Editing VSEPR theory

{{Short description|Model for predicting molecular geometry}}
[[File:Water-dimensions-from-Greenwood&Earnshaw-2D.png|thumb|Example of bent electron arrangement (water molecule). Shows location of unpaired electrons, bonded atoms, and bond angles.  The bond angle for water is 104.5°.]]

'''Valence shell electron pair repulsion''' ('''VSEPR''') '''theory''' ({{IPAc-en|ˈ|v|ɛ|s|p|ər|,_|v|ə|ˈ|s|ɛ|p|ər}} {{respell|VESP|ər}},<ref name="Petrucci" />{{rp|410}} {{respell|və|SEP|ər}}<ref name="H2009">{{cite book|first= H. Stephen |last=Stoker|title = General, Organic, and Biological Chemistry|publisher = Cengage Learning|year = 2009|isbn = 978-0-547-15281-3|page=119}}</ref>) is a [[conceptual model|model]] used in [[chemistry]] to predict the geometry of individual [[molecule]]s from the number of [[electron pair]]s surrounding their central atoms.<ref name="Jolly">{{cite book |last=Jolly |first=W. L. |title=Modern Inorganic Chemistry |publisher=McGraw-Hill |year=1984 |pages=[https://archive.org/details/trent_0116300649799/page/77 77–90] |isbn=978-0-07-032760-3 |url=https://archive.org/details/trent_0116300649799/page/77 }}</ref> It is also named the Gillespie-Nyholm theory after its two main developers, [[Ronald Gillespie]] and [[Ronald Sydney Nyholm|Ronald Nyholm]].

The premise of VSEPR is that the [[valence electron]] pairs surrounding an atom tend to repel each other. The greater the repulsion, the higher in energy (less stable) the molecule is. Therefore, the VSEPR-predicted [[molecular geometry]] of a molecule is the one that has as little of this repulsion as possible.  Gillespie has emphasized that the electron-electron repulsion due to the [[Pauli exclusion principle]] is more important in determining molecular geometry than the [[electrostatic repulsion]].<ref name="Fiftyyears">{{cite journal | last1 = Gillespie | first1 = R. J. | year = 2008 | title = Fifty years of the VSEPR model | journal = Coord. Chem. Rev. | volume = 252 | issue = 12–14| pages = 1315–1327 | doi=10.1016/j.ccr.2007.07.007}}</ref>

The insights of VSEPR theory are derived from topological analysis of the [[electron density]] of molecules. Such quantum chemical topology (QCT) methods include the [[electron localization function]] (ELF) and the [[atoms in molecules|quantum theory of atoms in molecules]] (AIM or QTAIM).<ref name="Fiftyyears"/><ref>{{cite journal | last1 = Bader | first1 = Richard F. W. | last2 = Gillespie | first2 = Ronald J. | last3 = MacDougall | first3 = Preston J. | year = 1988 | title = A physical basis for the VSEPR model of molecular geometry | journal = J. Am. Chem. Soc. | volume = 110 | issue = 22 | pages = 7329–7336 | doi=10.1021/ja00230a009| bibcode = 1988JAChS.110.7329B }}</ref>

==History==
The idea of a correlation between molecular geometry and number of valence electron pairs (both shared and unshared pairs) was originally proposed in 1939 by [[Ryutaro Tsuchida]] in Japan,<ref>{{cite journal|journal= Nippon Kagaku Kaishi|volume=60 |year=1939|issue=3|pages= 245–256|doi=10.1246/nikkashi1921.60.245|script-title=ja:新簡易原子價論 |trans-title=New simple valency theory|first=Ryutarō |last=Tsuchida|language=ja|title=A New Simple Theory of Valency |doi-access=free}}</ref> and was independently presented in a [[Bakerian Lecture]] in 1940 by [[Nevil Sidgwick]] and [[Herbert Marcus Powell|Herbert Powell]] of the [[University of Oxford]].<ref>{{cite journal | last1 = Sidgwick | first1 = N. V. | last2 = Powell | first2 = H. M. | year = 1940 | title = Bakerian Lecture. Stereochemical Types and Valency Groups | journal = Proc. R. Soc. A | volume = 176 | issue = 965| pages = 153–180 | doi=10.1098/rspa.1940.0084| bibcode = 1940RSPSA.176..153S | doi-access = free }}</ref> In 1957, [[Ronald Gillespie]] and [[Ronald Sydney Nyholm]] of [[University College London]] refined this concept into a more detailed theory, capable of choosing between various alternative geometries.<ref name="Gill1957">{{cite journal | last1=Gillespie|first1=R. J.|author1-link=Ronald Gillespie|last2=Nyholm|first2=R. S.|author2-link=Ronald Sydney Nyholm| year = 1957 | title = Inorganic stereochemistry | journal = Q. Rev. Chem. Soc. | volume = 11 |issue=4| page = 339|doi=10.1039/QR9571100339 }}</ref><ref>{{cite journal | year = 1970 | last1=Gillespie|first1=R. J.|author1-link=Ronald Gillespie|title = The electron-pair repulsion model for molecular geometry | journal = J. Chem. Educ. | volume = 47 | issue = 1 | page = 18 |doi=10.1021/ed047p18|bibcode=1970JChEd..47...18G}}</ref>

==Overview==
VSEPR theory is used to predict the arrangement of electron pairs around central atoms in molecules, especially simple and symmetric molecules. A central atom is defined in this theory as an atom which is bonded to two or more other atoms, while a terminal atom is bonded to only one other atom.<ref name="Petrucci" />{{rp|398}} For example, in the molecule [[methyl isocyanate]] (H<sub>3</sub>C-N=C=O), the two carbons and one nitrogen are central atoms, and the three hydrogens and one oxygen are terminal atoms.<ref name="Petrucci" />{{rp|416}} The geometry of the central atoms and their non-bonding electron pairs in turn determine the geometry of the larger whole molecule.

The number of electron pairs in the valence shell of a central atom is determined after drawing the [[Lewis structure]] of the molecule, and expanding it to show all bonding groups and [[lone pair]]s of electrons.<ref name=Petrucci>{{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 |isbn=978-0-13-014329-7}}</ref>{{rp|410–417}} In VSEPR theory, a [[double bond]] or [[triple bond]] is treated as a single bonding group.<ref name=Petrucci/> The sum of the number of atoms bonded to a central atom and the number of [[lone pair]]s formed by its nonbonding [[valence electron]]s is known as the central atom's steric number.

The electron pairs (or groups if multiple bonds are present) are assumed to lie on the surface of a sphere centered on the central atom and tend to occupy positions that minimize their mutual repulsions by maximizing the distance between them.<ref name=Petrucci/>{{rp|410–417}}<ref name=Miessler>{{cite book|first1=G. L. |last1=Miessler |first2=D. A. |last2=Tarr |title=Inorganic Chemistry |edition=2nd |publisher=Prentice-Hall |year=1999 |pages=54–62 |isbn=978-0-13-841891-5}}</ref> The number of electron pairs (or groups), therefore, determines the overall geometry that they will adopt. For example, when there are two electron pairs surrounding the central atom, their mutual repulsion is minimal when they lie at opposite poles of the sphere. Therefore, the central atom is predicted to adopt a ''linear'' geometry. If there are 3 electron pairs surrounding the central atom, their repulsion is minimized by placing them at the vertices of an equilateral triangle centered on the atom. Therefore, the predicted geometry is ''[[triangular|trigonal]]''. Likewise, for 4 electron pairs, the optimal arrangement is ''[[tetrahedron|tetrahedral]]''.<ref name=Petrucci/>{{rp|410–417}}

As a tool in predicting the geometry adopted with a given number of electron pairs, an often used physical demonstration of the principle of minimal electron pair repulsion utilizes inflated balloons. Through handling, balloons acquire a slight surface electrostatic charge that results in the adoption of roughly the same geometries when they are tied together at their stems as the corresponding number of electron pairs.  For example, five balloons tied together adopt the ''[[trigonal bipyramidal molecular geometry|trigonal bipyramidal]]'' geometry, just as do the five bonding pairs of a PCl<sub>5</sub> molecule.

===Steric number===
[[Image:Sulfur-tetrafluoride-2D-dimensions.png|thumb|Sulfur tetrafluoride has a steric number of 5.]]
The steric number of a central atom in a molecule is the number of atoms bonded to that central atom, called its [[coordination number]], plus the number of [[lone pair]]s of valence electrons on the central atom.<ref>{{cite book|first1=G. L. |last1=Miessler |first2=D. A. |last2=Tarr |title=Inorganic Chemistry |edition=2nd |publisher=Prentice-Hall |year=1999 |pages=55 |isbn=978-0-13-841891-5}}</ref> In the molecule [[Sulfur tetrafluoride|SF<sub>4</sub>]], for example, the central sulfur atom has four [[ligand]]s; the [[coordination number]] of sulfur is four. In addition to the four ligands, sulfur also has one lone pair in this molecule. Thus, the steric number is 4 + 1 = 5.

