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From densities to potentials: Benchmarking local exchange-correlation approximations

Visagan Ravindran1, Clio Johnson2, Neil D. Drummond2, Stewart J. Clark1, and Nikitas I. Gidopoulos1,*

  • *Contact author: nikitas.gidopoulos@durham.ac.uk
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Phys. Rev. B 114, 125121 – Published 21 August, 2026

DOI: https://doi.org/10.1103/w4tn-bjz9

Abstract

Using the Kohn-Sham (KS) inversion method of Hollins et al. [J. Phys.: Condens. Matter 29, 04LT01 (2017)], we invert densities from variational and diffusion quantum Monte Carlo (QMC) calculations to obtain benchmark QMC-KS potentials for a range of insulators and semiconductors, which we then compare to the KS potentials of popular density functional approximations (DFAs). Our results show that different DFAs yield similar electron densities, despite differences in their KS potentials, which originate primarily from the exchange and correlation contribution. We also find that the KS gap from the QMC density is typically larger than the KS gaps of most DFAs, with the exception of Hartree-Fock. Finally, the KS gap is sensitive to the inclusion of semicore states in the pseudopotentials, such that comparison with experiment should be done with caution.

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References (133)

  1. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  2. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
  3. A. D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Rev. A 38, 3098 (1988).
  4. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  5. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
  6. J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Climbing the density functional ladder: Nonempirical meta-generalized gradient approximation designed for molecules and solids, Phys. Rev. Lett. 91, 146401 (2003).
  7. J. Sun, A. Ruzsinszky, and J. P. Perdew, Strongly constrained and appropriately normed semilocal density functional, Phys. Rev. Lett. 115, 036402 (2015).
  8. A. P. Bartók and J. R. Yates, Regularized SCAN functional, J. Chem. Phys 150, 161101(R) (2019).
  9. J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, Accurate and numerically efficient r2SCAN meta-generalized gradient approximation, J. Phys. Chem. Lett. 11, 8208 (2020).
  10. A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys 98, 5648 (1993).
  11. J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys 118, 8207 (2003).
  12. J. P. Perdew, M. Ernzerhof, and K. Burke, Rationale for mixing exact exchange with density functional approximations, J. Chem. Phys. 105, 9982 (1996).
  13. R. van Leeuwen and E. J. Baerends, Exchange-correlation potential with correct asymptotic behavior, Phys. Rev. A 49, 2421 (1994).
  14. A. Görling, Kohn-Sham potentials and wave functions from electron densities, Phys. Rev. A 46, 3753 (1992).
  15. Q. Zhao, R. C. Morrison, and R. G. Parr, From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange-correlation potentials, and exchange-correlation energies, Phys. Rev. A 50, 2138 (1994).
  16. G. K.-L. Chan, D. J. Tozer, and N. C. Handy, Correlation potentials and functionals in Hartree-Fock-Kohn-Sham theory, J. Chem. Phys. 107, 1536 (1997).
  17. A. Savin, C. Umrigar, and X. Gonze, Relationship of Kohn-Sham eigenvalues to excitation energies, Chem. Phys. Lett. 288, 391 (1998).
