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Valence shell electron pair repulsion (VSEPR) theory is a model in chemistry used to predict the shape of individual 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" 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 developed.

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 Oxford Universitymarker. In 1957 Ronald Gillespie and Ronald Sydney Nyholm at University College Londonmarker refined this concept to build a more detailed theory capable of choosing between various alternative geometries.

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.

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.

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 , 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. 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 model.Landis, 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, (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 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.

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 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, and therefore their ability to repel other electron pairs, is greatest when the ligand has an electronegativity similar to, or greater than, the central atom. When the central atom 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, e.g. 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. 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.

See also



References

  1. Modern Inorganic Chemistry W.L. Jolly ISBN 0-07-032760-2
  2. VGS Box. Journal of Molecular Modeling, 1997, 3, 124-141.
  3. http://www.jstor.org/pss/97507 N.V.Sidgwick and H.M.Powell, Proc.Roy.Soc.A 176, 153-180 (1940) Bakerian Lecture. Stereochemical Types and Valency Groups
  4. R.J.Gillespie and R.S.Nyholm, Quart.Rev. 11, 339 (1957)
  5. R.J.Gillespie, J.Chem.Educ. 47, 18(1970)
  6. Models of molecular geometry, Gillespie R. J., Robinson E.A. Chem. Soc. Rev., 2005, 34, 396–407,
  7. Landis, C. K.; Cleveland, T.; Firman, T. K. Making sense of the shapes of simple metal hydrides. J. Am. Chem. Soc. 1995, 117, 1859-1860.
  8. Core Distortions and Geometries of the Difluorides and Dihydrides of Ca, Sr, and Ba Bytheway I, Gillespie R.J, Tang T.H., Bader R.F. Inorganic Chemistry, 34,9, 2407-2414, 1995
  9. 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
  10. Wells A.F. (1984) Structural Inorganic Chemistry 5th edition Oxford Science Publications ISBN 0-19-855370-6
  11. Catherine E. Housecroft, Alan G. Sharpe (2005), Inorganic Chemistry, Pearson Education, ISBN 0130399132


External links

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



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