Python library to perform tight-binding mean field Hubbard calculations on the conjugated π-networks of organic systems. Only carbon atoms are supported and each atom is modelled by a single pz orbital hosting a single electron.
The modelled Hamiltonian is the following:
where c†, c and n are respectively the creation, annihiliation and number operators, t is the hopping integral and U denotes the on-site Coulomb repulsion.
Python 3 (tested with 3.6 - 3.9) environment is required with the following libraries (parenthesis indicate tested versions; but the library should work with all recent versions):
- Standard python libraries:
numpy(1.17.2),scipy(1.3.1),matplotlib(3.2.1) - Atomistic simulation environment:
ase(3.18.1) - Python Tight Binding:
pythtb(1.7.2)
Note: the dependencies will be automatically installed via pip.
Option 1) Install the library and dependencies hosted on PyPI:
pip install tb-mean-field-hubbard
Option 2) Manual installation, such that you have direct access to the code and the notebook:
git clone https://github.com/eimrek/tb-mean-field-hubbard.git
cd tb-mean-field-hubbard
pip install -e .
On a normal desktop computer, installation of the python dependencies can take some minutes, while the tb-mean-field-hubbard should install in seconds.
Example jupyter notebook example.ipynb is provided that performs the calculation for the Clar's goblet molecule. The geometry is read from a xyz file. The whole notebook should run in a matter of seconds on a normal desktop computer.
The following image demonstrates a selection of the output for the calculation for parameters t=2.7 and U=3.0 (both in electronvolts).
In addition to the structure of Clar's goblet, the geom/ folder contains input geometries for triangulene, 4- and 5-rhombene, and several other systems.