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sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Electron counting rules</div> <p>In <a href="/wiki/Chemistry" title="Chemistry">chemistry</a> the <b>polyhedral skeletal electron pair theory</b> (PSEPT) provides <a href="/wiki/Electron_counting" title="Electron counting">electron counting</a> rules useful for predicting the structures of <a href="/wiki/Cluster_compound" class="mw-redirect" title="Cluster compound">clusters</a> such as <a href="/wiki/Boranes" title="Boranes">borane</a> and <a href="/wiki/Carborane" title="Carborane">carborane</a> clusters. The electron counting rules were originally formulated by <a href="/wiki/Kenneth_Wade" title="Kenneth Wade">Kenneth Wade</a>,<sup id="cite_ref-wade71_1-0" class="reference"><a href="#cite_note-wade71-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and were further developed by others including <a href="/wiki/Michael_Mingos" title="Michael Mingos">Michael Mingos</a>;<sup id="cite_ref-mingos72_2-0" class="reference"><a href="#cite_note-mingos72-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> they are sometimes known as <b>Wade's rules</b> or the <b>Wade–Mingos rules</b>.<sup id="cite_ref-welch13_3-0" class="reference"><a href="#cite_note-welch13-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The rules are based on a <a href="/wiki/Molecular_orbital" title="Molecular orbital">molecular orbital</a> treatment of the bonding.<sup id="cite_ref-Wade_4-0" class="reference"><a href="#cite_note-Wade-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-lecture_5-0" class="reference"><a href="#cite_note-lecture-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Nyholm_6-0" class="reference"><a href="#cite_note-Nyholm-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-mingos84_7-0" class="reference"><a href="#cite_note-mingos84-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> These rules have been extended and unified in the form of the <a href="/wiki/Jemmis_mno_rules" title="Jemmis mno rules">Jemmis <i>mno</i> rules</a>.<sup id="cite_ref-jemmis01_8-0" class="reference"><a href="#cite_note-jemmis01-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-jemmis02_9-0" class="reference"><a href="#cite_note-jemmis02-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Predicting_structures_of_cluster_compounds">Predicting structures of cluster compounds</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=1" title="Edit section: Predicting structures of cluster compounds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Re4CO122-.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Re4CO122-.svg/220px-Re4CO122-.svg.png" decoding="async" width="220" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Re4CO122-.svg/330px-Re4CO122-.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Re4CO122-.svg/440px-Re4CO122-.svg.png 2x" data-file-width="2316" data-file-height="1000" /></a><figcaption>The structure of the <a href="/wiki/Butterfly_cluster_compound" title="Butterfly cluster compound">butterfly cluster compound</a> [Re<sub>4</sub>(CO)<sub>12</sub>]<sup>2−</sup> conforms to the predictions of PSEPT.</figcaption></figure> <p>Different rules (4<i>n</i>, 5<i>n</i>, or 6<i>n</i>) are invoked depending on the number of electrons per vertex. </p><p>The 4<i>n</i> rules are reasonably accurate in predicting the structures of clusters having about 4 electrons per vertex, as is the case for many <a href="/wiki/Boranes" title="Boranes">boranes</a> and <a href="/wiki/Carborane" title="Carborane">carboranes</a>. For such clusters, the structures are based on <a href="/wiki/Deltahedra" class="mw-redirect" title="Deltahedra">deltahedra</a>, which are <a href="/wiki/Polyhedra" class="mw-redirect" title="Polyhedra">polyhedra</a> in which every face is triangular. The 4<i>n</i> clusters are classified as <i>closo-</i>, <i>nido-</i>, <i>arachno-</i> or <i>hypho-</i>, based on whether they represent a complete (<i>closo-</i>) <a href="/wiki/Deltahedron" title="Deltahedron">deltahedron</a>, or a deltahedron that is missing one (<i>nido-</i>), two (<i>arachno-</i>) or three (<i>hypho-</i>) vertices. </p><p>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 4<i>n</i> 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. </p><p>As the electron count increases further, the structures of clusters with 5n electron counts become unstable, so the 6<i>n</i> rules can be implemented. The 6<i>n</i> clusters have structures that are based on rings. </p><p>A molecular orbital treatment can be used to rationalize the bonding of cluster compounds of the 4<i>n</i>, 5<i>n</i>, and 6<i>n</i> types. </p> <div class="mw-heading mw-heading3"><h3 id="4n_rules">4<i>n</i> rules</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=2" title="Edit section: 4n rules"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Deltahedral-borane-cluster-array-numbered-3D-bs-17.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Deltahedral-borane-cluster-array-numbered-3D-bs-17.png/220px-Deltahedral-borane-cluster-array-numbered-3D-bs-17.png" decoding="async" width="220" height="503" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Deltahedral-borane-cluster-array-numbered-3D-bs-17.png/330px-Deltahedral-borane-cluster-array-numbered-3D-bs-17.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Deltahedral-borane-cluster-array-numbered-3D-bs-17.png/440px-Deltahedral-borane-cluster-array-numbered-3D-bs-17.png 2x" data-file-width="3478" data-file-height="7958" /></a><figcaption><a href="/wiki/Ball-and-stick_model" title="Ball-and-stick model">Ball-and-stick models</a> showing the structures of the <a href="/wiki/Boron" title="Boron">boron</a> skeletons of <a href="/wiki/Boranes" title="Boranes">borane</a> <a href="/wiki/Atom_cluster" class="mw-redirect" title="Atom cluster">clusters</a>.</figcaption></figure> <p>The following <a href="/wiki/Polyhedra" class="mw-redirect" title="Polyhedra">polyhedra</a> are <i>closo</i> polyhedra, and are the basis for the 4<i>n</i> rules; each of these have triangular faces.