Editing VSEPR theory (section)

==AXE method==
The "AXE method" of electron counting is commonly used when applying the VSEPR theory. The electron pairs around a central atom are represented by a formula AX<sub>m</sub>E<sub>n</sub>, where ''A'' represents the central atom and always has an implied subscript one.  Each ''X'' represents a ligand (an atom bonded to A). Each ''E'' represents a ''lone pair'' of electrons on the central atom.<ref name=Petrucci/>{{rp|410–417}} The total number of ''X'' and ''E'' is known as the steric number. For example, in a molecule AX<sub>3</sub>E<sub>2</sub>, the atom A has a steric number of 5.

When the [[substituent]] (X) atoms are not all the same, the geometry is still approximately valid, but the bond angles may be slightly different from the ones where all the outside atoms are the same.  For example, the double-bond carbons in alkenes like [[ethylene|C<sub>2</sub>H<sub>4</sub>]] are AX<sub>3</sub>E<sub>0</sub>, but the bond angles are not all exactly 120°.  Likewise, [[thionyl chloride|SOCl<sub>2</sub>]] is AX<sub>3</sub>E<sub>1</sub>, but because the X substituents are not identical, the X–A–X angles are not all equal.

Based on the steric number and distribution of ''X''s and ''E''s, VSEPR theory makes the predictions in the following tables.

===Main-group elements===
For [[main-group element]]s, there are stereochemically active [[lone pair]]s ''E'' whose number can vary from 0 to 3. Note that the geometries are named according to the atomic positions only and not the electron arrangement. For example, the description of AX<sub>2</sub>E<sub>1</sub> as a bent molecule means that the three atoms AX<sub>2</sub> are not in one straight line, although the lone pair helps to determine the geometry.

{| class="wikitable" style="margin:1em auto;"
!Steric <br> number
!Molecular geometry<ref name=PetrucTable>{{cite book|last1=Petrucci |first1=R. H. |first2=Harwood |last2=W. S. |first3=Herring |last3=F. G. |title=General Chemistry: Principles and Modern Applications |publisher=Prentice-Hall |edition=8th |year=2002 |pages=413–414 (Table 11.1) |isbn=978-0-13-014329-7}}</ref> <br> 0 lone pairs
!Molecular geometry<ref name=Petrucci/>{{rp|413–414}}<br> 1 lone pair
!Molecular geometry<ref name=Petrucci/>{{rp|413–414}}<br> 2 lone pairs
!Molecular geometry<ref name=Petrucci/>{{rp|413–414}}<br> 3 lone pairs
|-
!2 
| [[File:AX2E0-2D.png|128px]] <br> {{center|[[Linear (chemistry)|Linear]]}} || &nbsp; || &nbsp; || &nbsp;
|-
!3 
| [[File:AX3E0-side-2D.png|128px]] <br> {{center|[[Trigonal planar]]}} || [[File:AX2E1-2D.png|128px]] <br> {{center|[[Bent (chemistry)|Bent]]}} ||&nbsp; ||&nbsp;
|-
!4 