  18. K. Peirs, D. Van Neck, and M. Waroquier, Algorithm to derive exact exchange-correlation potentials from correlated densities in atoms, Phys. Rev. A 67, 012505 (2003).
  19. E. S. Kadantsev and M. J. Stott, Variational method for inverting the Kohn-Sham procedure, Phys. Rev. A 69, 012502 (2004).
  20. I. G. Ryabinkin and V. N. Staroverov, Determination of Kohn-Sham effective potentials from electron densities using the differential virial theorem, J. Chem. Phys. 137, 164113 (2012).
  21. D. S. Jensen and A. Wasserman, Numerical methods for the inverse problem of density functional theory, Int. J. Quantum Chem. 118, e25425 (2018).
  22. Y. Shi and A. Wasserman, Inverse Kohn-Sham density functional theory: Progress and challenges, J. Phys. Chem. Lett. 12, 5308 (2021).
  23. A. Kumar, R. Singh, and M. K. Harbola, Universal nature of different methods of obtaining the exact Kohn-Sham exchange-correlation potential for a given density, J. Phys. B: At. Mol. Opt. Phys. 52, 075007 (2019).
  24. J. Erhard, E. Trushin, and A. Görling, Numerically stable inversion approach to construct Kohn-Sham potentials for given electron densities within a Gaussian basis set framework, J. Chem. Phys. 156, 204124 (2022).
  25. A. Aouina, M. Gatti, S. Chen, S. Zhang, and L. Reining, Accurate Kohn-Sham auxiliary system from the ground-state density of solids, Phys. Rev. B 107, 195123 (2023).
  26. A. Aouina, P. Borlido, M. A. L. Marques, and S. Botti, Assessing exchange-correlation functionals for accurate densities of solids, J. Chem. Theory Comput. 20, 10852 (2024).
  27. A. Kaiser and S. Kümmel, Rethinking the Kohn-Sham inverse problem, J. Chem. Phys. 163, 104101 (2025).
  28. W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, Quantum Monte Carlo simulations of solids, Rev. Mod. Phys. 73, 33 (2001).
  29. J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45, 13244 (1992).
  30. J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23, 5048 (1981).
  31. D. M. Ceperley and B. J. Alder, Ground state of the electron gas by a stochastic method, Phys. Rev. Lett. 45, 566 (1980).
  32. M.-C. Kim, E. Sim, and K. Burke, Understanding and reducing errors in density functional calculations, Phys. Rev. Lett. 111, 073003 (2013).
  33. A. Wasserman, J. Nafziger, K. Jiang, M.-C. Kim, E. Sim, and K. Burke, The importance of being inconsistent, Annu. Rev. Phys. Chem. 68, 555 (2017).
  34. E. Sim, S. Song, and K. Burke, Quantifying density errors in DFT, J. Phys. Chem. Lett. 9, 6385 (2018).
  35. S. Vuckovic, S. Song, J. Kozlowski, E. Sim, and K. Burke, Density functional analysis: The theory of density-corrected DFT, J. Chem. Theory Comput. 15, 6636 (2019).
  36. R. J. Needs, M. D. Towler, N. D. Drummond, P. López Ríos, and J. R. Trail, Variational and diffusion quantum Monte Carlo calculations with the CASINO code, J. Chem. Phys. 152, 154106 (2020).
  37. S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. J. Probert, K. Refson, and M. C. Payne, First principles methods using CASTEP, Z. Kristallogr 220, 567 (2005).
  38. O. Madelung, Semiconductors - Basic Data, 2nd ed. (Springer, Berlin, Heidelberg, 1996).
  39. J. R. Trail and R. J. Needs, Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg, J. Chem. Phys. 122, 174109 (2005).
  40. N. D. Drummond, J. R. Trail, and R. J. Needs, Trail-Needs pseudopotentials in quantum Monte Carlo calculations with plane-wave/blip basis sets, Phys. Rev. B 94, 165170 (2016).
  41. L. Kleinman and D. M. Bylander, Efficacious form for model pseudopotentials, Phys. Rev. Lett. 48, 1425 (1982).
