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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 (/ˈvɛspər, vəˈsɛpər/ VESP-ər,[1]: 410  və-SEP-ər[2]) is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms.[3] It is also named the Gillespie-Nyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm but it is also called the Sidgwick-Powell theory after earlier work by Nevil Sidgwick and Herbert Marcus Powell.

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.[4]

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 quantum theory of atoms in molecules (AIM or QTAIM).[4][5]

History

[edit]

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,[6] and was independently presented in a Bakerian Lecture in 1940 by Nevil Sidgwick and Herbert Powell of the University of Oxford.[7] 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.[8][9]

Overview

[edit]

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.[1]: 398  For example, in the molecule methyl isocyanate (H3C-N=C=O), the two carbons and one nitrogen are central atoms, and the three hydrogens and one oxygen are terminal atoms.[1]: 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 pairs of electrons.[1]: 410–417  In VSEPR theory, a double bond or triple bond is treated as a single bonding group.[1] 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.

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.[1]: 410–417 [10] 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 trigonal. Likewise, for 4 electron pairs, the optimal arrangement is tetrahedral.[1]: 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 geometry, just as do the five bonding pairs of a PCl5 molecule.

Steric number

[edit]
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 pairs of valence electrons on the central atom.[11] In the molecule SF4, for example, the central sulfur atom has four ligands; 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

[edit]

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.[1]: 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.[10]

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.[1]: 410–417 [10]

A bond of higher bond order also exerts greater repulsion since the pi bond electrons contribute.[10] For example, in isobutylene, (H3C)2C=CH2, the H3C−C=C angle (124°) is larger than the H3C−C−CH3 angle (111.5°). However, in the carbonate ion, CO2−
3, all three C−O bonds are equivalent with angles of 120° due to resonance.

AXE method

[edit]

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 AXmEn, 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.[1]: 410–417  The total number of X and E is known as the steric number. For example, in a molecule AX3E2, 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 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 X–A–X angles are not all equal.

Based on the steric number and distribution of Xs and Es, VSEPR theory makes the predictions in the following tables.

Main-group elements

[edit]

For main-group elements, there are stereochemically active lone pairs 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 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.

Steric
number 		Molecular
geometry[12]
0 lone pairs 		Molecular
geometry[1]: 413–414 
1 lone pair 		Molecular
geometry[1]: 413–414 
2 lone pairs 		Molecular
geometry[1]: 413–414 
3 lone pairs
2
Linear
      
3
Trigonal planar
Bent
    
4
Tetrahedral
Trigonal pyramidal
Bent
  
5
Trigonal bipyramidal
Seesaw
T-shaped
Linear
6
Octahedral
Square pyramidal
Square planar
  
7
Pentagonal bipyramidal
Pentagonal pyramidal
Pentagonal planar
  
8
Square antiprismatic
 		    
Molecule
type 		Molecular
Shape[1]: 413–414  		Electron
Arrangement[1]: 413–414 
including lone pairs,
shown in yellow 		Geometry[1]: 413–414 
excluding lone pairs 		Examples
AX2E0 Linear BeCl2,[3] CO2[10]
AX2E1 Bent NO−
2,[3] SO2,[1]: 413–414  O3,[3] CCl2
AX2E2 Bent H2O,[1]: 413–414  OF2[13]: 448 
AX2E3 Linear XeF2,[1]: 413–414  I−
3,[13]: 483  XeCl2
AX3E0 Trigonal planar BF3,[1]: 413–414  CO2−
3,[13]: 368  CH
2O, NO−
3,[3] SO3[10]
AX3E1 Trigonal pyramidal NH3,[1]: 413–414  PCl3[13]: 407 
AX3E2 T-shaped ClF3,[1]: 413–414  BrF3[13]: 481 
AX4E0 Tetrahedral CH4,[1]: 413–414  PO3−
4, SO2−
4,[10] ClO−
4,[3] XeO4[13]: 499 
AX4E1 Seesaw or disphenoidal SF4[1]: 413–414 [13]: 45 
AX4E2 Square planar XeF4[1]: 413–414 
AX5E0 Trigonal bipyramidal PCl5,[1]: 413–414  PF5,[1]: 413–414 
AX5E1 Square pyramidal ClF5,[13]: 481  BrF5,[1]: 413–414  XeOF4[10]
AX5E2 Pentagonal planar XeF−
5[13]: 498 
AX6E0 Octahedral SF6[1]: 413–414 
AX6E1 Pentagonal pyramidal XeOF−
5,[14] IOF2−
5[14]
AX7E0 Pentagonal bipyramidal[10] IF7[10]
AX8E0 Square antiprismatic[10] IF−
8, XeF82- in (NO)2XeF8

Transition metals (Kepert model)

[edit]

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(H2O)6 are all octahedral for M = V3+, Mn3+, Co3+, Ni2+ and Zn2+, despite the fact that the electronic configurations of the central metal ion are d2, d4, d6, d8 and d10 respectively.[13]: 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 AXn with 0 lone pairs E.[15][13]: 542  This is often written MLn, where M = metal and L = ligand. The Kepert model predicts the following geometries for coordination numbers of 2 through 9:

Molecule
type 		Shape Geometry Examples
ML2 Linear HgCl2[3]
ML3 Trigonal planar
ML4 Tetrahedral NiCl2−
4
ML5 Trigonal bipyramidal Fe(CO)
5
Square pyramidal MnCl52−
ML6 Octahedral WCl6[13]: 659 
ML7 Pentagonal bipyramidal[10] ZrF3−
7
Capped octahedral MoF−
7
Capped trigonal prismatic TaF2−
7
ML8 Square antiprismatic[10] ReF−
8
Dodecahedral Mo(CN)4−
8
Bicapped trigonal prismatic ZrF4−
8
ML9 Tricapped trigonal prismatic ReH2−
9[13]: 254 
Capped square antiprismatic

Examples

[edit]

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(−1⁄3) ≈ 109° 28′.[16][17] This is referred to as an AX4 type of molecule. As mentioned above, A represents the central atom and X represents an outer atom.[1]: 410–417 

The ammonia molecule (NH3) has three pairs of electrons involved in bonding, but there is a lone pair of electrons on the nitrogen atom.[1]: 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 AX3E type molecule because the lone pair is represented by an E.[1]: 410–417  By definition, the molecular shape or geometry describes the geometric arrangement of the atomic nuclei only, which is trigonal-pyramidal for NH3.[1]: 410–417 

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.[10] The most common geometry for a steric number of 8 is a square antiprismatic geometry.[18]: 1165  Examples of this include the octacyanomolybdate (Mo(CN)4−
8) and octafluorozirconate (ZrF4−
8) anions.[18]: 1165  The nonahydridorhenate ion (ReH2−
9) in potassium nonahydridorhenate is a rare example of a compound with a steric number of 9, which has a tricapped trigonal prismatic geometry.[13]: 254 [18]

Steric numbers beyond 9 are very rare, and it is not clear what geometry is generally favoured.[19] 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.[18]: 1165, 1721 

Exceptions

[edit]

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

Some AX2E0 molecules

[edit]

The shapes of heavier Group 14 element alkyne analogues (RM≡MR, where M = Si, Ge, Sn or Pb) have been computed to be bent.[20][21][22]

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.[23] 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°).[24] 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.[24] 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.[24] Burford et al. showed through X-ray diffraction studies that Cl3Al–O–PCl3 has a linear Al–O–P bond angle and is therefore a non-VSEPR molecule.[25]

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−
6, TeBr2−
6, BiCl3−
6, BiBr3−
6 and BiI3−
6, are octahedral, rather than pentagonal pyramids, and the lone pair does not affect the geometry to the degree predicted by VSEPR.[26] Similarly, the octafluoroxenate ion (XeF2−
8) in nitrosonium octafluoroxenate(VI)[13]: 498 [27][28] 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;[24] another rationalization is the inert-pair effect.[13]: 214 

Square planar ML4 complexes

[edit]

The Kepert model predicts that ML4 transition metal molecules are tetrahedral in shape, and it cannot explain the formation of square planar complexes.[13]: 542  The majority of such complexes exhibit a d8 configuration as for the tetrachloroplatinate (PtCl2−
4) ion. The explanation of the shape of square planar complexes involves electronic effects and requires the use of crystal field theory.[13]: 562–4 

Complexes with strong d-contribution

[edit]
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.[29] Gillespie found that this interaction produces bonding pairs that also occupy the respective antipodal points (ligand opposed) of the sphere.[30][4] This phenomenon is an electronic effect resulting from the bilobed shape of the underlying sdx hybrid orbitals.[31][32] The repulsion of these bonding pairs leads to a different set of shapes.

Molecule type Shape Geometry Examples
ML2 Bent TiO2[29]
ML3 Trigonal pyramidal CrO3[33]
ML4 Tetrahedral TiCl4[13]: 598–599 
ML5 Square pyramidal Ta(CH3)5[34]
ML6 C3v Trigonal prismatic W(CH3)6[35]

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°).[36] It has been proposed by 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.[24][37]

Superheavy elements

[edit]

Relativistic effects on the electron orbitals of superheavy elements is predicted to influence the molecular geometry of some compounds. For instance, the 6d5/2 electrons in nihonium play an unexpectedly strong role in bonding, so NhF3 should assume a T-shaped geometry, instead of a trigonal planar geometry like its lighter congener BF3.[38] In contrast, the extra stability of the 7p1/2 electrons in tennessine are predicted to make TsF3 trigonal planar, unlike the T-shaped geometry observed for IF3 and predicted for AtF3;[39] similarly, OgF4 should have a tetrahedral geometry, while XeF4 has a square planar geometry and RnF4 is predicted to have the same.[40]

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[8]: 364–365  suggested that the decrease in the bond angle in the series NO+
2 (180°), NO2 (134°), 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 AX2E0.5 molecule, with a geometry intermediate between NO+
2 and NO−
2. Similarly, chlorine dioxide (ClO2) is an AX2E1.5 molecule, with a geometry intermediate between ClO+
2 and ClO−
2.[citation needed]

Finally, the methyl radical (CH3) is predicted to be trigonal pyramidal like the methyl anion (CH−
3), but with a larger bond angle (as in the trigonal planar methyl cation (CH+
3)). 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.[41]

See also

[edit]

References

[edit]

Further reading

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

VSEPR theory

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from Grokipedia
Valence Shell Electron Pair Repulsion (VSEPR) theory is a fundamental model in chemistry used to predict the three-dimensional of covalently bonded molecules and polyatomic ions by considering the repulsive interactions among electron pairs in the valence shell of the central atom. Developed by Ronald J. Gillespie and Ronald S. Nyholm in their 1957 paper "Inorganic ," the theory builds on earlier ideas from Sidgwick and Powell, refining them into a systematic approach that assumes pairs—both bonding and lone pairs—arrange themselves to minimize electrostatic repulsion, thereby determining the overall shape of the molecule. This model is particularly effective for main-group elements and provides qualitative predictions without requiring complex quantum mechanical calculations, making it a cornerstone of introductory inorganic and education. At its core, VSEPR theory classifies molecular geometries using the AXE notation, where A represents the central atom, X denotes the number of atoms bonded to it (ligands), and E indicates the number of lone pairs on the central atom. The total number of electron domains (X + E) dictates the , which may differ from the if lone pairs are present, as these occupy space but are not visible in the final structure. For instance, with two electron domains, the arrangement is linear (180° bond angle); three domains yield trigonal planar (120°); four domains result in tetrahedral (109.5°); five in trigonal bipyramidal (90° and 120° angles); and six in octahedral (90° angles). Lone pairs exert stronger repulsion than bonding pairs, distorting bond angles—for example, in (H₂O, AX₂E₂), the bent shape has a bond angle of about 104.5° rather than the ideal 109.5° of tetrahedral . While VSEPR excels at explaining geometries for simple molecules like (CH₄, tetrahedral) and (NH₃, trigonal pyramidal), it has limitations, particularly for complexes, molecules with multiple bonds, or those involving d-orbitals, where hybridization or field effects play larger roles. The theory does not predict bond lengths, strengths, or vibrational frequencies quantitatively and can falter in cases of significant π-bonding or hypervalent molecules, though refinements by Gillespie and others have addressed some exceptions, such as or T-shaped geometries for five-electron-domain species. Despite these constraints, VSEPR remains widely taught and applied due to its simplicity and accuracy for many common molecular structures.

Introduction

Definition and Scope

The Valence Shell Pair Repulsion (VSEPR) theory is a qualitative model in chemistry that predicts the three-dimensional of molecules by considering the arrangement of pairs around a central atom. It builds upon Lewis dot structures to determine how atoms are spatially oriented in a , focusing on the valence shell of the central atom. The core assumption of VSEPR theory is that the pairs—both bonding pairs and lone pairs—in the valence shell of the central atom repel one another due to electrostatic forces, leading to spatial arrangements that minimize these repulsions. This repulsion drives the pairs to adopt positions as far apart as possible, thereby defining the overall molecular shape. VSEPR theory primarily applies to compounds involving main-group elements and simple molecular species, where it provides reliable predictions without the need for computational intensity. Its scope extends to coordination compounds, where models like the Kepert extension adapt VSEPR principles to predict geometries around centers based on repulsions. Developed in the mid-20th century, VSEPR emerged as an accessible, non-mathematical alternative to quantum mechanical calculations for rationalizing molecular structures.

