Example 2: Acetaldehyde

Z-Matrices

Students

This is acetaldehyde.

Notice the pyrimidal shape of the three hydrogens and the V-shape of the hydrogen and oxygen.

Here is the numbered molecule. Use this as a reference when following along in the example. Notice that the black arrow means that atom H7 is coming out of the screen and towards you. The shaded arrow H6 is going into the monitor.

These pictures show the five atoms that make up one plane. The included atoms are both carbons, the oxygen, and two hydrogens, each from opposite ends. This geometry is important when finding the dihedral angles.

1. First we must decide which atom will be atom #1. Let's choose the carbon bonded to the oxygen and call it C1. Place this at the origin.

   C1

2. Next we must order the rest of the atoms. Designate the oxygen O2, the hydrogen atached to C1 to be H3, the other carbon as C4, and the other hydrogens as atoms H5, H6, and H7.
3. Now we must look at the oxygen. Using our reference charts, we find the double bond length equals, 1.22 angstroms.

   C1
   O2	1	1.22

4. Next look at atom H3. Its bond length to atom C1 equals 1.09 angstroms. The bond angle formed between the first three atoms equals 120.0 degrees.

   C1
   O2	1	1.22
   H3	1	1.09	2	120.0

5. Next we look at atom C4. Its bond length with atom C1 equals 1.54 angstroms. Its bond angle with atoms C1 and O2 equals 120.0 degrees. Its dihedral angle with atoms C1,O2,H3 equals 180.0 degrees.

   C1
   O2	1	1.22
   H3	1	1.09	2	120.0
   C4	1	1.54	2	120.0	3	180.0

6. Now we must find a way to describe the atoms that are not bonded to atom C1. To do this, we will describe them with reference to their bond length with the carbon, atom C4, in addition to the angles they form with atoms C1,O2.
7. Looking at atom H5, we find its bond length to atom C4 equals 1.09 angstroms. Its bond angle with atoms C1,C4 equals 110.0 degrees. Its dihedral angle with atoms C1,O2,C4 equals 000.0 degrees.

   C1
   O2	1	1.22
   H3	1	1.09	2	120.0
   C4	1	1.54	2	120.0	3	180.0
   H5	4	1.09	1	110.0	2	000.0

8. We will do the same for atom H6. Its bond length to atom C4 equals 1.09 angstroms. Its bond angle with atoms C1,C4 equals 110.0 degrees. Its dihedral angle with atoms C1,O2,C4 equals 120.0 degrees.

   C1
   O2	1	1.22
   H3	1	1.09	2	120.0
   C4	1	1.54	2	120.0	3	180.0
   H5	4	1.09	1	110.0	2	000.0
   H6	4	1.09	1	110.0	2	120.0

9. For atom H7, everything is the same as atom H6 except the dihedral angle formed with atoms C1,O2,C4. This angle will be -120.0 degrees since it is in the opposite direction as that of atom H6. Your final z-matrix for acetaldehyde is as follows:

   C1
   O2	1	1.22
   H3	1	1.09	2	120.0
   C4	1	1.54	2	120.0	3	180.0
   H5	4	1.09	1	110.0	2	000.0
   H6	4	1.09	1	110.0	2	120.0
   H7	4	1.09	1	110.0	2	-120.0

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