A more chemically intuitive way of writing the coordinates is to use the internal coordinates of a molecule (i.e. bond lengths, bond angles and torsion angles).

Internal coordinates are usually written as a Z-matrix.

Here is an example of a Z-matrix, for ethene (C₂H₄):

Atom	Atom		Distance		Bond		Torsion
number	type		(Å)		angle (º)		angle (º)
1	C
2	C	1	1.31
3	H	1	1.07	2	121.5
4	H	1	1.07	2	121.5	3	180.0
5	H	2	1.07	1	121.5	3	180.0
6	H	2	1.07	1	121.5	4	180.0

· The first line of the Z-matrix defines atom number 1 (a carbon atom here).

· Atom 2 is also a carbon atom, and is at a distance of 1.31Å from atom 1 (the approximate length of a carbon-carbon double bond).

· The third column defines the atom to which the distance in column 4 refers, i.e. atom 3 (a hydrogen) is 1.07Å from atom 1 (the length of the C-H bond).

· Similarly the atom numbers in columns 5 and 7 define which atoms are involved in the bond angle and torsion angle (values given in columns 6 and 8 respectively).

· So, for example, atom number 6 is a hydrogen. It is 1.07Å from atom 2, the bond angle involves atoms 6-2-1, and the torsion angle is for atoms 6-2-1-4.

· Notice here that all the torsion angles (HCCH) are 180°, showing that the molecule is planar.

Next: internal coordinates (continued)