Historical Development

The foundational ideas of what would become VSEPR theory emerged from the work of British chemists Nevil V. Sidgwick and Herbert M. Powell, who in 1940 proposed that the repulsion between electron pairs in the valence shell of a central atom determines the overall shape of simple molecules. In their Bakerian Lecture, they correlated the number of pairs (ranging from two to six) with geometric arrangements such as linear, trigonal planar, and octahedral structures, providing an early qualitative framework for predicting molecular geometries based on minimization. This approach built on prior valence concepts but emphasized stereochemical implications without invoking hybridization or detailed orbital interactions. The theory was formalized and refined in 1957 by Ronald J. Gillespie and Ronald S. Nyholm at , who introduced the valence shell electron pair repulsion (VSEPR) model as a systematic predictive tool for inorganic . In their seminal paper "Inorganic Stereochemistry," published in the Quarterly Reviews of the Chemical Society, they expanded on Sidgwick and Powell's ideas by incorporating the differential repulsions between bonding and lone electron pairs, enabling more accurate predictions for a wider range of main-group compounds. This work established VSEPR as a cornerstone of structural , emphasizing its simplicity and utility over quantum mechanical calculations at the time. By the 1960s, VSEPR had gained widespread acceptance in chemical education and research, appearing in major inorganic chemistry textbooks that disseminated the model to students and practitioners. For instance, it was integrated into discussions of molecular structure in texts like F. Albert Cotton and Geoffrey Wilkinson's Advanced Inorganic Chemistry (first edition, 1962), reflecting its rapid adoption as a standard teaching tool. In the 1970s, David L. Kepert extended the model to coordination compounds of transition metals, developing the Kepert model to account for ligand repulsions while treating d-electrons as stereochemically inactive, as detailed in his 1972 book The Early Transition Metals. Over subsequent decades, VSEPR's evolution included growing recognition of its limitations, particularly in explaining hypervalent molecules like SF6 or PCl5, where the model predicts expanded octets but struggles with the absence of d-orbital involvement confirmed by modern quantum calculations. Critiques from the onward highlighted these issues, prompting integrations with (MO) theory to provide a more complete picture of bonding and geometry, such as in hybrid models that combine VSEPR heuristics with MO-derived electron densities. This synthesis has refined VSEPR's role as an introductory predictive method while addressing its empirical shortcomings through computational validation.

Core Concepts

Valence Shell Electron Pairs

In VSEPR theory, the valence shell refers to the outermost of the central atom in a , encompassing the s involved in bonding and those remaining as non-bonding pairs. This shell includes bonding pairs, which are shared between the central atom and surrounding atoms, and lone pairs, which are localized entirely on the central atom without participation in bonding. These pairs collectively dictate the spatial arrangement of atoms by minimizing mutual repulsions within the valence shell. A prerequisite for applying VSEPR theory is the construction of a to identify the bonding and lone pairs around the central atom. The total s for the molecule are calculated by summing the s contributed by each atom, based on their positions in the periodic table (e.g., group number for main-group elements). For the central atom, the effective s include its own contribution plus one per monovalent atom (or adjusted for polyatomic ligands and molecular charge), which are then used to form bonds and place lone pairs. The total number of pairs around the central atom is determined by dividing these total s by 2, as each pair consists of two s. For example, in (H₂O), oxygen contributes 6 s, each contributes 1, yielding 8 total s and 4 pairs around oxygen (2 bonding, 2 lone). The foundational principle of VSEPR relies on the repulsion among these valence shell electron pairs, which adopt geometries that minimize electrostatic interactions. Lone pairs exert stronger repulsions than bonding pairs because their is more concentrated near the central atom, occupying greater effective and causing distortions in bond angles. In contrast, bonding pairs have their electron density delocalized between the central atom and ligands, resulting in less intense repulsions. Multiple bonds, such as double or triple bonds, are treated as a single effective bonding pair in this model, since the dominates the spatial repulsion while pi bonds lie in the nodal plane and contribute minimally to the overall . This approach simplifies predictions while capturing the essential in main-group compounds. The sum of bonding and lone pairs, known as the steric number, provides the basis for arranging these pairs , though the detailed of repulsions is considered separately.

Steric Number and Repulsion Strengths

In VSEPR theory, the steric number (SN) of a central atom is defined as the sum of the number of atoms directly bonded to it and the number of lone pairs residing on it, which corresponds to the total count of domains surrounding the atom (SN = A + E, where A represents bonded atoms and E represents lone pairs in the AXE classification system). This quantification provides a foundational metric for predicting by assessing the spatial arrangement needed to minimize repulsions. The concept builds directly on the principles outlined by Gillespie and Nyholm, who emphasized the role of pairs in dictating . Electron domains, or regions of high around the central atom, encompass both bonding pairs and lone pairs; notably, multiple bonds—such as double or triple bonds—are treated as a single domain equivalent to a for repulsion purposes, as the is concentrated in a similar directional lobe. This treatment simplifies the model while capturing the effective spatial occupancy, ensuring that the reflects the overall repulsion dynamics rather than bond multiplicity alone. Gillespie and Nyholm's framework underscores that these domains arrange to achieve the lowest possible energy configuration through mutual repulsion. The relative strengths of repulsions between electron domains follow a clear hierarchy: lone pair–lone pair (lp–lp) interactions are the strongest, exerting the greatest force due to the unshared s' larger effective volume; lone pair–bonding pair (lp–bp) repulsions are intermediate; and bonding pair–bonding pair (bp–bp) interactions are the weakest, as shared s are partially constrained by nuclear attraction from adjacent atoms. This ordering, central to VSEPR predictions, can be visualized through qualitative energy diagrams where lp–lp repulsions elevate the most significantly, followed by lp–bp, with bp–bp contributing the least distortion. The originates from the differential spatial demands of lone versus bonding pairs, as articulated in the foundational VSEPR model. The ideal geometries derived from the steric number minimize these repulsions by positioning domains as far apart as possible on the valence shell surface. For SN = 2, the arrangement is linear; for SN = 3, trigonal planar; for SN = 4, tetrahedral; for SN = 5, trigonal bipyramidal; and for SN = 6, octahedral. These configurations represent the baseline geometries before accounting for distortions, providing a systematic basis for VSEPR applications across main-group compounds.
Steric Number (SN)Ideal Electron Pair Geometry
2Linear
3Trigonal planar
4Tetrahedral
5Trigonal bipyramidal
6Octahedral

