This repository contains the code to reproduce the results of the following paper:

Michael F. Herbst and Bonan Sun
Efficient Krylov methods for linear response in plane-wave electronic structure calculations
arXiv prerint, arXiv:2505.02319, 2025, https://doi.org/10.48550/arXiv.2505.02319

Each directory contains the source code (and data, figures for Al40 and Fe2MnAl) for the corresponding system. For example, the structure of Al40/ is as follows and other directories are similar.

Al40
 ┣ data_logs
 ┃ ┣ Al_extracted.jld2    # saved results
 ┃ ┗ summary_tables.md    # summary of the results for Al40
 ┣ figures                # figures
 ┃ ┗ repeat10             # figures for length 10 Al supercell
 ┃ ┃ ┣ Al.eps
 ┃ ┃ ┣ ...
 ┣ Al40.jl                # main source for Al systems
 ┣ GeneratePlots.jl       # generate figures for Al40
 ┣ GenerateTables.jl      # generate tables for Al40
 ┗ test.jl                # testing script for a small system

The recommended way to install Julia is to install juliaup, a Julia version manager. See the juliaup repository or Julia official website for more instructions.

Once you have juliaup installed, we recommend using the same julia version as the one used to develop this code (1.10.3) to avoid any potential issues. Simply open a terminal from the directory of this repository and run the following command to start Julia with the correct version and activate the project environment:

juliaup add 1.10.3
julia +1.10.3 --project

Then run the following command in the Julia REPL activated above to install the dependencies:

using Pkg
Pkg.instantiate()

This will install all the required packages. Notably it will install not the main distribution of DFTK, but a branch of my fork. Though the methods proposed in the paper will be incorporated in the main distribution of DFTK in the future, this repository is meant to be self-contained and reproducible. This code may not work with the main distribution of DFTK.

Run a small test with

include("Al40/test.jl")

to see if everything is working. It should create a directory repeat3/ under Al40/data_logs/ with 3 .log files and 3 .jld2 files. It should also create one plot in Al40/figures/repeat3/. It should finish in less than 10 minutes on a modern laptop.

Note that generating figures requires LaTeX to be installed on your system. The tables and figures in the paper can be generated from saved results in Al40/data_logs/Al_extracted.jld2 and Fe2MnAl/data_logs/Fe2MnAl_extracted.jld2. Run

include("Al40/GeneratePlots.jl"); include("Al40/GenerateTables.jl")
include("Fe2MnAl/GeneratePlots.jl"); include("Fe2MnAl/GenerateTables.jl")

to generate all the tables and figures in the paper (except for Table 4 for silicon) by loading the saved results .jld2 files in Al40/data_logs/ and Fe2MnAl/data_logs/ since re-running all the tests would take thousands of core hours, see next section if you really want to do that or if you want to run part of the tests shown in the paper. See the table below for a description of the them.

For the Silicon system, run

include("silicon/test.jl"); include("silicon/GetTable.jl")

to reproduce the Tab. 4 in the paper from scratch. It will take 2~3 hours on a modern laptop.

To rerun the calculations for the metallic systems, let's take the Heusler alloy as an example. First run

include("Fe2MnAl/Fe2MnAl.jl"); setup_model(debug)

to import procedures and functions, and to run the self-consistent field (SCF) calculation to set up the model, either in debugging mode (debug="debug") or in production mode (debug="full"), where the former uses a small cutoff and the latter uses the same parameters as in the paper. After the SCF, the response calculation can be run with

run_gmres(; debug, restart, tol, adaptive, CG_tol_scale_choice, precon)

where:

• debug: boolean, default false. If true, run the calculation for the small system otherwise for the same system as in the paper.
• restart: integer, default 20. The restart parameter for GMRES.
• tol: float, default 1e-12. The tolerance for GMRES convergence.
• adaptive: boolean or string, default true. Possible values are true (adaptive strategies proposed in the paper) or "D10", "D100", "D10_n" (baseline methods, see Table 1 in the paper for the definition).
• CG_tol_scale_choice: string, default "agr". The strategy to choose the CG tolerances in case of adaptive=true. Possible values are "agr", "hdmd", "grt" (see Table 1 for the definition, "hdmd" refers to the bal strategy in the paper).
• precon: boolean, default false. If true, use the Kerker preconditioner.

Note that one GMRES run will generate a .log file and a .jld2 file in the data_logs/ directory. The .log file contains the output of the GMRES run, while the .jld2 file contains the results. Each would take 5~30 hours in debug="full" mode depending on the choice of the above parameters, e.g., how tight the tolerance is, which strategy is used etc.

For the aluminum system, similar procedures can be followed with the exception that one more parameter repeat is needed in both setup_model and run_gmres to specify the size of the supercell.

This is research code and therefore not necessarily user-friendly and actively maintained. If you have questions or encounter problems, get in touch!