Huckel Theory - Dimers

EmilJaffal

As an example of the Huckel method, we will examine the frontier orbitals (i.e. determine eigenfunctions) and their associated orbital energies (i.e. eigenvalues) of the dimers.

The central assumptions of Huckel theory are: Electrons are ignored (we say that “the sigma and pi electrons can be separated”, and assume that the pi electrons move around a core of the nuclei and the electrons). The molecular orbital wave function for the electrons is constructed from a linear combination of (normalised) p orbitals from the atoms. In Carbon, each atom contributes one such electron. And, all overlap integrals are neglected. The (diagonal) energy integral,

, is the same for all atoms i (of the same element). It is denoted by α.

Eigenvalues quantify the Huckel hamiltonian matrix. It doesn't take into account sigma bonding, therefore if the quantified EV ordering is consistent with our calculated ordering it is not hydrogen bonding that differs stabilization energies but the structure. If it differs from the simple huckel model, it is not just MOs. Here, we can differentiate between H-bonding or steric preference for each molecule. (I hypothesize that H-bonding takes precedence over steric hindrance in P2, not sure in P1).In the early days of quantum chemistry, before the age of computers, the Hückel theory was widely used, but in spite of its simplicity it is still in use, e.g., papers appear continually in Physics Reviews B using the Huckel theory in a solid-state ‘tight-binding’ format. The Hückel theory also plays a central role in a recent paper by Klein and Misra in their discussion of minimally Kekulenoid π–networks and reactivity of acyclics [144]. Additionally, graph-theoretical analysis of the Hückel theory [e.g .,145-148] has provided elegant answers to some questions that were previously left unanswered, such as why only a few (six to be precise [149]) conjugated molecules have only integers as eigenvalues or why some structurally quite different molecules possess identical sets of eigenvalues (that is, identical Hückel spectra) [150-158], etc. Graphs with identical spectra are called isospectral or cospectral graphs. For example, in Figure 19 we give graphs G7 and G8 of two structurally-different molecules - 1,4 - divinylbenzene and 2-phenylbutadiene - that possess identical Hückel spectra. Their vertex-adjacency matrices are given below the figure.

Huckel Theory downloaded from GitHub.

First, to introduce the polymers:
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P1
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UPDATE: Code to shorten all of the above process
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UPDATE DONE - LOOK BELOW FOR P2.
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P2
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UPDATE: Code to shorten all of the above process
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UPDATE DONE


Cite this as: Emil Jaffal, "Huckel Theory - Dimers" from the Notebook Archive (2023), https://notebookarchive.org/2023-05-475ui96

Huckel Theory - Dimers

First, to introduce the polymers:

P1

UPDATE: Code to shorten all of the above process

UPDATE DONE - LOOK BELOW FOR P2.

P2

UPDATE: Code to shorten all of the above process

UPDATE DONE

First, to introduce the polymers:


P1


UPDATE: Code to shorten all of the above process


UPDATE DONE - LOOK BELOW FOR P2.


P2


UPDATE: Code to shorten all of the above process


UPDATE DONE
