Inorganic Chemistry/Chemical Bonding/VSEPR theory

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.Jolly W. L. Modern Inorganic Chemistry McGraw-Hill 1984 77–90 978-0-07-032760-3 https://archive.org/details/trent_0116300649799/page/77 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 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.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 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.R.J.Gillespie and R.S.Nyholm, Quart.Rev. 11, 339 (1957)R.J.Gillespie, J.Chem.Educ. 47, 18(1970) 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 (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.Petrucci R. H. Harwood W. S. Herring F. G. General Chemistry: Principles and Modern Applications Prentice-Hall 8th 2002 978-0-13-014329-7410–417 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.410–417G. L. Miessler D. A. Tarr Inorganic Chemistry 2nd Prentice-Hall 1999 54–62 978-0-13-841891-5 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. Steric number thumb|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.G. L. Miessler D. A. Tarr Inorganic Chemistry 2nd Prentice-Hall 1999 55 978-0-13-841891-5 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 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.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 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 A bond of higher bond order also exerts greater repulsion since the pi bond electrons contribute. 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, CO 3 2−, 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 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.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 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 numberMolecular geometryPetrucci R. H. Harwood W. S. Herring F. G. General Chemistry: Principles and Modern Applications Prentice-Hall 8th 2002 413–414 (Table 11.1) 978-0-13-014329-7 0 lone pairsMolecular geometry413–414 1 lone pairMolecular geometry413–414 2 lone pairsMolecular geometry413–414 3 lone pairs2 128px Linear      3 128px Trigonal planar 128px Bent    4 128px Tetrahedral 128px Trigonal pyramidal 128px Bent   5 128px Trigonal bipyramidal 128px Seesaw 128px T-shaped 128px Linear6 128px Octahedral 128px Square pyramidal 128px Square planar  7 128px Pentagonal bipyramidal 128px Pentagonal pyramidal 128px Pentagonal planar  8 Square antiprismatic       Molecule type Shape413–414 Electron arrangement413–414 including lone pairs, shown in pale yellow Geometry413–414 excluding lone pairs Examples AX2E0 Linear 100px 100px BeCl2, CO2 AX2E1 Bent 100px 100px NO 2 -, SO2,413–414 O3, CCl2 AX2E2 Bent 100px 100px H2O,413–414 OF2448 AX2E3 Linear 100px 100px XeF2,413–414 I 3 -,483 XeCl2 AX3E0 Trigonal planar 100px 100px BF3,413–414 CO 3 2-,368 NO 3 -, SO3 AX3E1 Trigonal pyramidal 100px 100px NH3,413–414 PCl3407 AX3E2 T-shaped 100px 100px ClF3,413–414 BrF3481 AX4E0 Tetrahedral 100px 100px CH4,413–414 PO 4 3-, SO 4 2-, ClO 4 -, XeO4499 AX4E1 Seesaw or disphenoidal 100px 100px SF4413–41445 AX4E2 Square planar 100px 100px XeF4413–414 AX5E0 Trigonal bipyramidal 100px 100px PCl5413–414 AX5E1 Square pyramidal 100px 100px ClF5,481 BrF5,413–414 XeOF4 AX5E2 Pentagonal planar 100px 100px XeF 5 -498 AX6E0 Octahedral 100px 100px SF6413–414 AX6E1 Pentagonal pyramidal 100px 100px XeOF 5 -, IOF 5 2- E. Mean amplitudes of vibration of the pentagonal pyramidal XeOF 5 - and IOF 5 2- anions J. Fluorine Chem. 101 Baran 61–63 2000 10.1016/S0022-1139(99)00194-3 AX7E0 Pentagonal bipyramidal 100px 100px IF7 AX8E0 Square antiprismatic 100px 100px IF 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(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.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.Anderson O. P. Book reviews: Inorganic Stereochemistry (by David L. Kepert) Acta Crystallographica B 1983 39 527–528 10.1107/S0108768183002864 https://journals.iucr.org/b/issues/1983/04/00/a22157/a22157.pdf 14 September 2020 based on a systematic quantitative application of the common ideas regarding electron-pair repulsion free 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 100px HgCl2 ML3 Trigonal planar 100px ML4 Tetrahedral 100px NiCl 4 2- ML5 Trigonal bipyramidal 100px Fe(CO) 5 Square pyramidal 100px MnCl52− ML6 Octahedral 100px WCl6659 ML7 Pentagonal bipyramidal 100px ZrF 7 3- Capped octahedral 100px MoF 7 - Capped trigonal prismatic 100px TaF 7 2- ML8 Square antiprismatic 100px ReF 8 - Dodecahedral 100px Mo(CN) 8 4- Bicapped trigonal prismatic 100px ZrF 8 4- ML9 Tricapped trigonal prismatic 110px ReH 9 2-254 Capped square antiprismatic 110px Examples 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′. Brittin W. E. 1945 Valence Angle of the Tetrahedral Carbon Atom J. Chem. Educ. 22 3 145 10.1021/ed022p145 1945JChEd..22..145B "Angle Between 2 Legs of a Tetrahedron" https://web.archive.org/web/20181003122307/http://maze5.net/?page_id=367 2018-10-03 – Maze5.net This is referred to as an AX4 type of molecule. As mentioned above, A represents the central atom and X represents an outer atom.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.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.410–417 By definition, the molecular shape or geometry describes the geometric arrangement of the atomic nuclei only, which is trigonal-pyramidal for NH3.410–417 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. The most common geometry for a steric number of 8 is a square antiprismatic geometry. E. Wiberg A. F. Holleman Inorganic Chemistry Academic Press 2001 978-0-12-352651-91165 Examples of this include the octacyanomolybdate (Mo(CN) 8 4-) and octafluorozirconate (ZrF 8 4-) anions.1165 The nonahydridorhenate ion (ReH 9 2-) in potassium nonahydridorhenate is a rare example of a compound with a steric number of 9, which has a tricapped trigonal prismatic geometry.Housecroft C. E. Sharpe A. G. Inorganic Chemistry 2nd Pearson 2005 978-0-130-39913-7254 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 AX2E0 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. Silicon, germanium, tin and lead analogues of acetylenes Philip P. Power Chem. Commun. September 2003 17 2091–2101 10.1039/B212224C 13678155 Triple bonds between heavier Group 14 elements. A theoretical approach Shigeru Nagase Kaoru Kobayashi Nozomi Takagi J. Organomet. Chem. 6 October 2000 11 1–2 264–271 10.1016/S0022-328X(00)00489-7 A Stable Compound Containing a Silicon–Silicon Triple Bond Akira Sekiguchi Rei Kinjō Masaaki Ichinohe Science September 2004 305 5691 1755–1757 10.1126/science.1102209 15375262 2004Sci...305.1755S 24416825 http://people.ok.ubc.ca/wsmcneil/339/Sci2004.pdfDecember 2017 InternetArchiveBot yes Some AX2E2 molecules 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.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); 10.1063/1.1349424 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. 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.Models of molecular geometry, Gillespie R. J., Robinson E.A. Chem. Soc. Rev., 2005, 34, 396–407, 10.1039/b405359c 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, TeCl 6 2-, TeBr 6 2-, BiCl 6 3-, BiBr 6 3- and BiI 6 3-, are octahedra rather than pentagonal pyramids, and the lone pair does not affect the geometry to the degree predicted by VSEPR.Wells A.F. (1984) Structural Inorganic Chemistry 5th edition Oxford Science Publications 0-19-855370-6 One rationalization is that steric crowding of the ligands allows no room for the non-bonding lone pair; another rationalization is the inert pair effect. Similarly, the octafluoroxenate ion (XeF 8 2-) in nitrosonium octafluoroxenate(VI)498 A. H. M. Antiprismatic Coordination about Xenon: the Structure of Nitrosonium Octafluoroxenate(VI) W. Holloway Coyle 173 Science 4003 1238–1239 0036-8075 10.1126/science.173.4003.1238 Williams 17775218 Peterson Sep 1971 1971Sci...173.1238P Molecular origami: precision scale models from paper Robert M. Hanson University Science Books 1995 0-935702-30-X 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 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 (PtCl 4 2-) 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 d-contribution 200px|thumb|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. "Non-VSEPR" Structures and Bonding in d0 Systems Martin Kaupp Angew. Chem. Int. Ed. Engl. 2001 40 1 3534–3565 10.1002/1521-3773(20011001)40:19<3534::AID-ANIE3534>3.0.CO;2-# Gillespie found that this interaction produces bonding pairs that also occupy the respective antipodal points (ligand opposed) of the sphere. An Electron Localization Function Study of the Geometry of d0 Molecules of the Period 4 Metals Ca to Mn Ronald J. Gillespie Stéphane Noury Julien Pilmé Bernard Silvi Inorg. Chem. 2004 43 10 3248–3256 10.1021/ic0354015 15132634 Gillespie R. J. 2008 Fifty years of the VSEPR model Coord. Chem. Rev. 252 12–14 1315–1327 10.1016/j.ccr.2007.07.007 This phenomenon is an electronic effect resulting from the bilobed shape of the underlying sdx hybrid orbitals. 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 10.1021/ja00111a036 Landis C. R. Cleveland T. Firman T. K. 1996 Structure of W(CH3)6 Science 272 5259 179–183 10.1126/science.272.5259.179f free The repulsion of these bonding pairs leads to a different set of shapes. Molecule type Shape Geometry Examples ML2 Bent 100px VO 2 + ML3 Trigonal pyramidal 100px CrO3 ML4 Tetrahedral 100px TiCl4598–599 ML5 Square pyramidal 100px Ta(CH3)5 Coord. Chem. Rev. 197 2000 141–168 Atomic orbitals, symmetry, and coordination polyhedra R. Bruce King 10.1016/s0010-8545(99)00226-x ML6 C3v Trigonal prismatic 100px W(CH3)6Haalan A. Hammel A. Rydpal K. Volden H. V. J. Am. Chem. Soc. 1990 112 4547–4549 The coordination geometry of gaseous hexamethyltungsten is not octahedral 10.1021/ja00167a065 11 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. 10.1063/1.459748 Ab initio model potential study of the equilibrium geometry of alkaline earth dihalides: MX2 (M=Mg, Ca, Sr, Ba; X=F, Cl, Br, I) 1991 Seijo, Luis J. Chem. Phys. 94 3762 Barandiarán Zoila Huzinaga Sigeru 5 1991JChPh..94.3762S https://repositorio.uam.es/bitstream/10486/7315/1/41581_jchemphysseijo_91_jcp_94_3762.pdf 10486/7315 free 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". 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 NO 2 - ion (AX2E1, bent, bond angle approx. 120°) but intermediate between NO 2 - 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 ClO 2 - but intermediate between ClO 2 - and ClO 2 +. Finally the methyl radical (CH3) 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 CH3 is actually planar, although its distortion to a pyramidal geometry requires very little energy.Anslyn E.V. and Dougherty D.A., Modern Physical Organic Chemistry (University Science Books, 2006), p.57 References