===Degree of repulsion===
The overall geometry is further refined by distinguishing between ''bonding'' and ''nonbonding'' electron pairs. The bonding electron pair shared in a [[sigma bond]] with an adjacent atom lies further from the central atom than a nonbonding (lone) pair of that atom, which is held close to its positively charged nucleus. VSEPR theory therefore views repulsion by the lone pair to be greater than the repulsion by a bonding pair. As such, when a molecule has 2 interactions with different degrees of repulsion, VSEPR theory predicts the structure where lone pairs occupy positions that allow them to experience less repulsion. Lone pair–lone pair (lp–lp) repulsions are considered stronger than lone pair–bonding pair (lp–bp) repulsions, which in turn are considered stronger than bonding pair–bonding pair (bp–bp) repulsions, distinctions that then guide decisions about overall geometry when 2 or more non-equivalent positions are possible.<ref name=Petrucci/>{{rp|410–417}} For instance, when 5 valence electron pairs surround a central atom, they adopt a ''trigonal bipyramidal'' molecular geometry with two collinear ''axial'' positions and three ''equatorial'' positions. An electron pair in an axial position has three close equatorial neighbors only 90° away and a fourth much farther at 180°, while an equatorial electron pair has only two adjacent pairs at 90° and two at 120°. The repulsion from the close neighbors at 90° is more important, so that the axial positions experience more repulsion than the equatorial positions; hence, when there are lone pairs, they tend to occupy equatorial positions as shown in the diagrams of the next section for steric number five.<ref name=Miessler/>

The difference between lone pairs and bonding pairs may also be used to rationalize deviations from idealized geometries. For example, the H<sub>2</sub>O molecule has four electron pairs in its valence shell: two lone pairs and two bond pairs.  The four electron pairs are spread so as to point roughly towards the apices of a tetrahedron.  However, the bond angle between the two O–H bonds is only 104.5°, rather than the 109.5° of a regular tetrahedron, because the two lone pairs (whose density or probability envelopes lie closer to the oxygen nucleus) exert a greater mutual repulsion than the two bond pairs.<ref name=Petrucci/>{{rp|410–417}}<ref name=Miessler/>

A bond of higher [[bond order]] also exerts greater repulsion since the [[pi bond]] electrons contribute.<ref name=Miessler/> For example, in [[isobutylene]], (H<sub>3</sub>C)<sub>2</sub>C=CH<sub>2</sub>, the H<sub>3</sub>C−C=C angle (124°) is larger than the H<sub>3</sub>C−C−CH<sub>3</sub> angle (111.5°). However, in the [[carbonate]] ion, {{chem|CO|3|2−}}, all three C−O bonds are equivalent with angles of 120° due to [[resonance (chemistry)|resonance]].

==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]]
|
|}

==Examples==
The [[methane]] molecule (CH<sub>4</sub>) is tetrahedral because there are four pairs of electrons. The four hydrogen atoms are positioned at the vertices of a [[tetrahedron]], and the bond angle is [[Inverse trigonometric functions|cos<sup>−1</sup>]](−{{frac|1|3}})&nbsp;≈&nbsp;109°&nbsp;28′.<ref>{{cite journal | last1 = Brittin | first1 = W. E. | year = 1945 | title = Valence Angle of the Tetrahedral Carbon Atom | journal = J. Chem. Educ. | volume = 22 | issue = 3| page = 145 | doi=10.1021/ed022p145| bibcode = 1945JChEd..22..145B }}</ref><ref>[http://maze5.net/?page_id=367 "Angle Between 2 Legs of a Tetrahedron"] {{Webarchive|url=https://web.archive.org/web/20181003122307/http://maze5.net/?page_id=367 |date=2018-10-03 }} – Maze5.net</ref> This is referred to as an AX<sub>4</sub> type of molecule. As mentioned above, A represents the central atom and X represents an outer atom.<ref name=Petrucci/>{{rp|410–417}}

The [[ammonia]] molecule (NH<sub>3</sub>) has three pairs of electrons involved in bonding, but there is a lone pair of electrons on the nitrogen atom.<ref name=Petrucci/>{{rp|392–393}} It is not bonded with another atom; however, it influences the overall shape through repulsions. As in methane above, there are four regions of electron density. Therefore, the overall orientation of the regions of electron density is tetrahedral. On the other hand, there are only three outer atoms. This is referred to as an AX<sub>3</sub>E type molecule because the lone pair is represented by an E.<ref name=Petrucci/>{{rp|410–417}} By definition, the molecular shape or geometry describes the geometric arrangement of the atomic nuclei only, which is trigonal-pyramidal for NH<sub>3</sub>.<ref name=Petrucci/>{{rp|410–417}}