<sup id="cite_ref-Cotton&Wilkinson6th_10-0" class="reference"><a href="#cite_note-Cotton&Wilkinson6th-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The number of vertices in the cluster determines what polyhedron the structure is based on. </p> <table class="wikitable"> <tbody><tr> <th>Number of vertices </th> <th>Polyhedron </th></tr> <tr> <td>4 </td> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">Tetrahedron</a> </td></tr> <tr> <td>5 </td> <td><a href="/wiki/Triangular_bipyramid" title="Triangular bipyramid">Trigonal bipyramid</a> </td></tr> <tr> <td>6 </td> <td><a href="/wiki/Octahedron" title="Octahedron">Octahedron</a> </td></tr> <tr> <td>7 </td> <td><a href="/wiki/Pentagonal_bipyramid" title="Pentagonal bipyramid">Pentagonal bipyramid</a> </td></tr> <tr> <td>8 </td> <td>D<sub>2d</sub> (trigonal) dodecahedron (<a href="/wiki/Snub_disphenoid" title="Snub disphenoid">snub disphenoid</a>) </td></tr> <tr> <td>9 </td> <td><a href="/wiki/Triaugmented_triangular_prism" title="Triaugmented triangular prism">Tricapped trigonal prism</a> </td></tr> <tr> <td>10 </td> <td><a href="/wiki/Gyroelongated_square_bipyramid" title="Gyroelongated square bipyramid">Bicapped square antiprismatic molecular geometry</a> </td></tr> <tr> <td>11 </td> <td><a href="/wiki/Edge-contracted_icosahedron" title="Edge-contracted icosahedron">Edge-contracted icosahedron</a> (octadecahedron) </td></tr> <tr> <td>12 </td> <td><a href="/wiki/Icosahedron" title="Icosahedron">Icosahedron</a> (bicapped pentagonal antiprism) </td></tr></tbody></table> <p>Using the electron count, the predicted structure can be found. <i>n</i> is the number of vertices in the cluster. The 4<i>n</i> rules are enumerated in the following table. </p> <table class="wikitable"> <tbody><tr> <th>Electron count </th> <th>Name </th> <th>Predicted structure </th></tr> <tr> <td>4<i>n</i> − 2 </td> <td>Bicapped <i>closo</i> </td> <td><i>n</i> − 2 vertex <i>closo</i> polyhedron with 2 capped (<a href="/wiki/Augmentation_(geometry)" class="mw-redirect" title="Augmentation (geometry)">augmented</a>) faces </td></tr> <tr> <td>4<i>n</i> </td> <td>Capped <i>closo</i> </td> <td><i>n</i> − 1 vertex <i>closo</i> polyhedron with 1 face capped </td></tr> <tr> <td>4<i>n</i> + 2 </td> <td><i>closo</i> </td> <td><i>closo</i> polyhedron with <i>n</i> vertices </td></tr> <tr> <td>4<i>n</i> + 4 </td> <td><i>nido</i> </td> <td><i>n</i> + 1 vertex <i>closo</i> polyhedron with 1 missing vertex </td></tr> <tr> <td>4n + 6 </td> <td><i>arachno</i> </td> <td><i>n</i> + 2 vertex <i>closo</i> polyhedron with 2 missing vertices </td></tr> <tr> <td>4n + 8 </td> <td><i>hypho</i> </td> <td><i>n</i> + 3 vertex <i>closo</i> polyhedron with 3 missing vertices </td></tr> <tr> <td>4n + 10 </td> <td><i>klado</i> </td> <td><i>n</i> + 4 vertex <i>closo</i> polyhedron with 4 missing vertices </td></tr></tbody></table> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Pb9_Cluster.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Pb9_Cluster.png/150px-Pb9_Cluster.png" decoding="async" width="150" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Pb9_Cluster.png/225px-Pb9_Cluster.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Pb9_Cluster.png/300px-Pb9_Cluster.png 2x" data-file-width="974" data-file-height="913" /></a><figcaption><span class="chemf nowrap">Pb<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">10</sub></span></span></span></figcaption></figure> <p>When counting electrons for each cluster, the number of <a href="/wiki/Valence_electrons" class="mw-redirect" title="Valence electrons">valence electrons</a> is enumerated. For each <a href="/wiki/Transition_metal" title="Transition metal">transition metal</a> present, 10 electrons are subtracted from the total electron count. For example, in Rh<sub>6</sub>(CO)<sub>16</sub> the total number of electrons would be <span class="nowrap">6 × 9 + 16 × 2 − 6 × 10</span> = <span class="nowrap">86 – 60</span> = 26. Therefore, the cluster is a <i>closo</i> polyhedron because <span class="nowrap"><i>n</i> = 6</span>, with <span class="nowrap">4<i>n</i> + 2 = 26</span>. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:S4_Cluster.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/S4_Cluster.png/150px-S4_Cluster.png" decoding="async" width="150" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/S4_Cluster.png/225px-S4_Cluster.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/S4_Cluster.png/300px-S4_Cluster.png 2x" data-file-width="781" data-file-height="367" /></a><figcaption><span class="chemf nowrap">S<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span></figcaption></figure> <p>Other rules may be considered when predicting the structure of clusters: </p> <ol><li>For clusters consisting mostly of transition metals, any main group elements present are often best counted as ligands or interstitial atoms, rather than vertices.</li> <li>Larger and more electropositive atoms tend to occupy vertices of high connectivity and smaller more electronegative atoms tend to occupy vertices of low connectivity.</li> <li>In the special case of <a href="/wiki/Boranes" title="Boranes">boron hydride</a> clusters, each boron atom connected to 3 or more vertices has one terminal hydride, while a boron atom connected to two other vertices has two terminal hydrogen atoms. If more hydrogen atoms are present, they are placed in open face positions to even out the coordination number of the vertices.</li> <li>For the special case of transition metal clusters, <a href="/wiki/Ligands" class="mw-redirect" title="Ligands">ligands</a> are added to the metal centers to give the metals reasonable coordination numbers, and if any <a href="/wiki/Hydrogen" title="Hydrogen">hydrogen</a> <a href="/wiki/Atoms" class="mw-redirect" title="Atoms">atoms</a> are present they are placed in bridging positions to even out the coordination numbers of the vertices.</li></ol> <p>In general, <i>closo</i> structures with <i>n</i> vertices are <i>n</i>-vertex polyhedra. </p><p>To predict the structure of a <i>nido</i> cluster, the <i>closo</i> cluster with <i>n</i> + 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. </p><p>To predict the structure of an <i>arachno</i> cluster, the <i>closo</i> polyhedron with <i>n</i> + 2 vertices is used as the starting point, and the <i>n</i> + 1 vertex <i>nido</i> 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. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Os6corrected.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Os6corrected.png/150px-Os6corrected.png" decoding="async" width="150" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Os6corrected.png/225px-Os6corrected.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Os6corrected.png/300px-Os6corrected.png 2x" data-file-width="696" data-file-height="794" /></a><figcaption>Os<sub>6</sub>(CO)<sub>18</sub>, carbonyls omitted</figcaption></figure> <p>Example: <span class="chemf nowrap">Pb<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">10</sub></span></span></span> </p> <dl><dd>Electron count: 10 × Pb + 2 (for the negative charge) = 10 × 4 + 2 = 42 electrons.</dd> <dd>Since <i>n</i> = 10, 4<i>n</i> + 2 = 42, so the cluster is a <i>closo</i> bicapped square antiprism.</dd></dl> <p>Example: <span class="chemf nowrap">S<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2+</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">4</sub></span></span></span> </p> <dl><dd>Electron count: 4 × S – 2 (for the positive charge) = 4 × 6 – 2 = 22 electrons.</dd> <dd>Since <i>n</i> = 4, 4<i>n</i> + 6 = 22, so the cluster is <i>arachno</i>.</dd> <dd>Starting from an octahedron, a vertex of high connectivity is removed, and then a non-adjacent vertex is removed.</dd></dl> <p>Example: Os<sub>6</sub>(CO)<sub>18</sub> </p> <dl><dd>Electron count: 6 × Os + 18 × CO – 60 (for 6 osmium atoms) = 6 × 8 + 18 × 2 – 60 = 24</dd> <dd>Since <i>n</i> = 6, 4<i>n</i> = 24, so the cluster is capped <i>closo</i>.</dd> <dd>Starting from a trigonal bipyramid, a face is capped. The carbonyls have been omitted for clarity.</dd></dl> <figure typeof="mw:File/Thumb"><a href="/wiki/File:B5H5_cluster.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/B5H5_cluster.png/150px-B5H5_cluster.png" decoding="async" width="150" height="87" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/B5H5_cluster.png/225px-B5H5_cluster.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/B5H5_cluster.png/300px-B5H5_cluster.png 2x" data-file-width="861" data-file-height="501" /></a><figcaption><span class="chemf nowrap">B<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">5</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">4−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">5</sub></span></span></span>, hydrogen atoms omitted</figcaption></figure> <p>Example:<sup id="cite_ref-Cotton3_11-0" class="reference"><a href="#cite_note-Cotton3-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <span class="chemf nowrap">B<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">5</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">4−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">5</sub></span></span></span> </p> <dl><dd>Electron count: 5 × B + 5 × H + 4 (for the negative charge) = 5 × 3 + 5 × 1 + 4 = 24</dd> <dd>Since <i>n</i> = 5, 4<i>n</i> + 4 = 24, so the cluster is nido.</dd> <dd>Starting from an octahedron, one of the vertices is removed.</dd></dl> <p>The rules are useful in also predicting the structure of <a href="/wiki/Carborane" title="Carborane">carboranes</a>. Example: C<sub>2</sub>B<sub>7</sub>H<sub>13</sub> </p> <dl><dd>Electron count = 2 × C + 7 × B + 13 × H = 2 × 4 + 7 × 3 + 13 × 1 = 42</dd> <dd>Since n in this case is 9, 4<i>n</i> + 6 = 42, the cluster is <i>arachno</i>.</dd></dl> <p>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 <a href="/wiki/Deltahedron" title="Deltahedron">deltahedral</a> clusters are: </p> <ul><li><i>n</i>-vertex <i>closo</i>: <i>n</i> + 1 skeletal orbitals, 2<i>n</i> + 2 skeletal electrons</li> <li><i>n</i>-vertex <i>nido</i>: <i>n</i> + 2 skeletal orbitals, 2<i>n</i> + 4 skeletal electrons</li> <li><i>n</i>-vertex <i>arachno</i>: <i>n</i> + 3 skeletal orbitals, 2<i>n</i> + 6 skeletal electrons</li> <li><i>n</i>-vertex <i>hypho</i>: <i>n</i> + 4 skeletal orbitals, 2<i>n</i> + 8 skeletal electrons</li></ul> <p>The skeletal electron counts are determined by summing the total of the following number of electrons: </p> <ul><li>2 from each BH unit</li> <li>3 from each CH unit</li> <li>1 from each additional hydrogen atom (over and above the ones on the BH and CH units)</li> <li>the anionic charge electrons</li></ul> <div class="mw-heading mw-heading3"><h3 id="5n_rules">5<i>n</i> rules</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=3" title="Edit section: 5n rules"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As discussed previously, the 4<i>n</i> rule mainly deals with clusters with electron counts of <span class="nowrap">4<i>n</i> + <i>k</i></span>, in which approximately 4 <a href="/wiki/Electrons" class="mw-redirect" title="Electrons">electrons</a> 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 <a href="/wiki/Polyhedra" class="mw-redirect" title="Polyhedra">polyhedra</a>, in which each vertex is connected to 3 other vertices. The 3-connected polyhedra are the <a href="/wiki/Dual_polyhedron" title="Dual polyhedron">duals</a> of the deltahedra. The common types of 3-connected polyhedra are listed below. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:P4_diagram.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/67/P4_diagram.gif" decoding="async" width="105" height="93" class="mw-file-element" data-file-width="105" data-file-height="93" /></a><figcaption>5<i>n</i> cluster: P<sub>4</sub></figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:P4S3.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/P4S3.png/150px-P4S3.png" decoding="async" width="150" height="173" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/P4S3.png/225px-P4S3.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/P4S3.png/300px-P4S3.png 2x" data-file-width="409" data-file-height="472" /></a><figcaption>5<i>n</i> + 3 cluster: P<sub>4</sub>S<sub>3</sub></figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Phosphorus_trioxide.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Phosphorus_trioxide.svg/100px-Phosphorus_trioxide.svg.png" decoding="async" width="100" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Phosphorus_trioxide.svg/150px-Phosphorus_trioxide.