| [[File:AX4E0-2D.svg|128px]] <br> {{center|[[Tetrahedral molecular geometry|Tetrahedral]]}} || [[File:AX3E1-2D.png|128px]] <br> {{center|[[Trigonal pyramidal molecular geometry|Trigonal pyramidal]]}} || [[File:AX2E2-2D.png|128px]]  <br> {{center|[[Bent (chemistry)|Bent]]}} ||&nbsp; 
|-
!5 
| [[File:AX5E0-2D.png|128px]] <br> {{center|[[Trigonal bipyramidal molecular geometry|Trigonal bipyramidal]]}} || [[File:AX4E1-2D.png|128px]] <br> {{center|[[Seesaw (chemistry)|Seesaw]]}} || [[File:AX3E2-2D.png|128px]] <br> {{center|[[T-shaped (chemistry)|T-shaped]]}} || [[File:AX2E3-2D.png|128px]] <br> {{center|[[Linear (chemistry)|Linear]]}}
|-
!6 
| [[File:AX6E0-2D.svg|128px]]  <br> {{center|[[Octahedral molecular geometry|Octahedral]]}} || [[File:AX5E1-2D.png|128px]]  <br> {{center|[[Square pyramidal molecular geometry|Square pyramidal]]}} || [[File:AX4E2-2D.png|128px]] <br> {{center|[[Square planar]]}} || &nbsp;
|-
!7 
| [[File:AX7E0-2D.png|128px]] <br> {{center|[[Pentagonal bipyramidal molecular geometry|Pentagonal bipyramidal]]}} ||[[File:AX6E1-2D.png|128px]] <br> {{center|[[Pentagonal pyramidal molecular geometry|Pentagonal pyramidal]]}} ||[[File:AX5E2-2D.png|128px]] <br> {{center|[[Pentagonal planar molecular geometry|Pentagonal planar]]}} || &nbsp;
|-
!8 
| <br> {{center|[[Square antiprismatic molecular geometry|Square antiprismatic]]<br> }} || <br> &nbsp; || &nbsp; || &nbsp;
|}

{{Clear}}
{| class="wikitable" style="margin:1em auto;"
|- 
! Molecule <br>type
! Molecular Shape<ref name=Petrucci/>{{rp|413–414}}
! Electron Arrangement<ref name=Petrucci/>{{rp|413–414}} <br> <small>including lone pairs, shown in yellow</small>
! Geometry<ref name=Petrucci/>{{rp|413–414}} <br> <small>excluding lone pairs</small>
! Examples
|- 
! AX<sub>2</sub>E<sub>0</sub>
| [[Linear (chemistry)|Linear]]
| [[File:AX2E0-3D-balls.png|100px]]
| [[File:Linear-3D-balls.png|100px]]
| [[beryllium chloride|BeCl<sub>2</sub>]],<ref name=Jolly/> [[carbon dioxide|CO<sub>2</sub>]]<ref name=Miessler/>
|- 
! AX<sub>2</sub>E<sub>1</sub>
| [[Bent (chemistry)|Bent]]
| [[File:AX2E1-3D-balls.png|100px]]
| [[File:Bent-3D-balls.png|100px]]
| [[nitrite|{{chem|NO|2|-}}]],<ref name=Jolly/> [[sulfur dioxide|SO<sub>2</sub>]],<ref name=Petrucci/>{{rp|413–414}} [[ozone|O<sub>3</sub>]],<ref name=Jolly/> [[dichlorocarbene|CCl<sub>2</sub>]]
|-
! AX<sub>2</sub>E<sub>2</sub>
| [[Bent (chemistry)|Bent]]
| [[File:AX2E2-3D-balls.png|100px]]
| [[File:Bent-3D-balls.png|100px]]
| [[water (molecule)|H<sub>2</sub>O]],<ref name=Petrucci/>{{rp|413–414}} [[oxygen difluoride|OF<sub>2</sub>]]<ref name=Housecroft/>{{rp|448}}
|- 
! AX<sub>2</sub>E<sub>3</sub>
| [[Linear (chemistry)|Linear]]
| [[File:AX2E3-3D-balls.png|100px]]
| [[File:Linear-3D-balls.png|100px]]
| [[xenon difluoride|XeF<sub>2</sub>]],<ref name=Petrucci/>{{rp|413–414}} [[triiodide|{{chem|I|3|-}}]],<ref name=Housecroft/>{{rp|483}} [[xenon dichloride|XeCl<sub>2</sub>]]
|- 
! AX<sub>3</sub>E<sub>0</sub>
| [[Trigonal planar]]
| [[File:AX3E0-3D-balls.png|100px]]
| [[File:Trigonal-3D-balls.png|100px]]
| [[boron trifluoride|BF<sub>3</sub>]],<ref name=Petrucci/>{{rp|413–414}} [[carbonate|{{chem|CO|3|2-}}]],<ref name=Housecroft/>{{rp|368}} [[formaldehyde|{{chem|CH|2|O}}]], [[nitrate|{{chem|NO|3|-}}]],<ref name=Jolly/> [[sulfur trioxide|SO<sub>3</sub>]]<ref name=Miessler/>
|- 
! AX<sub>3</sub>E<sub>1</sub>
| [[Trigonal pyramid (chemistry)|Trigonal pyramidal]]
| [[File:AX3E1-3D-balls.png|100px]]
| [[File:Pyramidal-3D-balls.png|100px]]
| [[ammonia|NH<sub>3</sub>]],<ref name=Petrucci/>{{rp|413–414}} [[phosphorus trichloride|PCl<sub>3</sub>]]<ref name=Housecroft/>{{rp|407}}
|- 
! AX<sub>3</sub>E<sub>2</sub>
| [[T-shaped molecular geometry|T-shaped]]
| [[File:AX3E2-3D-balls.png|100px]]
| [[File:T-shaped-3D-balls.png|100px]]
| [[chlorine trifluoride|ClF<sub>3</sub>]],<ref name=Petrucci/>{{rp|413–414}} [[bromine trifluoride|BrF<sub>3</sub>]]<ref name=Housecroft/>{{rp|481}}
|- 
! AX<sub>4</sub>E<sub>0</sub>
| [[Tetrahedral molecular geometry|Tetrahedral]]
| [[File:AX4E0-3D-balls.png|100px]]
| [[File:Tetrahedral-3D-balls.png|100px]]
| [[methane|CH<sub>4</sub>]],<ref name=Petrucci/>{{rp|413–414}} [[phosphate|{{chem|PO|4|3-}}]], [[sulfate|{{chem|SO|4|2-}}]],<ref name=Miessler/> [[perchlorate|{{chem|ClO|4|-}}]],<ref name=Jolly/> [[xenon tetroxide|XeO<sub>4</sub>]]<ref name=Housecroft/>{{rp|499}}
|- 
! AX<sub>4</sub>E<sub>1</sub>
| [[Seesaw (chemistry)|Seesaw]] or [[disphenoid]]al
| [[File:AX4E1-3D-balls.png|100px]]
| [[File:Seesaw-3D-balls.png|100px]]
| [[sulfur tetrafluoride|SF<sub>4</sub>]]<ref name=Petrucci/>{{rp|413–414}}<ref name=Housecroft/>{{rp|45}}
|- 
! AX<sub>4</sub>E<sub>2</sub>
| [[Square planar molecular geometry|Square planar]]
| [[File:AX4E2-3D-balls.png|100px]]
| [[File:Square-planar-3D-balls.png|100px]]
| [[xenon tetrafluoride|XeF<sub>4</sub>]]<ref name=Petrucci/>{{rp|413–414}}
|- 
! AX<sub>5</sub>E<sub>0</sub>
| [[Trigonal bipyramidal molecular geometry|Trigonal bipyramidal]]
| [[File:Trigonal-bipyramidal-3D-balls.png|100px]]
| [[File:Trigonal-bipyramidal-3D-balls.png|100px]]
| [[phosphorus pentachloride|PCl<sub>5</sub>]],<ref name=Petrucci/>{{rp|413–414}} [[phosphorus pentafluoride|PF<sub>5</sub>]],<ref name=Petrucci/>{{rp|413–414}}
|- 
! AX<sub>5</sub>E<sub>1</sub>
| [[Square pyramidal molecular geometry|Square pyramidal]]
| [[File:AX5E1-3D-balls.png|100px]]
| [[File:Square-pyramidal-3D-balls.png|100px]]
| [[chlorine pentafluoride|ClF<sub>5</sub>]],<ref name=Housecroft/>{{rp|481}} [[bromine pentafluoride|BrF<sub>5</sub>]],<ref name=Petrucci/>{{rp|413–414}} [[xenon oxytetrafluoride|XeOF<sub>4</sub>]]<ref name=Miessler/>
