VSEPR theory
Valence shell electron pair repulsion (VSEPR) theory (/ˈvɛspər, vəˈsɛpər/ VESPər,^{: 410 } vəSEPər) 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 GillespieNyholm theory after its two main developers, Ronald Gillespie and Ronald Nyholm.
The premise of VSEPR is that the valence electron pairs surrounding an atom tend to repel each other. The greater the repulsion, the higher in energy (less stable) the molecule is. Therefore, the VSEPRpredicted molecular geometry of a molecule is the one that has as little of this repulsion as possible. Gillespie has emphasized that the electronelectron 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.^{: 398 } For example in the molecule methyl isocyanate (H_{3}CN=C=O), the two carbons and one nitrogen are central atoms, and the three hydrogens and one oxygen are terminal atoms.^{: 416 } The geometry of the central atoms and their nonbonding 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.^{: 410–417 } 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 (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.^{: 410–417 } 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.^{: 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 PCl_{5} 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 SF_{4}, 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
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 nonequivalent positions are possible.^{: 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.
The difference between lone pairs and bonding pairs may also be used to rationalize deviations from idealized geometries. For example, the H_{2}O molecule has four electron pairs in its valence shell: two lone pairs and two bond pairs. The four electron pairs are spread so as to point roughly towards the apices of a tetrahedron. However, the bond angle between the two O–H bonds is only 104.5°, rather than the 109.5° of a regular tetrahedron, because the two lone pairs (whose density or probability envelopes lie closer to the oxygen nucleus) exert a greater mutual repulsion than the two bond pairs.^{: 410–417 }
A bond of higher bond order also exerts greater repulsion since the pi bond electrons contribute. For example in isobutylene, (H_{3}C)_{2}C=CH_{2}, the H_{3}C−C=C angle (124°) is larger than the H_{3}C−C−CH_{3} angle (111.5°). However, in the carbonate ion, CO^{2−}
_{3}, 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_{n}E_{m}, 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.^{: 410–417 } The total number of X and E is known as the steric number. For example in a molecule AX_{3}E_{2}, 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 doublebond carbons in alkenes like C_{2}H_{4} are AX_{3}E_{0}, but the bond angles are not all exactly 120°. Likewise, SOCl_{2} is AX_{3}E_{1}, 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.
Maingroup elements
For maingroup elements, there are stereochemically active lone pairs E whose number can vary between 0 to 3. Note that the geometries are named according to the atomic positions only and not the electron arrangement. For example, the description of AX_{2}E_{1} as a bent molecule means that the three atoms AX_{2} are not in one straight line, although the lone pair helps to determine the geometry.
Steric number 
Molecular geometry 0 lone pairs 
Molecular geometry^{: 413–414 } 1 lone pair 
Molecular geometry^{: 413–414 } 2 lone pairs 
Molecular geometry^{: 413–414 } 3 lone pairs 

2  

3  


4  



5  



6  



7  



8 
Molecule type 
Molecular Shape^{: 413–414 }  Electron Arrangement^{: 413–414 } including lone pairs, shown in yellow 
Geometry^{: 413–414 } excluding lone pairs 
Examples 

