Anyone can help to calculate with Huckel methods the matrix that gives the energies of the pro penal c=c-c=o
Dear Mohamed, unfortunately I am not able to help with this concern. However, there are bellow two links that may be useful for you.
1) http://scitation.aip.org/content/aip/journal/jcp/48/9/10.1063/1.1669730
2) http://www.sciencedirect.com/science/article/pii/0009261475802727
Best regards and good luck with your research!
The matrix for this system will be very similar to the butadiene case. Unfortunately writing matrices here is difficult, but let me give a try. The matrix for butadiene:
| a-e , b , 0, 0 |
| b, a-e , b , 0 |
| 0 , b , a-e , b|
| 0 , 0 , b , a-e|
where a is alpha, b is beta and e is energy in the common notation for Huckel systems. Now, since we have O instead of C as the last atom we rewrite this matrix as:
| a-e , b , 0, 0 |
| b, a-e , b , 0 |
| 0 , b , a-e , bCO|
| 0 , 0 , bCO , aO-e|
where bCO is the beta parameter for the interaction between C and O and aO is the alpha parameter for O.
To solve this set of equations we need to know the values of bCO and aO - these are fitted to high-level QM using calcualtions for various systems. You can take the simple set suggested many yers ago from: http://pubs.acs.org/doi/pdf/10.1021/jo01311a060 which gives you:
bCO = 1.06*b (taken from the k_C-O1 value)
aO = a + 0.97*b (taken from the k_O1 value)
Substituting these value into the second matrix gives you a set of equation that can be easily solved using the standard algorithm for solving Huckel equations. Obviously the energetic levels as well as the total Energy will depend on a and b.
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