Polyhedral skeletal electron pair theory: Difference between revisions

Revision as of 12:37, 6 September 2015

Latest revision as of 16:33, 23 July 2025

(48 intermediate revisions by 28 users not shown)

Line 1:

{{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, 792-793|volume=1971|issue=15 {{DOI|pages=792–793 |doi=10.1039/C29710000792}}</ref> and were further developed by others including [[Michael Mingos|D. M. P. 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. MINGOS|last=Mingos |year = 1972|journal=Nature Physical Science |volume=236, 99-102|issue=68 {{doi|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/MingosWade–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, 3615-3616|issue=35 {{DOI|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|authorlast=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|authorlast=Girolami, |first=G.|date=Fall 2008}} These notes contained original material that served as the basis of the sections on the 4n4''n'', 5n5''n'', and 6n6''n'' rules.</ref><ref name=Nyholm>{{cite journal|title=Nyholm Memorial Lectures|authorlast=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|authorlast=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==

[[File:Re4CO122-.svg|thumb|The structure of the [[butterfly cluster compound]] [Re₄(CO)₁₂]^2-2− conforms to the predictions of PSEPT.]]

Different rules (4n4''n'', 5n5''n'', or 6n6''n'') are invoked depending on the number of electrons per vertex.

The 4n4''n'' rules are reasonably accurate in predicting the structures of clusters having about 4 electrons per vertex, as is the case for many [[boraneboranes]]s and [[carborane]]s. For such clusters, the structures are based on [[deltahedra]], which are [[polyhedra]] in which every face is triangular. The 4n4''n'' clusters are classified as ''closo-'', ''nido-'', ''arachno-'' or ''hypho-,'', based on whether they represent a complete (''closo-'') [[deltahedron]], or a deltahedron that is missing one (''nido-''), two (''arachno-'') or three (''hypho-'') vertices.

However, hypho clusters are relatively uncommon due to the fact that the electron count is high enough to start to fill antibonding orbitals and destabilize the 4n4''n'' structure. If the electron count is close to 5 electrons per vertex, the structure often changes to one governed by the 5n rules, which are based on 3-connected polyhedra.

As the electron count increases further, the structures of clusters with 5n electron counts become unstable, so the 6n6''n'' rules can be implemented. The 6n6''n'' clusters have structures that are based on rings.

A molecular orbital treatment can be used to rationalize the bonding of cluster compounds of the 4n4''n'', 5n5''n'', and 6n6''n'' types.

[[File:Re4CO122-.svg|thumb|The structure of the [[butterfly cluster]] [Re₄(CO)₁₂]^2- conforms to the predictions of PSEPT.]]

===4n rules===

===4n4''n'' rules===

The following [[polyhedra]] are closo polyhedra, and are the basis for the 4n rules; each of these have triangular faces.<ref name="Cotton&Wilkinson6th">{{Cotton&Wilkinson6th}}</ref> The number of vertices in the cluster determines what polyhedron the structure is based on.

[[File:Deltahedral-borane-cluster-array-numbered-3D-bs-17.png|thumb|[[:en:Ball-and-stick model|Ball-and-stick model]]s showing the structures of the [[:en:Boron|boron]] skeletons of [[:en:Boranes|borane]] [[:en:Atom cluster|clusters]].]]

The following [[polyhedra]] are ''closo'' polyhedra, and are the basis for the 4n4''n'' rules; each of these have triangular faces.<ref name="Cotton&Wilkinson6th">{{Cotton&Wilkinson6th}}</ref> The number of vertices in the cluster determines what polyhedron the structure is based on.

{| class="wikitable"

Line 41 ⟶ 44:

|-

| 10

| [[Gyroelongated square bipyramid|Bicapped square antiprismantiprismatic molecular geometry]]

|-

| 11

Line 50 ⟶ 53:

|}

Using the electron count, the predicted structure can be found. ''n'' is the number of vertices in the cluster. The 4n4''n'' rules are enumerated in the following table.

