Example of z-matrix

Normally, one would not construct a z-matrix by hand, but use a drawing or modelling program (MODEL, SYBYL). All modelling programs have an interface to MOPAC, which means they will construct an input file. See the chapter 'Programs' for details.

In many cases however, especially in transition state modelling, it is necessary to make changes in the arbitrary z-matrices constructed by programs, e.g. to add certain variables or to introduce symmetry.
Therefore we will discuss the z-matrix in some more detail. The examples below follow the MOPAC input file format, the Gamess format will be discussed in Example 3.

A crude z-matrix for cyclopropane would look like this:

C   0.00    0.00    0.00  0  0  0
C   1.35    0.00    0.00  1  0  0
C   1.35   60.00    0.00  2  1  0
H   1.10  110.00  120.00  3  2  1
H   1.10  110.00  240.00  3  2  1
H   1.10  110.00  120.00  2  1  3
H   1.10  110.00  240.00  2  1  3
H   1.10  110.00  120.00  1  2  3
H   1.10  110.00  240.00  1  2  3
The first three atoms are defined by two distances and an angle.
The last three numbers on each line show the definition 'path': Carbon3, is defined by the distance to atom 2 (also a carbon), and an angle C3-C2-C1.
In general, the connectivity of the molecule will be followed in the z-matrix, and dihedrals will represent actual torsion angles, but this is not mandatory.
Any geometrical distance, angle or dihedral can be used, provided that all atoms are defined unambiguously and no conflicts arise.

A dihedral is required for the fourth atom.
Atom4, the first hydrogen, is defined by:
a distance of 1.10 A to carbon 3,
an angle H4-C3-C2 of 110.0 degrees and
a dihedral angle H4-C3-C2-C1 of 120.0 degrees.
Atom 5 follows the same path over atoms 3, 2, and 1. Only lower numbers than the current line, so already defined atoms, can be used in a path.
The remaining hydrogens are also defined over the carbon they are attached to.

In this z-matrix there are 3N-6, 21 variables.
However, because of symmetry, cyclopropane has only three degrees of freedom: the C-C distance, the C-H distance, and the H-C-H (or H-C-C) bond angle. The simplification can be accomplished by using dummy atoms and by applying symmetry.
See the part 1D:Applying symmetry and dummy atoms in MOPAC input files.

Or try to interpret a more complicated z-matrix.


Back to text of paragraph 1C.