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  • When constructing a Z-matrix, you should follow these steps:
    1. Draw the molecule.
    2. Assign one atom to be #1.
    3. 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.
    4. Starting with atom #1, list the atoms you numbered, in order, down your paper, one right under the other.
    5. 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 the origin.
    6. To identify the second atom, you must only define its bond length to the first atom. Use the reference charts given.
    7. 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 three atoms.)
    8. 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 #5.
    9. 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:

    1. The bond length of each kind of bond varies very little from one particular compound to another.
    2. Single bonds of first-row elements (C, N, O, F) to hydrogen are all about 1 Å.
    3. Single bonds between first-row atoms are all about 1.5 Å.
    4. Double and triple bonds are shorter: 1.2 to 1.3 Å in first-row elements.
    5. Second-row, and higher, atoms (S, P, Cl, etc.) form correspondingly longer bonds.

    Normal Bond Lengths (in angstroms)

    H-C     1.09
    H-N     1.00
    H-O     0.96
    C-C     1.54
    C-N     1.47
    C-O     1.43
    C-Cl     1.76
    C-Br     1.94
    C-I     2.14
    C=C     1.35
    C=N     1.30
    C=O     1.22
    C (triple)C     1.20
    C(triple)N     1.16
    N-F		1.33
    H-P		1.40

    Bond Angles:

    1. Angles with all single bonds: 110 degrees
    2. Angles with a double bond: 120 degrees
    3. Angles with a triple bond: 180 degrees

    Dihedral Angles:

    1. Angles with all single bonds: 120 degrees
    2. Angles with a double bond: 180 degrees

    More Hints:

    • 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

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    Shodor logoThe Shodor Education Foundation, Inc.
    in cooperation with the
    National Center for Supercomputing Applications

    © Copyright 1999-2000 The Shodor Education Foundation, Inc.