A robust and efficient line search for self-consistent field iterations

Supporting information containing structures, raw data and computational scripts for the paper:

Michael F. Herbst and Antoine Levitt
A robust and efficient line search for self-consistent field iterations
Preprint on arxiv (2109.14018)

The code in this repository has been used to run all calculations and produce all plots of the above paper. It relies on DFTK version 0.3.10 and ASE. For more details see this blog article.

In particular:

• The subfolders contain the employed structures (as QuantumEspresso input files, ASE JSON files and/or CIF files) and computational parameters of the numerical tests conducted for the paper. See in particular the <case>/config.jl file for the computational parameters of each test case (kinetic energy cutoff, k-Point sampling, smearing).
• analyse.jl contains the code to produce the plots of the paper.
• common.jl contains the routines to setup and run the calculations.
• plot_all_summaries.jl plots the summary.svg plots of each subfolder which provide an overview of the convergence over all damping strategies considered.

Running the code and reproducing the plots

Running the code requires an installation of Julia 1.6.0, of DFTK and of ASE. With this setup can generate the plots of the paper by executing:

julia --project=@. -e "import Pkg; Pkg.instantiate()"  # Install dependencies
julia run.jl      # Generate data
julia analyse.jl  # Generate plots

Be aware that generating the data takes a long time (like two weeks on a couple of cluster nodes). The raw data is, however, included in the repository, such that the plotting works without running the calculations beforehand.

List of test systems

Folder	System	Preconditioner	Anderson?	Comments
Al_nodiis	Al8 supercell	×	×	randomised initial guess
Al_nodiis_Kerker	Al8 supercell	Kerker	×	randomised initial guess
Al	Al40 supercell	×	Anderson	randomised initial guess
Al_Kerker	Al40 supercell	Kerker	Anderson	randomised initial guess
AlVac	Al40 surface	×	Anderson
AlVac_Kerker	Al40 surface	Kerker	Anderson
----	----	----	----	----
GaAs	Ga40As40 supercell	×	Anderson	randomised initial guess
----	----	----	----	----
CoFeMnGa	CoFeMnGa	Kerker	Anderson	FM initial guess
Fe2CrGa	Fe2CrGa	Kerker	Anderson	FM initial guess
Fe2CrGa_nodiis	Fe2CrGa	Kerker	×	FM initial guess
Fe2MnAl	Fe2MnAl	Kerker	Anderson	FM initial guess
FeNiF6	FeNiF6	Kerker	Anderson	FM initial guess
Mn2RuGa	Mn2RuGa	Kerker	Anderson	FM initial guess
Mn3Si	Mn3Si	Kerker	Anderson	FM initial guess
Mn3Si_AFM	Mn3Si	Kerker	Anderson	AFM initial guess
Cr19	Cr19 defect	Kerker	Anderson	FM initial guess
WFe	Fe28W8 multilayer	Kerker	Anderson	FM initial guess
----	----	----	----	----
Fe2CrGa_40guess	Fe2CrGa	Kerker	Anderson	started within the stagnating region
Fe2CrGa_maxcond02	Fe2CrGa	Kerker	Anderson	using maximal conditioning 10² in Anderson
Fe2CrGa_maxcond04	Fe2CrGa	Kerker	Anderson	using maximal conditioning 10⁴ in Anderson
Fe2CrGa_maxcond06	Fe2CrGa	Kerker	Anderson	using maximal conditioning 10⁶ in Anderson
Fe2CrGa_maxcond08	Fe2CrGa	Kerker	Anderson	using maximal conditioning 10⁸ in Anderson
Fe2CrGa_maxcond10	Fe2CrGa	Kerker	Anderson	using maximal conditioning 10¹⁰ in Anderson

Further details on the comments:

• randomised initial guess: Some random noise is added to DFTK's default superposition of Gaussian atomic densities guess
• FM initial guess: Superposition of Gaussian atomic densities, spin polarisation in all transition metals is aligned.
• AFM initial guess: Superposition of Gaussian atomic densities, spin polarisation alters between transition metals.
• started within the stagnating region: SCF is restarted after 40 steps within the stagnating region of the Fe2CrGa calculation, see details in the article.
• using maximal conditioning 10ˣ in Anderson: To regularise the Anderson linear system, we truncate iterates in case the conditioning increases beyond the indicated threshold in those runs.