{| class="wikitable"

Line 58 ⟶ 61:

! Predicted structure

|-

| 4n4''n'' − 2

| Bicapped ''closo''

| ''n'' − 2 vertex ''closo'' polyhedron with 2 capped ([[augmentation (geometry)|augmented]]) faces

|-

| 4n4''n''

| Capped ''closo''

| ''n'' − 1 vertex ''closo'' polyhedron with 1 face capped

|-

| 4n4''n'' + 2

| ''closo''

| Closo

| Closo''closo'' polyhedron with ''n'' vertices

|-

| 4n4''n'' + 4

| ''nido''

| Nido

| ''n'' + 1 vertex ''closo'' polyhedron with 1 missing vertex

|-

| 4n + 6

| ''arachno''

| Arachno

| ''n'' + 2 vertex ''closo'' polyhedron with 2 missing vertices

|-

| 4n + 8

| ''hypho''

| Hypho

| ''n'' + 3 vertex ''closo'' polyhderonpolyhedron with 3 missing vertices

|-

| 4n + 10

| ''klado''

| ''n'' + 4 vertex ''closo'' polyhedron with 4 missing vertices

|}

[[File:Pb9 Cluster.png|thumb|150px|Rightright|{{chem|Pb_|10^|2−}}]]

When counting electrons for each cluster, the number of [[valence electrons]] is enumerated. For each [[transition metal]] present, 10 electrons are subtracted from the total electron count. For example, in Rh₆(CO)₁₆ the total number of electrons would be {{nowrap|6( × 9) + 16( × 2) -− 6( × 10)}} = {{nowrap|86 – 6(10)60}} = 26. Therefore, the cluster is a ''closo'' polyhedron because {{nowrap|1=''n'' = 6}}, with 4n{{nowrap|1=4''n'' + 2 = 26}}.

[[File:S4 Cluster.png|thumb|150px|Rightright|{{chem|S_|4^|2+}}]]

Other rules may be considered when predicting the structure of clusters:

# For clusters consisting mostly of transition metals, any ''main group elements'' present are often best counted as ligands or interstitial atoms, rather than vertices.

# Larger and more electropositive atoms tend to occupy vertices of high connectivity and smaller more electronegative atoms tend to occupy vertices of low connectivity.

# In the special case of [[Boranes|boron hydride]] clusters, each boron atom connected to 3 or more vertices has one terminal hydride, while a boron atom connected to 2two other vertices has 2two terminal hydrogenshydrogen atoms. If more hydrogenshydrogen atoms are present, they are placed in open face positions to even out the coordination number of the vertices.

# For the special case of transition metal clusters, [[ligands]] are added to the metal centers to give the metals reasonable coordination numbers, and if any [[hydrogen]] [[atoms]] are present they are placed in bridging positions to even out the ''coordination numbers'' of the vertices.

In general, ''closo'' structures with ''n'' vertices are ''n''-vertex polyhedra.

To predict the structure of a ''nido'' cluster, the ''closo'' cluster with ''n ''&nbsp;+ &nbsp;1 vertices is used as a starting point; if the cluster is composed of small atoms a high connectivity vertex is removed, while if the cluster is composed of large atoms a low connectivity vertex is removed.

To predict the structure of an ''arachno'' cluster, the ''closo'' polyhedron with ''n ''&nbsp;+ &nbsp;2 vertices is used as the starting point, and the ''n''&nbsp;+&nbsp;1 vertex ''nido'' complex is generated by following the rule above; a second vertex adjacent to the first is removed if the cluster is composed of mostly small atoms, a second vertex not adjacent to the first is removed if the cluster is composed mostly of large atoms.

[[File:Os6corrected.png|thumb|150px|Os₆(CO)₁₈, carbonyls omitted]]

Example: {{chem|Pb_|10^|2−}}

:Electron count: 10( × Pb) + 2 (for the negative charge) = 10( × 4) + 2 = 42 electrons.

:Since ''n'' = 10, 4n4''n'' + 2 = 42, so the cluster is a ''closo'' bicapped square antiprism.

Example: {{chem|S_|4^|2+}}

:Electron count: 4( × S) – 2 (for the positive charge) = 4( × 6) – 2 = 22 electrons.

:Since ''n'' = 4, 4n4''n'' + 6 = 22, so the cluster is ''arachno''.

:Starting from an octahedron, a vertex of high connectivity is removed, and then a non-adjacent vertex is removed.

Example: Os₆(CO)₁₈

:Electron count: 6( × Os) + 18( × CO) – 60 (for 6 osmium atoms) = 6( × 8) + 18( × 2) – 60 = 24

:Since ''n'' = 6, 4n4''n'' = 24, so the cluster is capped ''closo''.

