https://github.com/jarvist/teclo.jl
Tight Binding calculation of the Density of States of disordered materials
https://github.com/jarvist/teclo.jl
density-of-states disorder julia statistical-mechanics tight-binding urbach-tail
Last synced: about 2 months ago
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Tight Binding calculation of the Density of States of disordered materials
- Host: GitHub
- URL: https://github.com/jarvist/teclo.jl
- Owner: jarvist
- License: mit
- Created: 2014-12-07T18:08:20.000Z (over 10 years ago)
- Default Branch: master
- Last Pushed: 2017-11-15T00:31:07.000Z (over 7 years ago)
- Last Synced: 2024-04-18T14:38:47.950Z (about 1 year ago)
- Topics: density-of-states, disorder, julia, statistical-mechanics, tight-binding, urbach-tail
- Language: Jupyter Notebook
- Homepage:
- Size: 40 KB
- Stars: 1
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
Sturm und Drang / Storm and Urge
=====
Calculation of electronic densities of states for conjugated polymer chains, with off-diagonal disorder parameterised by statistical mechanics.
* Given an arbitrary effective potential energy landscape U=f(\theta). [The Urge]
* Specified as a functional form ( `U(theta)=( E0 * sin(theta*pi/180.0)^2 ) #P3HT like` ) [1]
* OR read in from tabulated data (i.e. a Quantum-Chemical potential energy scan), fitting a Chebyshev Polynomial [2] with a Vandermonde matrix [3] via the excellent ApproxFun [4] package.
* Integrate (monte carlo direct sampling) to get a (statistical mechanical) partition function, Z=\sum e^{U/kBT}
* Use this partition function to generate random samples of \theta
* Use a model for the transfer integral between two neighbouring units (i.e. monomers in a polymer chain, J~cos(theta)) to build a tridiagonal tight-binding Hamiltonian
* Solve this tridiagonal Hamiltonian with `Sturm sequence` methods, which are linear in time and require no memory. [The Storm]
Method developed in these codes are discussed in these talk slides, but I'm afraid it's pretty incoherent without the talk (and not much better with...).
https://speakerdeck.com/jarvist/2016-03-pvcdt-jarvistmoorefrost-from-atoms-to-solar-cells?slide=82
The only published application of this method we applied it to the P3HT system, treating the P3HT as non-interacting chains. Unfortunately, we found that it didn't agree particularly well with the detailed Molecular Dynamics of the rest of the paper. I suspect this is due to the poor model for the inter-monomer potential (we need an effective potential that includes steric hindrance + entropic effects of the sidechains).
Parameter free calculation of the subgap density of states in poly(3-hexylthiophene)
Jarvist M. Frost, James Kirkpatrick, Thomas Kirchartz and Jenny Nelson
Faraday Discuss., 2014,174, 255-266
http://dx.doi.org/10.1039/C4FD00153B
# Teclo
Extension of these methods to molecular crystals.
* If tri-diagonal, use linear scaling Sturm sequencies to generate a historgrammed DoS
* If not - currently just standard linear algebra methods. Though perhaps Arrowhead methods for 2D/3D systems in the future?
# References
* [1] This should really be a 'free energy' not a potential, taking in an entropic contribution + all enthalpic contributions. However, you can approximate it by using the torsional potential as you would use in part of a molecular dynamics forcefield. For instance for P3HT, Raos FF paper (Moreno et al. J.Phys.Chem.B 2010), contains a 'full' potential energy Fig 4.a. puts a barrier at 90 degress of ~3.0 kCal / mol = 126 meV.
* [2] The Numerical Recipes description is pretty useful. https://en.wikipedia.org/wiki/Approximation_theory#Chebyshev_approximation
* [3] Mathematicians keep all the good stuff to themselves. A superior method of fitting a polynomial, with a specially constructed matrix. https://en.wikipedia.org/wiki/Vandermonde_matrix#Applications
* [4] https://github.com/ApproxFun/ApproxFun.jl