AX_{2}E_{0}  Linear  BeCl_{2}, CO_{2}  
AX_{2}E_{1}  Bent  NO^{−} _{2}, SO_{2},^{: 413–414 } O_{3}, CCl_{2}  
AX_{2}E_{2}  Bent  H_{2}O,^{: 413–414 } OF_{2}^{: 448 }  
AX_{2}E_{3}  Linear  XeF_{2},^{: 413–414 } I^{−} _{3},^{: 483 } XeCl_{2}  
AX_{3}E_{0}  Trigonal planar  BF_{3},^{: 413–414 } CO^{2−} _{3},^{: 368 } CH^{} _{2}O, NO^{−} _{3}, SO_{3}  
AX_{3}E_{1}  Trigonal pyramidal  NH_{3},^{: 413–414 } PCl_{3}^{: 407 }  
AX_{3}E_{2}  Tshaped  ClF_{3},^{: 413–414 } BrF_{3}^{: 481 }  
AX_{4}E_{0}  Tetrahedral  CH_{4},^{: 413–414 } PO^{3−} _{4}, SO^{2−} _{4}, ClO^{−} _{4}, XeO_{4}^{: 499 }  
AX_{4}E_{1}  Seesaw or disphenoidal  SF_{4}^{: 413–414 }^{: 45 }  
AX_{4}E_{2}  Square planar  XeF_{4}^{: 413–414 }  
AX_{5}E_{0}  Trigonal bipyramidal  PCl_{5},^{: 413–414 } PF_{5}, ^{: 413–414 }  
AX_{5}E_{1}  Square pyramidal  ClF_{5},^{: 481 } BrF_{5},^{: 413–414 } XeOF_{4}  
AX_{5}E_{2}  Pentagonal planar  XeF^{−} _{5}^{: 498 }  
AX_{6}E_{0}  Octahedral  SF_{6}^{: 413–414 }  
AX_{6}E_{1}  Pentagonal pyramidal  XeOF^{−} _{5}, IOF^{2−} _{5}  
AX_{7}E_{0}  Pentagonal bipyramidal  IF_{7}  
AX_{8}E_{0}  Square antiprismatic  IF^{−} _{8}, XeF_{8}^{2} in (NO)_{2}XeF_{8} 
Transition metals (Kepert model)
The lone pairs on transition metal atoms are usually stereochemically inactive, meaning that their presence does not change the molecular geometry. For example, the hexaaquo complexes M(H_{2}O)_{6} are all octahedral for M = V^{3+}, Mn^{3+}, Co^{3+}, Ni^{2+} and Zn^{2+}, despite the fact that the electronic configurations of the central metal ion are d^{2}, d^{4}, d^{6}, d^{8} and d^{10} respectively.^{: 542 } The Kepert model ignores all lone pairs on transition metal atoms, so that the geometry around all such atoms corresponds to the VSEPR geometry for AX_{n} with 0 lone pairs E.^{: 542 } This is often written ML_{n}, 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 

ML_{2}  Linear  HgCl_{2}  
ML_{3}  Trigonal planar  
ML_{4}  Tetrahedral  NiCl^{2−} _{4}  
ML_{5}  Trigonal bipyramidal  Fe(CO)^{} _{5}  
Square pyramidal  MnCl_{5}^{2−}  
ML_{6}  Octahedral  WCl_{6}^{: 659 }  
ML_{7}  Pentagonal bipyramidal  ZrF^{3−} _{7}  
Capped octahedral  MoF^{−} _{7}  
Capped trigonal prismatic  TaF^{2−} _{7}  
ML_{8}  Square antiprismatic  ReF^{−} _{8}  
Dodecahedral  Mo(CN)^{4−} _{8}  
Bicapped trigonal prismatic  ZrF^{4−} _{8}  
ML_{9}  Tricapped trigonal prismatic  ReH^{2−} _{9}^{: 254 }  
Capped square antiprismatic 
Examples
The methane molecule (CH_{4}) 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′. This is referred to as an AX_{4} type of molecule. As mentioned above, A represents the central atom and X represents an outer atom.^{: 410–417 }
The ammonia molecule (NH_{3}) has three pairs of electrons involved in bonding, but there is a lone pair of electrons on the nitrogen atom.^{: 392–393 } It is not bonded with another atom; however, it influences the overall shape through repulsions. As in methane above, there are four regions of electron density. Therefore, the overall orientation of the regions of electron density is tetrahedral. On the other hand, there are only three outer atoms. This is referred to as an AX_{3}E type molecule because the lone pair is represented by an E.^{: 410–417 } By definition, the molecular shape or geometry describes the geometric arrangement of the atomic nuclei only, which is trigonalpyramidal for NH_{3}.^{: 410–417 }
Steric numbers of 7 or greater are possible, but are less common. The steric number of 7 occurs in iodine heptafluoride (IF_{7}); the base geometry for a steric number of 7 is pentagonal bipyramidal. The most common geometry for a steric number of 8 is a square antiprismatic geometry.^{: 1165 } Examples of this include the octacyanomolybdate (Mo(CN)^{4−}
_{8}) and octafluorozirconate (ZrF^{4−}
_{8}) anions.^{: 1165 } The nonahydridorhenate ion (ReH^{2−}
_{9}) in potassium nonahydridorhenate is a rare example of a compound with a steric number of 9, which has a tricapped trigonal prismatic geometry.^{: 254 }
Steric numbers beyond 9 are very rare, and it is not clear what geometry is generally favoured. 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.^{: 1165, 1721 }
Exceptions
There are groups of compounds where VSEPR fails to predict the correct geometry.
Some AX_{2}E_{0} molecules
The shapes of heavier Group 14 element alkyne analogues (RM≡MR, where M = Si, Ge, Sn or Pb) have been computed to be bent.
Some AX_{2}E_{2} molecules
One example of the AX_{2}E_{2} geometry is molecular lithium oxide, Li_{2}O, a linear rather than bent structure, which is ascribed to its bonds being essentially ionic and the strong lithiumlithium repulsion that results. Another example is O(SiH_{3})_{2} with an Si–O–Si angle of 144.1°, which compares to the angles in Cl_{2}O (110.9°), (CH_{3})_{2}O (111.7°), and N(CH_{3})_{3} (110.9°). 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. In O(SiH_{3})_{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 ligandligand repulsion by the relatively large SiH_{3} ligand. Burford et al showed through Xray diffraction studies that Cl_{3}Al–O–PCl_{3} has a linear Al–O–P bond angle and is therefore a nonVSEPR molecule.
Some AX_{6}E_{1} and AX_{8}E_{1} molecules
Some AX_{6}E_{1} molecules, e.g. xenon hexafluoride (XeF_{6}) and the Te(IV) and Bi(III) anions, TeCl^{2−}
_{6}, TeBr^{2−}
_{6}, BiCl^{3−}
_{6}, BiBr^{3−}
_{6} and BiI^{3−}
_{6}, 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 (XeF^{2−}
_{8}) in nitrosonium octafluoroxenate(VI)^{: 498 } 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 nonbonding lone pair; another rationalization is the inertpair effect.^{: 214 }
Square planar ML_{4} complexes
The Kepert model predicts that ML_{4} transition metal molecules are tetrahedral in shape, and it cannot explain the formation of square planar complexes.^{: 542 } The majority of such complexes exhibit a d^{8} configuration as for the tetrachloroplatinate (PtCl^{2−}
_{4}) ion. The explanation of the shape of square planar complexes involves electronic effects and requires the use of crystal field theory.^{: 562–4 }
Complexes with strong dcontribution
Some transition metal complexes with low d electron count have unusual geometries, which can be ascribed to d subshell bonding interaction. Gillespie found that this interaction produces bonding pairs that also occupy the respective antipodal points (ligand opposed) of the sphere. This phenomenon is an electronic effect resulting from the bilobed shape of the underlying sd^{x} hybrid orbitals. The repulsion of these bonding pairs leads to a different set of shapes.
Molecule type  Shape  Geometry  Examples 

