Polyhedral skeletal electron pair theory: Difference between revisions

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In [[chemistry]] the '''polyhedral skeletal electron pair theory''' (PSEPT) provides [[electron counting]] rules useful for predicting the structures of [[cluster compound|clusters]] such as [[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|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 |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 |pages=3615–3616 |doi=10.1039/C3CC00069A}}</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. |year=1976|volume=18|pages=1–66|doi=10.1016/S0065-2792(08)60027-8}}</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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;''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: