### Cyclohexane z-matrix

The chair conformation of cyclohexane contains a symmetry axis (S_{6}),
and perpendicular to it, a number of C_{2} axes. These axes
lie in the 'mean' plane of the carbon skeleton, which disects the
carbon-carbon bonds.

The main difference between cyclohexane and cyclopropane is the
fact that this plane is not a mirror plane. Therefore, there are more
independent degrees of freedom.

One way to place dummy atoms is to take the points where the S_{6}
axis crosses the two planes, parallel to the 'mean' plane, defined
by two sets of three C atoms:

the C1-C3-C5 plane and the C2-C4-C6 plane.

The distance between XX1 and XX2 is the variable which determines
the puckering of the ring, i.e. the distance of each C to the
'mean' plane.

The degrees of freedom (variables) are:

- the XX1-XX2 distance (determines the C-C-C bond angle)
- the C-XX distance (determines C-C bond length)
- the C-H
_{ax} bond distance
- the C-H
_{eq} bond distance
- the H-C-H bond angle
- the H-C-C-H torsion angles (insofar not determined by the previous variables)

In the input file below, one such a scheme is implemented.

There are six variables, of which two deserve an explanation: the hydrogen
angles.

For the axial ones: H9-C3-XX1 is close to 90 degrees, but not exactly 90 by
definition.

The equatorial H15 angle is the second variable. In combination these two
angles determine the H-C-H angle and the H-C-C-H torsion angles.

All torsion angles in the z-matrix are constants!
AM1 T=3600 SYMMETRY NOINTER NOXYZ
z-matrix for cyclohexane
with symmetry
XX 0.00 0 0.00 0 0.00 0 0 0 0 two dummy atoms
XX 1.00 1 0.00 0 0.00 0 1 0 0
C 1.40 1 90.00 0 0.00 0 1 2 0 the carbon skeleton
C 1.40 0 90.00 0 120.00 0 1 2 3 three around XX1
C 1.40 0 90.00 0 240.00 0 1 2 3
C 1.40 0 90.00 0 60.00 0 2 1 5 three around XX2
C 1.40 0 90.00 0 120.00 0 2 1 6
C 1.40 0 90.00 0 240.00 0 2 1 6
H 1.10 1 90.00 1 180.00 0 3 1 2 three axial H's
H 1.10 0 90.00 0 180.00 0 4 1 2 on XX1 side
H 1.10 0 90.00 0 180.00 0 5 1 2
H 1.10 0 90.00 0 180.00 0 6 2 1 three on XX2 side
H 1.10 0 90.00 0 180.00 0 7 2 1
H 1.10 0 90.00 0 180.00 0 8 2 1
H 1.10 1 160.00 1 0.00 0 3 1 2 six equatorial H's
H 1.10 0 160.00 0 0.00 0 4 1 2
H 1.10 0 160.00 0 0.00 0 5 1 2
H 1.10 0 160.00 0 0.00 0 6 2 1
H 1.10 0 160.00 0 0.00 0 7 2 1
H 1.10 0 160.00 0 0.00 0 8 2 1
0 0.00
3 1 4 5 6 7 8 symmetry lines
9 1 10 11 12 13 14
9 2 10 11 12 13 14
15 1 16 17 18 19 20
15 2 16 17 18 19 20

The result, together with a discussion, can be found on a
separate page.
If you have developed an alternative way of applying symmetry in the
z-matrix, please let me know!