- #1

chem5432

- 1

- 0

**1. Write the complete secular equation using the AO basis in terms of alphas and betas**

I'm to use the following:

alphaH for a 1s H

alphaO' for a 2s O

alphaO for a 2p O

The only non zero off-diagonal matrix elements are

<2px|H|1sA>=<2px|H|1sB>= beta cos (theta/2)

<2py|H|1sA>=-<2py|H|1sB>= beta sin (theta/2)

<2s|H|1sA>=<2s|H|1sB>= beta'

Where theta is the internal angle and beta and beta' are parameters

## Homework Equations

The basic form of the secular determinant:

[ alpha1-E beta12

beta 12 alpha2-E]

## The Attempt at a Solution

I understand the basic Huckel method for a simple molecule like C3H8. However, I cannot find a good explanation for how the extended Huckel method works on molecules with oxygen. It is my understanding that the extended huckel method treats sigma and pi electrons equally. I am unsure of how to write the matrix to accommodate the oxygen as 2s and 2p.

I figured that on the diagonal would be alphaH-E, then something about O in the middle, and then alphaH-E on the bottom. I do not know how to assign the middle matrix element for O since there are two alphas for O. Additionally, I do not understand how to apply the non zero off-diagonal matrix elements (the betas) since I do not know how to distinguish between the 2s and 2p of O, and I don't know why/how to use the 2px and 2py. I think both Hs would see the same effect from O, so the matrix should be symmetric.

Any pointers on how to get this set up will be greatly appreciated. I'm also new here so if someone can direct me to a page on formatting (for Greek letters and writing out matrices), that would be helpful!

Last edited: