I am currently in a computational physics course and am working on a final project involving carbon dimers. The reason this topic is applicable in my class is that once I figure out the physics involved, the problem involves using a lot of the numerical methods I learned in class. I am solid on the numerical methods, but a complete novice in terms of solid-state physics and quantum mechanics. I previously posted this https://www.physicsforums.com/showthread.php?t=361408" in the Homework and Coursework Questions forum, but wasn't getting any replies, so I am rethinking my approach to getting help on this.(adsbygoogle = window.adsbygoogle || []).push({});

Can someone explain to me what an empirical tight-binding Hamiltonian is?

I understand that in classical mechanics the Hamiltonian represents the energy of the system.

In the tight binding model, I assume it still represents the energy, but in what way?

Is the tight-binding hamiltonian the same as the Hamiltonian in the Schrödinger equation?

Why would the tight binding Hamiltonian be represented as a matrix?

In the case above, does empirical imply that the values used in the matrix should be measure?

(for example, the off-diagonal elements are supposed to be described by a set of orthogonal sp^{3}two-center hopping parameters, [tex]V_{ss\sigma}[/tex],

[tex]V_{sp\sigma}[/tex], [tex]V_{pp\sigma}[/tex], and [tex]V_{pp\pi}[/tex], scaled with interatomic separation r as a function of s(r); and the on-site elements are the atomic orbital energies of the corresponding atom.)

Should the Hamiltonian matrix have dimensions 8x8 because carbon is tetravalent and I am attempting to construct a Hamiltonian for C_{2}?

What does off-site element mean? Does it refer to the diagonal elements of the matrix?

Any help would greatly be appreciated.

Also, if anyone here hasn't seen my thread in the coursework forum, but think they might be able to help, please do. Any kind of human-to-human interaction is better than trying to figure this stuff out through journals and wikipedia.

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# Tight-binding Hamiltonian

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