VSEPR theoryFrom Wikipedia, the free encyclopediaValence shell electron pair repulsion (VSEPR) rules are a model in chemistry used to predict the shape ofindividual molecules based upon the extent of electron-pair electrostatic repulsion.It is also named Gillespie–Nyholm theory after its two main developers. The acronym "VSEPR" is sometimes pronounced "vesper" forease of pronunciation; however, the phonetic pronunciation is technically more correct.The premise of VSEPR is that the valence electron pairs surrounding an atom mutually repel each other, andwill therefore adopt an arrangement that minimizes this repulsion, thus determining the molecular geometry.The number of atoms bonded to a central atom plus the number of lone pairs of its nonbonding valenceelectrons is called its steric number.VSEPR theory is usually compared and contrasted with valence bond theory, which addresses molecularshape through orbitals that are energetically accessible for bonding. Valence bond theory concerns itself withthe formation of sigma and pi bonds. Molecular orbital theory is another model for understanding how atomsand electrons are assembled into molecules and polyatomic ions.VSEPR theory has long been criticized for not being quantitative, and therefore limited to the generation of"crude", even though structurally accurate, molecular geometries of covalent molecules. However, molecularmechanics force fields based on VSEPR have also been developed. Contents [hide]1 History2 Description3 AXE method4 Examples5 Exceptions o 5.1 Transition metal compounds o 5.2 Some AX2E0 molecules o 5.3 Some AX2E2 molecules o 5.4 Some AX6E1 and AX8E1molecules6 Odd-electron molecules7 VSEPR and localized orbitals8 See also9 References
10 Further reading11 External linksHistoryThe idea of a correlation between molecular geometry and number of valence electrons (both shared andunshared) was first presented in a Bakerian Lecture in 1940 by Nevil Sidgwick and Herbert Powell atthe University of Oxford. In 1957 Ronald Gillespie and Ronald Sydney Nyholm at University CollegeLondon refined this concept to build a more detailed theory capable of choosing between various alternativegeometries.DescriptionThe VSEPR rules mainly involve predicting the layout of electron pairs surrounding one or more central atomsin a molecule, which are bonded to two or more other atoms. The geometry of these central atoms in turndetermines the geometry of the larger whole.The number of electron pairs in the valence shell of a central atom is determined by drawing the Lewisstructure of the molecule, expanded to show all lone pairs of electrons, alongside protruding and projectingbonds. Where two or more resonance structures can depict a molecule, the VSEPR model is applicable to anysuch structure. For the purposes of VSEPR theory, the multiple electron pairs in a double bond or triplebond are treated as though they were a single "pair".These electron pairs are assumed to lie on the surface of a sphere centered on the central atom, and sincethey are negatively charged, tend to occupy positions that minimizes their mutual electrostatic repulsions bymaximizing the distance between them. The number of electron pairs, therefore, determine the overallgeometry that they will adopt.For example, when there are two electron pairs surrounding the central atom, their mutual repulsion is minimalwhen they lie at opposite poles of the sphere. Therefore, the central atom is predicted to adopta linear geometry. If there are 3 electron pairs surrounding the central atom, their repulsion is minimized byplacing them at the vertices of an equilateral triangle centered on the atom. Therefore, the predicted geometryis trigonal. Likewise, for 4 electron pairs, the optimal arrangement is tetrahedral.This overall geometry is further refined by distinguishing between bonding and nonbonding electron pairs. Abonding electron pair is involved in a sigma bond with an adjacent atom, and, being shared with that otheratom, lies farther away from the central atom than does a nonbonding pair (lone pair), which is held close to thecentral atom by its positively-charged nucleus. Therefore, the repulsion caused by the lone pair is greater thanthe repulsion caused by the bonding pair. As such, when the overall geometry has two sets of positions thatexperience different degrees of repulsion, the lone pair(s) will tend to occupy the positions that experience less
repulsion. In other words, the lone pair-lone pair (lp-lp) repulsion is considered to be stronger than the lonepair-bonding pair (lp-bp) repulsion, which in turn is stronger than the bonding pair-bonding pair (bp-bp)repulsion. Hence, the weaker bp-bp repulsion is preferred over the lp-lp or lp-bp repulsion.This distinction becomes important when the overall geometry has two or more non-equivalent positions. Forexample, when there are 5 electron pairs surrounding the central atom, the optimal arrangement is a trigonalbipyramid. In this geometry, two positions lie at 180° angles to each other and 90° angles to the other 3adjacent positions, whereas the other 3 positions lie at 120° to each other and at 90° to the first two positions.The first two positions therefore experience more repulsion than the last three positions. Hence, when there areone or more lone pairs, the lone pairs will tend to occupy the last three positions first.The difference between lone pairs and bonding pairs may also be used to rationalize deviations from idealizedgeometries. For example, the H2O molecule has four electron pairs in its valence shell: two lone pairs and twobond 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 regulartetrahedron, because the two lone pairs (whose density or probability envelopes lie closer to the oxygennucleus) exert a greater mutual repulsion than the two bond pairs.AXE methodThe "AXE method" of electron counting is commonly used when applying the VSEPR theory. The A representsthe central atom and always has an implied subscript one. The X represents the number of sigmabonds between the central atoms and outside atoms. Multiple covalent bonds (double, triple, etc.) count asone X. The E represents the number of lone electron pairs surrounding the central atom. The sum of X and E,known as the steric number, is also associated with the total number of hybridized orbitals used by valencebond theory.Based on the steric number and distribution of Xs and Es, VSEPR theory makes the predictions in thefollowing tables. Note that the geometries are named according to the atomic positions only and not theelectron arrangement. For example the description of AX2E1 as bent means that AX2 is a bent molecule withoutreference to the lone pair, although the lone pair helps to determine the geometry.