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Phosphorus_trioxide.svg/200px-Phosphorus_trioxide.svg.png 2x" data-file-width="520" data-file-height="494" /></a><figcaption>5<i>n</i> + 6 cluster: P<sub>4</sub>O<sub>6</sub></figcaption></figure> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>Number of vertices</th> <th>Type of 3-connected polyhedron </th></tr> <tr> <td>4</td> <td><a href="/wiki/Tetrahedron" title="Tetrahedron">Tetrahedron</a> </td></tr> <tr> <td>6</td> <td><a href="/wiki/Triangular_prism" title="Triangular prism">Trigonal prism</a> </td></tr> <tr> <td>8</td> <td><a href="/wiki/Cube" title="Cube">Cube</a> </td></tr> <tr> <td>10</td> <td><a href="/wiki/Pentagonal_prism" title="Pentagonal prism">Pentagonal prism</a> </td></tr> <tr> <td>12</td> <td>D<sub>2d</sub> pseudo-octahedron (dual of snub disphenoid) </td></tr> <tr> <td>14</td> <td>Dual of triaugmented triangular prism (K<sub>5</sub> <a href="/wiki/Associahedron" title="Associahedron">associahedron</a>) </td></tr> <tr> <td>16</td> <td><a href="/wiki/Square_truncated_trapezohedron" class="mw-redirect" title="Square truncated trapezohedron">Square truncated trapezohedron</a> </td></tr> <tr> <td>18</td> <td>Dual of edge-contracted icosahedron </td></tr> <tr> <td>20</td> <td><a href="/wiki/Dodecahedron" title="Dodecahedron">Dodecahedron</a> </td></tr></tbody></table> <p>The 5<i>n</i> rules are as follows. </p> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>Total electron count</th> <th>Predicted structure </th></tr> <tr> <td>5<i>n</i></td> <td><i>n</i>-vertex 3-connected polyhedron </td></tr> <tr> <td>5<i>n</i> + 1</td> <td><i>n</i> – 1 vertex 3-connected polyhedron with one vertex inserted into an edge </td></tr> <tr> <td>5<i>n</i> + 2</td> <td><i>n</i> – 2 vertex 3-connected polyhedron with two vertices inserted into edges </td></tr> <tr> <td>5<i>n</i> + <i>k</i></td> <td><i>n</i> − <i>k</i> vertex 3-connected polyhedron with <i>k</i> vertices inserted into edges </td></tr></tbody></table> <p>Example: P<sub>4</sub> </p> <dl><dd>Electron count: 4 × P = 4 × 5 = 20</dd> <dd>It is a 5<i>n</i> structure with <i>n</i> = 4, so it is tetrahedral</dd></dl> <p>Example: P<sub>4</sub>S<sub>3</sub> </p> <dl><dd>Electron count 4 × P + 3 × S = 4 × 5 + 3 × 6 = 38</dd> <dd>It is a 5<i>n</i> + 3 structure with <i>n</i> = 7. Three vertices are inserted into edges</dd></dl> <p>Example: P<sub>4</sub>O<sub>6</sub> </p> <dl><dd>Electron count 4 × P + 6 × O = 4 × 5 + 6 × 6 = 56</dd> <dd>It is a 5<i>n</i> + 6 structure with <i>n</i> = 10. Six vertices are inserted into edges</dd></dl> <div class="mw-heading mw-heading3"><h3 id="6n_rules">6<i>n</i> rules</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=4" title="Edit section: 6n rules"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div><p> As more electrons are added to a 5<i>n</i> cluster, the number of electrons per vertex approaches 6. Instead of adopting structures based on 4<i>n</i> or 5<i>n</i> rules, the clusters tend to have structures governed by the 6<i>n</i> rules, which are based on rings. The rules for the 6<i>n</i> structures are as follows.</p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cyclooctasulfur_structural_formula_3D.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Cyclooctasulfur_structural_formula_3D.svg/220px-Cyclooctasulfur_structural_formula_3D.svg.png" decoding="async" width="220" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Cyclooctasulfur_structural_formula_3D.svg/330px-Cyclooctasulfur_structural_formula_3D.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Cyclooctasulfur_structural_formula_3D.svg/440px-Cyclooctasulfur_structural_formula_3D.svg.png 2x" data-file-width="389" data-file-height="187" /></a><figcaption>S<sub>8</sub> crown</figcaption></figure> <table class="wikitable" style="text-align:center"> <tbody><tr> <th>Total electron count</th> <th>Predicted structure </th></tr> <tr> <td>6<i>n</i> – k</td> <td><i>n</i>-membered ring with <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num"><i>k</i></span>⁄<span class="den">2</span></span> transannular bonds </td></tr> <tr> <td>6<i>n</i> – 4</td> <td><i>n</i>-membered ring with 2 transannular bonds </td></tr> <tr> <td>6<i>n</i> – 2</td> <td><i>n</i>-membered ring with 1 transannular bond </td></tr> <tr> <td>6<i>n</i></td> <td><i>n</i>-membered ring </td></tr> <tr> <td>6<i>n</i> + 2</td> <td><i>n</i>-membered chain (<i>n</i>-membered ring with 1 broken bond) </td></tr></tbody></table> <p>Example: S<sub>8</sub> </p> <dl><dd>Electron count = 8 × S = 8 × 6 = 48 electrons.</dd> <dd>Since <i>n</i> = 8, 6<i>n</i> = 48, so the cluster is an 8-membered ring.</dd></dl> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hexane-2D-Skeletal.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Hexane-2D-Skeletal.svg/220px-Hexane-2D-Skeletal.svg.png" decoding="async" width="220" height="55" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Hexane-2D-Skeletal.svg/330px-Hexane-2D-Skeletal.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Hexane-2D-Skeletal.svg/440px-Hexane-2D-Skeletal.svg.png 2x" data-file-width="728" data-file-height="181" /></a><figcaption>6<i>n</i> + 2 cluster: hexane</figcaption></figure> <p>Hexane (C<sub>6</sub>H<sub>14</sub>) </p> <dl><dd>Electron count = 6 × C + 14 × H = 6 × 4 + 14 × 1 = 38</dd> <dd>Since <i>n</i> = 6, 6<i>n</i> = 36 and 6<i>n</i> + 2 = 38, so the cluster is a 6-membered chain.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Isolobal_vertex_units">Isolobal vertex units</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=5" title="Edit section: Isolobal vertex units"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Provided a vertex unit is <a href="/wiki/Isolobal_principle" title="Isolobal principle">isolobal</a> with BH then it can, in principle at least, be substituted for a BH unit, even though BH and CH are not isoelectronic. The CH<sup>+</sup> unit is isolobal, hence the rules are applicable to carboranes. This can be explained due to a <a href="/wiki/Frontier_orbital" class="mw-redirect" title="Frontier orbital">frontier orbital</a> treatment.<sup id="cite_ref-Cotton&Wilkinson6th_10-1" class="reference"><a href="#cite_note-Cotton&Wilkinson6th-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Additionally there are isolobal transition-metal units. For example, Fe(CO)<sub>3</sub> provides 2 electrons. The derivation of this is briefly as follows: </p> <ul><li>Fe has 8 valence electrons.