The AXE system of determining the shape of the molecules

The AXE system

American General Chemistry textbooks – but for some reasom not British ones – adopt the excellent AXmEn system, where A is the central atom, m the number of ligands X, and n the number of nonbonded lone-pairs of electrons, E, about the central atom.

In this system:

methane, CH4, is AX4
ammonia, H3N:, is AX3E1
water, H2O, is AX2E2

Note that different AXmEn designations can give rise to the same overall geometry or shape:

For example:

AX2E1 and AX2E2 both give rise to bent or angular geometries
AX2 and AX2E3 both give rise to linear geometries

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Patterns in AXE Space

The AXE system gives rise to a pattern, from which the various atomic geometric shapes can be determined/assigned:

Determining the Shape of Simple Molecules or Ions

• A molecule consists of 2 or more atoms joined by covalent bonds.
• The shape of a molecule is a description of the way the atoms in the molecule occupy space.
• A diatomic molecule, a molecule composed of only 2 atoms, must always be linear in shape as the centers of the 2 atoms will always be in a straight line.
• 'Electron Cloud' Repulsion Theory (Valence Shell Electron Pair Repulsion, VSEPR) is used to predict shapes and bond angles of simple molecules

1. an 'electron cloud' may be a single, double or triple bond, or a lone pair of electrons
2. a lone pair of electrons is a non-bonding pair of electrons
3. 'electron clouds' are negatively charged since the electrons are negatively charged, so electron clouds repel one another and try to get as far away from each other as possible
4. lone pairs of electrons exert a greater repelling effect than bonding pairs do
5. lone pair-bonding pair repulsion is greater than bonding pair-bonding pair repulsion
6. lone pair-lone pair repulsion > lone pair-bonding pair repulsion > bonding pair-bonding pair repulsion

Total Number of electron pairs	Arrangement of electron pairs	Number of bonding pairs of electrons	Number of lone pairs of electrons	Shape of Molecule	Name of Shape	Bond Angle	Examples
not applicable	linear	1	not applicable		linear	180o	H2, HCl
2	linear	2	0		linear	180o	CO2, HCN
3	trigonal planar	3	0		triganol planar	120o	BCl3, AlCl3
4	tetrahedral	4	0		tetrahedral	109.5o	CH4, SiF4
		3	1		trigonal pyramidal	<109.5o (bond angles in ammonia, NH3, are 107o)	NH3, PCl3
		2	2		bent	<109.5o (bond angles in water, H2O, are 105o)	H2O, SCl2
5	trigonal bipyramidal	5	0		trigonal bipyramidal	120o in the trigonal planar part of the molecule, 90o for the others	PCl5
6	octahedral	6	0		octahedral	90o	SF6