Steric Basic geometry 1 lone pair 2 lone pairs 3 lone pairs No. 0 lone pair2 Linear (CO2)3 Trigonal planar (BCl3) Bent (SO2)4 Bent (H2O) Tetrahedral (CH4) Trigonal pyramidal (NH3)5 Trigonal bipyramidal (PCl5) Seesaw (SF4) T-shaped (ClF3) Linear (I3-)
AX5E2 Pentagonal planar XeF5-AX6E0 Octahedral SF6, WCl6 PentagonalAX6E1 XeOF5−, IOF52−  pyramidal PentagonalAX7E0 IF7 bipyramidal SquareAX8E0 ZrF84-, ReF8- antiprismatic Tricapped trigonal prismaticAX9E0 OR ReH2− capped square 9 antiprismatic † Electron arrangement including lone pairs, shown in pale yellow
‡ Observed geometry (excluding lone pairs)When the substituent (X) atoms are not all the same, the geometry is still approximately valid, but the bondangles may be slightly different from the ones where all the outside atoms are the same. For example, thedouble-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 XAX angles are not all equal.As a tool in predicting the geometry adopted with a given number of electron pairs, an often used physicaldemonstration of the principle of minimal electrostatic repulsion utilizes inflated balloons. Through handling,balloons acquire a slight surface electrostatic charge that results in the adoption of roughly the samegeometries when they are tied together at their stems as the corresponding number of electron pairs. Forexample, five balloons tied together adopt the trigonal bipyramidal geometry, just as do the five bonding pairsof a PCl5 molecule (AX5) or the two bonding and three non-bonding pairs of a XeF2 molecule (AX2E3). Themolecular geometry of the former is also trigonal bipyramidal, whereas that of the latter is linear.ExamplesThe methane molecule (CH4) is tetrahedral because there are four pairs of electrons. The four hydrogen atomsare positioned at the vertices of a tetrahedron, and the bond angle is cos−1(-1/3) ≈ 109°28. This is referred toas an AX4 type of molecule. As mentioned above, A represents the central atom and X represents all of theouter atoms.The ammonia molecule (NH3) has three pairs of electrons involved in bonding, but there is a lone pair ofelectrons on the nitrogen atom. It is not bonded with another atom; however, it influences the overall shapethrough repulsions. As in methane above, there are four regions of electron density. Therefore, the overallorientation 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. The observedshape of the molecule is a trigonal pyramid, because the lone pair is not "visible" in experimental methods usedto determine molecular geometry. The shape of a molecule is found from the relationship of the atoms eventhough it can be influenced by lone pairs of electrons.A steric number of seven or greater is possible, but it occurs in uncommon compounds such as iodineheptafluoride (IF7) . The base geometry for a steric number of 7 is pentagonal bipyramidal.The most common geometry for a steric number of eight is a square antiprismatic geometry. Examples of thisinclude the octacyanomolybdate (Mo(CN)4−8) and octafluorozirconate (ZrF4− 8) anions.The nonahydridorhenate ion (ReH2−9) in potassium nonahydridorhenate is a rare example of a compound with a steric number of nine, which has a
tricapped trigonal prismatic geometry.Another example is the octafluoroxenate ion (XeF2− 8) in nitrosonium octafluoroxenate(VI) , although in this case one of the electron pairs is a lone pair, andtherefore the molecule actually has a distorted square antiprismatic geometry.Possible geometries for steric numbers of 10, 11, or 12 are bicapped square antiprismatic, octadecahedral,and icosahedral, respectively. No compounds with steric numbers this high involvingmonodentate ligands exist,and those involving multidentate ligands can often be analysed more simply as complexes with lower stericnumbers when some multidentate ligands are treated as a unit.ExceptionsThere are groups of compounds where VSEPR fails to predict the correct geometry.Transition metal compoundsHexamethyltungsten, a transition metal compound whose geometry is different from that predicted by VSEPR.Many transition metal compounds do not have the geometries predicted by VSEPR, which can be ascribed tothere being no lone pairs in the valence shell and the interaction of core d electrons with the ligands. Thestructure of some of these compounds, including metal hydrides and alkyl complexes suchas hexamethyltungsten, can be predicted correctly using the VALBOND theory, which is based on sd hybridorbitals and the 3-center-4-electron bondingmodel. Crystal field theory is another theory that can oftenpredict the geometry of coordination complexes.Some AX2E0 moleculesThe carbon atoms in mercury(II) fulminatehave bent geometries despite having no lone pairs.
The gas phase structures of the triatomic halides of the heavier members of group 2, (i.e., calcium, strontiumand 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 proposedby Gillespie that this is caused by interaction of the ligands with the electron core of the metal atom, polarisingit so that the inner shell is not spherically symmetric, thus influencing the moleculargeometry. Disilynes are also bent, despite having no lone pairs, as are the carbon atoms in mercury(II)fulminate.Some AX2E2 moleculesOne example is molecular lithium oxide, Li2O, which is linear rather than being bent, and this has beenascribed to the bondings being in essence ionic, leading to strong repulsion between the lithium atoms. 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°). Gillespies rationalisation is that the localisation of the lone pairs, andtherefore their ability to repel other electron pairs, is greatest when the ligand has an electronegativity similarto, 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 strongerligand-ligand repulsion (-SiH3 is a relatively large ligand compared to the examples above), gives the larger-than-expected Si-O-Si bond angle.Some AX6E1 and AX8E1 moleculesXenon hexafluoride, which has a regular octahedral geometry despite containing a lone pair.Some AX6E1 molecules, e.g. xenon hexafluoride (XeF6) and the Te(IV) and Bi(III) anions, TeCl62−, TeBr62−,BiCl63−, BiBr63− and BiI63−, are regular octahedra and the lone pair does not affect the geometry. Onerationalization is that steric crowding of the ligands allows no room for the non-bonding lone pair; anotherrationalization is the inert pair effect. Similarly, the octafluoroxenate anion (XeF82-) is a square antiprism andnot a distorted square antiprism (as predicted by VSEPR theory for an AX8E1 molecule), despite having a lonepair.
Odd-electron moleculesThe VSEPR theory can be extended to molecules with an odd number of electrons by treating the unpairedelectron as a "half electron pair". In effect, the odd electron has an influence on the geometry which is similar toa full electron pair, but less pronounced so that the geometry may be intermediate between the molecule with afull 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 theNO2- ion (AX2E1, bent, bond angle approx. 120°) but intermediatebetween NO2- and NO2+ (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 ClO2+.Finally the methyl radical (CH3) is predicted to be trigonal pyramidal like the methyl anion (CH3-) but with alarger bond angle as in the trigonal planar methyl cation (CH3+). However in this case the VSEPR prediction isnot quite true as CH3 is actually planar, although its distortion to a pyramidal geometry requires very littleenergy.VSEPR and localized orbitalsThe VSEPR theory places each pair of valence electrons in a bond or a lone pair found in a local region of themolecule. Molecular orbital theory yields a set of orbitals that have the symmetry of the molecule and that aredelocalized over several atoms. However these orbitals can be transformed into an equivalent set of localizedmolecular orbitals.In the water molecule for example, molecular orbital calculations yield two lone pairs, one an s-p hybrid in theplane of the molecule and one a pure p orbital perpendicular to this plane. These orbitals can be combined intotwo sp3 nonbonding orbitals, equivalent to each other, which can be compared to the lone pairs of VSEPRtheory. Likewise, there are two calculated bonding orbitals each extending over all three atoms, which can becombined into two localized orbitals, one for each bond.The delocalized and localized orbitals provide completely equivalent descriptions of the ground state, since thetotal wavefunction for all electrons is a Slater determinant, which is unchanged by the transformation of theorbitals.