</li> <li>Each carbonyl group is a net 2 electron donor after the internal <a href="/wiki/Sigma_bond" title="Sigma bond">σ</a>- and <a href="/wiki/Pi_bond" title="Pi bond">π-bonding</a> are taken into account making 14 electrons.</li> <li>3 pairs are considered to be involved in Fe–CO <a href="/wiki/Sigma_bond" title="Sigma bond">σ-bonding</a> and 3 pairs are involved in <a href="/wiki/Pi_bond" title="Pi bond">π</a>-backbonding from Fe to CO reducing the 14 to 2.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Bonding_in_cluster_compounds">Bonding in cluster compounds</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=6" title="Edit section: Bonding in cluster compounds"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt><i>closo</i>-<span class="chemf nowrap">B<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span></span></dt></dl> <figure typeof="mw:File/Thumb"><a href="/wiki/File:B6H6MOdiagram.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/B6H6MOdiagram.jpg/200px-B6H6MOdiagram.jpg" decoding="async" width="200" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9f/B6H6MOdiagram.jpg/300px-B6H6MOdiagram.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9f/B6H6MOdiagram.jpg/400px-B6H6MOdiagram.jpg 2x" data-file-width="640" data-file-height="512" /></a><figcaption>MO diagram of <span class="chemf nowrap">B<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline"></sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span>H<span class="nowrap"><span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">2−</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">6</sub></span></span></span> 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.</figcaption></figure> <dl><dd>The boron atoms lie on each vertex of the octahedron and are sp hybridized.<sup id="cite_ref-Cotton3_11-1" class="reference"><a href="#cite_note-Cotton3-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-jemmis02_9-1" class="reference"><a href="#cite_note-jemmis02-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The orbital diagram breaks down as follows:</dd></dl> <dl><dd><dl><dd>The 18 framework molecular orbitals, (MOs), derived from the 18 boron atomic orbitals are: <ul><li>1 bonding MO at the center of the cluster and 5 antibonding MOs from the 6 sp-radial hybrid orbitals</li> <li>6 bonding MOs and 6 antibonding MOs from the 12 tangential p-orbitals.</li></ul></dd></dl></dd> <dd>The total skeletal bonding orbitals is therefore 7, i.e. <span class="nowrap"><i>n</i> + 1</span>.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Transition_metal_clusters">Transition metal clusters</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=7" title="Edit section: Transition metal clusters"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Transition metal clusters use the d orbitals for <a href="/wiki/Chemical_bond" title="Chemical bond">bonding</a>. Thus, they have up to nine bonding orbitals, instead of only the four present in boron and main group clusters.<sup id="cite_ref-king_12-0" class="reference"><a href="#cite_note-king-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-RCR_13-0" class="reference"><a href="#cite_note-RCR-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> PSEPT also applies to <a href="/wiki/Metallaborane" title="Metallaborane">metallaboranes</a> </p> <div class="mw-heading mw-heading3"><h3 id="Clusters_with_interstitial_atoms">Clusters with interstitial atoms</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=8" title="Edit section: Clusters with interstitial atoms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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 [Fe<sub>6</sub>C(CO)<sub>16</sub>]<sup>2-</sup>. In such cases, the rules of electron counting assume that the interstitial atom contributes all valence electrons to cluster bonding. In this way, [Fe<sub>6</sub>C(CO)<sub>16</sub>]<sup>2-</sup> is equivalent to [Fe<sub>6</sub>(CO)<sub>16</sub>]<sup>6-</sup> or [Fe<sub>6</sub>(CO)<sub>18</sub>]<sup>2-</sup>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_Also">See Also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=9" title="Edit section: See Also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Styx_rule" title="Styx rule">Styx rule</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=10" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-wade71-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-wade71_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFWade1971" class="citation journal cs1"><a href="/wiki/Kenneth_Wade" title="Kenneth Wade">Wade, K.</a> (1971). 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(2013). "The significance and impact of Wade's rules". <i>Chem. Commun</i>. <b>49</b> (35): 3615–3616. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FC3CC00069A">10.1039/C3CC00069A</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/23535980">23535980</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Chem.+Commun.&rft.atitle=The+significance+and+impact+of+Wade%27s+rules&rft.volume=49&rft.issue=35&rft.pages=3615-3616&rft.date=2013&rft_id=info%3Adoi%2F10.1039%2FC3CC00069A&rft_id=info%3Apmid%2F23535980&rft.aulast=Welch&rft.aufirst=Alan+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></span> </li> <li id="cite_note-Wade-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wade_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWade1976" class="citation journal cs1"><a href="/wiki/Kenneth_Wade" title="Kenneth Wade">Wade, K.</a> (1976). "Structural and Bonding Patterns in Cluster Chemistry". <i>Adv. Inorg. Chem. Radiochem</i>. 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Res.</a></i> <b>17</b> (9): 311–319. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Far00105a003">10.1021/ar00105a003</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Acc.+Chem.+Res.&rft.atitle=Polyhedral+Skeletal+Electron+Pair+Approach&rft.volume=17&rft.issue=9&rft.pages=311-319&rft.date=1984&rft_id=info%3Adoi%2F10.1021%2Far00105a003&rft.aulast=Mingos&rft.aufirst=D.+M.