AXE Notation and Geometry Prediction

Notation for Main-Group Elements

The AXE notation provides a systematic way to classify molecules and predict their geometries under the VSEPR theory for compounds of main-group elements, particularly those in the p-block. In this scheme, "A" denotes the central atom, "X" represents each surrounding atom directly bonded to the central atom (often called ligands), and "E" stands for each lone pair of electrons residing on the central atom. This notation simplifies the analysis by focusing on the total number of electron domains around the central atom, treating both bonding pairs and lone pairs as repelling entities. To apply AXE notation, the process begins with constructing the of the molecule, which reveals the central atom, the bonds to surrounding atoms (counted as X), and any non-bonding pairs on the central atom (counted as E). The steric number (SN) is then determined as the sum SN = X + E, corresponding to the total pairs in the valence shell; this dictates the geometry, such as linear for SN=2, trigonal planar for SN=3, or octahedral for SN=6. The follows by positioning the X groups around this arrangement, with E pairs ideally placed to maximize separation and minimize repulsion, often in less sterically demanding locations. For instance, in cases of higher SN like 5 or 6, lone pairs may preferentially occupy equatorial positions in trigonal bipyramidal or axial/equatorial distinctions in octahedral arrangements due to varying repulsion strengths. Common classifications illustrate the notation's utility. (CO₂) is AX₂, featuring a central carbon bonded to two oxygens with no lone pairs, yielding a with a 180° bond angle. (NH₃) is AX₃E, with bonded to three hydrogens and one , resulting in a trigonal pyramidal shape derived from a tetrahedral , with H-N-H angles of approximately 107°. tetrafluoride (XeF₄) exemplifies AX₄E₂, where bonds to four fluorines and has two lone pairs, leading to a square planar from an octahedral arrangement, with F-Xe-F angles of 90°. These examples highlight how AXE notation guides predictions for p-block central atoms. The AXE notation assumes octet adherence or expanded octets without significant d-orbital participation, making it primarily valid for main-group elements in the p-block where valence electrons occupy s and p orbitals. It does not account for cases involving transition metals or substantial d-orbital involvement, which are addressed separately.

Extension to Transition Metals

The Kepert model, introduced by D. L. Kepert in 1972, adapts VSEPR theory specifically for predicting the coordination geometries of complexes by considering ligands as the dominant electron domains that generate repulsions. In this framework, the geometry is determined primarily by the (CN), which equates to the number of ligand attachments (denoted as X in an AXE-type notation, where E=0 due to the negligible stereochemical role of lone pairs on the central metal). This approach treats the metal center as a point from which ligands repel each other to minimize , much like electron pairs in standard VSEPR, but it emphasizes the positional arrangement on a spherical surface around the metal. Key differences from VSEPR applications to main-group elements arise because transition metal complexes typically ignore metal-centered lone pairs, concentrating instead on inter-ligand repulsions, which enables higher coordination numbers such as 7–9 that are stabilized by d-orbital participation. The model accommodates variable bond types (ionic or covalent) between metal and ligands, and repulsion strengths follow a similar hierarchy to VSEPR—close approaches between ligands are disfavored—but geometries often exhibit angular distortions influenced by crystal field stabilization energies. Notation is adapted for simplicity, using MLn_n to indicate the metal (M) and number of ligands (n = CN), for instance, ML4_4 for square planar arrangements common in d8^8 configurations like Ni(II) complexes. Illustrative examples highlight the model's predictive power: for CN=6, the octahedral geometry (ML6_6) is standard, as in hexaamminecobalt(III) ion, [Co(NH3_3)6_6]3+^{3+}, where six equivalent ligands occupy positions to maximize separation at 90° and 180° angles. For certain electronic configurations, such as d0^0 or d10^{10}, the model predicts trigonal prismatic ML6_6 structures over octahedral, exemplified by the layered sulfide MoS2_2 (where Mo is effectively six-coordinate to S) or the alkyl complex [Ta(CH3_3)6_6]−^-, due to reduced repulsion in the prismatic arrangement for these cases. The steric number here aligns directly with the , serving as the basis for these predictions.

