo|2|Cl|8|4-}}), and molybdenum formate ({{chem|Mo|2|(O|2|CH)|4}})|last1=Norman|first1=Joe G. Jr.|last2=Ryan|first2=P. Barry|journal=J. Comput. Chem.|year=1980|volume=1|issue=1|pages=59–63|doi=10.1002/jcc.540010107|s2cid=98503129}}
• {{cite journal|title=Electron correlation and the nature of the sextuple bond in the dimolybdenum molecule|last1=Atha|first1=P. M.|last2=Hillier|first2=I. H.|last3=Guest|first3=M. F.|journal=Chem. Phys. Lett.|year=1980|volume=75|issue=1|pages=84–86|doi=10.1016/0009-2614(80)80469-6|bibcode=1980CPL....75...84A}}
• {{cite journal|title= Theoretical study of the electronic structure of the transition metal dimers, Sc₂, Cr₂, Mo₂ and Ni₂|last1=Wood|first1=Carol|last2=Doran|first2=Mark|last3=Hillier|first3=Ian H.|last4=Guest|first4=Martyn F.|journal= Faraday Symposia of the Chemical Society|year=1980|volume=14|pages=159–169|doi=10.1039/fs9801400159}}

{{refend}}

{{Chemical bonding theory}}

Category:Chemical bonding