+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></span> </li> <li id="cite_note-jemmis01-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-jemmis01_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJemmisBalakrishnarajanPancharatna2001" class="citation journal cs1">Jemmis, Eluvathingal D.; Balakrishnarajan, Musiri M.; Pancharatna, Pattath D. (2001). "A Unifying Electron-counting rule for Macropolyhedral Boranes, Metallaboranes, and Metallocenes". <i><a href="/wiki/J._Am._Chem._Soc." class="mw-redirect" title="J. Am. Chem. Soc.">J. Am. Chem. Soc.</a></i> <b>123</b> (18): 4313–4323. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fja003233z">10.1021/ja003233z</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11457198">11457198</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Am.+Chem.+Soc.&rft.atitle=A+Unifying+Electron-counting+rule+for+Macropolyhedral+Boranes%2C+Metallaboranes%2C+and+Metallocenes&rft.volume=123&rft.issue=18&rft.pages=4313-4323&rft.date=2001&rft_id=info%3Adoi%2F10.1021%2Fja003233z&rft_id=info%3Apmid%2F11457198&rft.aulast=Jemmis&rft.aufirst=Eluvathingal+D.&rft.au=Balakrishnarajan%2C+Musiri+M.&rft.au=Pancharatna%2C+Pattath+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></span> </li> <li id="cite_note-jemmis02-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-jemmis02_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-jemmis02_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJemmisBalakrishnarajanPancharatna2002" class="citation journal cs1">Jemmis, Eluvathingal D.; Balakrishnarajan, Musiri M.; Pancharatna, Pattath D. (2002). "Electronic Requirements for Macropolyhedral Boranes". <i><a href="/wiki/Chem._Rev." class="mw-redirect" title="Chem. Rev.">Chem. 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Albert Cotton">Cotton, F. Albert</a>; <a href="/wiki/Geoffrey_Wilkinson" title="Geoffrey Wilkinson">Wilkinson, Geoffrey</a>; Murillo, Carlos A.; Bochmann, Manfred (1999), <i>Advanced Inorganic Chemistry</i> (6th ed.), New York: Wiley-Interscience, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-19957-5" title="Special:BookSources/0-471-19957-5"><bdi>0-471-19957-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+Inorganic+Chemistry&rft.place=New+York&rft.edition=6th&rft.pub=Wiley-Interscience&rft.date=1999&rft.isbn=0-471-19957-5&rft.au=Cotton%2C+F.+Albert&rft.au=Wilkinson%2C+Geoffrey&rft.au=Murillo%2C+Carlos+A.&rft.au=Bochmann%2C+Manfred&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></span> </li> <li id="cite_note-Cotton3-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Cotton3_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Cotton3_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCotton1990" class="citation book cs1">Cotton, Albert (1990). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780471510949/page/205"><i>Chemical Applications of Group Theory</i></a></span>. John Wiley & Sons. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/isbn_9780471510949/page/205">205–251</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-51094-7" title="Special:BookSources/0-471-51094-7"><bdi>0-471-51094-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+Applications+of+Group+Theory&rft.pages=205-251&rft.pub=John+Wiley+%26+Sons&rft.date=1990&rft.isbn=0-471-51094-7&rft.aulast=Cotton&rft.aufirst=Albert&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_9780471510949%2Fpage%2F205&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></span> </li> <li id="cite_note-king-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-king_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKingRouvray1977" class="citation journal cs1">King, R. B.; Rouvray, D. H. (1977). "Chemical Applications of Group Theory and Topology.7. A Graph-Theoretical Interpretation of the Bonding Topology in Polyhedral Boranes, Carboranes, and Metal Clusters". <i><a href="/wiki/J._Am._Chem._Soc." class="mw-redirect" title="J. Am. Chem. Soc.">J. Am. Chem. Soc.</a></i> <b>99</b> (24): 7834–7840. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fja00466a014">10.1021/ja00466a014</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=J.+Am.+Chem.+Soc.&rft.atitle=Chemical+Applications+of+Group+Theory+and+Topology.7.+A+Graph-Theoretical+Interpretation+of+the+Bonding+Topology+in+Polyhedral+Boranes%2C+Carboranes%2C+and+Metal+Clusters&rft.volume=99&rft.issue=24&rft.pages=7834-7840&rft.date=1977&rft_id=info%3Adoi%2F10.1021%2Fja00466a014&rft.aulast=King&rft.aufirst=R.+B.&rft.au=Rouvray%2C+D.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></span> </li> <li id="cite_note-RCR-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-RCR_13-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKostikovaKorolkov1985" class="citation journal cs1">Kostikova, G. P.; Korolkov, D. V. (1985). "Electronic Structure of Transition Metal Cluster Complexes with Weak- and Strong-field Ligands". <i>Russ. Chem. 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(2006). "Cluster Compounds: Inorganometallic Compounds Containing Transition Metal & Main Group Elements". <i>Encyclopedia of Inorganic Chemistry</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F0470862106.ia097">10.1002/0470862106.ia097</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0470860782" title="Special:BookSources/0470860782"><bdi>0470860782</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Cluster+Compounds%3A+Inorganometallic+Compounds+Containing+Transition+Metal+%26+Main+Group+Elements&rft.btitle=Encyclopedia+of+Inorganic+Chemistry&rft.date=2006&rft_id=info%3Adoi%2F10.1002%2F0470862106.ia097&rft.isbn=0470860782&rft.aulast=Fehlner&rft.aufirst=Thomas+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="General_references">General references</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&action=edit&section=11" title="Edit section: General references"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGreenwoodEarnshaw1997" class="citation book cs1"><a href="/wiki/Norman_Greenwood" title="Norman Greenwood">Greenwood, Norman N.