# 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-O1 and X-C-O2 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, CO2. 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

Atom Distance to atom Angle Dihedral angle
N1 symbol N2 N1-N2 special
option
N3 N1-N2-N3 special
option
N4 N1-N2-N3-N4 special
option
no. no. Å no. degree no. degree
1
2
3
4

Allowed special options are

• #<atom number> to re-use a variable
• -#<atom number> to re-use a dihedral angle, but with the sign changed
• f to "fix" the value
Do not use more than one option per parameter. A geometry parameter re-using a fixed value will be fixed automatically.

### Z-Matrix as Program Input

 (WebLab Viewer must be installed) Erase form content

### Send in

To have your solution checked, please send in the Z-matrix (Gaussian input) for CO2X .

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