- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Efficient periodic density functional theory calculations of charged molecules and surfaces using Coulomb kernel truncation

Sudarshan Vijay1,*,†, Martin Schlipf1, Henrique Miranda1, Ferenc Karsai1, Merzuk Kaltak1, Martijn Marsman1, and Georg Kresse1,2,‡

  • *Contact author: sudarshan.vijay@vasp.at; sudarshan.vijay @iitb.ac.in
  • †Present address: Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra 400076, India.
  • ‡Contact author: georg.kresse@univie.ac.at
PDF

Phys. Rev. B 112, 045409 – Published 10 July, 2025

DOI: https://doi.org/10.1103/cd6s-cdkf

Abstract

Density functional theory (DFT) calculations of charged molecules and surfaces are critical to applications in electrocatalysis, energy materials, and related fields of materials science. DFT implementations such as the Vienna ab initio simulation package (vasp) compute the electrostatic potential under three-dimensional (3D) periodic boundary conditions, necessitating charge neutrality. In this work, we implement 0D and 2D periodic boundary conditions to facilitate DFT calculations of charged molecules and surfaces, respectively. We implement these boundary conditions using the Coulomb kernel truncation method. Our implementation computes the potential under 0D and 2D boundary conditions by selectively subtracting unwanted long-range interactions in the potential computed under 3D boundary conditions. By combining the Coulomb kernel truncation method with a computationally efficient padding approach, we remove nonphysical potentials from vacuum in 0D and 2D systems. To illustrate the computational efficiency of our method, we perform large supercell calculations of the formation energy of a charged chlorine defect on a sodium chloride (001) surface and perform long-timescale molecular dynamics simulations on a stepped gold (211) water electrode-electrolyte interface.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (36)

