VSEPR theory

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 ( ,) 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 (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.

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).

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, 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. In VSEPR theory, a double bond or triple bond is treated as a single bonding group. 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. 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 (domains). The formula is:

:<math>\text{SN} = \frac{V + M - C + A}{2}</math>

where:

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

Example<br>

For the xenon tetrafluoride molecule (XeF₄):

• Xenon (group 18) has 8 valence electrons (V = 8).
• There are 4 bonded fluorine atoms, each contributing 1 electron (M = 4).
• The molecule is neutral (C = 0, A = 0).

:<math>\text{SN} = \frac{8 + 4 - 0 + 0}{2} = 6 \text{ electron pairs}</math>

A steric number of 6 corresponds to an octahedral electron geometry. Since there are 4 bonded atoms, the molecule contains 2 lone pairs (6 − 4 = 2), 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 (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. <br> 0 lone pairs

!Molecular<br>geometry

|-

! AX₇E₀

| Pentagonal bipyramidal This is referred to as an AX₄ type of molecule. As mentioned above, A represents the central atom and X represents an outer atom. Examples of this include the octacyanomolybdate () and octafluorozirconate () anions. 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.

Some AX₂E₂ molecules

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&ndash;lithium repulsion that results. 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°). 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&ndash;ligand repulsion by the relatively large -SiH₃ ligand.

Some AX₆E₁ and AX₈E₁ molecules

200px|thumb|[[Xenon hexafluoride, which has a distorted octahedral geometry]]

Some AX₆E₁ molecules, e.g. xenon hexafluoride (XeF₆) and the Te(IV) and Bi(III) anions, , , , and , are octahedral, rather than pentagonal pyramids, and the lone pair does not affect the geometry to the degree predicted by VSEPR. Similarly, the octafluoroxenate ion () in nitrosonium octafluoroxenate(VI) 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; Gillespie found that this interaction produces bonding pairs that also occupy the respective antipodal points (ligand opposed) of the sphere. The repulsion of these bonding pairs leads to a different set of shapes.

{| class="wikitable" style="margin:1em auto;"

|-

! Molecule type

! Shape

! Geometry

! Examples

|-

! ML₂

| Bent

| 100px

| TiO₂

|-

! ML₄

| Tetrahedral

| 100px

| TiCl₄

|-

! ML₆

| C_3v Trigonal prismatic

| 100px

| W(CH₃)₆

|}

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°). 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.

Superheavy elements

Relativistic effects on the electron orbitals of superheavy elements is predicted to influence the molecular geometry of some compounds. For instance, the 6d_5/2 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. In contrast, the extra stability of the 7p_1/2 electrons in tennessine are predicted to make TsF₃ trigonal planar, unlike the T-shaped geometry observed for IF₃ and predicted for AtF₃; similarly, OgF₄ should have a tetrahedral geometry, while XeF₄ has a square planar geometry and RnF₄ is predicted to have the same.

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

Finally, the methyl radical (CH₃) is predicted to be trigonal pyramidal like the methyl anion (), but with a larger bond angle (as in the trigonal planar methyl cation ()). 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.

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 (MOT)
• Thomson problem
• Valence Bond Theory (VBT)
• Valency interaction formula

References

Further reading

External links

• VSEPR AR—3D VSEPR Theory Visualization with Augmented Reality app
• 3D Chem—Chemistry, structures, and 3D molecules
• Indiana University Molecular Structure Center (IUMSC)