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Total energies of atoms from integral-equation radial solver

Jānis Užulis1*, Andris Gulans1*

1 Department of Physics, University of Latvia, LV-1004 Riga, Latvia

* Corresponding authors emails: janis.uzulis@lu.lv, andris.gulans@lu.lv
DOI10.24435/materialscloud:2w-ev [version v1]

Publication date: Feb 11, 2022

How to cite this record

Jānis Užulis, Andris Gulans, Total energies of atoms from integral-equation radial solver, Materials Cloud Archive 2022.25 (2022), doi: 10.24435/materialscloud:2w-ev.


We present a numerical tool for solving the non-relativistic Kohn-Sham problem for spherically-symmetric atoms. It treats the Schrödinger equation as an integral equation relying heavily on convolutions. The solver supports different types of exchange-correlation functionals including screened and long-range corrected hybrids. We implement a new method for treating range separation based on the complementary error function kernel. The present tool is applied in spin-restricted non-relativistic total energy calculations of atoms. A comparison with ultra-precise reference data[Cinal, JOMC 58, 1571 (2020)] shows a 14-digit agreement for Hartree-Fock results. We provide further benchmark data obtained with 5 different exchange-correlation functionals: VWN5 (the local-density approximation), PBE (the generalized gradient approximation), PBE0 and B3LYP (hybrids with a Fock exchange) and LC-BLYP (hybrid with a long-range corrected exchange).

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File name Size Description
49.8 MiB There are 3 types of text files in the archive: Z.input, Z.out and Z.wave_fun.dat, where Z is the nuclear charge of an atom. Z.input contains the input data. Z.out contains the standard output including the total energies and orbital energies. Z.wave_fun.dat contains the radial parts of all calculated orbitals. The shell occupancies are defined in Z.input and also printed in Z.out.


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

Preprint (Paper in which the method is described)
J. Užulis, A. Gulans, Radial Kohn-Sham problem via integral-equation approach, (in preparation)
Software (The software with which the data are obtained)


density-functional theory atoms hybrids high-precision hartree-fock

Version history:

2022.25 (version v1) [This version] Feb 11, 2022 DOI10.24435/materialscloud:2w-ev