Steric numbers of 7 or greater are possible, but are less common. The steric number of 7 occurs in [[iodine heptafluoride]] (IF<sub>7</sub>); the base geometry for a steric number of 7 is pentagonal bipyramidal.<ref name=Miessler/> The most common geometry for a steric number of 8 is a [[square antiprism]]atic geometry.<ref name="wiberg">{{cite book| first1 = E.| last1 = Wiberg| first2 = A. F.|last2= Holleman| title = Inorganic Chemistry| publisher = Academic Press| year = 2001| isbn = 978-0-12-352651-9}}</ref>{{rp|1165}} Examples of this include the octacyanomolybdate ({{chem|Mo(CN)|8|4-}}) and octafluorozirconate ({{chem|ZrF|8|4-}}) anions.<ref name="wiberg" />{{rp|1165}} The nonahydridorhenate ion ({{chem|ReH|9|2-}}) in [[potassium nonahydridorhenate]] is a rare example of a compound with a steric number of 9, which has a tricapped trigonal prismatic geometry.<ref name=Housecroft>{{cite book|last1=Housecroft |first1=C. E. |last2=Sharpe |first2=A. G. |title=Inorganic Chemistry|edition=2nd |publisher=Pearson |date=2005 |isbn=978-0-130-39913-7}}</ref>{{rp|254}}<ref name="wiberg" />

Steric numbers beyond 9 are very rare, and it is not clear what geometry is generally favoured.<ref>{{cite book |last=Wulfsberg |first=Gary |author-link= |date=2000 |title=Inorganic Chemistry |url= |location= |publisher=University Science Books |page=107 |isbn=9781891389016}}</ref> Possible geometries for steric numbers of 10, 11, 12, or 14 are [[gyroelongated square bipyramid|bicapped square antiprismatic]] (or bicapped [[dodecadeltahedral]]), [[edge-contracted icosahedron|octadecahedral]], [[regular icosahedron|icosahedral]], and bicapped [[hexagonal antiprism]]atic, respectively. No compounds with steric numbers this high involving [[denticity|monodentate]] ligands exist, and those involving multidentate ligands can often be analysed more simply as complexes with lower steric numbers when some multidentate ligands are treated as a unit.<ref name="wiberg" />{{rp|1165,1721}}

==Exceptions==
There are groups of compounds where VSEPR fails to predict the correct geometry.

===Some AX<sub>2</sub>E<sub>0</sub> molecules===

The shapes of heavier Group 14 element alkyne analogues (RM≡MR, where M = Si, Ge, Sn or Pb) have been computed to be bent.<ref>{{cite journal| title = Silicon, germanium, tin and lead analogues of acetylenes| first = Philip P.| last = Power| journal = [[ChemComm|Chem. Commun.]]| date = September 2003| issue = 17| pages = 2091–2101| doi = 10.1039/B212224C| pmid = 13678155}}</ref><ref>{{cite journal| title = Triple bonds between heavier Group 14 elements. A theoretical approach| first1 = Shigeru| last1 = Nagase| first2 = Kaoru| last2 = Kobayashi| first3 = Nozomi| last3 = Takagi| journal = [[Journal of Organometallic Chemistry|J. Organomet. Chem.]]| date = 6 October 2000| volume = 11 | issue = 1–2| pages = 264–271| doi = 10.1016/S0022-328X(00)00489-7}}</ref><ref>{{cite journal| title = A Stable Compound Containing a Silicon–Silicon Triple Bond| first1 = Akira| last1 = Sekiguchi| first2 = Rei| last2 = Kinjō| first3 = Masaaki| last3 = Ichinohe| journal = [[Science (journal)|Science]]| date = September 2004| volume = 305| issue = 5691| pages = 1755–1757| doi = 10.1126/science.1102209| pmid = 15375262| bibcode = 2004Sci...305.1755S| s2cid = 24416825| url = http://people.ok.ubc.ca/wsmcneil/339/Sci2004.pdf}}{{dead link|date=December 2017 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>

