Extended Huckel Calculation with Water

In summary, the secular equation for the extended Huckel method for molecules with oxygen treats sigma and pi electrons equally, assigning alphaH-E on the diagonal, alphaO' for 2s O in the middle, and alphaO for 2p O on the bottom. The non-zero off-diagonal elements, beta and beta', are applied based on the internal angle, theta, and are used to distinguish between the 2s and 2p orbitals. The matrix is symmetric as both hydrogen atoms are affected in the same way by oxygen.
  • #1
chem5432
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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!
 
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  • #2
The secular equation using the AO basis in terms of alphas and betas is as follows:[ alphaH - E beta cos (theta/2) beta' beta cos (theta/2) alphaO' - E 0 beta' 0 alphaO - E]
 

Related to Extended Huckel Calculation with Water

1. What is the purpose of performing an Extended Huckel Calculation with Water?

The purpose of performing an Extended Huckel Calculation with Water is to determine the electronic structure and molecular orbitals of a water molecule, which can provide valuable insights into its chemical and physical properties.

2. How is the Extended Huckel method different from the regular Huckel method?

The Extended Huckel method takes into account the interactions between the water molecule and its surrounding environment, while the regular Huckel method only considers the interactions within the molecule itself.

3. What are the limitations of using the Extended Huckel method?

The Extended Huckel method is limited to small molecules and does not take into account the effects of molecular vibrations or temperature on the electronic structure. It also assumes a static and rigid structure of the molecule.

4. How is the calculation performed?

The calculation involves solving the Schrodinger equation using a set of approximations and parameters specific to the Extended Huckel method. This is typically done using computer programs or software.

5. What are some applications of Extended Huckel Calculation with Water?

Extended Huckel Calculation with Water has many applications in fields such as chemistry, materials science, and biochemistry. It can be used to study the properties of water clusters, solvation effects, and the electronic structure of biomolecules in aqueous environments.

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