Molecular Geometries

Basic Shapes and Bond Angles

The Valence Shell Pair Repulsion (VSEPR) theory determines the arrangement of electron pairs around a central atom, leading to specific electron geometries based on the steric number (SN), defined as the total number of bonding pairs and lone pairs in the valence shell. These geometries minimize repulsions between electron pairs, resulting in characteristic ideal bond angles. The basic electron geometries for SN = 2 to 6 are as follows:
Steric Number (SN)Electron GeometryIdeal Bond Angles
2Linear180°
3Trigonal planar120°
4Tetrahedral109.5°
5Trigonal bipyramidal90° (axial-equatorial), 120° (equatorial-equatorial), 180° (axial-axial)
6Octahedral90° (adjacent), 180° (opposite)
These angles arise from the equal repulsion assumption among electron pairs, with the tetrahedral angle specifically derived from the of four equivalent positions around a point. Molecular geometries are obtained by considering only the positions of the bonding pairs (denoted as X in AXE notation, where A is the central atom and E represents lone pairs), while lone pairs occupy the remaining positions in the electron but are not visible in the molecular structure. Lone pairs exert stronger repulsions than bonding pairs due to their higher , often occupying positions that minimize interactions, such as equatorial sites in trigonal bipyramidal arrangements over axial ones to reduce 90° repulsions. The resulting molecular shapes for common AXE configurations (SN = 2–6) are summarized below, with ideal bond angles matching the parent electron unless distorted:
SNAXE NotationMolecular GeometryDescription of 3D Arrangement
2AX2LinearTwo atoms aligned opposite the central atom along a straight line.
3AX3Trigonal planarThree atoms in a plane, equally spaced around the central atom.
AX2EBentTwo atoms with a , forming a V-shape in the plane of the trigonal arrangement.
4AX4Four atoms at the vertices of a , all equivalent.
AX3ETrigonal pyramidalThree atoms forming a with the central atom at the apex.
AX2E2BentTwo atoms with two s, resulting in an angular structure.
5AX5Trigonal bipyramidalThree equatorial atoms in a plane (120° apart) and two axial atoms perpendicular (90° to equatorial).
AX4EFour atoms: two axial, two equatorial, resembling a seesaw with the central atom as fulcrum.
AX3E2T-shapedThree atoms: two axial and one equatorial, forming a T configuration.
AX2E3LinearTwo atoms in axial positions, with three equatorial s.
6AX6Six atoms at the vertices of an , all equivalent positions.
AX5ESquare pyramidalFive atoms: four basal in a square plane, one apical perpendicular.
AX4E2Square planarFour atoms in a square plane, with lone pairs trans to each other.
In these arrangements, axial positions in trigonal bipyramidal are distinct from equatorial ones, with axial bonds forming 90° angles to the equatorial plane and 180° to the opposite axial bond, influencing placement to favor less crowded equatorial sites. Observed bond angles often deviate from ideal values due to the greater effective size of compared to bonding pairs, which compress adjacent bond angles to reduce repulsion. For instance, in a tetrahedral (SN=4), the presence of one or more reduces the X-A-X angle below 109.5°, such as to approximately 104.5° in cases with two . Multiple bonds, treated as single domains in basic VSEPR, can slightly expand bond angles due to their higher and reduced repulsion in certain directions, though this effect is minor and secondary to influences. These deviations highlight the qualitative nature of VSEPR in prioritizing repulsion hierarchies over exact predictions.

Illustrative Examples

(BF₃) serves as a foundational example of VSEPR application for main-group elements. The molecule has a total of 24 valence electrons: contributes 3, and each contributes 7. The places as the central atom bonded to three atoms via single bonds, with no lone pairs on and three lone pairs on each ; this results in three bonding pairs around the central atom. Using AXE notation, BF₃ is classified as AX₃ (A = central atom, X = bonding pair, E = lone pair), with a steric number of 3. The is trigonal planar, and since there are no lone pairs, the is also trigonal planar, with ideal bond angles of 120°. Experimental verification via confirms F-B-F bond angles of exactly 120°. Methane (CH₄) illustrates VSEPR for a tetrahedral arrangement without lone pairs. It possesses 8 valence electrons: carbon provides 4, and each hydrogen provides 1. The Lewis structure features carbon centrally bonded to four hydrogens with single bonds and no lone pairs on carbon. This corresponds to AX₄ notation, with a steric number of 4. The electron and molecular geometries are both tetrahedral, predicting bond angles of 109.5°. Microwave spectroscopy measurements yield H-C-H bond angles of 109.47°, closely matching the VSEPR prediction and underscoring the model's accuracy for saturated hydrocarbons. Sulfur tetrafluoride (SF₄) demonstrates VSEPR effects of a , leading to distorted geometries. With 34 valence electrons (sulfur contributes 6, each fluorine 7), the shows sulfur central with four single bonds to fluorines and one on sulfur. Designated AX₄E, the steric number is 5, yielding a trigonal bipyramidal geometry. The occupies an equatorial position to minimize repulsion, resulting in a ; the two axial fluorines form bonds at approximately 173° to each other, the two equatorial F-S-F is about 102°, and the axial-equatorial F-S-F angles are roughly 87° due to -bond pair repulsions stronger than bond pair-bond pair interactions. Gas-phase confirms these distortions, with axial F-S-F at 173.1° and equatorial F-S-F near 101.6°.

