VSEPR method
by Gérard Dupuis and Nicole Berland
Lycée Faidherbe - LILLE



Also available : French version




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Introduction

The molecular constitution is all of the atoms linked with bonds. In the Lewis formula the bonds are represented with a dash between the two bonded atoms and a lone electron pair with a dash on the considered atom. The molecular geometrical shape is the arrangement of these atoms in the space. A lot of physical or chemical properties are the consequence of particular geometrical shape. In this chapter we are going to study the geometrical shape for some molecules or ions. We'll only see the simple cases where we can distinguish without ambiguity a central atom (noted A) and its peripheral atoms (noted X). We won't study molecules with a central atom which belongs to transition elements.

Experimental results

SO2 is very more soluble in water than CO2. This difference of behaviour in the macroscopic scale is explained in the microscopic scale by the geometrical shape of these molecules. CO2 and SO2 have each other two oxygen atoms bonded to a central atom. The IR spectrum shows that CO2 is linear whereas SO2 is triangular. So, the dipolar moment of SO2 is not equal to zero and this molecule can act with H2O, whereas the dipolar moment of CO2 is equal to zero because of the compensation of the dipolar moments of bonds.

CO2

SO2

A lot of physical and chemical methods determinate the molecular geometrical shape : RX, electronic and neutronic diffraction, UV, IR, Raman, microwave spectroscopy. RMN and RPE also permit to obtain precious information notably in the dynamic molecular estate. At the present time, we know with precision the bond lenghts and the angles between bonds for a lot of molecules. One of the important aspects for geometrical shape is to explain and to forsee this shape for selected molecules

Principles of the VSEPR method

Origin
In 1957 the canadian chemist R.J Gillespie (university Mc Master Hamilton, Ontario) took back british N. Sigdwick and H. Powell idea, and developped the theory of the valence shell electron pair repulsion VSEPR. This method prolongs in the geometrical shape aspect the description of the chemical bond by G. N. Lewis (1916).

The electrons in the valence shell of most stable molecules and ions are paired (some rare molecules like NO2 have unpaired electrons). The Pauli principle shows that only the electrons which own opposite spin quantic numbers move in the same space region, because they are described by the same orbital. These electrons can be grouped together in pairs. In the Lewis model, the bond between two atoms is described by a bonding electron pair. The electron pairs no employed in a bond are lone pairs or non bonding electron pair. Afterwards X indicate an atom attached to the central atom A and E a non-bonding pair on the central atom. In first approximation, mutiple bonds are treated like a single bond with only one shared pairs

Atoms attached to A : X

Non-bonding pair on A : E

Number

n

m

Basic principle
The first approximation of the theory is to liken electron pairs to ponctual electric charges. Each pair which belongs to the valence shell moves to a comparable distance from the atom center, so on the same sphere whose the center is the atom A. On this sphere, the position of the pairs is the consequence of their mutual repulsions. Although this is not an electrostatic interaction between ponctual charges (because the behaviour of electrons are governed by quantum mechanics) we obtain a correct result if we search the arrangement that gives maximum distances between electron pairs. At this first level of approximation, we don't distinguich bonding and non bonding electron pairs. In these conditions, the arrangement that minimizes the pair repulsions depends only the sum (m + n), and so, if we stop at the number six, we see these following geometrical figures.

m + n

Overall geometry

2

Linear

3

Trigonal

4

Tetrahedral

5

Trigonal bipyramidal

6

Octahedral

For these five geometrical figures, we'll see more arrangements of the electron pairs. We'll see molecules with single or multiple bonds.

The different arrangement of pairs

Linear arrangement

For example, molecules with simple bonds :

Beryllium, an element of the second column of the periodic classification, has for electronical configuration : [He] 2s2. It has two single bonds with two atoms in BeCl2.

BeCl2

AX2

For example, molecules with multiple bonds :

CO2

CS2

HCN

AX2

AX2

AX2

Exercise : draw the Lewis structure for the following molecules and verify their family and geometrical shape.

AX2

COS, C2H2

Trigonal arrangement

We distinguish two families :

AX3

AX2E

Trigonal planar

Bent

For example, molecules with single bonds :

B

Sn

[He] 2s2 2p1

[Kr] 4d10 5s2 5p2

BCl3

SnCl2

AX3

AX2E

Molecules with multiple bonds :

S

O

N

[Ne] 3s2 3p4

[He] 2s2 2p4

[He] 2s2 2p3

SO3

O3

NSF

AX3

AX2E

AX2E

Exercise : draw the Lewis structure for the following molecules and ions and verifiy their family and geometrical shape.