:Starting from a trigonal bipyramid, a face is capped. The carbonyls have been omitted for clarity.

[[File:B5H5 cluster.png|thumb|150px|{{chem|B_|5|H_|5^|4−}}, hydrogenshydrogen atoms omitted]]

Example:<ref name=Cotton3>{{cite book| last = Cotton| first = Albert| title = Chemical Applications of Group Theory| year = 1990| publisher = John Wiley & Sons| pages = [https://archive.org/details/isbn_9780471510949/page/205 205–251]| isbn = 0-471-51094-7| url-access = registration| url = https://archive.org/details/isbn_9780471510949/page/205}}</ref> {{chem|B|5|H|5|4−}}

Example:<ref name=Cotton3>{{cite book

| last= Cotton| first = Albert| title = Chemical Applications of Group Theory

| year = 1990|publisher = John Wiley & Sons

| pages = 205–251| isbn = 0-471-51094-7}}</ref> B₅H₅⁴⁻

:Electron count: 5( × B) + 5( × H) + 4 (for the negative charge) = 5( × 3) + 5( × 1) + 4 = 24

:Since ''n'' = 5, 4n4''n'' + 4 = 24, so the cluster is nido.

:Starting from an octahedron, one of the vertices is removed.

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

Example: C₂B₇H₁₃

:Electron count = 2( × C) + 7( × B) + 13( × H) = 2( × 4) + 3(7) × 3 + 13( × 1) = 42

:Since n in this case is 9, 4n4''n'' + 6 = 42, the cluster is ''arachno''.

The bookkeeping for deltahedral clusters is sometimes carried out by counting skeletal electrons instead of the total number of electrons. The skeletal orbital (electron pair) and skeletal electron counts for the four types of [[deltahedron|deltahedral]] clusters are:

*''n''-vertex ''closo'': (''n'' + 1) skeletal orbitals, (2n2''n'' + 2) skeletal electrons

*''n''-vertex ''nido'': (''n'' + 2) skeletal orbitals, (2n2''n'' + 4) skeletal electrons

*''n''-vertex ''arachno'': (''n'' + 3) skeletal orbitals, (2n2''n'' + 6) skeletal electrons

*''n''-vertex ''hypho'': (''n'' + 4) skeletal orbitals, (2n2''n'' + 8) skeletal electrons

The skeletal electron counts are determined by summing the total of the following number of electrons:

Line 142 ⟶ 146:

*the anionic charge electrons

===5n5''n'' rules===

As discussed previously, the 4n4''n'' rule mainly deals with clusters with electron counts of 4n{{nowrap|4''n'' + ''k''}}, in which approximately 4 [[electrons]] are on each vertex. As more electrons are added per vertex, the number of the electrons per vertex approaches 5. Rather than adopting structures based on deltahedra, the 5n-type clusters have structures based on a different series of polyhedra known as the 3-connected [[polyhedra]], in which each vertex is connected to 3 other vertices. The 3-connected polyhedra are the [[dual polyhedron|duals]] of the deltahedra. The common types of 3-connected polyhedra are listed below.

[[File:P4 diagram.gif|thumb|150px|right|5n5''n'' cluster: P₄]]

[[File:P4S3 diagram.gifpng|thumb|150px|right|5n5''n'' + 3 cluster: P₄S₃]]

[[File:Phosphorus trioxide.svg|thumb|100px|right|5n5''n'' + 6 cluster: P₄O₆]]

{|class = "wikitable" style="text-align:center"

|-

Line 159 ⟶ 163:

|10||[[Pentagonal prism]]

|-

|12||D_2d Pseudopseudo-octahedron (dual of snub disphenoid)

|-

|14||Dual of triaugmented triangular prism (K₅ [[associahedron]])

|-

|16||Square [[Square truncated trapezohedron]]

|-

|18||Dual of edge-contracted icosahedron

Line 170 ⟶ 174:

|}

The 5n5''n'' rules are as follows.