Limitations and Exceptions

Deviations in Hypervalent Molecules

Hypervalent molecules, in which the central atom from the p-block appears to exceed the by accommodating more than eight valence electrons, challenge the foundational assumptions of the valence shell electron pair repulsion (VSEPR) theory. While VSEPR successfully extends to these cases by assigning steric numbers greater than four—treating all and lone s as repelling domains—it provides only an approximate model for their geometries and . For instance, in XeF₂, the central atom has a steric number of 5 (AX₂E₃ notation), leading to a predicted trigonal bipyramidal geometry with the two pairs axial and three lone pairs equatorial, resulting in a linear molecular shape. This prediction aligns with experimental observations, yet the structure involves 10 valence electrons around , which VSEPR accommodates phenomenologically without explaining the mechanism. The bonding in such hypervalent species is better rationalized through models like the 3-center-4-electron (3c-4e) bond, where four electrons are delocalized over three atomic centers, effectively describing the F-Xe-F unit in XeF₂ as two such bonds supplemented by two lone pairs on . This approach, building on early proposals by Rundle and Pimentel, avoids reliance on d-orbital hybridization, which quantum calculations show contributes negligibly to . Similarly, for XeF₄ (AX₄E₂, steric number 6), VSEPR predicts an octahedral electron geometry with two lone pairs trans to each other, yielding a square planar molecular shape, which matches experiment. The four Xe–F bonds are characterized by 3c-4e interactions, forming two linear F–Xe–F units, highlighting VSEPR's limitation in distinguishing bond types and electron sharing. Quantum chemical analyses indicate that the valence electron population on the central atom remains close to eight, with significant charge transfer from ligands rendering largely ionic in character. Further examples illustrate VSEPR's qualitative successes amid subtle deviations. In IF₇ (AX₇E₀, steric number 7), the theory predicts a pentagonal bipyramidal geometry, with five equatorial fluorine atoms in a plane and two axial, and the observed structure confirms this, featuring ideal 72° equatorial angles and 90° axial-equatorial angles. Nonetheless, experimental bond lengths show axial I-F bonds shorter (≈1.79 Å) than equatorial (≈1.86 Å), a distortion attributed to varying repulsion strengths or partial 3c-4e character in the equatorial plane, which simple VSEPR pairwise repulsions do not fully predict. For [XeF₈]²⁻ (AX₈E₀, steric number 8), VSEPR suggests a square antiprismatic or dodecahedral arrangement, and crystallographic data reveal a slightly distorted square antiprism, with bond angles deviating by a few degrees from ideality due to ligand crowding and anion charge effects. These cases underscore VSEPR's utility as an empirical tool for main-group hypervalent geometries but its inadequacy for precise electron distributions. In contemporary understanding, VSEPR serves as a heuristic for predicting shapes in hypervalent molecules but is superseded by (MO) theory or advanced valence bond methods for detailed electronic structure, particularly when electron counts exceed eight. MO descriptions reveal multicenter delocalizations and recoupled pair bonds that rationalize octet expansion without d-orbital involvement, aligning with topological analyses showing concentrations consistent with 3c-4e motifs. Ronald Gillespie, a pioneer of VSEPR, emphasized that while the theory effectively models domain repulsions, hypervalency arises from close-packing and rather than expanded valence shells, rendering the irrelevant for these compounds. This perspective reconciles VSEPR's predictive power with the nuanced bonding realities of hypervalent p-block . Additionally, VSEPR struggles with molecules involving significant multiple bonds, such as (H₂C=C=CH₂), where the cumulative double bonds lead to a perpendicular arrangement not fully predicted by simple electron domain repulsions, as π-bonding effects dominate.

Cases Involving d-Orbitals and Relativistic Effects

VSEPR theory encounters significant limitations when applied to transition metal complexes where d-orbitals play a prominent role in determining geometry. For four-coordinate d^8 metal complexes such as [Ni(CN)_4]^{2-}, VSEPR predicts a tetrahedral arrangement based on minimizing electron pair repulsions around the central atom. However, these complexes often adopt a square planar geometry due to the large crystal field stabilization energy arising from the splitting of d-orbitals in a square planar ligand field, which favors pairing of electrons in lower-energy orbitals. This deviation highlights how VSEPR overlooks the energetic contributions from d-electron configurations and ligand field effects. Another key failure occurs in octahedral transition metal complexes subject to the Jahn-Teller effect, where electronically degenerate ground states lead to structural distortions. For instance, the d^9 Cu^{2+} in [Cu(H_2O)_6]^{2+} exhibits an elongated tetragonal geometry, with two axial Cu-O bonds significantly longer than the four equatorial ones (approximately 2.4 vs. 1.96 ). VSEPR would predict a regular octahedral shape for this AX_6 system, assuming equivalent lone pair and bond pair repulsions, but the distortion arises from the uneven occupation of degenerate e_g d-orbitals, lowering the overall energy. Such effects are not captured by VSEPR, which treats all pairs as equivalent in repulsion strength. In superheavy elements, relativistic effects further challenge VSEPR predictions by altering orbital energies and bonding patterns through spin-orbit coupling and orbital contraction/expansion. For oganesson (element 118), the difluoride OgF_2 is theoretically predicted to adopt a bent rather than the linear AX_2 structure expected from VSEPR for a central atom with two bonding pairs and three lone pairs. This deviation stems from strong relativistic stabilization of the 7s orbital and significant spin-orbit splitting of the 7p orbitals, which modifies the repulsion and hybridization, leading to a bond angle closer to 90° in computational models. Overall, these cases underscore a fundamental critique of VSEPR: it neglects metal- π-bonding interactions and d-orbital participation, which are crucial in transition metals and heavier elements. Models like or the Kepert extension, which incorporate ligand repulsions in non-spherical fields, are necessary for better accuracy, though even they have limitations in highly relativistic regimes.