</a>; Earnshaw, Alan (1997). <i>Chemistry of the Elements</i> (2nd ed.). <a href="/wiki/Butterworth-Heinemann" title="Butterworth-Heinemann">Butterworth-Heinemann</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-037941-8" title="Special:BookSources/978-0-08-037941-8"><bdi>978-0-08-037941-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemistry+of+the+Elements&rft.edition=2nd&rft.pub=Butterworth-Heinemann&rft.date=1997&rft.isbn=978-0-08-037941-8&rft.aulast=Greenwood&rft.aufirst=Norman+N.&rft.au=Earnshaw%2C+Alan&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCotton,_F._AlbertWilkinson,_GeoffreyMurillo,_Carlos_A.Bochmann,_Manfred1999" class="citation cs2"><a href="/wiki/F._Albert_Cotton" title="F. Albert Cotton">Cotton, F. Albert</a>; <a href="/wiki/Geoffrey_Wilkinson" title="Geoffrey Wilkinson">Wilkinson, Geoffrey</a>; Murillo, Carlos A.; Bochmann, Manfred (1999), <i>Advanced Inorganic Chemistry</i> (6th ed.), New York: Wiley-Interscience, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-19957-5" title="Special:BookSources/0-471-19957-5"><bdi>0-471-19957-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+Inorganic+Chemistry&rft.place=New+York&rft.edition=6th&rft.pub=Wiley-Interscience&rft.date=1999&rft.isbn=0-471-19957-5&rft.au=Cotton%2C+F.+Albert&rft.au=Wilkinson%2C+Geoffrey&rft.au=Murillo%2C+Carlos+A.&rft.au=Bochmann%2C+Manfred&rfr_id=info%3Asid%2Fen.wikipedia.org%3APolyhedral+skeletal+electron+pair+theory" class="Z3988"></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output 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abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Organometallics" title="Template:Organometallics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Organometallics" title="Template talk:Organometallics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Organometallics" title="Special:EditPage/Template:Organometallics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Organometallic_chemistry" style="font-size:114%;margin:0 4em"><a href="/wiki/Organometallic_chemistry" title="Organometallic chemistry">Organometallic chemistry</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Principles</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Crystal_field_theory" title="Crystal field theory">Crystal field theory</a></li> <li><a href="/wiki/Ligand_field_theory" title="Ligand field theory">Ligand field theory</a></li> <li><a href="/wiki/18-electron_rule" title="18-electron rule">18-electron rule</a></li> <li><a href="/wiki/D_electron_count" title="D electron count">d electron count</a></li> <li><a class="mw-selflink selflink">Polyhedral skeletal electron pair theory</a></li> <li><a href="/wiki/Isolobal_principle" title="Isolobal principle">Isolobal principle</a></li> <li><a href="/wiki/Pi_backbonding" title="Pi backbonding">π backbonding</a></li> <li><a href="/wiki/Dewar%E2%80%93Chatt%E2%80%93Duncanson_model" title="Dewar–Chatt–Duncanson model">Dewar–Chatt–Duncanson model</a></li> <li><a href="/wiki/Hapticity" title="Hapticity">Hapticity</a></li> <li><a href="/wiki/Spin_states_(d_electrons)" title="Spin states (d electrons)">spin states</a></li> <li><a href="/wiki/Agostic_interaction" title="Agostic interaction">Agostic interaction</a></li> <li><a href="/wiki/Metal%E2%80%93ligand_multiple_bond" title="Metal–ligand multiple bond">Metal–ligand multiple bond</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Reactions</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Oxidative_addition" title="Oxidative addition">Oxidative addition</a> / <a href="/wiki/Reductive_elimination" title="Reductive elimination">reductive elimination</a></li> <li><a href="/wiki/Migratory_insertion" title="Migratory insertion">Migratory insertion</a></li> <li><a href="/wiki/Beta-Hydride_elimination" class="mw-redirect" title="Beta-Hydride elimination">β-hydride elimination</a></li> <li><a href="/wiki/Transmetalation" title="Transmetalation">Transmetalation</a></li> <li><a href="/wiki/Carbometalation" title="Carbometalation">Carbometalation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of compounds</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gilman_reagent" title="Gilman reagent">Gilman reagents</a></li> <li><a href="/wiki/Grignard_reagent" title="Grignard reagent">Grignard reagents</a></li> <li><a href="/wiki/Cyclopentadienyl_complex" title="Cyclopentadienyl complex">Cyclopentadienyl complexes</a></li> <li><a href="/wiki/Transition_metal_indenyl_complex" title="Transition metal indenyl complex">Transition metal indenyl complexes</a></li> <li><a href="/wiki/Transition_metal_fullerene_complex" title="Transition metal fullerene complex">Transition metal fullerene complexes</a></li> <li><a href="/wiki/Metallocene" title="Metallocene">Metallocenes</a></li> <li><a href="/wiki/Metal_tetranorbornyl" title="Metal tetranorbornyl">Metal tetranorbornyls</a></li> <li><a href="/wiki/Sandwich_compound" title="Sandwich compound">Sandwich compounds</a></li> <li><a href="/wiki/Half_sandwich_compound" title="Half sandwich compound">Half sandwich compounds</a></li> <li><a href="/wiki/Transition_metal_acyl_complexes" title="Transition metal acyl complexes">Transition metal acyl complexes</a></li> <li><a href="/wiki/Transition_metal_carbene_complex" title="Transition metal carbene complex">Transition metal carbene complexes</a></li> <li><a href="/wiki/Transition_metal_carbyne_complex" title="Transition metal carbyne complex">Transition metal carbyne complexes</a></li> <li><a href="/wiki/Transition_metal_alkene_complex" title="Transition metal alkene complex">Transition metal alkene complexes</a></li> <li><a href="/wiki/Transition_metal_alkyne_complex" title="Transition metal alkyne complex">Transition metal alkyne complexes</a></li> <li><a href="/wiki/Transition-metal_allyl_complex" title="Transition-metal allyl complex">Transition-metal allyl complexes</a></li> <li><a href="/wiki/Metal_carbido_complex" title="Metal carbido complex">Transition metal carbides</a></li> <li><a href="/wiki/Arene_complexes_of_univalent_gallium,_indium,_and_thallium" title="Arene complexes of univalent gallium, indium, and thallium">Arene complexes of univalent gallium, indium, and thallium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Carbonylation" title="Carbonylation">Carbonylation</a></li> <li><a href="/wiki/Cativa_process" title="Cativa process">Cativa process</a></li> <li><a href="/wiki/Grignard_reaction" title="Grignard