===Some AX<sub>2</sub>E<sub>2</sub> molecules===
One example of the AX<sub>2</sub>E<sub>2</sub> geometry is molecular [[lithium oxide]], Li<sub>2</sub>O, a linear rather than bent structure, which is ascribed to its bonds being essentially ionic and the strong lithium-lithium repulsion that results.<ref>{{cite journal | last1 = Bellert | first1 = D. | last2 = Breckenridge | first2 = W. H. | year = 2001 | title = A spectroscopic determination of the bond length of the LiOLi molecule: Strong ionic bonding | journal = [[J. Chem. Phys.]] | volume = 114 | issue = 7| page = 2871 | doi = 10.1063/1.1349424 | bibcode = 2001JChPh.114.2871B }}</ref> Another example is O(SiH<sub>3</sub>)<sub>2</sub> with an Si–O–Si angle of 144.1°, which compares to the angles in Cl<sub>2</sub>O (110.9°), (CH<sub>3</sub>)<sub>2</sub>O (111.7°), and N(CH<sub>3</sub>)<sub>3</sub> (110.9°).<ref name="Gillespie&Robinson"/> Gillespie and Robinson rationalize the Si–O–Si bond angle based on the observed ability of a ligand's lone pair to most greatly repel other electron pairs when the ligand electronegativity is greater than or equal to that of the central atom.<ref name = "Gillespie&Robinson">{{cite journal | last1 = Gillespie | first1 = R. J. | last2 = Robinson | first2 = E. A. | year = 2005 | title = Models of molecular geometry | journal = [[Chem. Soc. Rev.]] | volume = 34 | issue = 5| pages = 396–407 | doi = 10.1039/b405359c | pmid = 15852152 }}</ref> In O(SiH<sub>3</sub>)<sub>2</sub>, the central atom is more electronegative, and the lone pairs are less localized and more weakly repulsive.  The larger Si–O–Si bond angle results from this and strong ligand-ligand repulsion by the relatively large -SiH<sub>3</sub> ligand.<ref name="Gillespie&Robinson"/>  Burford et al. showed through X-ray diffraction studies that Cl<sub>3</sub>Al–O–PCl<sub>3</sub> has a linear Al–O–P bond angle and is therefore a non-VSEPR molecule.<ref>{{cite journal |last1=Burford |first1=Neil |last2=Phillips |first2=Andrew |last3=Schurko |first3=Robert |last4=Wasylishen |first4=Roderick |last5=Richardson |first5=John |title=Isolation and comprehensive solid state characterization of Cl<sub>3</sub>Al–O–PCl<sub>3</sub> |journal=Chemical Communications |date=1997 |volume=1997 |issue=24 |pages=2363–2364 |doi=10.1039/A705781D |url=https://doi.org/10.1039/A705781D |access-date=3 April 2024|url-access=subscription }}</ref>

===Some AX<sub>6</sub>E<sub>1</sub> and AX<sub>8</sub>E<sub>1</sub> molecules===
[[File:Xenon-hexafluoride-3D-SF.png|200px|thumb|[[Xenon hexafluoride]], which has a distorted octahedral geometry]]
Some AX<sub>6</sub>E<sub>1</sub> molecules, e.g. [[xenon hexafluoride]] (XeF<sub>6</sub>) and the Te(IV) and Bi(III) anions, {{chem|TeCl|6|2-}}, {{chem|TeBr|6|2-}}, {{chem|BiCl|6|3-}}, {{chem|BiBr|6|3-}} and {{chem|BiI|6|3-}}, are octahedral, rather than pentagonal pyramids, and the lone pair does not affect the geometry to the degree predicted by VSEPR.<ref>{{cite book|last=Wells |first=A. F. |date=1984 |title=Structural Inorganic Chemistry |edition=5th |publisher=Oxford Science Publications |isbn=978-0-19-855370-0}}</ref> Similarly, the octafluoroxenate ion ({{chem|XeF|8|2-}}) in [[nitrosonium octafluoroxenate(VI)]]<ref name=Housecroft/>{{rp|498}}<ref name="Peterson1971">{{Cite journal | first3 = A.| first2 = H. | first4 = M.| title = Antiprismatic Coordination about Xenon: the Structure of Nitrosonium Octafluoroxenate(VI)| first1 = W.| last2 = Holloway| last3 = Coyle| volume = 173| journal = [[Science (journal)|Science]]| issue = 4003| pages = 1238–1239| issn = 0036-8075| doi = 10.1126/science.173.4003.1238| last4 = Williams| pmid = 17775218| last1 = Peterson| date = Sep 1971|bibcode = 1971Sci...173.1238P | s2cid = 22384146 }}</ref><ref>{{cite book| title = Molecular origami: precision scale models from paper| first1 = Robert M.| last1 = Hanson| publisher = University Science Books| year = 1995| isbn = 978-0-935702-30-9}}</ref> is a square antiprism with minimal distortion, despite having a lone pair. One rationalization is that steric crowding of the ligands allows little or no room for the non-bonding lone pair;<ref name = "Gillespie&Robinson"/> another rationalization is the [[inert-pair effect]].<ref name=Housecroft/>{{rp|214}}

===Square planar ML<sub>4</sub> complexes===
The Kepert model predicts that ML<sub>4</sub> transition metal molecules are tetrahedral in shape, and it cannot explain the formation of square planar complexes.<ref name=Housecroft/>{{rp|542}} The majority of such complexes exhibit a d<sup>8</sup> configuration as for the [[potassium tetrachloroplatinate|tetrachloroplatinate]] ({{chem|PtCl|4|2-}}) ion. The explanation of the shape of square planar complexes involves electronic effects and requires the use of [[crystal field theory]].<ref name=Housecroft/>{{rp|562–4}}