ML_{2}  Bent  TiO_{2}  
ML_{3}  Trigonal pyramidal  CrO_{3}  
ML_{4}  Tetrahedral  TiCl_{4}^{: 598–599 }  
ML_{5}  Square pyramidal  Ta(CH_{3})_{5}  
ML_{6}  C_{3v} Trigonal prismatic  W(CH_{3})_{6} 
The gas phase structures of the triatomic halides of the heavier members of group 2, (i.e., calcium, strontium and barium halides, MX_{2}), are not linear as predicted but are bent, (approximate X–M–X angles: CaF_{2}, 145°; SrF_{2}, 120°; BaF_{2}, 108°; SrCl_{2}, 130°; BaCl_{2}, 115°; BaBr_{2}, 115°; BaI_{2}, 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 NhF_{3} should assume a Tshaped geometry, instead of a trigonal planar geometry like its lighter congener BF_{3}. In contrast, the extra stability of the 7p_{1/2} electrons in tennessine are predicted to make TsF_{3} trigonal planar, unlike the Tshaped geometry observed for IF_{3} and predicted for AtF_{3}; similarly, OgF_{4} should have a tetrahedral geometry, while XeF_{4} has a square planar geometry and RnF_{4} is predicted to have the same.
Oddelectron 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^{: 364–365 } suggested that the decrease in the bond angle in the series NO^{+}
_{2} (180°), NO_{2} (134°), NO^{−}
_{2} (115°) indicates that a given set of bonding electron pairs exert a weaker repulsion on a single nonbonding electron than on a pair of nonbonding electrons. In effect, they considered nitrogen dioxide as an AX_{2}E_{0.5} molecule, with a geometry intermediate between NO^{+}
_{2} and NO^{−}
_{2}. Similarly, chlorine dioxide (ClO_{2}) is an AX_{2}E_{1.5} molecule, with a geometry intermediate between ClO^{+}
_{2} and ClO^{−}
_{2}.^{[citation needed]}
Finally, the methyl radical (CH_{3}) 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 CH_{3} 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