reaction">Grignard reaction</a></li> <li><a href="/wiki/Monsanto_process" title="Monsanto process">Monsanto process</a></li> <li><a href="/wiki/Olefin_metathesis" title="Olefin metathesis">Olefin metathesis</a></li> <li><a href="/wiki/Shell_higher_olefin_process" title="Shell higher olefin process">Shell higher olefin process</a></li> <li><a href="/wiki/Ziegler%E2%80%93Natta_catalyst" title="Ziegler–Natta catalyst">Ziegler–Natta process</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related branches of <a href="/wiki/Chemistry" title="Chemistry">chemistry</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Organic_chemistry" title="Organic chemistry">Organic chemistry</a></li> <li><a href="/wiki/Inorganic_chemistry" title="Inorganic chemistry">Inorganic chemistry</a></li> <li><a href="/wiki/Bioinorganic_chemistry" title="Bioinorganic chemistry">Bioinorganic chemistry</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img 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bond">3c–4e</a></li></ul></li> <li><a href="/wiki/Agostic_interaction" title="Agostic interaction">Agostic</a></li> <li><a href="/wiki/Bent_bond" title="Bent bond">Bent</a></li> <li><a href="/wiki/Coordinate_covalent_bond" title="Coordinate covalent bond">Coordinate (dipolar)</a></li> <li><a href="/wiki/Pi_backbonding" title="Pi backbonding">Pi backbond</a></li> <li><a href="/wiki/Metal%E2%80%93ligand_multiple_bond" title="Metal–ligand multiple bond">Metal–ligand multiple bond</a></li> <li><a href="/wiki/Charge-shift_bond" title="Charge-shift bond">Charge-shift</a></li> <li><a href="/wiki/Hapticity" title="Hapticity">Hapticity</a></li> <li><a href="/wiki/Conjugated_system" title="Conjugated system">Conjugation</a></li> <li><a href="/wiki/Hyperconjugation" title="Hyperconjugation">Hyperconjugation</a></li> <li><a href="/wiki/Aromaticity" title="Aromaticity">Aromaticity</a> <ul><li><a href="/wiki/Homoaromaticity" title="Homoaromaticity">homo</a></li> <li><a href="/wiki/Bicycloaromaticity" title="Bicycloaromaticity">bicyclo</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Metallic_bonding" title="Metallic bonding">Metallic</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Metal_aromaticity" title="Metal aromaticity">Metal aromaticity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ionic_bonding" title="Ionic bonding">Ionic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li class="mw-empty-elt"></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Ligatio-covalens.svg" class="mw-file-description"><img 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class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Van_der_Waals_force" title="Van der Waals force">Van der Waals<br />forces</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/London_dispersion_force" title="London dispersion force">London dispersion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Hydrogen_bond" title="Hydrogen bond">Hydrogen</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Low-barrier_hydrogen_bond" title="Low-barrier hydrogen bond">Low-barrier</a></li> <li><a href="/wiki/Resonance-assisted_hydrogen_bond" class="mw-redirect" title="Resonance-assisted hydrogen bond">Resonance-assisted</a></li> <li><a href="/wiki/Symmetric_hydrogen_bond" title="Symmetric hydrogen bond">Symmetric</a></li> <li><a href="/wiki/Dihydrogen_bond" title="Dihydrogen bond">Dihydrogen bonds</a></li> <li><a href="/wiki/C%E2%80%93H%C2%B7%C2%B7%C2%B7O_interaction" title="C–H···O interaction">C–H···O interaction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Non-covalent_interactions" class="mw-redirect" title="Non-covalent interactions">Noncovalent</a><br />other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mechanically_interlocked_molecular_architectures" title="Mechanically interlocked molecular architectures">Mechanical</a></li> <li><a href="/wiki/Halogen_bond" title="Halogen bond">Halogen</a></li> <li><a href="/wiki/Chalcogen_bond" title="Chalcogen bond">Chalcogen</a></li> <li><a href="/wiki/Metallophilic_interaction" title="Metallophilic interaction">Metallophilic</a> (<a href="/wiki/Aurophilicity" title="Aurophilicity">aurophilic</a>)</li> <li><a href="/wiki/Intercalation_(chemistry)" title="Intercalation (chemistry)">Intercalation</a></li> <li><a href="/wiki/Stacking_(chemistry)" title="Stacking (chemistry)">Stacking</a></li> <li><a href="/wiki/Cation%E2%80%93pi_interaction" class="mw-redirect" title="Cation–pi interaction">Cation–pi</a></li> <li><a href="/wiki/Cation%E2%80%93pi_interaction#Anion–π_interaction" class="mw-redirect" title="Cation–pi interaction">Anion–pi</a></li> <li><a href="/wiki/Salt_bridge_(protein_and_supramolecular)" title="Salt bridge (protein and supramolecular)">Salt bridge</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Bond_cleavage" title="Bond cleavage">Bond cleavage</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Heterolysis_(chemistry)" title="Heterolysis (chemistry)">Heterolysis</a></li> <li><a href="/wiki/Homolysis_(chemistry)" title="Homolysis (chemistry)">Homolysis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Electron_counting" title="Electron counting">Electron counting</a> rules</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aromaticity" title="Aromaticity">Aromaticity</a> <ul><li><a href="/wiki/H%C3%BCckel%27s_rule" title="Hückel's rule">Hückel's rule</a></li> <li><a href="/wiki/Baird%27s_rule" title="Baird's rule">Baird's rule</a></li> <li><a href="/wiki/M%C3%B6bius_aromaticity" title="Möbius aromaticity">Möbius</a></li> <li><a href="/wiki/Spherical_aromaticity" title="Spherical aromaticity">spherical</a></li></ul></li> <li><a class="mw-selflink selflink">Polyhedral skeletal electron pair theory</a></li> <li><a href="/wiki/Jemmis_mno_rules" title="Jemmis mno rules">Jemmis mno rules</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&oldid=1251328776">https://en.wikipedia.org/w/index.php?title=Polyhedral_skeletal_electron_pair_theory&oldid=1251328776</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Chemical_bonding" title="Category:Chemical bonding">Chemical bonding</a></li><li><a href="/wiki/Category:Inorganic_chemistry" title="Category:Inorganic 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