Special Applications

Odd-Electron Molecules

Odd-electron molecules, or free radicals, pose a unique challenge to the standard VSEPR theory because they possess an odd total number of valence electrons, leading to an that cannot be neatly paired into full electron domains around the central atom. This disrupts the conventional counting of bonding and domains, as the occupies an orbital but exerts only partial repulsive force compared to a complete . To extend VSEPR to these species, the is conceptualized as a "phantom " or a fractional electron domain equivalent to 0.5 of a standard domain, which accounts for its reduced steric demand and weaker repulsion. This adaptation modifies the AXE notation by incorporating the 0.5 E term, allowing of geometries where the bond angles are intermediate between those of even-electron analogs—for instance, larger than in the corresponding AX2E species due to diminished lone-pair repulsion. The modified steric number reflects this fractional contribution, enabling the theory to approximate the arrangement of atoms. A representative example is (NO2), which has 17 valence electrons and features a central atom bonded to two oxygen atoms with an on nitrogen, denoted as AX2E0.5. VSEPR predicts a with an O-N-O bond angle of approximately 134°, consistent with the experimental value of 134.1°. Another illustrative case is (ClO2), with 19 valence electrons and a central atom, classified as AX2E1.5 (two bonding domains, one full , and one half lone pair from the ). This arrangement yields a bent structure with an O-Cl-O bond angle of about 117°, aligning closely with observed data. Despite these successes, VSEPR adaptations for odd-electron molecules have limitations, particularly when the is delocalized across the structure, leading to less precise geometric predictions. In such scenarios, the model is often complemented by quantum computational approaches, such as , for more accurate descriptions.

Inorganic and Organometallic Complexes

In , VSEPR theory successfully predicts the geometry of hypervalent main-group compounds such as (IF5), classified as AX5E with five bonding pairs and one on the central iodine atom, resulting in a square pyramidal molecular shape that minimizes lone-pair/bond-pair repulsions. This structure features bond angles close to 90° in the basal plane and approximately 81° for the axial-equatorial interactions, consistent with the octahedral electron-pair geometry. VSEPR also anticipates fluxional behavior in certain pentacoordinate species with steric number 5, where pseudorotation facilitates rapid exchange between apical and equatorial positions, averaging the ligand environments on the NMR timescale. In , VSEPR theory encounters significant limitations due to the role of delocalized π-bonding and metal-ligand interactions that deviate from simple electron-pair repulsion models. For instance, (Fe(C5H5)2) exhibits a parallel sandwich geometry driven by η5-coordination of the cyclopentadienyl ligands and d-orbital overlap with the iron center, rather than the localized bonding assumed by VSEPR. Similarly, π-ligand effects distort predictions in bent metallocenes such as bis(cyclopentadienyl)titanium dichloride (Cp2TiCl2), where the Cp ligands impose a bent structure (Cp-M-Cp angle ~134°) through back-donation and steric factors, overriding expectations of a linear or trigonal arrangement based on steric number alone. Advanced applications extend VSEPR to higher coordination numbers, such as in seven-coordinate complexes like heptafluorozirconate ([ZrF7]3-), which adopts a capped octahedral geometry to accommodate seven ligands while minimizing repulsions, with the capping fluoride positioned over a triangular face of the . For heavy metal complexes, relativistic effects—particularly scalar relativistic contraction of s-orbitals—require adjustments to VSEPR predictions, as they stabilize more compact geometries and influence bond angles in compounds involving elements like or mercury. The Kepert model provides a foundational extension of VSEPR for these coordination compounds by focusing solely on ligand-bonding electron pairs, independent of metal d-electron configuration. Practically, VSEPR and its modifications guide the rational design of inorganic and organometallic complexes for and materials applications, predicting stable geometries to target specific reactivity profiles, though experimental validation through techniques like and vibrational is essential to confirm structures and account for dynamic behaviors.

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