Z-matrix

The Z-matrix is a way to represent a system built of atoms. It provides a description of each atom in a molecule in terms of its atomic number, bond length, bond angle, and dihedral angle, the so-called internal coordinates.

Z-matrices can be converted to cartesian coordinates and back, the information content is identical. They are used for creating input geometries for molecular systems in many molecular modelling and computational chemistry programs. A skillfull choice of internal coordinates can make the interpretation of results straightforward. Also, since Z-matrices contain molecular connectivity information, quantum chemical calculations such as geometry optimization may be performed faster, because an educated guess is available for an initial Hessian matrix, and more natural internal coordinates are used rather than Catesians.

Example

The methane molecule can be described by the following cartesian coordinates (in angstroms):

C     0.000000     0.000000     0.000000
H     0.000000     0.000000     1.089000
H     1.026719     0.000000    -0.363000
H    -0.513360    -0.889165    -0.363000
H    -0.513360     0.889165    -0.363000

The corresponding Z-matrix, which statrs from the carbon atom, could look like this:

C
H   1 1.089000     
H   1 1.089000  2  109.4710      
H   1 1.089000  2  109.4710  3  120.0000   
H   1 1.089000  2  109.4710  3  240.0000