VSEPR theory

Valence shell electron pair repulsion 'theory' is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. 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 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.
The insights of VSEPR theory are derived from topological analysis of the electron density of molecules. Such quantum chemical topology methods include the electron localization function and the quantum theory of atoms in molecules.

History

The idea of a correlation between molecular geometry and number of valence electron pairs was originally proposed in 1939 by Ryutaro Tsuchida in Japan, and was independently presented in a Bakerian Lecture in 1940 by Nevil Sidgwick and Herbert Powell of the University of Oxford. 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.

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. For example, in the molecule methyl isocyanate, the two carbons and one nitrogen are central atoms, and the three hydrogens and one oxygen are terminal atoms. 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. In VSEPR theory, a double bond or triple bond is treated as a single bonding group. 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 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. The number of electron pairs, 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.
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

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. 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.
Alternatively, the steric number can be determined for main-group elements using an algebraic electron-counting formula. This method sums the relevant valence electrons and divides by 2 to determine the number of electron pairs. The formula is:
where:

V is the number of valence electrons on the central atom.
M M is the number of atoms bonded to the central atom by single bonds.
C is the charge of the cation.
A is the charge of the anion.

Example
For the xenon tetrafluoride molecule :

Xenon has 8 valence electrons.
There are 4 bonded fluorine atoms, each contributing 1 electron.
The molecule is neutral.

A steric number of 6 corresponds to an octahedral electron geometry. Since there are 4 bonded atoms, the molecule contains 2 lone pairs, resulting in a square planar molecular geometry.

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 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 repulsions are considered stronger than lone pair–bonding pair repulsions, which in turn are considered stronger than bonding pair–bonding pair repulsions, distinctions that then guide decisions about overall geometry when 2 or more non-equivalent positions are possible. 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.
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 exert a greater mutual repulsion than the two bond pairs.
A bond of higher bond order also exerts greater repulsion since the pi bond electrons contribute. For example, in isobutylene, ₂C=CH₂, the H₃C−C=C angle is larger than the H₃C−C−CH₃ angle. However, in the carbonate ion,, all three C−O bonds are equivalent with angles of 120° due to 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_mE_n, where A represents the central atom and always has an implied subscript one. Each X represents a ligand. Each E represents a lone pair of electrons on the central atom. 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 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

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 0 lone pairs	Molecular geometry 1 lone pair	Molecular geometry 2 lone pairs	Molecular geometry 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	Electron Arrangement including lone pairs, shown in yellow	Geometry excluding lone pairs	Examples
AX₂E₀	Linear			BeCl₂, CO₂
AX₂E₁	Bent			nitrite\|, SO₂, O₃, CCl₂
AX₂E₂	Bent			H₂O, OF₂
AX₂E₃	Linear			XeF₂, triiodide\|, XeCl₂
AX₃E₀	Trigonal planar			BF₃, carbonate\|, formaldehyde\|, nitrate\|, SO₃
AX₃E₁	Trigonal pyramidal			NH₃, PCl₃
AX₃E₂	T-shaped			ClF₃, BrF₃
AX₄E₀	Tetrahedral			CH₄, phosphate\|, sulfate\|, perchlorate\|, XeO₄
AX₄E₁	Seesaw or disphenoidal			SF₄
AX₄E₂	Square planar			XeF₄
AX₅E₀	Trigonal bipyramidal			PCl₅, PF₅,
AX₅E₁	Square pyramidal			ClF₅, BrF₅, XeOF₄
AX₅E₂	Pentagonal planar			Tetramethylammonium pentafluoroxenate\|
AX₆E₀	Octahedral			SF₆
AX₆E₁	Pentagonal pyramidal			,
AX₇E₀	Pentagonal bipyramidal			IF₇
AX₈E₀	Square antiprismatic			, XeF₈^2- in ₂XeF₈