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>; 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=mingos84>{{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=jemmis01>{{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=jemmis02>{{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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===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==