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Inorganic Chemistry/Chemical Bonding/VSEPR theory

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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.[1] It is also named the Gillespie-Nyholm 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 and will, therefore, adopt an arrangement that minimizes this repulsion. This in turn decreases the molecule's energy and increases its stability, which determines the molecular geometry.

History

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The idea of a correlation between molecular geometry and number of valence electrons (both shared and unshared) was first presented in a Bakerian Lecture in 1940 by Nevil Sidgwick and Herbert Powell at the University of Oxford.[2] In 1957 Ronald Gillespie and Ronald Sydney Nyholm at University College London refined this concept to build a more detailed theory capable of choosing between various alternative geometries.[3][4]

Overview

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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.[5]: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.[5]: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.[5]:410–417 In VSEPR theory, a double bond or triple bond is treated as a single bonding group.[5] 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.[5]:410–417[6] 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.[5]: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

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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.[7] 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

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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.[5]: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.[6]

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.[5]:410–417[6]

A bond of higher bond order also exerts greater repulsion since the pi bond electrons contribute.[6] 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

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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 AXnEm, 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.[5]: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

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For main-group 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 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[8]
0 lone pairs 		Molecular geometry[5]:413–414
1 lone pair 		Molecular geometry[5]:413–414
2 lone pairs 		Molecular geometry[5]: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 		Shape[5]:413–414 Electron arrangement[5]:413–414
including lone pairs, shown in pale yellow 		Geometry[5]:413–414
excluding lone pairs 		Examples
AX2E0 Linear     BeCl2,[1] CO2[6]
AX2E1 Bent     NO2-,[1] SO2,[5]:413–414 O3,[1] CCl2
AX2E2 Bent     H2O,[5]:413–414 OF2[9]:448
AX2E3 Linear     XeF2,[5]:413–414 I3-,[9]:483 XeCl2
AX3E0 Trigonal planar     BF3,[5]:413–414 CO2−3,[9]:368 NO3-,[1] SO3[6]
AX3E1 Trigonal pyramidal     NH3,[5]:413–414 PCl3[9]:407
AX3E2 T-shaped     ClF3,[5]:413–414 BrF3[9]:481
AX4E0 Tetrahedral     CH4,[5]:413–414 PO3−4, SO2−4,[6] ClO4-,[1] XeO4[9]:499
AX4E1 Seesaw or disphenoidal     SF4[5]:413–414[9]:45
AX4E2 Square planar     XeF4[5]:413–414
AX5E0 Trigonal bipyramidal     PCl5[5]:413–414
AX5E1 Square pyramidal     ClF5,[9]:481 BrF5,[5]:413–414 XeOF4[6]
AX5E2 Pentagonal planar     XeF5-[9]:498
AX6E0 Octahedral     SF6[5]:413–414
AX6E1 Pentagonal pyramidal     XeOF5-,[10] IOF2−5[10]
AX7E0 Pentagonal bipyramidal[6]     IF7[6]
AX8E0 Square antiprismatic[6]     IF8-

Transition metals (Kepert model)

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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.[9]: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.[11][9]: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[1]
ML3 Trigonal planar  
ML4 Tetrahedral   NiCl2−4
ML5 Trigonal bipyramidal   Fe(CO)5
Square pyramidal   MnCl52−
ML6 Octahedral   WCl6[9]:659
ML7 Pentagonal bipyramidal[6]   ZrF3−7
Capped octahedral   MoF7-
Capped trigonal prismatic   TaF2−7
ML8 Square antiprismatic[6]   ReF8-
Dodecahedral   Mo(CN)4−8
Bicapped trigonal prismatic   ZrF4−8
ML9 Tricapped trigonal prismatic   ReH2−9[9]:254
Capped square antiprismatic  

Examples

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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′.[12][13] This is referred to as an AX4 type of molecule. As mentioned above, A represents the central atom and X represents an outer atom.[5]: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.[5]: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.[5]:410–417 By definition, the molecular shape or geometry describes the geometric arrangement of the atomic nuclei only, which is trigonal-pyramidal for NH3.[5]: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.[6] The most common geometry for a steric number of 8 is a square antiprismatic geometry.[14]:1165 Examples of this include the octacyanomolybdate (Mo(CN)4−8) and octafluorozirconate (ZrF4−8) anions.[14]: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.[9]:254[14]

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.[14]:1165,1721

Exceptions

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

Some AX2E0 molecules

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The shapes of heavier Group 14 element alkyne analogues (RM≡MR, where M = Si, Ge, Sn or Pb) have been computed to be bent.[15][16][17]

Some AX2E2 molecules

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One example is molecular lithium oxide, Li2O, which is linear rather than being bent, and this has been ascribed to the bonding's being in essence ionic, leading to strong repulsion between the lithium atoms.[18]
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°). Gillespie's rationalisation is that the localisation of the lone pairs, and therefore their ability to repel other electron pairs, is greatest when the ligand has an electronegativity similar to, or greater than, that of the central atom.[19] When the central atom is more electronegative, as in O(SiH3)2, the lone pairs are less well-localised and have a weaker repulsive effect. This fact, combined with the stronger ligand-ligand repulsion (-SiH3 is a relatively large ligand compared to the examples above), gives the larger-than-expected Si-O-Si bond angle.[19]

Some AX6E1 and AX8E1 molecules

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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 octahedra rather than pentagonal pyramids, and the lone pair does not affect the geometry to the degree predicted by VSEPR.[20] One rationalization is that steric crowding of the ligands allows no room for the non-bonding lone pair;[19] another rationalization is the inert pair effect.[21] Similarly, the octafluoroxenate ion (XeF2−8) in nitrosonium octafluoroxenate(VI)[9]:498[22][23] is a square antiprism and not a bicapped trigonal prism (as predicted by VSEPR theory for an AX8E1 molecule), despite having a lone pair.

Square planar ML4 complexes

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The Kepert model predicts that ML4 transition metal molecules are tetrahedral in shape, and it cannot explain the formation of square planar complexes.[9]: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.[9]:562-4

Complexes with strong d-contribution

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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.[24] Gillespie found that this interaction produces bonding pairs that also occupy the respective antipodal points (ligand opposed) of the sphere.[25][26] This phenomenon is an electronic effect resulting from the bilobed shape of the underlying sdx hybrid orbitals.[27][28] The repulsion of these bonding pairs leads to a different set of shapes.

Molecule type Shape Geometry Examples
ML2 Bent   VO+2
ML3 Trigonal pyramidal   CrO3
ML4 Tetrahedral   TiCl4[9]:598–599
ML5 Square pyramidal   Ta(CH3)5[29]
ML6 C3v Trigonal prismatic   W(CH3)6[30]

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°).[31] 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.[19][32]

Odd-electron molecules

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The VSEPR theory can be extended to molecules with an odd number of electrons by treating the unpaired electron as a "half electron pair". In effect, the odd electron has an influence on the geometry which is similar to a full electron pair, but less pronounced so that the geometry may be intermediate between the molecule with a full electron pair and the molecule with one less electron pair on the central atom.

For example, nitrogen dioxide (NO2) is an AX2E0.5 molecule, with an unpaired electron on the central nitrogen. VSEPR predicts a geometry similar to the NO2- ion (AX2E1, bent, bond angle approx. 120°) but intermediate between NO2- and NO+2 (AX2E0, linear, 180°). In fact NO2 is bent with an angle of 134° which is closer to 120° than to 180°, in qualitative agreement with the theory.

Similarly chlorine dioxide (ClO2, AX2E1.5) has a geometry similar to ClO2- but intermediate between ClO2- and ClO+2.

Finally the methyl radical (CH3) is predicted to be trigonal pyramidal like the methyl anion (CH3-) 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.[33]

References

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  1. ↑ a b c d e f g Jolly, W. L. (1984). Modern Inorganic Chemistry. McGraw-Hill. pp. 77–90. ISBN 978-0-07-032760-3.
  2. ↑ http://rspa.royalsocietypublishing.org/content/176/965/153.abstract N.V.Sidgwick and H.M.Powell, Proc.Roy.Soc.A 176, 153–180 (1940) Bakerian Lecture. Stereochemical Types and Valency Groups
  3. ↑ R.J.Gillespie and R.S.Nyholm, Quart.Rev. 11, 339 (1957)
  4. ↑ R.J.Gillespie, J.Chem.Educ. 47, 18(1970)
  5. ↑ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae 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.
  6. ↑ a b c d e f g h i j k l m n Miessler, G. L.; Tarr, D. A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. pp. 54–62. ISBN 978-0-13-841891-5.
  7. ↑ Miessler, G. L.; Tarr, D. A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. p. 55. ISBN 978-0-13-841891-5.
  8. ↑ Petrucci, R. H.; W. S., Harwood; F. G., Herring (2002). General Chemistry: Principles and Modern Applications (8th ed.). Prentice-Hall. pp. 413–414 (Table 11.1). ISBN 978-0-13-014329-7.
  9. ↑ a b c d e f g h i j k l m n o p q r Housecroft, C. E.; Sharpe, A. G. (2005). Inorganic Chemistry (2nd ed.). Pearson. ISBN 978-0-130-39913-7.
  10. ↑ a b Baran, E. (2000). "Mean amplitudes of vibration of the pentagonal pyramidal XeOF5- and IOF2−5 anions". J. Fluorine Chem. 101: 61–63. doi:10.1016/S0022-1139(99)00194-3.
  11. ↑ Anderson, O. P. (1983). "Book reviews: Inorganic Stereochemistry (by David L. Kepert)" (PDF). Acta Crystallographica B. 39: 527–528. doi:10.1107/S0108768183002864. Retrieved 14 September 2020. based on a systematic quantitative application of the common ideas regarding electron-pair repulsion
  12. ↑ Brittin, W. E. (1945). "Valence Angle of the Tetrahedral Carbon Atom". J. Chem. Educ. 22 (3): 145. Bibcode:1945JChEd..22..145B. doi:10.1021/ed022p145.
  13. ↑ "Angle Between 2 Legs of a Tetrahedron" Template:Webarchive – Maze5.net
  14. ↑ a b c d Wiberg, E.; Holleman, A. F. (2001). Inorganic Chemistry. Academic Press. ISBN 978-0-12-352651-9.
  15. ↑ Power, Philip P. (September 2003). "Silicon, germanium, tin and lead analogues of acetylenes". Chem. Commun. (17): 2091–2101. doi:10.1039/B212224C. PMID 13678155.
  16. ↑ Nagase, Shigeru; Kobayashi, Kaoru; Takagi, Nozomi (6 October 2000). "Triple bonds between heavier Group 14 elements. A theoretical approach". J. Organomet. Chem. 11 (1–2): 264–271. doi:10.1016/S0022-328X(00)00489-7.
  17. ↑ Sekiguchi, Akira; Kinjō, Rei; Ichinohe, Masaaki (September 2004). "A Stable Compound Containing a Silicon–Silicon Triple Bond" (PDF). Science. 305 (5691): 1755–1757. Bibcode:2004Sci...305.1755S. doi:10.1126/science.1102209. PMID 15375262. S2CID 24416825. [dead link]
  18. ↑ A spectroscopic determination of the bond length of the LiOLi molecule: Strong ionic bonding, D. Bellert, W. H. Breckenridge, J. Chem. Phys. 114, 2871 (2001); doi:10.1063/1.1349424
  19. ↑ a b c d Models of molecular geometry, Gillespie R. J., Robinson E.A. Chem. Soc. Rev., 2005, 34, 396–407, doi: 10.1039/b405359c
  20. ↑ Wells A.F. (1984) Structural Inorganic Chemistry 5th edition Oxford Science Publications ISBN 0-19-855370-6
  21. ↑ Template:Housecroft2nd
  22. ↑ Peterson, W.; Holloway, H.; Coyle, A.; Williams, M. (Sep 1971). "Antiprismatic Coordination about Xenon: the Structure of Nitrosonium Octafluoroxenate(VI)". Science. 173 (4003): 1238–1239. Bibcode:1971Sci...173.1238P. doi:10.1126/science.173.4003.1238. ISSN 0036-8075. PMID 17775218. {{cite journal}}: Cite has empty unknown parameter: |month= (help)
  23. ↑ Hanson, Robert M. (1995). Molecular origami: precision scale models from paper. University Science Books. ISBN 0-935702-30-X.
  24. ↑ Kaupp, Martin (2001). ""Non-VSEPR" Structures and Bonding in d0 Systems". Angew. Chem. Int. Ed. Engl. 40 (1): 3534–3565. doi:10.1002/1521-3773(20011001)40:19<3534::AID-ANIE3534>3.0.CO;2-#.
  25. ↑ Gillespie, Ronald J.; Noury, Stéphane; Pilmé, Julien; Silvi, Bernard (2004). "An Electron Localization Function Study of the Geometry of d0 Molecules of the Period 4 Metals Ca to Mn". Inorg. Chem. 43 (10): 3248–3256. doi:10.1021/ic0354015. PMID 15132634.
  26. ↑ Gillespie, R. J. (2008). "Fifty years of the VSEPR model". Coord. Chem. Rev. 252 (12–14): 1315–1327. doi:10.1016/j.ccr.2007.07.007.
  27. ↑ Landis, C. R.; Cleveland, T.; Firman, T. K. (1995). "Making sense of the shapes of simple metal hydrides". J. Am. Chem. Soc. 117 (6): 1859–1860. doi:10.1021/ja00111a036.
  28. ↑ Landis, C. R.; Cleveland, T.; Firman, T. K. (1996). "Structure of W(CH3)6". Science. 272 (5259): 179–183. doi:10.1126/science.272.5259.179f.
  29. ↑ King, R. Bruce (2000). "Atomic orbitals, symmetry, and coordination polyhedra". Coord. Chem. Rev. 197: 141–168. doi:10.1016/s0010-8545(99)00226-x.
  30. ↑ Haalan, A.; Hammel, A.; Rydpal, K.; Volden, H. V. (1990). "The coordination geometry of gaseous hexamethyltungsten is not octahedral". J. Am. Chem. Soc. 112 (11): 4547–4549. doi:10.1021/ja00167a065.
  31. ↑ Template:Greenwood&Earnshaw
  32. ↑ Seijo, Luis; Barandiarán, Zoila; Huzinaga, Sigeru (1991). "Ab initio model potential study of the equilibrium geometry of alkaline earth dihalides: MX2 (M=Mg, Ca, Sr, Ba; X=F, Cl, Br, I)" (PDF). J. Chem. Phys. 94 (5): 3762. Bibcode:1991JChPh..94.3762S. doi:10.1063/1.459748. hdl:10486/7315.
  33. ↑ Anslyn E.V. and Dougherty D.A., Modern Physical Organic Chemistry (University Science Books, 2006), p.57
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