|-
! AX<sub>5</sub>E<sub>2</sub>
| [[Pentagonal planar molecular geometry|Pentagonal planar]]
| [[File:AX5E2-3D-balls.png|100px]]
| [[File:Pentagonal-planar-3D-balls.png|100px]]
| [[Tetramethylammonium pentafluoroxenate|{{chem|XeF|5|-}}]]<ref name=Housecroft/>{{rp|498}}
|-
! AX<sub>6</sub>E<sub>0</sub>
| [[Octahedral molecular geometry|Octahedral]]
| [[File:AX6E0-3D-balls.png|100px]]
| [[File:Octahedral-3D-balls.png|100px]]
| [[sulfur hexafluoride|SF<sub>6</sub>]]<ref name=Petrucci/>{{rp|413–414}}
|- 
! AX<sub>6</sub>E<sub>1</sub>
| [[Pentagonal pyramidal molecular geometry|Pentagonal pyramidal]]
| [[File:AX6E1-3D-balls.png|100px]]
| [[File:Pentagonal-pyramidal-3D-balls.png|100px]]
| {{chem|XeOF|5|-}},<ref name=Baran2000/> {{chem|IOF|5|2-}}<ref name=Baran2000>{{Cite journal| first1 = E. | title = Mean amplitudes of vibration of the pentagonal pyramidal {{chem|XeOF|5|-}} and {{chem|IOF|5|2-}} anions | journal = J. Fluorine Chem. | volume = 101| last1 = Baran | pages = 61–63 | year = 2000 | doi = 10.1016/S0022-1139(99)00194-3}}</ref>
|-
! AX<sub>7</sub>E<sub>0</sub>
| [[Pentagonal bipyramidal molecular geometry|Pentagonal bipyramidal]]<ref name=Miessler/>
| [[File:AX7E0-3D-balls.png|100px]]
| [[File:Pentagonal-bipyramidal-3D-balls.png|100px]]
| [[iodine heptafluoride|IF<sub>7</sub>]]<ref name=Miessler/>
|-
! AX<sub>8</sub>E<sub>0</sub>
| [[Square antiprismatic molecular geometry|Square antiprismatic]]<ref name=Miessler/>
| [[File:AX8E0-3D-balls.png|100px]]
| [[File:Square-antiprismatic-3D-balls.png|100px]]
| {{chem|IF|8|-}}, XeF<sub>8</sub><sup>2-</sup> in [[Nitrosonium octafluoroxenate(VI)|(NO)<sub>2</sub>XeF<sub>8</sub>]]
|}

===Transition metals (Kepert model)===
The lone pairs on [[transition metal]] atoms are usually stereochemically inactive, meaning that their presence does not change the molecular geometry. For example, the hexaaquo complexes M(H<sub>2</sub>O)<sub>6</sub> are all octahedral for M = V<sup>3+</sup>, Mn<sup>3+</sup>, Co<sup>3+</sup>, Ni<sup>2+</sup> and Zn<sup>2+</sup>, despite the fact that the electronic configurations of the central metal ion are d<sup>2</sup>, d<sup>4</sup>, d<sup>6</sup>, d<sup>8</sup> and d<sup>10</sup> respectively.<ref name=Housecroft/>{{rp|542}} The Kepert model ignores all lone pairs on transition metal atoms, so that the geometry around all such atoms corresponds to the VSEPR geometry for AX<sub>n</sub> with 0 lone pairs E.<ref>{{cite journal |last1=Anderson |first1=O. P. |title=Book reviews: Inorganic Stereochemistry (by David L. Kepert) |journal=Acta Crystallographica B |date=1983 |volume=39 |pages=527–528 |doi=10.1107/S0108768183002864 |url=https://journals.iucr.org/b/issues/1983/04/00/a22157/a22157.pdf |access-date=14 September 2020 |quote=based on a systematic quantitative application of the common ideas regarding electron-pair repulsion|doi-access=free }}</ref><ref name=Housecroft/>{{rp|542}} This is often written ML<sub>n</sub>, where M = metal and L = ligand. The Kepert model predicts the following geometries for coordination numbers of 2 through 9:

{| class="wikitable" style="margin:1em auto;"
|- 
! Molecule <br>type
! Shape
! Geometry
! Examples
|- 
! ML<sub>2</sub>
| [[Linear (chemistry)|Linear]]
| [[File:Linear-3D-balls.png|100px]]
| [[mercury(II) chloride|HgCl<sub>2</sub>]]<ref name=Jolly/>
|- 
! ML<sub>3</sub>
| [[Trigonal planar]]
| [[File:Trigonal-3D-balls.png|100px]]
|
|- 
! ML<sub>4</sub>
| [[Tetrahedral molecular geometry|Tetrahedral]]
| [[File:Tetrahedral-3D-balls.png|100px]]
| [[Tetrachloronickelate|{{chem|NiCl|4|2-}}]]
|- 
! rowspan="2"| ML<sub>5</sub>
| [[Trigonal bipyramidal molecular geometry|Trigonal bipyramidal]]
| [[File:Trigonal-bipyramidal-3D-balls.png|100px]]
| [[Iron pentacarbonyl|{{chem|Fe(CO)|5}}]]
|-
| [[Square pyramidal molecular geometry|Square pyramidal]]
| [[File:Square-pyramidal-3D-balls.png|100px]]
| MnCl<sub>5</sub><sup>2−</sup>
|-
! ML<sub>6</sub>
| [[Octahedral molecular geometry|Octahedral]]
| [[File:Octahedral-3D-balls.png|100px]]
| [[tungsten hexachloride|WCl<sub>6</sub>]]<ref name=Housecroft/>{{rp|659}}
|-
! rowspan="3"| ML<sub>7</sub>
| [[Pentagonal bipyramidal molecular geometry|Pentagonal bipyramidal]]<ref name=Miessler/>
| [[File:Pentagonal-bipyramidal-3D-balls.png|100px]]
| {{chem|ZrF|7|3-}}
|-
| [[Capped octahedral molecular geometry|Capped octahedral]]
| [[File:Face-capped octahedron.png|100px]]
| {{chem|MoF|7|-}}
|-
| [[Capped trigonal prismatic molecular geometry|Capped trigonal prismatic]]
| [[File:MonocappTrigPrism.CapRightps.png|100px]]
| {{chem|TaF|7|2-}}
|-
! rowspan="3"| ML<sub>8</sub>
| [[Square antiprismatic molecular geometry|Square antiprismatic]]<ref name=Miessler/>
| [[File:Square-antiprismatic-3D-balls.png|100px]]
| {{chem|ReF|8|-}}
|-
| [[Dodecahedral molecular geometry|Dodecahedral]]
| [[File:Snub disphenoid.png|100px]]
| {{chem|Mo(CN)|8|4-}}
|-
| [[Bicapped trigonal prismatic molecular geometry|Bicapped trigonal prismatic]]
| [[File:Square face bicapped trigonal prism.png|100px]]
| {{chem|ZrF|8|4-}}
|-
! rowspan="2"| ML<sub>9</sub>
| [[Tricapped trigonal prismatic molecular geometry|Tricapped trigonal prismatic]]
| [[File:AX9E0-3D-balls.png|110px]]
| [[Potassium nonahydridorhenate|{{chem|ReH|9|2-}}]]<ref name=Housecroft/>{{rp|254}}
|-
| [[Capped square antiprismatic molecular geometry|Capped square antiprismatic]]
| [[File:Monocapped square antiprism.png|110px]]
|
|}