AX3

AX2E

BF3 , H2CO , COCl2 , C2H4 , (CO3)2-

SO2

Tetrahedral

We distinguish three families :

AX4

AX3E

AX2E2

Tetrahedral

Trigonal pyramidal

Bent

For example molecules with simple bonds :

Si

P

O

[Ne] 3s2 3p2

[Ne] 3s2 3p3

[He] 2s2 2p4

SiF4

PCl3

Cl2O

AX4

AX3E

AX2E2

For example molecules with multiple bonds :

P

S

[Ne] 3s2 3p1

[Ne] 3s2 3p4

POCl3

(SO4)2-

AX4

AX4

Exercise : draw the Lewis structure for the following molecules and ions. Verify their family and geometrical shape.

AX4

AX3E

AX2E2

CH4 , (NH4)+ , (S2O3)2-

NH3 , PH3 , (H3O)+

H2O , H2S , (NH2)-

Trigonal bipyramidal

The corners of the bipyramid aren't equivalent. We can split in axial (a) or equatorial (e) corners.

The problem can be resolve if we refine the hypothesis of the method. The non bonding and bonding pairs can be differently treated, indeed the position in the space of bonding pairs is controled by the field of the two bonding atoms, but the position of non bonding pairs is controled by only one atom : the central atom. And so, the volum of a non bonding E is higher than this of bonding S. The repulsion between pairs follows the order :

E-E (x) > E-S (y) > S-S (z)

A practical parameter to assess the importance of the repulsion between the pairs is the angle a between the directions of these pairs. This parameter allow to compare the energies of the two arrangements (1) and (2) when we count the interactions with the previous inegalities. If we only count the interactions when a £ 90° (we disregard the other one) we obtain :

Arrangement (1)

Arrangement (2)

The pair E acts with 2 atomes X

The pair E acts with 3 atomes X

The first arrangement is stabler than the second. The molecules that belong to this first arrangement, are called "disphenoïd" molecules, like SF4. Experimentally we don't know stereoisomer for this molecule.

A same study for the other possible trigonal bipyramidal shapes, shows that the lone pairs must preferably occupy the equatorial positions.

AX5

AX4E

AX3E2

AX2E3

Trigonal bipyramidal

Seesaw

T-shaped

Linear

For example molecules with single bonds :

P

S

Cl

I

[Ne] 3s2 3p3

[Ne] 3s2 3p4

[Ne] 3s2 3p5

[Kr] 4 d10 5s2 5p5

PCl5

SF4

ClF3

I3-

AX5

AX4E

AX3E

AX2E3

Molecules and ions with multiple bonds :

S

I

[Ne] 3s2 3p4

[Kr] 4 d105s2 5p5

SOF4

IO2F2-

AX5

AX4E

Exercise : draw the Lewis structure for these following molecules or ions, and verify their family and geometrical shape.

AX5

AX4E

PF3Cl2 , XeO3F2

XeO2F2

Octahedral arrangement

We observe these families :

AX6

AX5E

AX4E2

Octahedral

Square pyramidal

Square planar

For example, molecules with single bonds :

S

Br

I

[Ne] 3s2 3p4

[Kr] 3 d10 4s2 4p5

[Kr] 4 d10 5s2 5p5

SF6

BrF5

ICl4-

AX6

AX5E

AX4E2

Molecules with multiple bonds :

I

Xe

[Kr] 4 d10 5s2 5p5

 [Kr] 4 d10 5s2 5p6

IOF5

XeOF4

AX6

AX5E

Second order effects

Influence of the nature of electron pairs on the angles between bonds
It's logical to admit that the non-bonding pairs, less confined in the internuclear space than bonding pairs, occupy a higher volume. And so, we see a diminution of the angles between the bonds when we observe in the order CH4, NH3 and H2O.

CH4

NH3

H2O

109,5°

107°

104,5°

We observe the same evolution for the ionic derivatives of NH3 :

NH4+

NH3

NH2-

109,5°

107°

104°

Influence of the volume of the multiple bonds
The geometric form depends only on s bond. So we can class the molecules with p bonds in the same groups that these with only s bonds. But the volume occupied by the electrons depends on the number of p bonds, and then we observe a diminution of the opposite angle of the p bond.

For example in the trigonal arrangement, the molecules like HCHO and COCl2 have an angle between single bonds inferior to 120°.