  42. N. D. Drummond, M. D. Towler, and R. J. Needs, Jastrow correlation factor for atoms, molecules, and solids, Phys. Rev. B 70, 235119 (2004).
  43. E. Hernández, M. J. Gillan, and C. M. Goringe, Basis functions for linear-scaling first-principles calculations, Phys. Rev. B 55, 13485 (1997).
  44. D. Alfè and M. J. Gillan, Efficient localized basis set for quantum Monte Carlo calculations on condensed matter, Phys. Rev. B 70, 161101 (2004).
  45. Y. Kwon, D. M. Ceperley, and R. M. Martin, Effects of backflow correlation in the three-dimensional electron gas: Quantum Monte Carlo study, Phys. Rev. B 58, 6800 (1998).
  46. P. López Ríos, A. Ma, N. D. Drummond, M. D. Towler, and R. J. Needs, Inhomogeneous backflow transformations in quantum Monte Carlo calculations, Phys. Rev. E 74, 066701 (2006).
  47. See Supplemental Material at http://link.aps.org/supplemental/10.1103/w4tn-bjz9 for additional computational details, convergence tests, and supporting numerical results.
  48. A. Baldereschi, Mean-value point in the Brillouin zone, Phys. Rev. B 7, 5212 (1973).
  49. V. Stevanovic, A Python code for calculating the mean-value (Baldereschi's) point for any crystal structure, arXiv:2405.00925.
  50. C. J. Umrigar, K. G. Wilson, and J. W. Wilkins, Optimized trial wave functions for quantum Monte Carlo calculations, Phys. Rev. Lett. 60, 1719 (1988).
  51. N. D. Drummond and R. J. Needs, Variance-minimization scheme for optimizing Jastrow factors, Phys. Rev. B 72, 085124 (2005).
  52. J. Toulouse and C. J. Umrigar, Optimization of quantum Monte Carlo wave functions by energy minimization, J. Chem. Phys. 126, 084102 (2007).
  53. C. J. Umrigar, J. Toulouse, C. Filippi, S. Sorella, and R. G. Hennig, Alleviation of the fermion-sign problem by optimization of many-body wave functions, Phys. Rev. Lett. 98, 110201 (2007).
  54. D. M. Ceperley and M. H. Kalos, Quantum many-body problems, in Monte Carlo Methods in Statistical Physics, edited by K. Binder, 2nd ed. (Springer-Verlag, Heidelberg, 1979), p. 145.
  55. J. Casulleras and J. Boronat, Unbiased estimators in quantum Monte Carlo methods: Application to liquid He4, Phys. Rev. B 52, 3654 (1995).
  56. S. Baroni and S. Moroni, Reptation quantum Monte Carlo: A method for unbiased ground-state averages and imaginary-time correlations, Phys. Rev. Lett. 82, 4745 (1999).
  57. T. W. Hollins, S. J. Clark, K. Refson, and N. I. Gidopoulos, A local Fock-exchange potential in Kohn-Sham equations, J. Phys.: Condens. Matter 29, 04LT01 (2017).
  58. S. J. Clark, T. W. Hollins, K. Refson, and N. I. Gidopoulos, Self-interaction free local exchange potentials applied to metallic systems, J. Phys.: Condens. Matter 29, 374002 (2017).
  59. T. J. Callow, N. N. Lathiotakis, and N. I. Gidopoulos, Density-inversion method for the Kohn-Sham potential: Role of the screening density, J. Chem. Phys. 152, 164114 (2020).
  60. S. Bousiadi, N. I. Gidopoulos, and N. N. Lathiotakis, Density inversion method for local basis sets without potential auxiliary functions: Inverting densities from RDMFT, Phys. Chem. Chem. Phys. 24, 19279 (2022).
  61. V. Ravindran, N. I. Gidopoulos, and S. J. Clark, Local exchange-correlation potentials by density inversion in solids, Phys. Rev. B 112, 085208 (2025).
  62. R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients, Comput. J. 7, 149 (1964).
  63. N. I. Gidopoulos, Progress at the interface of wave-function and density-functional theories, Phys. Rev. A 83, 040502(R) (2011).
