VSEPR theory

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Valence shell electron pair repulsion (VSEPR) theory is a model used, in chemistry, to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms.[1] It is also named GillespieNyholm theory after its two main developers. The acronym "VSEPR" is pronounced "vesper"[2] or "vuh-seh-per"[3] by some chemists.

The premise of VSEPR is that the valence electron pairs surrounding an atom tend to repel each other, and will therefore adopt an arrangement that minimizes this repulsion, thus determining the molecule's geometry. The sum of the number of atoms bonded to a central atom and the number of lone pairs formed by its nonbonding valence electrons is known as the central atom's steric number.

VSEPR theory is usually compared with valence bond theory, which addresses molecular shape through orbitals that are energetically accessible for bonding. Valence bond theory concerns itself with the formation of sigma and pi bonds. Molecular orbital theory is another model for understanding how atoms and electrons are assembled into molecules and polyatomic ions.

VSEPR theory has long been criticized for not being quantitative, and therefore limited to the generation of "crude" (though structurally accurate) molecular geometries of covalently-bonded molecules. However, molecular mechanics force fields based on VSEPR have also been developed.[4]


The idea of a correlation between molecular geometry and number of valence electrons (both shared and unshared) was originally proposed in 1939 by Ryutaro Tsuchida in Japan,[citation needed] and was independently presented in a Bakerian Lecture in 1940 by Nevil Sidgwick and Herbert Powell of the University of Oxford.[5] 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.[6][7]


VSEPR theory is used to predict the arrangement of electron pairs around non-hydrogen atoms in molecules, especially simple and symmetric molecules, where these key, central atoms participate in bonding to 2 or more other atoms; the geometry of these key atoms and their non-bonding electron pairs in turn determine the geometry of the larger whole.

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 pairs of electrons.[8] In VSEPR theory, a double bond or triple bond are treated as a single bonding group.[8]

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 minimizes their mutual repulsions by maximizing the distance between them.[8][9] 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.[10] The number of electron pairs (or groups), therefore, determine 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 trigonal. Likewise, for 4 electron pairs, the optimal arrangement is tetrahedral.[8]

Degree of repulsion[edit]

This 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.[8] For instance, when 5 ligands or lone pairs surround a central atom, a trigonal bipyramidal molecular geometry is specified. In this geometry, the 2 collinear "axial" positions lie 180° apart from one another, and 90° from each of 3 adjacent "equatorial" positions; these 3 equatorial positions lie 120° apart from each other and experience only two closer proximity 90° neighbors (the axial positions). The axial positions therefore experience more repulsion than the equatorial positions; hence, when there are lone pairs, they tend to occupy equatorial positions.[9]

The difference between lone pairs and bonding pairs may also be used to rationalize deviations from idealized geometries. For example, the H2O 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.[8][9]

A generalization of the distinction can be made by the consideration of a variant of Bent's rule: electron pairs of more electropositive ligands constitute greater repulsion. This then explains for example, why the Cl in PClF4 prefers the equatorial position and why the bond angle in oxygen difluoride (103.8°) is smaller than that of water (104.5°). Lone pairs are then considered to be a special case of this rule, held by a "ghost ligand" in the limit of electropositivity.

AXE method[edit]

The "AXE method" of electron counting is commonly used when applying the VSEPR theory. The A represents the central atom and always has an implied subscript one. The X represents the number of ligands (atoms bonded to A). The E represents the number of lone electron pairs surrounding the central atom.[8] The sum of X and E is known as the steric number.

Based on the steric number and distribution of X's and E's, VSEPR theory makes the predictions in the following tables. Note that the geometries are named according to the atomic positions only and not the electron arrangement. For example the description of AX2E1 as a bent molecule means that the three atoms AX2 are not in one straight line, although the lone pair helps to determine the geometry.

Molecular geometry[11]
0 lone pair
Molecular geometry[11]
1 lone pair
Molecular geometry[11]
2 lone pairs
Molecular geometry[11]
3 lone pairs
2 AX2E0-2D.png
Linear (CO2)
3 AX3E0-side-2D.png
Trigonal planar (BCl3)
Bent (SO2)
4 AX4E0-2D.png
Tetrahedral (CH4)
Trigonal pyramidal (NH3)
Bent (H2O)
5 AX5E0-2D.png
Trigonal bipyramidal (PCl5)
Seesaw (SF4)
T-shaped (ClF3)
Linear (I
6 AX6E0-2D.png
Octahedral (SF6)
Square pyramidal (BrF5)
Square planar (XeF4)
7 AX7E0-2D.png
Pentagonal bipyramidal (IF7)[9]
Pentagonal pyramidal (XeOF
Pentagonal planar (XeF
Square antiprismatic

9 Tricapped trigonal prismatic (ReH2−
Capped square antiprismatic[citation needed]
10 Bicapped square antiprismatic OR
Bicapped dodecadeltahedral[15]
11 Octadecahedral[15]      
12 Icosahedral[15]      
14 Bicapped hexagonal antiprismatic[15]      

Molecule Type Shape[11] Electron arrangement[11] Geometry[11] Examples
AX2E0 Linear AX2E0-3D-balls.png Linear-3D-balls.png BeCl2,[1] HgCl2,[1] CO2[9]
AX2E1 Bent AX2E1-3D-balls.png Bent-3D-balls.png NO
,[1] SO2,[11] O3,[1] CCl2
AX2E2 Bent AX2E2-3D-balls.png Bent-3D-balls.png H2O,[11] OF2[16]
AX2E3 Linear AX2E3-3D-balls.png Linear-3D-balls.png XeF2,[11] I
,[17] XeCl2
AX3E0 Trigonal planar AX3E0-3D-balls.png Trigonal-3D-balls.png BF3,[11] CO2−
,[18] NO
,[1] SO3[9]
AX3E1 Trigonal pyramidal AX3E1-3D-balls.png Pyramidal-3D-balls.png NH3,[11] PCl3[19]
AX3E2 T-shaped AX3E2-3D-balls.png T-shaped-3D-balls.png ClF3,[11] BrF3[20]
AX4E0 Tetrahedral AX4E0-3D-balls.png Tetrahedral-3D-balls.png CH4,[11] PO3−
, SO2−
,[9] ClO
,[1] XeO4[21]
AX4E1 Seesaw (also called disphenoidal) AX4E1-3D-balls.png Seesaw-3D-balls.png SF4[11][22]
AX4E2 Square planar AX4E2-3D-balls.png Square-planar-3D-balls.png XeF4[11]
AX5E0 Trigonal bipyramidal Trigonal-bipyramidal-3D-balls.png Trigonal-bipyramidal-3D-balls.png PCl5[11]
AX5E1 Square pyramidal AX5E1-3D-balls.png Square-pyramidal-3D-balls.png ClF5,[20] BrF5,[11] XeOF4[9]
AX5E2 Pentagonal planar AX5E2-3D-balls.png Pentagonal-planar-3D-balls.png XeF
AX6E0 Octahedral AX6E0-3D-balls.png Octahedral-3D-balls.png SF6,[11] WCl6[23]
AX6E1 Pentagonal pyramidal AX6E1-3D-balls.png Pentagonal-pyramidal-3D-balls.png XeOF
,[12] IOF2−
AX7E0 Pentagonal bipyramidal[9] AX7E0-3D-balls.png Pentagonal-bipyramidal-3D-balls.png IF7[9]
AX8E0 Square antiprismatic[9] AX8E0-3D-balls.png Square-antiprismatic-3D-balls.png IF
, ZrF4−
, ReF
AX9E0 Tricapped trigonal prismatic (as drawn)
OR capped square antiprismatic
AX9E0-3D-balls.png AX9E0-3D-balls.png ReH2−
† Electron arrangement including lone pairs, shown in pale yellow
‡ Observed geometry (excluding lone pairs)

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 C2H4 are AX3E0, but the bond angles are not all exactly 120°. Likewise, SOCl2 is AX3E1, but because the X substituents are not identical, the XAX angles are not all equal.

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 geometry, just as do the five bonding pairs of a PCl5 molecule (AX5) or the two bonding and three non-bonding pairs of a XeF2 molecule (AX2E3). The molecular geometry of the former is also trigonal bipyramidal, whereas that of the latter is linear.


The methane molecule (CH4) 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 cos−1(−13) ≈ 109°28'.[24][25] This is referred to as an AX4 type of molecule. As mentioned above, A represents the central atom and X represents an outer atom.[8]

The ammonia molecule (NH3) has three pairs of electrons involved in bonding, but there is a lone pair of electrons on the nitrogen atom.[26] 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 AX3E type molecule because the lone pair is represented by an E.[8] By definition, the molecular shape or geometry describes the geometric arrangement of the atomic nuclei only, which is trigonal-pyramidal for NH3.[8]

Steric numbers of 7 or greater are possible, but are less common. The steric number of 7 occurs in iodine heptafluoride (IF7); the base geometry for a steric number of 7 is pentagonal bipyramidal.[9] The most common geometry for a steric number of 8 is a square antiprismatic geometry.[27] Examples of this include the octacyanomolybdate (Mo(CN)4−
) and octafluorozirconate (ZrF4−
) anions.[27]

The nonahydridorhenate ion (ReH2−
) in potassium nonahydridorhenate is a rare example of a compound with a steric number of 9, which has a tricapped trigonal prismatic geometry.[14][28] Another example is the octafluoroxenate ion (XeF2−
) in nitrosonium octafluoroxenate(VI),[13][29][30] although in this case one of the electron pairs is a lone pair, and therefore the molecule actually has a distorted square antiprismatic geometry.

