Z-Matrix Main Page
First year chemistry curriculum concepts
Second year chemistry curriculum concepts
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Z-matrix to Cartesian Converter
Cartesian Converter Example
Help Instructions for the Z-matrix to Cartesian Converter
Glossary of Terms
SUCCEED's Computational Chemistry
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When constructing a Z-matrix, you should follow these steps:
- Draw the molecule.
- Assign one atom to be #1.
- From the first atom, assign all other atoms a sequential number. When
assigning atoms, you must be careful to assign them in an order that is easy
to use. This will become clearer as you experiment with different molecules.
- Starting with atom #1, list the atoms you numbered, in order, down your
paper, one right under the other.
- Place the atom designated as #1 at the origin of your coordinate
system. The first atom does not have any defining measurements since it is at
- To identify the second atom, you must only define its bond length to the
first atom. Use the reference charts given.
- For the third atom, you must define a bond length to atom #1 and a bond
angle between atom #3 and atoms #1 and #2. (Bond angles are the angles between
- Remember that you can only use previously defined atoms when defining your
current atom. This means that you can not reference atom #7 when defining atom
- To identify atom #4 and all other atoms, you must include a bond length,
bond angle and a dihedral angle. (Dihedral angles are the angles between an
atom and the plane created by three other atoms.) This is done by using
neighboring atoms to the atom you are describing. Again, the reference charts
are helpful in locating bond lengths and angles.
Bond Length Hints:
- The bond length of each kind of bond varies very little from one
particular compound to another.
- Single bonds of first-row elements (C, N, O, F) to hydrogen are all about
- Single bonds between first-row atoms are all about 1.5 Å.
- Double and triple bonds are shorter: 1.2 to 1.3 Å in first-row
- Second-row, and higher, atoms (S, P, Cl, etc.) form correspondingly
Normal Bond Lengths (in angstroms)
C (triple)C 1.20
- Angles with all single bonds: 110 degrees
- Angles with a double bond: 120 degrees
- Angles with a triple bond: 180 degrees
- Angles with all single bonds: 120 degrees
- Angles with a double bond: 180 degrees
- Remember that you can ONLY use previously defined atoms to identify the
atom you are working on.
- Angles can be positive and negative to represent directions. If one atom
is going into the screen and another is coming out of the screen, one angle
should be defined as negative and the other as positive. It does not matter
which you chose to be positive or negative.
Z-Matrix Converter http://www.shodor.org/chemviz/zmatrices/babel/html.