Calculate Harmonic Freq of graphene and graphite block

[taylaron]

Greetings,
I'm looking for a way to calculate the molecular harmonics of a sheet of graphene. Any suggestions or tips would be greatly appreciated. How to approach this task with a hexagonal lattice and using atomic-scale objects leaves me stuck wondering how to do it.

Wiki briefly describes Graphene as:

"Graphene is a one-atom-thick planar sheet of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. The term graphene was coined as a combination of graphite and the suffix -ene by Hanns-Peter Boehm,[1][2] who described single-layer carbon foils in 1962.[3] Graphene is most easily visualized as an atomic-scale chicken wire made of carbon atoms and their bonds. The crystalline or "flake" form of graphite consists of many graphene sheets stacked together.
The carbon-carbon bond length in graphene is about 0.142 nanometers. Graphene sheets stack to form graphite with an interplanar spacing of 0.335 nm, which means that a stack of 3 million sheets would be only one millimeter thick. Graphene is the basic structural element of some carbon allotropes including graphite, charcoal, carbon nanotubes and fullerenes."http://en.wikipedia.org/wiki/Graphene#photoopt"

A college student's intro to Graphene presentation
http://www.int.washington.edu/REU/2008/Presentations/Friedline.pdf"

As for a Block of graphite, would the harmonic frequency be related to that of any randomly-oriented carbon bond since graphite blocks are not homogeneous in their molecular structure?

I have no education on quantum physics and my math skills are limited to calculus for the time being. Thank you for your time.

Regards,
-Taylaron

 

[Navin A S]

The fundamental vibrations of graphene can be calculated using a variety of methods such as the tight-binding model and density functional theory. The basic idea is to solve the Schrödinger equation for the electrons in the system, and then use the resulting wave functions to calculate the vibrational frequencies. This is a complex calculation, and therefore it is usually done numerically, either on a computer or with a software package such as VASP, Gaussian, Quantum Espresso, or SIESTA. In addition, there are also approximate methods such as the harmonic approximation, which assumes that the potential energy of the system can be approximated by a local quadratic form. This approximation simplifies the problem significantly and can be solved analytically. The result is a collection of eigenvalues (frequencies) and eigenvectors (displacement vectors) which can be used to calculate the vibrational modes of the system. Finally, there are also experimental techniques such as Raman spectroscopy, which can be used to measure the vibrational frequencies of graphene.