Possible geometries for steric numbers of 10, 11, 12, or 14 are bicapped square antiprismatic (or bicapped dodecadeltahedral), octadecahedral, icosahedral, and bicapped hexagonal antiprismatic, respectively. No compounds with steric numbers this high involving 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.[15]


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

Some AX2E0 molecules[edit]

The gas phase structures of the triatomic halides of the heavier members of group 2, (i.e., calcium, strontium and barium halides, MX2), are not linear as predicted but are bent, (approximate X-M-X angles: CaF2, 145°; SrF2, 120°; BaF2, 108°; SrCl2, 130°; BaCl2, 115°; BaBr2, 115°; BaI2, 105°).[31] It has been proposed by Gillespie that this is caused by interaction of the ligands with the electron core of the metal atom, polarising it so that the inner shell is not spherically symmetric, thus influencing the molecular geometry.[32][33] Ab initio calculations have been cited to propose that contributions from d orbitals in the shell below the valence shell are responsible.[34] Disilynes are also bent, despite having no lone pairs.[35]

Some AX2E2 molecules[edit]

One example of the AX2E2 geometry is molecular lithium oxide, Li2O, a linear rather than bent structure, which is ascribed to its bonds being essentially ionic and the strong lithium-lithium repulsion that results.[36] Another example is O(SiH3)2 with an Si-O-Si angle of 144.1°, which compares to the angles in Cl2O (110.9°), (CH3)2O (111.7°), and N(CH3)3 (110.9°).[32] 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.[32] In O(SiH3)2, 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 -SiH3 ligand.[32]

Some AX6E1 and AX8E1 molecules[edit]

Xenon hexafluoride, which has a distorted octahedral geometry.

Some AX6E1 molecules, e.g. xenon hexafluoride (XeF6) and the Te(IV) and Bi(III) anions, TeCl2−
, TeBr2−
, BiCl3−
, BiBr3−
and BiI3−
, are octahedra, rather than pentagonal pyramids, and the lone pair does not affect the geometry to the degree predicted by VSEPR.[37] One rationalization is that steric crowding of the ligands allows little or no room for the non-bonding lone pair;[32] another rationalization is the inert pair effect.[38]

Transition metal molecules[edit]

Hexamethyltungsten, a transition metal compound whose geometry is different from main group coordination.

Many transition metal compounds have unusual geometries, which can be ascribed to ligand-core interaction.[39] As explained by Gillespie, ligands can be weakly-interacting or strongly-interacting. Molecules with weakly-interacting ligands share the same shapes as their main group analogues (without the presence of stereochemically active lone pairs). Strongly-interacting ligands however, polarize the atomic core and produce bonding pairs that also occupy the region on the opposite side of the atom.[39] This is similar to predictions based on sd hybrid orbitals[40][41] using the VALBOND theory. The repulsion of these double-sided regions leads to a different prediction of shapes.

Molecule Type Shape Geometry Examples
AX2 Bent Bent-3D-balls.png VO2+
AX3 Trigonal pyramidal Pyramidal-3D-balls.png CrO3
AX4 Tetrahedral Tetrahedral-3D-balls.png TiCl4[42]
AX5 Square pyramidal Square-pyramidal-3D-balls.png Ta(CH3)5[43]
AX6 Trigonal prismatic Prismatic TrigonalP.png W(CH3)6

Another anomaly is the square planar shape associated with d8 molecules with weakly-interacting ligands. This can be rationalized by considering the increased crystal field stabilization energy as compared to a tetrahedral geometry.

Odd-electron molecules[edit]

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[44] suggested that the decrease in the bond angle in the series NO+
(180°), NO2 (134°), NO
(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 AX2E0.5 molecule with a geometry intermediate between NO+
and NO
. Similarly chlorine dioxide (ClO2) is AX2E1.5 with a geometry intermediate between ClO+
and ClO
.[citation needed]

Finally the methyl radical (CH3) is predicted to be trigonal pyramidal like the methyl anion (CH
), but with a larger bond angle as in the trigonal planar methyl cation (CH+
). However in this case the VSEPR prediction is not quite true, as CH3 is actually planar, although its distortion to a pyramidal geometry requires very little energy.[45]

VSEPR and orbital hybridisation[edit]

The VSEPR theory is frequently taught in conjunction with orbital hybridisation as the two give similar predictions. However, the two are unrelated as the former is based on the Pauli exclusion principle while the latter is based on the Schrödinger equation. The key difference between the VSEPR theory and orbital hybridisation is that the latter includes bonding interactions; in this respect, the relationship between the two can be compared to that between crystal field theory and ligand field theory.

See also[edit]


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Further reading[edit]

  • Chemistry: Foundations and Applications. J. J. Lagowski, ed. New York: Macmillan, 2004. ISBN 0-02-865721-7. Volume 3, pages 99–104.

External links[edit]

  • 3D Chem - Chemistry, Structures, and 3D Molecules
  • IUMSC - Indiana University Molecular Structure Center