# Exercise 5

### Topic: Z-matrix with dummy atom

*Dummy atoms* are auxiliary points in three-dimensional
space which facilitate the definition of the proper structural
parameters and thus the construction of a Z-matrix.
Dummy atoms neither feature a charged nucleus nor a basis set.
They are fully ignored in the determination of the molecule's
symmetry and in quantum chemical calculations.
Dummy atoms are invoked by the symbol "X".

In this exercise a dummy atom shall be used to avoid bond angles
of 180 degrees in the Z-matrix of carbon dioxide.
Since that molecule is linear the O-C-O angle has 180 degrees.
For geometry optimizations in user-specified internal coordinates
Gaussian94 does not accept angles of 180 and 0 degrees in the
Z-matrix.
With the help of a dummy atom it is easy to devide the O-C-O
angle into two parts of less than 180°. Just use the angles
X-C-O_{1} and X-C-O_{2} in the Z-matrix.
The figure below shows a possible solution with a purple
colored dummy atom.

### Exercise

Construct a Z-matrix for carbon dioxide, CO_{2}.
Use a dummy atom to avoid an angle of 0 or 180 degrees in the
Z-matrix.
Additionally, linearity of the molecular structure shall be
preserved with the two C-O bonds remaining at equal length
during geometry optimization.
Use a C-O distance of 1.143 Å.
This value results from a Hartree-Fock geometry optimization using
basis set 6-31G(d).

### Remark

Gaussian94 accepts bond angles of 0 and 180 degrees if
*redundant coordinates* are used.
In this case Gaussian will automatically define its own set of
structural parameters.
Since this course also aims at an improved ability of handling
three-dimensional structures and molecular symmetry we will
refrain from using this automatic tool.

### Hints

The distance C-X can be chosen arbitrarily, e.g. a value of
1.5 Å works fine.
The number of free parameters to be calculated in an geometry
optimization **must not enlarge** by using a dummy
atom!
Otherwise the geometry optimization would not converge.
So fix a suitable number of structure parameters or define
common variables.

### Z-Matrix

### Send in

To have your solution checked, please send in the Z-matrix
(Gaussian input) for CO_{2}X .

Copyright © 2003
N.
Rösch,
Technische
Universität München