Generating molecular graph Laplacian based on Hückel theory

While studying graphs and graph Laplacians from *"Laplacian eigenvectors of graphs: Perron-Frobenius and Faber-Krahn type theorems."*, I encountered a type of graph Laplacians that rise from quantum chemistry. This matrix is consists of off-diagonal elements called resonance integrals and diagonal terms called Coulomb integrals. This is a sparse matrix, meaning that the matrix elements corresponding to non-connected atoms are zero. It is further mentioned that 



> 
> ... the entries of this matrix, H, are tabulated for different atoms and
>  bonds.
> 
> 
> 


I was looking online to find some table that gives this information and write a package to compute this matrix given a SMILES entry. As an alternative, I also looked for an already existing package that provides this matrix. The only thing I found was the implementation of the extended Hückel method in RDKit, which requires molecule conformation as input (apparently, eHM needs atom coordinates).


I was wondering if anyone can point me to such a table or python package or let me know if I'm missing something.




You're describing simple [Hückel theory](https://en.wikipedia.org/wiki/H%C3%BCckel_method). This is usually applied to $\pi$-conjugated systems to understand the stabilization in conjugated and aromatic molecules.


There are a variety of Python packages, for example:


* Felix Plasser wrote one for his [blog](http://chemical-quantum-images.blogspot.com/2007/08/h-package.html) and the current location is at his [homepage](https://homepage.univie.ac.at/felix.plasser/chemprogs/python.htm)
* [Randle Taylor](http://randlet.com) has a [SHMO](https://github.com/randlet/SHMO) package on GitHub, including a [GUI called Orbis](https://github.com/randlet/Orbis)


I believe the version from Plasser will read in files using Open Babel's python interface, so certainly you could handle SMILES.


People would perturb the $\alpha$ (atom site energies) and $\beta$ (bond interaction) parameters in various ways. It's hard to find good tabulations of these, but the best appears to be:
"A brief review and table of semiempirical parameters used in the Hueckel molecular orbital method" [J. Chem. Eng. Data **1967** *122* pp. 235-246](https://doi.org/10.1021/je60033a020)


You mention the somewhat related [Extended Hückel theory (EHT)](https://en.wikipedia.org/wiki/Extended_H%C3%BCckel_method). This considers both $\sigma$ and $\pi$ bonds and is thus a lot more useful, although as you mention you need coordinates to calculate overlap values, etc.


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