Example 4: Butane

Z-Matrices

Students

This is Butane.

Steps:

Here is the numbered molecule. Use this as a reference when following along in the example. Notice that the black arrow means that the atom is coming out of the screen and towards you. The shaded arrows mean that the atom is going into the monitor.

1. First we must decide which atom will be atom C1. We'll pick the carbon to the left and call it C1. Place this at the origin.

   C1

2. Next we must order the rest of the atoms. Designate the other carbons C2, C3 and C4. The rest of the hydrogens will be H5 through H14.
3. Now we must look at the C2 atom. Using our reference charts, we find the single bond length between two carbons equals, 1.54 angstroms.

   C1
   C2	1	1.54

4. Next look at atom C3. Its bond length to atom C2 equals 1.54 angstroms. The bond angle formed between the first three atoms equals 110.0 degrees.

   C1
   C2	1	1.54
   C3	2	1.54	1	110.0

5. Next we look at atom C4. As before, its bond length with atom C3 equals 1.54 angstroms. Its bond angle with atoms C2 and C3 equals 110.0 degrees. Its dihedral angle with atoms C1,C2,C3 equals 120.0 degrees.

   C1
   C2	1	1.54
   C3	2	1.54	1	110.0
   C4	3	1.54	2	110.0	1	120.0

6. Atom H5 is the first hydrogen atom we will look at. We can see that it forms a 1.09 angstrom bond length with atom C1. It also forms a 110.0 bond angle with atoms C1 and C2 and a 120.0 degree dihedral angle with atoms C1,C2, and C3. Thus, the z-matrix now looks like this:

   C1
   C2	1	1.54
   C3	2	1.54	1	110.0
   C4	3	1.54	2	110.0	1	120.0
   H5	1	1.09	2	110.0	3	120.0

7. All of the hydrogens will have the same measurements, but will reference different atoms. Remember to only use previously defined atoms when identifying your current atom. Your final z-matrix should look like this:

   C1
   C2	1	1.54
   C3	2	1.54	1	110.0
   C4	3	1.54	2	110.0	1	120.0
   H5	1	1.09	2	110.0	3	120.0
   H6	1	1.09	2	110.0	3	120.0
   H7	1	1.09	2	110.0	3	120.0
   H8	2	1.09	3	110.0	4	120.0
   H9	2	1.09	3	110.0	4	120.0
   H10	3	1.09	2	110.0	1	120.0
   H11	3	1.09	2	110.0	1	120.0
   H12	4	1.09	3	110.0	2	120.0
   H13	4	1.09	3	110.0	2	120.0
   H14	4	1.09	3	110.0	2	120.0

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