HCHO

COCl2

115,8°

111,3°

In the tetraedric arrangement we observe a diminution of the angle between single bonds when in this order the central atom owns only single bonds, one double bond and one triple bond like in : SiF4, POF3 and NSF3.

SiF4

POF3

NSF3

109,5°

102°

98°

In the trigonal bipyramidal arrangement the angle FOF is inferior to 120° in SOF4.

SOF4

110°

Influence of the difference of electronegativity between atoms

There are two cases :

The first appears when for a same central atom we compare the angles between bonds with atoms X whose electronegativity increases like : PI3, PBr3, PCl3, PF3.

c (I)

c (Br)

c (Cl)

c (F)

2,66

2,96

3,16

3,98

c (I) < c (Br) < c (Cl) < c (F)

PI3

PBr3

PCl3

PF3

102°

101,5°

100,3°

97,8°

We observe a decrease of these angles. Indeed, the bonding electron pairs are moved near X which have a higher electronegativity than A, and then, confined near X, these pairs exert lower repulsions and the angles decrease.

The second case appears when for same bonding atoms X, we compare the angles between bonds for central atoms A whose electronegativity increases like AsH3, PH3, NH3.

c (As)

c (P)

c (N)

2,17

2,19

3,04

c (As) < c (P) < c (N)

AsH3

PH3

NH3

91,58°

93,83°

107°

We observe an increase of these angles. Indeed, the bonding electron pairs are moved near A which has an higher electronegativity than X and then confined near A these pairs exert higher repulsions and the angles increase.

Addition of the two effects : volume and electronegativity
The two effects seen can partially add or compensate. In molecules like C2H4 and C2F2H2, the angles between simple bonds are lower than 120°. This is because the volume of the double bonds is higher than the volume of single bonds. In C2F2H2 this diminution is higher than in C2H4 because F has an electronegativity higher than H and then the bonding pairs confined near F exert lower repulsions.

C2H4

C2H2F2

118°

109°

Non equivalence between axial and equatorial positions in trigonal bipyramidal geometry
We have already seen, that the equatorial and axial positions aren't equivalent in molecules like PF5 or PCl5. The interaction between bonding electron pairs in equatorial position is less than in axial position. So there is a decrease of the length for the equatorial bonds and an increase for the axial bonds.

Bond

P-Cléq

P-Clax

d (nm)

0,202

0,214

The non equivalence between axial and equatorial positions is visible when the bonding atoms X are different. For example, in PF3Cl2, Cl has a lower electronegativity than F and the electron pair that provides the bond between P and Cl occupies a higher volume than this between P and F and so, the molecule with Cl in equatorial positions is the stablest.

PCl5

PF3Cl2

PCl5

PF3Cl2

Remark : The same effect is observed in the octahedral arrangement. For AX5E molecules like BrF5 (square pyramidal), we observe a small diminution of the angle between bonds Br-Feq and Br-Fax (85° instead of 90°) due to a higher volume occupied by the non-bonding pair and the axial bond is longer that the equatorial ones.

Bond

Br-Feq

Br-Fax

d (nm)

0,177

0,168

Limits of VSEPR method

The VSEPR method often permits the correct prediction for the local arrangement of electron pairs arround an atom when this one is the central atom without ambiguity but for complex molecules it's more difficult to forsee the global geometry. For example it's impossible to forsee that C2H4 is a flat molecule or that in (allenes) the substituants are in perpendicular plane.

Morever, molecules aren't static objects, this is clear in molecules with pyramidal atoms like NH3 or PH3 . It exists some phenomenons more complex too, like the exchange between axial and equatorial positions in trigonal bipyramidal geometry (Berry's pseudo-rotation).


References

R. J Gillespie et R. S Nyholm - Quart. Rev., 1957, 11, 339.
R. J Gillespie - Actualité chimique, 1973, 4, 27.
R. J Gillespie - Molecular geometry, 1972. Van Nostrand Reihold, Londres.
G. Fontaine - Bulletin de l'union des physiciens n° 591 p. 559-568.
J. Sala- Pala - Bulletin de l'union des physiciens n° 648 p. 201-244.
N. N Greenwood and A. Earnshaw - Chemistry of the elements Pergamon Press 1984.

Links

VSEPR Theorie - Caroline Röhr, Universität Freiburg
VSEPR - by M. Lerner, Oregon State University
VSEPR - by Mark Winter, University of Sheffield
VSEPR - by John J. Nash, Purdue University


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