Julia code performing the numerical simulation from our paper on robust response calculations for metals, available on arXiv. The framework described in this paper is implemented by default in DFTK. For the metals, we run DFTK with MPI, see Timings and parallelization.

Dependencies

Julia 1.7 with the following Julia libraries:

• DFTK.jl v0.5.5 for the simulation environment (this code might not work with more recent versions of DFTK);
• ForwardDiff.jl for the generation of the perturbation δV from atomic displacements (with random seed fixed to reproduce the same results from the paper);
• MPI, LinearAlgebra, IterativeSolvers, Random for related computations;
• Dates, DataFrames, JLD2, JSON, PGFPlots, Latexify, LaTeXStrings, Plots, TimerOutputs for saving and reading results.

Organisation

Numerical examples are gathered as follows:

• the silicon examples can be found in silicon/;
• the metallic examples can be found in metals/system where system is either Al40 or Fe2MnAl, with default extra bands and with number of extra bands suggested by the adaptive algorithm from the appendix;
• the comparision with a shifted Sternheimer equation from section 4.3 can be found in compare_shifted_sternheimer. In each folder, you will find .log files of the SCF calculations, as well as the response calculations, and .json files which store the data we need to generate the plots.

Usage

To perform the computations, first open the Julia shell with julia --project from the location of this repository and then run

using Pkg
Pkg.instantiate()

to install the required dependencies.

To run the computations, two different cases arise:

• for silicon, open the Julia shell with julia --project from the silicon/ folder and then run include("silicon.jl");
• for the metals, first go, in your terminal, to the location of the system you want (e.g. metals/Fe2MnAl, metals/Al40 or compare_shifted_sternheimer/) and then run for instance mpiexecjl -n 8 julia Fe2MnAl.jl. /!\ this take about an hour /!\

To generate all the plots from the paper, open the Julia shell with julia --project from the location of this repository and then run include("all_plot.jl"). Plots can be generated without running the computations first as the .json files are already saved in the repo, and the pdf files will be generated in the associated folders.

To run the adaptive algorithm from Section 6, open the Julia shell with julia --project from the location of this repository and then run include("run_adaptive_algorithm.jl"). Note thas this requires to first run the computations for Al40 et Fe2MnAl in the metals folder in order to generate the scfres.jld files which store the data and are too large to be stored in the repo.

Contact

This is research code, not necessarily user-friendly, actively maintened or extremely robust. If you have questions or encounter problems, get in touch!