{|class = "wikitable" style="text-align:center"

Line 176 ⟶ 180:

!Total electron count!!Predicted structure

|-

|5n5''n''||''n''-vertex 3-connected polyhedron

|-

|5n5''n'' + 1||n–1''n'' – 1 vertex 3-connected polyhedron with one vertex inserted into an edge

|-

|5n5''n'' + 2||n–2''n'' – 2 vertex 3-connected polyhedron with two vertices inserted into edges

|-

|5n5''n'' + ''k''||''n-'' − ''k'' vertex 3-connected polyhedron with ''k'' vertices inserted into edges

|}

Example: P₄

:Electron count: 4( × P) = 4( × 5) = 20

:It is 5na 5''n'' structure with ''n'' = 4, so it is tetrahedral

Example: P₄S₃

:Electron count 4( × P) + 3( × S) = 4( × 5) + 3( × 6) = 38

:It is 5na 5''n'' + 3 structure with ''n'' = 7. Three vertices are inserted into edges

Example: P₄O₆

:Electron count 4( × P) + 6( × O) = 4( × 5) + 6( × 6) = 56

:It is 5na 5''n'' + 6 structure with ''n'' = 10. Six vertices are inserted into edges

===6n6''n'' rules===

As more electrons are added to a 5n5''n'' cluster, the number of electrons per vertex approaches 6. Instead of adopting structures based on 4n4''n'' or 5n5''n'' rules, the clusters tend to have structures governed by the 6n6''n'' rules, which are based on rings. The rules for the 6n6''n'' structures are as follows.[[File:Cyclooctasulfur structural formula 3D.svg|thumb|S₈ crown]]

{|class = "wikitable" style="text-align:center"

Line 204 ⟶ 208:

!Total electron count!!Predicted structure

|-

|6n–k6''n'' – k||''n''-membered ring with {{frac|''k/''|2}} trans-annulartransannular bonds

|-

|6n–46''n'' – 4||''n''-membered ring with 2 trans-annulartransannular bonds

|-

|6n–26''n'' – 2||''n''-membered ring with 1 trans-annulartransannular bond

|-

|6n6''n''||''n''-membered ring

|-

|6n6''n'' + 2||''n''-membered chain (''n''-membered ring with 1 broken bond)

|}

Example: S₈

:Electron count = 8( × S) = 8( × 6) = 48 electrons.

:Since ''n'' = 8, 6n6''n'' = 48, so the cluster is an 8 -membered ring.

[[File:Hexane skeletal.svg|thumb|6n6''n'' + 2 cluster: hexane]]

Hexane (C₆H₁₄)

:Electron count = 6( × C) + 14( × H) = 6( × 4) + 14( × 1) = 38

:Since ''n'' = 6, 6n6''n'' = 36 and 6n6''n'' + 2 = 38, so the cluster is a 6 -membered chain.

===Isolobal vertex units===

Provided a vertex unit is [[Isolobal principle|isolobal]] with BH then it can, in principle at least, be substituted for a BH unit, even though that BH and CH are not isoelectronic. The CH⁺ unit is isolobal, hence the reason why the rules are applicable to carboranes.<br/> This can be explained due to a [[frontier orbital]] treatment.<ref name="Cotton&Wilkinson6th"/> Additionally there are isolobal transition-metal units. For example, Fe(CO)₃ provides 2 electrons. The derivation of this is briefly as follows:

Additionally there are isolobal transition metal units. For example Fe(CO)₃ provides 2 electrons. The derivation of this is briefly as follows:

*Fe has 8 valence electrons.

*Each carbonyl group is a net 2 electron donor after the internal [[sigma bond|σ]]- and [[pi bond|π -bonding]] are taken into account making 14 electrons.

*3 pairs are considered to be involved in Fe – COFe–CO [[sigma bond|σ-bonding]] and 3 pairs are involved in [[pi bond|π]] back bonding-backbonding from Fe to CO reducing the 14 to 2.

==Bonding in cluster compounds==

;''closo''-{{chem|B|6|H|6|2−}}

===Polyhedron===

[[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.]]

'''B₂H₆'''

[[File:B6H6MOdiagram.jpg|thumb|200px|left|MO diagram of B₆H₆²⁻ 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:

[[File:B2H6MOdiagram.JPG|thumb|Molecular-orbital (MO) diagram of B₂H₆. Atoms and their corresponding orbitals are colored the same. Green MOs symbolize bonding, while red symbolize anti-bonding.]]The bonding in diborane is best described by treating each B as sp³ [[Orbital hybridisation|hybridized]]. Two sp³ hybrid orbitals on each boron form the bonds to the terminal hydrogens. The remaining sp³ orbitals create the bonds with the bridging hydrogens. Because the angles in the diborane structure are not tetrahedral the orbitals also likely contain some sp² character.

