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 (H3C-N=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 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.: 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 PCl5 molecule.
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.
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.: 410–417
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.: 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.
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. 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 (ZrF4−8) anions.: 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.: 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
There are groups of compounds where VSEPR fails to predict the correct geometry.
The shapes of heavier Group 14 element alkyne analogues (RM≡MR, where M = Si, Ge, Sn or Pb) have been computed to be bent.
The Kepert model predicts that ML4 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 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.: 562–4
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 sdx hybrid orbitals. The repulsion of these bonding pairs leads to a different set of shapes.
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°), 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.
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Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
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Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Miessler, G. L.; Tarr, D. A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. pp. 54–62. ISBN 978-0-13-841891-5. 978-0-13-841891-5
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Miessler, G. L.; Tarr, D. A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. pp. 54–62. ISBN 978-0-13-841891-5. 978-0-13-841891-5
Miessler, G. L.; Tarr, D. A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. pp. 54–62. ISBN 978-0-13-841891-5. 978-0-13-841891-5
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Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
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Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Jolly, W. L. (1984). Modern Inorganic Chemistry. McGraw-Hill. pp. 77–90. ISBN 978-0-07-032760-3. 978-0-07-032760-3
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
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Housecroft, C. E.; Sharpe, A. G. (2005). Inorganic Chemistry (2nd ed.). Pearson. ISBN 978-0-130-39913-7. 978-0-130-39913-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Housecroft, C. E.; Sharpe, A. G. (2005). Inorganic Chemistry (2nd ed.). Pearson. ISBN 978-0-130-39913-7. 978-0-130-39913-7
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Housecroft, C. E.; Sharpe, A. G. (2005). Inorganic Chemistry (2nd ed.). Pearson. ISBN 978-0-130-39913-7. 978-0-130-39913-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
Housecroft, C. E.; Sharpe, A. G. (2005). Inorganic Chemistry (2nd ed.). Pearson. ISBN 978-0-130-39913-7. 978-0-130-39913-7
Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
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Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
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Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. ISBN 978-0-13-014329-7. 978-0-13-014329-7
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