Huckel method for cyclooctatetraene (C8H8)

  • Thread starter JorisL
  • Start date
  • Tags
    Method
In summary, the student is studying quantum chemistry and has difficulty applying the Hückel or tight binding method. They can calculate the energies using the Frost-Musulin diagrams, but the problem is finding expressions for the molecular orbitals. They can use symmetry considerations and the pairing theorem to find some of the orbitals. However, they are not able to get any further because they need to use normality of the orbital, which they are not able to do because c_4 = 0.
  • #1
JorisL
492
189
Hi

I'm studying for my course of quantum chemistry and I have some issues with applying the Hückel or thight binding method.

I can calculate the energies with ease using Frost-Musulin diagrams.
The problem is finding expressions for the molecular orbitals.
I can use symmetry considerations and the pairing theorem to find some of the orbitals.

This is an overview of what I got until now.

The energies are determined using a frost-musulin diagram.
They are [tex]E_1 = \alpha +2\beta\, ,E_2 = E_3 = \alpha +\sqrt{2}\beta\, ,E_4 = E_5=\alpha\, ,E_6=E_7 = \alpha -\sqrt{2}\beta\, ,E_8=\alpha -2\beta[/tex] where [tex]E_1,\, E_2\, and\, E_3[/tex] correspond to bondig orbitals.
[tex]E_4\, and\, E_5[/tex] correspond with nonbonding orbitals and the other energies are anti-bonding.

The molecular orbitals (MO's) are denoted by [tex]\phi_i[/tex] where the i corresponds with the energy. They consist of the atomic orbitals (AO's) denoted by [tex]\chi_i[/tex].

Because the lowest and highest energy orbitals must contain all symmetry, all Atomic orbitals should be included. The ring is perfectly symmetrical so they all have the same sign and coefficient for the lowest energy.

[tex]\phi_1 = \frac{1}{2\sqrt{2}}\left(\chi_1 +\chi_2 +\chi_3 +\chi_4 +\chi_5 +\chi_6 +\chi_7 +\chi_8\right)[/tex]

Because of the pairing theorem I know the highest energy orbital has a similar form only with alternating signs.

[tex]\phi_8 = \frac{1}{2\sqrt{2}}\left(\chi_1 -\chi_2 +\chi_3 -\chi_4 +\chi_5 -\chi_6 +\chi_7 -\chi_8\right)[/tex]

Know I will try to use some symmetry, the pairing theorem and some simple calculus to determine the other orbitals.

The image in the attachment shows how I named the atoms.

I assume for orbital [tex]\phi_2[/tex] that it has a nodal plane through atom 1 and 5. For [tex]\phi_3[/tex] I'll assume a nodal plane perpendicular to that i.e. through 3 and 7.

I know that [tex]E_{tot} = 2\cdot E_1 + 4\cdot E_2 + 2\cdot E_4 = 8\alpha +2\beta (2+2\sqrt{2})[/tex]
Hence the sum [tex]\sum_{k,l}p_kl = 2+2\sqrt{2}[/tex].
Because of symmetry I state that the bond order is equal for all neighbours i.e. [tex]p_{12} = \frac{2+2\sqrt{2}}{8} = \frac{1+\sqrt{2}}{4}[/tex]

But I can't get any further with this.
I can use normality of the orbital to say that
[tex]1 = \int dV \phi^*_2\phi_2 = c_1^2+c_2^2+c_3^2+c_4^2+c_5^2+c_6^2+c_7^2+c_8^2[/tex]

Furthermore [tex]c_1 = c_5 = 0[/tex] because of the nodal plane.
Also [tex]c_2=c_4=-c_6=-c_8[/tex] and [tex]c_3=-c_7[/tex] from symmetry.

When I use this information about the coefficients and the bond order between 1 and 2, I find found that [tex]c_4 = 0[/tex] and consequently that [tex]c_3 = \infty[/tex]

I have no idea what else I can use because when I want to use the fact that the electron density is uniform as well, I need to include the 2 non-bonding orbitals as well.

Am I looking in the right direction? Or should I start over in another way?

Joris
 
Physics news on Phys.org
  • #2
This may be a stupid question, but can't you just write down the whole tight binding Hamiltonian as a N x N matrix and then diagonalize it? Using Python/scipy or Matlab or your favorite numerical scripting language this could probably be done in about 20 lines of code.
 
  • #3
Of course I can do that. But the exercise is made in such a way that we have to use symmetry etc. And I can use the practice. I don't always find the correct symmetry element/operation I have to use.
 

What is the Huckel method for cyclooctatetraene?

The Huckel method for cyclooctatetraene is a computational approach used to determine the electronic structure and properties of this molecule. It is based on the principles of molecular orbital theory and uses mathematical calculations to predict the behavior of electrons in the molecule.

How does the Huckel method work?

The Huckel method works by assigning a set of parameters to each atom in the molecule based on its atomic number. These parameters are then used to calculate the energies of the molecular orbitals in the molecule. By solving the Schrödinger equation, the Huckel method can determine the molecular orbitals and their corresponding energies, allowing for the prediction of the molecule's properties.

What are the benefits of using the Huckel method for cyclooctatetraene?

The Huckel method is a useful tool for studying cyclooctatetraene because it allows for the prediction of important properties such as bond energy, bond length, and electron density. It also provides insight into the stability and reactivity of the molecule, making it a valuable tool for understanding its behavior in chemical reactions.

What are the limitations of the Huckel method?

While the Huckel method is a useful tool for predicting the properties of cyclooctatetraene, it does have some limitations. It assumes that the molecule is planar and has a conjugated pi system, which may not always be the case. It also does not account for the effects of molecular vibrations and other factors that may affect the molecule's properties.

How is the Huckel method applied in real-world applications?

The Huckel method is widely used in the field of computational chemistry and has been applied in various industries, including pharmaceuticals, materials science, and organic electronics. It is also used in academic research to study the electronic properties of other molecules and to design new compounds with specific properties.

Similar threads

Replies
1
Views
2K
Replies
3
Views
745
  • Advanced Physics Homework Help
Replies
4
Views
303
  • Quantum Physics
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
8
Views
6K
  • Math Proof Training and Practice
Replies
16
Views
5K
  • Math Proof Training and Practice
6
Replies
175
Views
20K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
2K
Back
Top