## 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 C_{3}-C_{2}-C_{1}.

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 H_{4}-C_{3}-C_{2} of 110.0
degrees and

a dihedral angle
H_{4}-C_{3}-C_{2}-C_{1} 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.