Polyhedral skeletal electron pair theory: Difference between revisions

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{{Short description|Electron counting rules}}

In [[chemistry]] the '''polyhedral skeletal electron pair theory''' (PSEPT) provides [[electron counting]] rules useful for predicting the structures of [[cluster compound|clusters]] such as [[Boranes|borane]] and [[carborane]] clusters. The electron counting rules were originally formulated by [[Kenneth Wade]],<ref name=wade71>{{cite journal|title=The structural significance of the number of skeletal bonding electron-pairs in carboranes, the higher boranes and borane anions, and various transition-metal carbonyl cluster compounds|author-link=Kenneth Wade |first=K. |last=Wade |journal=J. Chem. Soc. D |date=1971 |volume=1971|issue=15 |pages=792–793 |doi=10.1039/C29710000792}}</ref> and were further developed by others including [[Michael Mingos]];<ref name=mingos72>{{cite journal|title=A General Theory for Cluster and Ring Compounds of the Main Group and Transition Elements |author-link=Michael Mingos|first=D. M. P. |last=Mingos |year = 1972|journal=Nature Physical Science |volume=236 |issue=68 |pages=99–102 |doi=10.1038/physci236099a0|bibcode=1972NPhS..236...99M }}</ref> and others; they are sometimes known as '''Wade's rules''' or the '''Wade–Mingos rules'''.<ref name=welch13>{{cite journal|title=The significance and impact of Wade's rules |first=Alan J. |last=Welch |journal=Chem. Commun. |date=2013|volume=49 |issue=35 |pages=3615–3616 |doi=10.1039/C3CC00069A|pmid=23535980 }}</ref> The rules are based on a [[molecular orbital]] treatment of the bonding.<ref name=Wade>{{cite journal|title=Structural and Bonding Patterns in Cluster Chemistry|last=Wade |first=K.|authorlink=Kenneth Wade|journal=Adv. Inorg. Chem. Radiochem. |series=Advances in Inorganic Chemistry and Radiochemistry |year=1976|volume=18|pages=1–66|doi=10.1016/S0065-2792(08)60027-8|isbn=9780120236183 }}</ref><ref name=lecture>{{cite journal|title= Lecture notes distributed at the University of Illinois, Urbana-Champaign|last=Girolami |first=G.|date=Fall 2008}} These notes contained original material that served as the basis of the sections on the 4''n'', 5''n'', and 6''n'' rules.</ref><ref name=Nyholm>{{cite journal|title=Nyholm Memorial Lectures|last=Gilespie |first=R. J.|journal=[[Chemical Society Reviews|Chem. Soc. Rev.]]|year=1979|volume=8|issue=3|pages=315–352|doi=10.1039/CS9790800315}}</ref><ref name=Mingosmingos84>{{cite journal|title=Polyhedral Skeletal Electron Pair Approach|last=Mingos |first=D. M. P.|authorlink=D. M. P. Mingos|journal=[[Acc. Chem. Res.]]|year=1984|volume=17|issue=9|pages=311–319|doi=10.1021/ar00105a003}}</ref> These rules have been extended and unified in the form of the [[Jemmis mno rules|Jemmis ''mno'' rules]].<ref name=mnorulesjemmis01>{{cite journal|title=A Unifying Electron-counting rule for Macropolyhedral Boranes, Metallaboranes, and Metallocenes|journal=[[J. Am. Chem. Soc.]]|year=2001|volume=123|issue=18|pmid=11457198|pages=4313–4323|doi=10.1021/ja003233z|last1=Jemmis|first1=Eluvathingal D.|last2=Balakrishnarajan|first2=Musiri M.|last3=Pancharatna|first3=Pattath D.}}</ref><ref name=mnoreviewjemmis02>{{cite journal|title=Electronic Requirements for Macropolyhedral Boranes|journal=[[Chem. Rev.]]|year=2002|volume=102|issue=1|pages=93–144|doi=10.1021/cr990356x|last1=Jemmis|first1=Eluvathingal D.|last2=Balakrishnarajan|first2=Musiri M.|last3=Pancharatna|first3=Pattath D.|pmid=11782130}}</ref>

==Predicting structures of cluster compounds==

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The rules are useful in also predicting the structure of [[carborane]]s.

Example: C₂B₇H₁₃

:Electron count = 2 × C + 7 × B + 13 × H = 2 × 4 + 37 × 73 + 13 × 1 = 42

:Since n in this case is 9, 4''n'' + 6 = 42, the cluster is ''arachno''.

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;''closo''-{{chem|B|6|H|6|2−}}

[[File:B6H6MOdiagram.jpg|thumb|200px|MO diagram of {{chem|B|6|H|6|2−}} showing the orbitals responsible for forming the cluster. Pictorial representations of the orbitals are shown; the MO sets of T and E symmetry will each have two or one additional pictorial representation, respectively, that are not shown here.]]

:The boron atoms lie on each vertex of the octahedron and are sp hybridized.<ref name=Cotton3 /> One sp-hybrid radiates away from the structure forming the bond with the hydrogen atom. The other sp-hybrid radiates into the center of the structure forming a large bonding molecular orbital at the center of the cluster. The remaining two unhybridized orbitals lie along the tangent of the sphere like structure creating more bonding and antibonding orbitals between the boron vertices.<ref name="mnorulesjemmis02"/> The orbital diagram breaks down as follows:

::The 18 framework molecular orbitals, (MOs), derived from the 18 boron atomic orbitals are:

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===Transition metal clusters===

Transition metal clusters use the d orbitals for [[Chemical bond|bonding]]. Thus, they have up to nine bonding orbitals, instead of only the four present in boron and main group clusters.<ref name=king>{{cite journal|title=Chemical Applications of Group Theory and Topology.7. A Graph-Theoretical Interpretation of the Bonding Topology in Polyhedral Boranes, Carboranes, and Metal Clusters|last1=King |first1=R. B. |last2=Rouvray |first2=D. H.|journal=[[J. Am. Chem. Soc.]]|year=1977|volume=99|issue=24|pages=7834–7840|doi=10.1021/ja00466a014}}</ref><ref name=RCR>{{cite journal|last1=Kostikova |first1=G. P. |last2=Korolkov |first2=D. V.|title=Electronic Structure of Transition Metal Cluster Complexes with Weak- and Strong-field Ligands|journal=Russ. Chem. Rev.|year=1985|volume=54|issue=4|pages=591–619|doi=10.1070/RC1985v054n04ABEH003040|bibcode = 1985RuCRv..54..344K |s2cid=250797537 }}</ref> PSEPT also applies to [[metallaborane]]s

===Clusters with interstitial atoms===

Owing their large radii, transition metals generally form clusters that are larger than main group elements. One consequence of their increased size, these clusters often contain atoms at their centers. A prominent example is [Fe₆C(CO)₁₆]^2-. In such cases, the rules of electron counting assume that the interstitial atom contributes all valence electrons to cluster bonding. In this way, [Fe₆C(CO)₁₆]^2- is equivalent to [Fe₆(CO)₁₆]^6- or [Fe₆(CO)₁₈]^2-.<ref>{{cite book |doi=10.1002/0470862106.ia097|chapter=Cluster Compounds: Inorganometallic Compounds Containing Transition Metal & Main Group Elements|title=Encyclopedia of Inorganic Chemistry|year=2006|last1=Fehlner|first1=Thomas P.|isbn=0470860782}}</ref>

==See also==

* [[Styx rule]]

==References==