An implementation of the methodology pioneered by Alkauskas et al. for computing nonradiative recombination rates from first principles. The code includes various utilities for processing first principles calculations and preparing the input for computing capture coefficients. More details on the implementation of the code can be found in our recent paper. Documentation for the code is hosted on Read the Docs.

NONRAD is implemented in python and can be installed through pip. Dependencies are kept to a minimum and include standard packages such as numpy, scipy, and pymatgen.

As always with python, it is highly recommended to use a virtual environment. To install NONRAD, issue the following command,

$ pip install nonrad

or to install directly from github,

$ pip install git+https://github.com/mturiansky/nonrad

NONRAD can use numba to accelerate certain calculations. If numba is already installed, it will be used; otherwise, it can be installed by specifying [fast] during installation with pip, e.g.

$ pip install nonrad[fast]

To install NONRAD for development purposes, clone the repository

$ git clone https://github.com/mturiansky/nonrad && cd nonrad

then install the package in editable mode with development dependencies

$ pip install -e .[dev]

pytest is used for unittesting. To run the unittests, issue the command pytest nonrad from the base directory. Unittests should run correctly with and without numba installed.

A tutorial notebook that describes the various steps is available here. The basic steps are summarized below:

0. Perform a first-principles calculation of the target defect system. A good explanation of the methodology can be found in this Review of Modern Physics. A high quality calculation is necessary as input for the nonradiative capture rate as the resulting values can differ by orders of magnitude depending on the input values.
1. Calculate the potential energy surfaces for the configuration coordinate diagram. This is facilitated using the get_cc_structures function. Extract the relevant parameters from the configuration coordinate diagram, aided by get_dQ, get_PES_from_vaspruns, and get_omega_from_PES.
2. Calculate the electron-phonon coupling matrix elements, using the method of your choice (see our paper for details on this calculation with VASP). Extraction of the matrix elements are facilitated by the get_Wif_from_wavecars or the get_Wif_from_WSWQ function.
3. Calculate scaling coefficients using sommerfeld_parameter and/or charged_supercell_scaling.
4. Perform the calculation of the nonradiative capture coefficient using get_C.

To contribute, see the above section on installing for development. Contributions are welcome and any potential change or improvement should be submitted as a pull request on Github. Potential contribution areas are:

• implement a command line interface
• add more robust tests for various functions

If you use our code to calculate nonradiative capture rates, please consider citing

@article{alkauskas_first-principles_2014,
	title = {First-principles theory of nonradiative carrier capture via multiphonon emission},
	volume = {90},
	doi = {10.1103/PhysRevB.90.075202},
	number = {7},
	journal = {Phys. Rev. B},
	author = {Alkauskas, Audrius and Yan, Qimin and Van de Walle, Chris G.},
	month = aug,
	year = {2014},
	pages = {075202},
}

and

@article{turiansky_nonrad_2021,
	title = {Nonrad: {Computing} nonradiative capture coefficients from first principles},
	volume = {267},
	doi = {10.1016/j.cpc.2021.108056},
	journal = {Comput. Phys. Commun.},
	author = {Turiansky, Mark E. and Alkauskas, Audrius and Engel, Manuel and Kresse, Georg and Wickramaratne, Darshana and Shen, Jimmy-Xuan and Dreyer, Cyrus E. and Van de Walle, Chris G.},
	month = oct,
	year = {2021},
	pages = {108056},
}

If you use the functionality for the Sommerfeld parameter in 2 and 1 dimensions, then please cite

@article{turiansky_dimensionality_2024,
    title = {Dimensionality Effects on Trap-Assisted Recombination: The {{Sommerfeld}} Parameter},
    shorttitle = {Dimensionality Effects on Trap-Assisted Recombination},
    author = {Turiansky, Mark E and Alkauskas, Audrius and Van De Walle, Chris G},
    year = {2024},
    month = may,
    journal = {J. Phys.: Condens. Matter},
    volume = {36},
    number = {19},
    pages = {195902},
    doi = {10.1088/1361-648X/ad2588},
}