VSEPR theory

'''Valence shell electron pair repulsion (VSEPR) theory''' is a model (abstract)|model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion''Modern Inorganic Chemistry'' WL Jolly ISBN 0-07-032760-2 It is also named '''Ronald Gillespie|Gillespie-Sir Ronald Sydney Nyholm|Nyholm theory''' after its two main developers The acronym "VSEPR" is sometimes pronounced "vesper" for ease of pronunciation
The premise of VSEPR is that the valence electron pairs surrounding an atom mutually repel each other and will therefore adopt an arrangement that minimizes this repulsion thus determining the molecular geometry The number of electron pairs surrounding an atom both bonding and nonbonding is called its steric number
VSEPR theory is usually compared and contrasted with valence bond theory which addresses molecular shape through orbitals that are energetically accessible for bonding Valence bond theory concerns itself with the formation of sigma and pi bonds Molecular orbital theory is another model for understanding how atoms and 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 molecular mechanics force fields based on VSEPR have also been developedVGS Box Journal of Molecular Modeling 1997 3, 124-141

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 Sidgwick and Powellhttp://wwwjstororg/pss/97507 NVSidgwick and HMPowell ProcRoySocA 176 153-180 (1940) Bakerian Lecture Stereochemical Types and Valency Groups In 1957 Gillespie and Ronald Nyholm|Nyholm] refined this concept to build a more detailed theory capable of choosing between various alternative geometriesRJGillespie and RSNyholm QuartRev 11, 339 (1957) RJGillespie JChemEduc 47, 18(1970)

Description

VSEPR theory mainly involves predicting the layout of electron pairs surrounding one or more central atoms in a molecule which are bonded to two or more other atoms The geometry of these central atoms in turn determines the geometry of the larger whole
The number of electron pairs in the valence shell of a central atom is determined by drawing the Lewis structure of the molecule expanded to show all lone pairs of electrons alongside protruding and projecting bonds Where two or more resonance structures can depict a molecule the VSEPR model is applicable to any such structure For the purposes of VSEPR theory the multiple electron pairs in a multiple bond 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 since they are negatively charged tend to occupy positions that minimizes their mutual electrostatic repulsions by maximising the distance between them The number of electron pairs therefore determine 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 a triangle centered on the atom Therefore the predicted geometry is trigonal Similarly for 4 electron pairs the optimal arrangement is tetrahedral
This overall geometry is further refined by distinguishing between bonding and nonbonding electron pairs A bonding electron pair is involved in a sigma bond with an adjacent atom and being shared with that other atom lies farther away from the central atom than does a nonbonding pair (lone pair) which is held close to the central atom by its positively-charged nucleus Therefore the repulsion caused by the lone pair is greater than the repulsion caused by the bonding pair As such when the overall geometry has two sets of positions that experience 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 lone pair-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 For example when there are 5 electron pairs surrounding the central atom the optimal arrangement is a trigonal bipyramid In this geometry two positions lie at 180° angles to each other and 90° angles to the other 3 adjacent 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 are one or more lone pairs the lone pairs will tend to occupy the last three positions first

AXE Method

The "AXE method" of electron counting is commonly used when applying the VSEPR theory The A represents the central atom and always has an implied subscript one The X represents the number of sigma bonds between the central atoms and outside atoms Multiple covalent bonds (double triple etc) count as one 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 valence bond theory
Based on the steric number and distribution of X's and E's VSEPR theory makes the following predictions:

Steric No	Basic Geometry 0 lone pair	1 lone pair	2 lone pairs	3 lone pairs
2	linear
3	trigonal planar	bent
4	tetrahedral	trigonal pyramid	bent
5	trigonal bipyramid	seesaw	T-shaped	linear
6	octahedral	square pyramid	square planar
7	pentagonal bipyramid	pentagonal pyramid

Molecule Type	Shape	Electron arrangement†	Geometry‡	Examples
AX1En	Diatomic			HF O2
AX2E0	Linear			BeCl2 HgCl2 CO2
AX2E1	Bent			NO2− SO2 O3
AX2E2	Bent			H2O OF2
AX2E3	Linear			XeF2 I3−
AX3E0	Trigonal planar			BF3 CO32− NO3− SO3
AX3E1	Trigonal pyramidal			NH3 PCl3
AX3E2	T-shaped			ClF3 BrF3
AX4E0	Tetrahedral			CH4 PO43− SO42− ClO4−
AX4E1	Seesaw			SF4
AX4E2	Square Planar			XeF4
AX5E0	Trigonal Bipyramidal			PCl5
AX5E1	Square Pyramidal			ClF5 BrF5
AX6E0	Octahedral			SF6
AX6E1	Pentagonal pyramidal			XeOF|5}}− 2−
AX7E0	Pentagonal bipyramidal			IF7

† 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 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° Similarly SOCl₂ is AX₃E₁ but because the X substituents are not identical the XAX angles are not all equal

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' This is referred to as an AX₄ type of molecule As mentioned above A represents the central atom and X represents all of the outer atoms
The ammonia molecule (NH₃) has three pairs of electrons involved in bonding but there is a lone pair of electrons on the nitrogen atom 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. The observed shape of the molecule is a trigonal pyramid because the lone pair is not "visible" in experimental methods used to determine molecular geometry The shape of a molecule is found from the relationship of the atoms even though it can be influenced by lone pairs of electrons
A steric number of seven is possible but it occurs in uncommon compounds such as iodine heptafluoride The base geometry for this is pentagonal bipyramidal
The most common geometry for a steric number of eight is a square antiprismatic geometry Examples of this include the octafluoroxenate ion (XeF) in nitrosonium octafluoroxenate octacyanomolybdate (Mo(CN)) and octafluorozirconate (ZrF)

Exceptions

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

Transition metal compounds

Many transition metal compounds do not have geometries explained by VSEPR which can be ascribed to there being no lone pairs in the valence shell and the interaction of core d electrons with the ligands Models of molecular geometry Gillespie R. J., Robinson EA Chem Soc Rev 2005 34, 396–407 The structure of some of these compounds including metal hydrides and alkyl complexes such as hexamethyltungsten can be predicted correctly using the VALBOND theory which is based on sd hybrid orbitals and the 3-center-4-electron bonding modelLandis C. K.; Cleveland T.; Firman T. K. Making sense of the shapes of simple metal hydrides J Am. Chem Soc 1995 117 1859-1860Landis C. K.; Cleveland T.; Firman T. K. Structure of W(CH₃)₆ Science 1996 272 182-183 Crystal field theory is another theory that can often predict the geometry of coordination complexes

Group 2 halides

The gas phase structures of the triatomic halides of the heavier members of group 2 (ie 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 caused by interaction of the ligands with the electron core of the metal atom polarising it so that the inner shell is not spherically symmetric thus influencing the molecular geometry Core Distortions and Geometries of the Difluorides and Dihydrides of Ca, Sr, and Ba Bytheway I, Gillespie RJ Tang TH Bader RF Inorganic Chemistry 349 2407-2414 1995

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 being essentially ionic leading to strong repulsion between the lithium atomsA spectroscopic determination of the bond length of the LiOLi : Strong ionic bonding D. Bellert W. H. Breckenridge J. Chem Phys 114 2871 (2001); doi:101063/113494243)₂ with an Si-O-Si angle of 1441° which compares to the angles in Cl₂O (1109°) (CH₃)₂O (1117°)and N(CH₃)₃ (1109°) Gillespies 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 the central atomatom is more electronegative as in O(SiH₃)₂ the lone pairs are less well localised have a weaker repulsive effect and this 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

Some AX₆E₁molecules

Some AX₆E₁ molecules eg 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 Wells AF (1984) Structural Inorganic Chemistry 5th edition Oxford Science Publications ISBN 0-19-855370-6 One rationalisation is that steric crowding of the ligands allows no room for the non-bonding lone pairinert pair effectCatherine E. Housecroft Alan G. Sharpe (2005) Inorganic Chemistry Pearson Education ISBN 0130399132

See also

• Molecular geometry
• Linear combination of atomic orbitals
• Molecular modelling
• List of software for mechanics modeling|Software for molecular modeling]
• Valency interaction formula

References

External links

• 3D Chem - Chemistry Structures and 3D Molecules
• IUMSC - Indiana University Molecular Structure Center