'''Closo-B₆H₆²⁻'''

[[File:B6H6MOdiagram.jpg|thumb|200px|left|MO diagram of B₆H₆²⁻ 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="mnorules"/>

The orbital diagram breaks down as follows

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

*1 bonding MO at the center of the cluster and 5 antibonding MOs from the 6 sp radial hybrid orbitals

*6 bonding MOs and 6 antibonding MOs from the 12 tangential p orbitals.

The total skeletal bonding orbitals is therefore 7, i.e. (n+1).

'''Main group atom clusters'''

The bonding in other main group cluster compounds follow similar rules as those described for the boron cluster bonding. The atoms at the vertex [[Orbital hybridisation|hybridize]] in a way which allows the lowest energy structure to form.

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

*1 bonding MO at the center of the cluster and 5 antibonding MOs from the 6 sp radial hybrid orbitals

*6 bonding MOs and 6 antibonding MOs from the 12 tangential p orbitals.

::The total18 skeletalframework bondingmolecular orbitals, is(MOs), thereforederived 7,from i.e.the (n+1).18 boron atomic orbitals are:

::*1 bonding MO at the center of the cluster and 5 antibonding MOs from the 6 sp -radial hybrid orbitals

::*6 bonding MOs and 6 antibonding MOs from the 12 tangential p -orbitals.

:The total skeletal bonding orbitals is therefore 7, i.e. ({{nowrap|''n'' + 1)}}.

===Transition metal clusters===

Transition metal clusters use the d orbitals for [[Chemical bond|bonding]]. Thus, sothey 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|authorlast1=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 Therename=RCR>{{cite isjournal|last1=Kostikova also|first1=G. moreP. bonding|last2=Korolkov flexibility|first2=D. inV.|title=Electronic transitionStructure metalof clustersTransition dependingMetal onCluster whetherComplexes vertexwith metalWeak- electronand pairsStrong-field areLigands|journal=Russ. involvedChem. inRev.|year=1985|volume=54|issue=4|pages=591–619|doi=10.1070/RC1985v054n04ABEH003040|bibcode cluster= bonding1985RuCRv..54..344K or|s2cid=250797537 appear}}</ref> as lonePSEPT pairs.also applies to [[metallaborane]]s

The cluster chlorides and carbonyls of transition metals will be briefly discussed here as they represent opposite ends of the [[spectrochemical series]] and show important features of the differences between transition metal clusters with different ligands.<ref name=RCR>{{cite journal|author=Kostikova, G.P., Korol'kov, D. V.|title=Electronic Structure of Transition Metal Cluster Complexes with Weak- and Strong-field Ligands|journal=Russian Chemical Reviews|year=1985|volume=54|issue=4|pages=591–619|doi=10.1070/RC1985v054n04ABEH003040|bibcode = 1985RuCRv..54..344K }}</ref> In chloride clusters the energy splitting of the valence d orbitals increases upon formation of the [[Cluster chemistry|cluster]]. The number and symmetry of these orbitals are dependent upon the type and structure of each individual cluster complex.<ref name=RCR /> Conversely in the carbonyl clusters the energy splitting of the valence d orbitals is greater before the formation of the cluster.<ref name=RCR />

===Clusters with interstitial atoms===

<gallery caption="MO diagram clusters metal chlorides and metal carbonyls" widths="250px" heights="300px" perrow="2">

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>

Image:TMclusterCl.JPG| General MO diagram of metal chloride structures. Green MOs represent bonding orbitals while red represent anti-bonding orbitals. The labeling on the MOs is as follows: s-sigma, p-pi, d-delta bonding, with * denoting anti-bonding interactions.

Image:TMclusterCO.JPG| General MO diagram for metal carbonyl clusters. Green MOs represent bonding orbitals while red represent anti-bonding orbitals. The labeling on the MOs is as follows:s-sigma, p-pi, d-delta bonding with * denoting anti-bonding interactions.

==See also==

</gallery>

* [[Styx rule]]

==References==

Line 274 ⟶ 263:

{{Organometallics}}

{{Chemical bonds}}

{{DEFAULTSORT:Polyhedral Skeletal Electron Pair Theory}}

Line 279 ⟶ 269:

[[Category:Inorganic chemistry]]

[[Category:Organometallic chemistry]]

[[Category:Cluster chemistry]]