A library for checking exact conditions in density functional theory (DFT) approximations.

Update: 08/23/2024

Vaibhav Khanna et al. 2024 Examining the Impact of Local Condition Violations on Energy Computations in DFT have found that several local conditions: deriv_lower_bd_check, deriv_upper_bd_check_1,deriv_upper_bd_check_2, and second_deriv_check can be sensitive to the number of $r_s$ grids used in evaluations due to the numerical derivates taken with respect to this variable. We suggest users more carefully scan through finer $r_s$ grid meshes until "fraction violated" appears converged. In some cases, over $500000$ grids have been required, but this depends on the functional of choice.

Please see examples/local_conditions/local_conditions_runs_w_update.py for info on changing such values from the default ones used in our paper.

Installation (Linux)

Before continuing, a python virtual environment is recommended. To install, use the following example command:

git clone https://github.com/pedersor/dft_exconditions.git
cd dft_exconditions
pip install .

Background and usage

Each DFT exact condition (constraint) that we consider has a corresponding local condition (further details will be provided in a forthcoming paper). Such local conditions can be assessed for a given exchange-correlation (XC) approximation using a grid search over applicable variables. For instance, using the PBE functional we can check our default set of exact conditions using

cd examples/local_conditions
python3 local_conditions_runs.py --func_id gga_c_pbe --condition_string negativity_check 

Running the above code produces an output out/gga_c_pbe.csv. Here, by default, our grid search is over density variables $r_s \in [0.0001, 5], s \in [0, 5], \zeta \in [0, 1]$. Further details and customization can be found in local_condition_checks.default_search_variables. In the output csv we see that PBE correlation is always negative with these density variables.

Exact conditions can also be assessed for given system densities. For instance, we may check whether various atomic self-consistent densities violate exact conditions in approximations. In the following we test neutral atoms H-Ar and their cations and also report the error in ionization energies (IEs).

cd examples/exact_conditions
python3 ie_runs.py --xc sogga11

Running the above code produces the outputs ie_checks_SOGGA11.csv and ie_errs_SOGGA11.csv. The former enumerates over the systems and checks whether various exact conditions are satisfied and the latter provides the IE error in the DFT approximation.

Analysis and visualization over obtained results can be found in analysis/. Other code such as examples/densities/examples.py is used to reproduce figures that will appear in a forthcoming paper.

Cite

Please cite this work as:

@article{pederson2023reassessing,
  title={Reassessing the role of exact conditions in density functional theory},
  author={Pederson, Ryan and Burke, Kieron},
  journal={arXiv preprint arXiv:2303.01766},
  year={2023}
}

Disclaimer

This library is in alpha.