===Complexes with strong d-contribution===
[[File:Hexamethyl-tungsten-3D-balls.png|200px|thumb|[[Hexamethyltungsten]], a transition metal complex whose geometry is different from main-group coordination]]
Some transition metal complexes with low d electron count have unusual geometries, which can be ascribed to d subshell bonding interaction.<ref name="d0kaupp">{{cite journal | title = "Non-VSEPR" Structures and Bonding in d<sup>0</sup> Systems | first = Martin | last = Kaupp | journal = [[Angewandte Chemie|Angew. Chem. Int. Ed. Engl.]] | year = 2001 | volume = 40 | issue = 1 | pages = 3534–3565 | doi =  10.1002/1521-3773(20011001)40:19<3534::AID-ANIE3534>3.0.CO;2-#| pmid = 11592184 | url = http://www.chimdocet-inorganica.it/SITO_ESERCIZI/Complementi/COMP1/VSEPREccezioni.pdf}}</ref> [[Ronald Gillespie|Gillespie]] found that this interaction produces bonding pairs that also occupy the respective [[antipodal point]]s (ligand opposed) of the sphere.<ref>{{cite journal | title = An Electron Localization Function Study of the Geometry of d<sup>0</sup> Molecules of the Period 4 Metals Ca to Mn | first1 = Ronald J. | last1 = Gillespie | first2 =  Stéphane | last2 =  Noury | first3 = Julien | last3 = Pilmé | first4 =  Bernard | last4 =  Silvi | journal = [[Inorganic Chemistry (journal)|Inorg. Chem.]] | year = 2004 | volume = 43 | issue = 10 | pages = 3248–3256 | doi =  10.1021/ic0354015| pmid = 15132634 }}</ref><ref name="Fiftyyears"/> This phenomenon is an electronic effect resulting from the bilobed shape of the underlying sd<sup>x</sup> [[hybridization (chemistry)|hybrid orbitals]].<ref>{{cite journal | last1 = Landis | first1 = C. R. | last2 = Cleveland | first2 = T. | last3 = Firman | first3 = T. K. | year = 1995 | title = Making sense of the shapes of simple metal hydrides | journal = [[J. Am. Chem. Soc.]] | volume = 117 | issue = 6| pages = 1859–1860 | doi=10.1021/ja00111a036| bibcode = 1995JAChS.117.1859L }}</ref><ref>{{cite journal | last1 = Landis | first1 = C. R. | last2 = Cleveland | first2 = T. | last3 = Firman | first3 = T. K. | year = 1996 | title = Structure of W(CH<sub>3</sub>)<sub>6</sub> | journal = [[Science (journal)|Science]] | volume = 272 | issue = 5259| pages = 179–183 |doi=10.1126/science.272.5259.179f| doi-access = free }}</ref> The repulsion of these bonding pairs leads to a different set of shapes.

{| class="wikitable" style="margin:1em auto;"
|- 
! Molecule type
! Shape
! Geometry
! Examples
|- 
! ML<sub>2</sub>
| [[Bent molecular geometry|Bent]]
| [[File:Bent-3D-balls.png|100px]]
| [[Titanium dioxide|TiO<sub>2</sub>]]<ref name="d0kaupp"/>
|- 
! ML<sub>3</sub>
| [[Trigonal pyramidal molecular geometry|Trigonal pyramidal]]
| [[File:Pyramidal-3D-balls.png|100px]]
| [[Chromium trioxide|CrO<sub>3</sub>]]<ref name=cdoi>{{Cite journal | doi = 10.1021/ja077984d| title = Probing the Electronic and Structural Properties of Chromium Oxide Clusters {{chem|(CrO|3|)|''n''|-}} and (CrO<sub>3</sub>)<sub>''n''</sub> (''n''&nbsp;= 1–5): Photoelectron Spectroscopy and Density Functional Calculations| journal = Journal of the American Chemical Society| volume = 130| issue = 15| pages = 5167–77| year = 2008| last1 = Zhai | first1 = H. J. | last2 = Li | first2 = S. | last3 = Dixon | first3 = D. A. | last4 = Wang | first4 = L. S. |pmid = 18327905}}</ref>
|-
! ML<sub>4</sub>
| [[Tetrahedral molecular geometry|Tetrahedral]]
| [[File:Tetrahedral-3D-balls.png|100px]]
| [[titanium tetrachloride|TiCl<sub>4</sub>]]<ref name=Housecroft/>{{rp|598–599}}
|- 
! ML<sub>5</sub>
| [[Square pyramidal molecular geometry|Square pyramidal]]
| [[File:Square-pyramidal-3D-balls.png|100px]]
| [[Pentamethyltantalum|Ta(CH<sub>3</sub>)<sub>5</sub>]]<ref>{{cite journal |journal= Coord. Chem. Rev. |volume= 197 |year= 2000 |pages= 141–168 |title= Atomic orbitals, symmetry, and coordination polyhedra |first= R. Bruce |last= King | doi = 10.1016/s0010-8545(99)00226-x }}</ref>
|- 
! ML<sub>6</sub>
| ''C<sub>3v</sub>'' [[Trigonal prismatic molecular geometry|Trigonal prismatic]]
| [[File:Prismatic_TrigonalP.png|100px]]
| [[Hexamethyltungsten|W(CH<sub>3</sub>)<sub>6</sub>]]<ref>{{cite journal|last1=Haalan |first1=A. |last2=Hammel |first2=A.|last3=Rydpal |first3=K. |last4=Volden |first4=H. V.|journal=[[J. Am. Chem. Soc.]]|year=1990|volume=112|pages= 4547–4549|title=The coordination geometry of gaseous hexamethyltungsten is not octahedral|doi=10.1021/ja00167a065|issue=11|bibcode=1990JAChS.112.4547H }}</ref>
|}

The gas phase structures of the triatomic halides of the heavier members of [[alkaline earth metal|group 2]], (i.e., calcium, strontium and barium halides, MX<sub>2</sub>), are not linear as predicted but are bent, (approximate X–M–X angles: [[calcium fluoride|CaF<sub>2</sub>]], 145°; [[strontium fluoride|SrF<sub>2</sub>]], 120°; [[barium fluoride|BaF<sub>2</sub>]], 108°; [[strontium chloride|SrCl<sub>2</sub>]], 130°; [[barium chloride|BaCl<sub>2</sub>]], 115°; [[barium bromide|BaBr<sub>2</sub>]], 115°; [[barium iodide|BaI<sub>2</sub>]], 105°).<ref name = "Greenwood">{{Greenwood&Earnshaw}}</ref> It has been proposed by [[Ronald Gillespie|Gillespie]] that this is also caused by bonding interaction of the ligands with the d subshell of the metal atom, thus influencing the molecular geometry.<ref name = "Gillespie&Robinson"/><ref>{{cite journal | doi = 10.1063/1.459748 | title = Ab initio model potential study of the equilibrium geometry of alkaline earth dihalides: MX<sub>2</sub> (M=Mg, Ca, Sr, Ba; X=F, Cl, Br, I) | year = 1991 | author = Seijo, Luis | journal = [[J. Chem. Phys.]] | volume = 94 | pages = 3762 | last2 = Barandiarán | first2 = Zoila | last3 = Huzinaga | first3 = Sigeru | issue = 5| bibcode = 1991JChPh..94.3762S | url = https://repositorio.uam.es/bitstream/10486/7315/1/41581_jchemphysseijo_91_jcp_94_3762.pdf | hdl = 10486/7315 | hdl-access = free }}</ref>

===Superheavy elements===
[[Relativistic quantum chemistry|Relativistic effects]] on the electron orbitals of [[superheavy element]]s is predicted to influence the molecular geometry of some compounds. For instance, the 6d<sub>5/2</sub> electrons in [[nihonium]] play an unexpectedly strong role in bonding, so NhF<sub>3</sub> should assume a T-shaped geometry, instead of a trigonal planar geometry like its lighter congener BF<sub>3</sub>.<ref>{{cite journal |last1=Seth |first1=Michael |last2=Schwerdtfeger |first2=Peter |first3=Knut |last3=Fægri |date=1999 |title=The chemistry of superheavy elements. III. Theoretical studies on element 113 compounds |journal=Journal of Chemical Physics |volume=111 |issue=14 |pages=6422–6433 |doi=10.1063/1.480168 |bibcode=1999JChPh.111.6422S|s2cid=41854842 |doi-access=free |hdl=2292/5178 |hdl-access=free }}</ref> In contrast, the extra stability of the 7p<sub>1/2</sub> electrons in [[tennessine]] are predicted to make TsF<sub>3</sub> trigonal planar, unlike the T-shaped geometry observed for IF<sub>3</sub> and predicted for [[Astatine|At]]F<sub>3</sub>;<ref>{{Cite journal |last1=Bae |first1=Ch. |last2=Han |first2=Y.-K. |last3=Lee |first3=Yo. S. |doi=10.1021/jp026531m |title=Spin−Orbit and Relativistic Effects on Structures and Stabilities of Group 17 Fluorides EF<sub>3</sub> (E = I, At, and Element 117): Relativity Induced Stability for the ''D<sub>3h</sub>'' Structure of (117)F<sub>3</sub> |journal=The Journal of Physical Chemistry A |volume=107 |issue=6 |pages=852–858 |date=18 January 2003 |bibcode=2003JPCA..107..852B}}</ref> similarly, [[Oganesson|Og]]F<sub>4</sub> should have a tetrahedral geometry, while XeF<sub>4</sub> has a square planar geometry and [[Radon|Rn]]F<sub>4</sub> is predicted to have the same.<ref name=fluoride>{{cite journal|journal=Journal of Physical Chemistry A|volume=103|issue=8|pages=1104–1108|date=1999|title=Structures of RgFn (Rg = Xe, Rn, and Element 118. n = 2, 4.) Calculated by Two-component Spin-Orbit Methods. A Spin-Orbit Induced Isomer of (118)F<sub>4</sub>|first1=Young-Kyu|last1=Han|first2=Yoon Sup|last2=Lee|doi=10.1021/jp983665k|bibcode=1999JPCA..103.1104H}}</ref>

