Also available : French version

Essentials before you start

This page is written in basic HTML. No plug-ins are required to view this page. You can save the molecule file with the right mouse button. You will be able to see the molecule without connection with a visualization program like RasMol. In order to view molecular structures on line you will have to configure your browser and to acquire CHIME plug-in.
More information : click HERE

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.

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.

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

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

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.

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

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.

For example, molecules with multiple bonds :

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

Trigonal arrangement

We distinguish two families :

For example, molecules with single bonds :

Molecules with multiple bonds :

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

We distinguish three families :

For example molecules with simple bonds :

For example molecules with multiple bonds :

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

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 :

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 :

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.

For example molecules with single bonds :

Molecules and ions with multiple bonds :

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

We observe these families :

For example, molecules with single bonds :

Molecules with multiple bonds :

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.

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.

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.

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.

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