  1. S.-J. Shin, D. H. Kim, G. Bae, S. Ringe, H. Choi, H.-K. Lim, C. H. Choi, and H. Kim, On the importance of the electric double layer structure in aqueous electrocatalysis, Nat. Commun. 13, 174 (2022).
  2. P. Lindgren, G. Kastlunger, and A. A. Peterson, Electrochemistry from the atomic scale, in the electronically grand-canonical ensemble, J. Chem. Phys. 157, 180902 (2022).
  3. E. W. C. Spotte-Smith, R. L. Kam, D. Barter, X. Xie, T. Hou, S. Dwaraknath, S. M. Blau, and K. A. Persson, Toward a mechanistic model of solid-electrolyte interphase formation and evolution in lithium-ion batteries, ACS Energy Lett. 7, 1446 (2022).
  4. N. Kumar, K. Leung, and D. J. Siegel, Crystal surface and state of charge dependencies of electrolyte decomposition on LiMn2O4 cathode, J. Electrochem. Soc. 161, E3059 (2014).
  5. H. P. Komsa, N. Berseneva, A. V. Krasheninnikov, and R. M. Nieminen, Charged point defects in the flatland: Accurate formation energy calculations in two-dimensional materials, Phys. Rev. X 4, 031044 (2014).
  6. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van de Walle, First-principles calculations for point defects in solids, Rev. Mod. Phys. 86, 253 (2014).
  7. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  8. P. P. Ewald, Die Berechnung optischer und elektrostatischer Gitterpotentiale, Ann. Phys. (Leipzig) 369, 253 (1921).
  9. S. W. de Leeuw, J. W. Perram, and E. R. Smith, Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants, Proc. R. Soc. Lond. A 373, 27 (1980).
  10. L. Bengtsson, Dipole correction for surface supercell calculations, Phys. Rev. B 59, 12301 (1999).
  11. J. Neugebauer and M. Scheffler, Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on Al(111), Phys. Rev. B 46, 16067 (1992).
  12. T. Sohier, M. Calandra, and F. Mauri, Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene, Phys. Rev. B 96, 075448 (2017).
  13. G. Makov and M. C. Payne, Periodic boundary conditions in ab initio calculations, Phys. Rev. B 51, 4014 (1995).
  14. M. R. Jarvis, I. D. White, R. W. Godby, and M. C. Payne, Supercell technique for total-energy calculations of finite charged and polar systems, Phys. Rev. B 56, 14972 (1997).
  15. C. A. Rozzi, D. Varsano, A. Marini, E. K. Gross, and A. Rubio, Exact Coulomb cutoff technique for supercell calculations, Phys. Rev. B 73, 205119 (2006).
  16. Y. Mokrousov, G. Bihlmayer, and S. Blügel, Full-potential linearized augmented plane-wave method for one-dimensional systems: Gold nanowire and iron monowires in a gold tube, Phys. Rev. B 72, 045402 (2005).
  17. S. Lany and A. Zunger, Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAS, Phys. Rev. B 78, 235104 (2008).
  18. O. Andreussi and N. Marzari, Electrostatics of solvated systems in periodic boundary conditions, Phys. Rev. B 90, 245101 (2014).
  19. K. Mathew, R. Sundararaman, K. Letchworth-Weaver, T. A. Arias, and R. G. Hennig, Implicit solvation model for density-functional study of nanocrystal surfaces and reaction pathways, J. Chem. Phys. 140, 084106 (2014).
  20. R. Sundararaman, W. A. Goddard, and T. A. Arias, Grand canonical electronic density-functional theory: Algorithms and applications to electrochemistry, J. Chem. Phys. 146, 114104 (2017).
  21. J. S. Hub, B. L. De Groot, H. Grubmüller, and G. Groenhof, Quantifying artifacts in Ewald simulations of inhomogeneous systems with a net charge, J. Chem. Theory Comput. 10, 381 (2014).
  22. J. A. Gauthier, C. F. Dickens, H. H. Heenen, S. Vijay, S. Ringe, and K. Chan, Unified approach to implicit and explicit solvent simulations of electrochemical reaction energetics, J. Chem. Theory Comput. 15, 6895 (2019).
  23. S. Ismail-Beigi, Truncation of periodic image interactions for confined systems, Phys. Rev. B 73, 233103 (2006).
  24. N. D. M. Hine, J. Dziedzic, P. D. Haynes, and C.-K. Skylaris, Electrostatic interactions in finite systems treated with periodic boundary conditions: Application to linear-scaling density functional theory, J. Chem. Phys. 135, 204103 (2011).
  25. J. Ihm, A. Zunger, and M. L. Cohen, Momentum-space formalism for the total energy of solids, J. Phys. C 12, 4409 (1979).
  26. I. Dabo, B. Kozinsky, N. E. Singh-Miller, and N. Marzari, Electrostatics in periodic boundary conditions and real-space corrections, Phys. Rev. B 77, 115139 (2008).
  27. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  28. D. M. Heyes, M. Barber, and J. H. R. Clarke, Molecular dynamics computer simulation of surface properties of crystalline potassium chloride, J. Chem. Soc. Faraday Trans. 2 73, 1485 (1977).
  29. C. Freysoldt, J. Neugebauer, and C. G. Van De Walle, Fully Ab initio finite-size corrections for charged-defect supercell calculations, Phys. Rev. Lett. 102, 016402 (2009).
  30. H. P. Komsa and A. Pasquarello, Finite-size supercell correction for charged defects at surfaces and interfaces, Phys. Rev. Lett. 110, 095505 (2013).
  31. S. Nosé, A unified formulation of the constant temperature molecular dynamics methods, J. Chem. Phys. 81, 511 (1984).
  32. R. Jinnouchi, J. Lahnsteiner, F. Karsai, G. Kresse, and M. Bokdam, Phase transitions of hybrid perovskites simulated by machine-learning force fields trained on-the-fly with Bayesian inference, Phys. Rev. Lett. 122, 225701 (2019).
  33. B. Hammer, L. B. Hansen, and J. K. Nørskov, Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals, Phys. Rev. B 59, 7413 (1999).
  34. S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem. 27, 1787 (2006).
  35. S. Vijay, Efficient periodic density functional theory calculations of charged molecules and surfaces using Coulomb kernel truncation [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.15494936.
  36. R. Jinnouchi, F. Karsai, and G. Kresse, Absolute standard hydrogen electrode potential and redox potentials of atoms and molecules: machine learning aided first principles calculations, Chem. Sci. 16, 2335 (2025).

Outline

Information

Phys. Rev. B 112, 045409– Published 10 July, 2025
  • Received 6 January 2025
  • Revised 29 April 2025
  • Accepted 21 May 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation