# Z-matrix of a series of 5 colinear atoms

How can I write a Z-matrix for the following complex?

  O==C==O  H--O
\
H


I have managed to write:

O
C   1  a
O   2  a     1  180
H   3  d     2  180    1  ?
O   4  b     3  180    2  ?
H   5  b     4    t    3  ?


but I don't know how to specify the dihedral angles indicated with ?. Are they all zero? Or completely unspecified? If so, will I be able to do a coordinate optimization with these variables or will it be a problem?

You cannot have bond angles of 0 or 180 degrees in a Z-matrix. This is because the dihedral becomes degenerate. To solve this, you can add 'dummy atoms' which provide an auxiliary point of reference to remove the 180 degree angle. These atoms are usually denoted $\ce{X}$ or $\ce{Xx}$ in computational chemistry suites. Usually, dummy atoms are placed at 90 degrees to a pair of atoms and the third collinear atom is then defined with a bond angle of 90 degrees and a dihedral of 0 or 180 degrees with respect to the previous 3 atoms.

## Example

To illustrate what I'm talking about, here's a schematic of your pair of molecules, with three dummy atoms:

This could have a Z-matrix like:

O   1
C   1    a
Xx  2  1.0  1  90
O   2    b  3  90     1  180
Xx  4  1.0  2  90     3  0
H   4    c  5  90     2  180
Xx  6  1.0  4  90     5  0
O   6    d  7  90     4  180
H   8    e  6  104.5  7  180


## Notes

There are no hard and fast rules about how many you should use (obviously we could simply define subsequent dihedrals in terms of the leftmost dummy atom) however it's best to strive for locality so that small changes in some variable don't correspond to large displacements elsewhere, in which case rounding errors or large gradients can ruin your day. You could also have defined all of the dihedrals in your molecule with respect to that convenient non-collinear hydrogen, however this is the Z-matrix equivalent of spaghetti code.

You will note that I use different letters for each variable. This is because forcing the $\ce{H-O}$ and $\ce{C=O}$ bonds to be of equal length is probably an unrealistic constraint for a geometry optimisation of this system.

Finally, note that dummy atoms do not take part in the electronic structure of a molecule, so feel free to put them in anywhere and set the dummy atom 'bond' length to whatever you want. 1.0 Ångström is traditional as far as I know.

## P.S.

Molden has a complete, if idiosyncratic graphical Z-matrix editor.

• Nice answer (beat me to it to boot!). To others tuning in, stay away from using Molden's auto-Z-matrix generator. It will likely give you junk. May 8 '12 at 9:44
• @LordStryker - this is a fair observation. Molden is best used for constructing Z-matrices manually or through the 'reorder Z-matrix' command, which lets one rebuild an iffy Z-matrix by simply clicking on the atoms in the desired order. May 8 '12 at 9:56

You can use SMILES in Avogadro or openbabel and it produces 3D coordinates that you can edit. And you can create Gaussian, NWChem, gamess... inputs.

• How does that relate to Z-matrices? Can Avogadro or openbabel produce Z-matrices from 3D coordinates? Are they then in “reasonable” physical order?
– F'x
Jun 8 '12 at 8:06
• @F'x Yes, both Open Babel and Avogadro automatically create Z-matrices with "reasonable" physical order. For some definition of reasonable. For your question, I think the answer above is much better - it can be very hard to optimize so many collinear atoms. Sep 12 '14 at 18:02