==Odd-electron molecules==
The VSEPR theory can be extended to molecules with an odd number of electrons by treating the unpaired electron as a "half electron pair"—for example, Gillespie and Nyholm<ref name="Gill1957"/>{{rp|364–365}} suggested that the decrease in the bond angle in the series [[Nitronium ion|{{chem|NO|2|+}}]] (180°), [[Nitrogen dioxide|NO<sub>2</sub>]] (134°), [[Nitrite|{{chem|NO|2|-}}]] (115°) indicates that a given set of bonding electron pairs exert a weaker repulsion on a single non-bonding electron than on a pair of non-bonding electrons. In effect, they considered nitrogen dioxide as an AX<sub>2</sub>E<sub>0.5</sub> molecule, with a geometry intermediate between {{chem|NO|2|+}} and {{chem|NO|2|-}}. Similarly, [[chlorine dioxide]] (ClO<sub>2</sub>) is an AX<sub>2</sub>E<sub>1.5</sub> molecule, with a geometry intermediate between [[Chloryl|{{chem|ClO|2|+}}]] and [[chlorite|{{chem|ClO|2|-}}]].{{citation needed|date=May 2014}}

Finally, the [[methyl radical]] (CH<sub>3</sub>) is predicted to be trigonal pyramidal like the methyl anion ({{chem|CH|3|-}}), but with a larger bond angle (as in the trigonal planar methyl cation ({{chem|CH|3|+}})). However, in this case, the VSEPR prediction is not quite true, as CH<sub>3</sub> is actually planar, although its distortion to a pyramidal geometry requires very little energy.<ref>{{cite book|last1=Anslyn |first1=E. V. |last2=Dougherty |first2=D. A. |title=Modern Physical Organic Chemistry |publisher=University Science Books |date=2006 |page=57|isbn=978-1891389313}}</ref>

==See also==
* [[Bent's rule]] (effect of ligand electronegativity)
* [[Comparison of software for molecular mechanics modeling]]
* [[Linear combination of atomic orbitals]]
* [[Molecular geometry]]
* [[Molecular modelling]]
* [[Molecular orbital theory|Molecular Orbital Theory]] (MOT)
* [[Thomson problem]]
* [[Valence bond theory|Valence Bond Theory]] (VBT)
* [[Valency interaction formula]]

==References==
{{reflist|30em}}

==Further reading==
* {{cite book |title=Chemistry: Foundations and Applications |editor-first=J. J. |editor-last=Lagowski |location=New York |publisher=Macmillan |date=2004 |isbn=978-0-02-865721-9 |volume=3 |pages=[https://archive.org/details/chemistryfoundat0000unse/page/99 99–104] |url-access=registration |url=https://archive.org/details/chemistryfoundat0000unse/page/99 }}

==External links==
{{Wikibooks|A-level Chemistry/OCR (Salters)|Molecular geometry#Molecular_geometry_and_lone_pairs|Molecular geometry and lone pairs}}
* [https://itunes.apple.com/us/app/vsepr-ar/id1441723400 VSEPR AR]{{dead link|date=March 2025|bot=medic}}{{cbignore|bot=medic}}—3D VSEPR Theory Visualization with Augmented Reality app
* [http://www.3dchem.com/ 3D Chem]—Chemistry, structures, and 3D molecules
* [http://arquivo.pt/wayback/20160523113736/http://www.iumsc.indiana.edu/ Indiana University Molecular Structure Center (IUMSC)]

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