  64. E. H. Lieb, Density functionals for Coulomb systems, Int. J. Quantum Chem. 24, 243 (1983).
  65. Q. Wu and W. Yang, A direct optimization method for calculating density functionals and exchange-correlation potentials from electron densities, J. Chem. Phys. 118, 2498 (2003).
  66. T. J. P. Irons, J. W. Furness, M. S. Ryley, J. Zemen, T. Helgaker, and A. M. Teale, Connections between variation principles at the interface of wave-function and density-functional theories, J. Chem. Phys. 147, 134107 (2017).
  67. T. Gould, Toward routine Kohn-Sham inversion using the “Lieb-response” approach, J. Chem. Phys. 158, 064102 (2023).
  68. A. Kumar and M. K. Harbola, A general penalty method for density-to-potential inversion, Int. J. Quantum Chem. 120, e26400 (2020),.
  69. K. H. Hellwege and A. M. Hellwege, Ferroelectrics and related substances, in Landolt-Börnstein (Springer-Verlag, Berlin, 1969), Vol. 3.
  70. J. J. Wang, F. Y. Meng, X. Q. Ma, M. X. Xu, and L. Q. Chen, Lattice, elastic, polarization, and electrostrictive properties of BaTiO3 from first-principles, J. Appl. Phys. 108, 034107 (2010).
  71. Y. A. Abramov, V. G. Tsirelson, V. E. Zavodnik, S. A. Ivanov, and I. D. Brown, The chemical bond and atomic displacements in SrTiO3 from X-ray diffraction analysis, Acta Crystallogr., Sect. B: Struct. Sci. 51, 942 (1995).
  72. S. Sasaki, K. Fujino, and Y. Tákeuchi, X-ray determination of electron-density distributions in oxides, MgO, MnO, CoO, and NiO, and atomic scattering factors of their constituent atoms, Proc. Jpn. Acad., Ser. B 55, 43 (1979).
  73. S. Chiesa, D. M. Ceperley, R. M. Martin, and M. Holzmann, Finite-size error in many-body simulations with long-range interactions, Phys. Rev. Lett. 97, 076404 (2006).
  74. J. P. Perdew and K. Schmidt, Jacob's ladder of density functional approximations for the exchange-correlation energy, AIP Conf. Proc. 577, 1 (2001).
  75. R. T. Sharp and G. K. Horton, A variational approach to the unipotential many-electron problem, Phys. Rev. 90, 317 (1953).
  76. J. D. Talman and W. F. Shadwick, Optimized effective atomic central potential, Phys. Rev. A 14, 36 (1976).
  77. S. Kümmel and L. Kronik, Orbital-dependent density functionals: Theory and applications, Rev. Mod. Phys. 80, 3 (2008).
  78. A. Seidl, A. Görling, P. Vogl, J. A. Majewski, and M. Levy, Generalized Kohn-Sham schemes and the band-gap problem, Phys. Rev. B 53, 3764 (1996).
  79. J. P. Perdew, W. Yang, K. Burke, Z. Yang, E. K. U. Gross, M. Scheffler, G. E. Scuseria, T. M. Henderson, I. Y. Zhang, A. Ruzsinszky, H. Peng, J. Sun, E. Trushin, and A. Görling, Understanding band gaps of solids in generalized Kohn-Sham theory, Proc. Natl. Acad. Sci. USA 114, 2801 (2017).
  80. Z.-H. Yang, H. Peng, J. Sun, and J. P. Perdew, More realistic band gaps from meta-generalized gradient approximations: Only in a generalized Kohn-Sham scheme, Phys. Rev. B 93, 205205 (2016).
  81. Y. Jin, N. Q. Su, Z. Chen, and W. Yang, Introductory lecture: When the density of the noninteracting reference system is not the density of the physical system in density functional theory, Faraday Discuss. 224, 9 (2020).
  82. R. Garrick, A. Natan, T. Gould, and L. Kronik, Exact generalized Kohn-Sham theory for hybrid functionals, Phys. Rev. X 10, 021040 (2020).
  83. J. S. Lin, A. Qteish, M. C. Payne, and V. Heine, Optimized and transferable nonlocal separable ab initio pseudopotentials, Phys. Rev. B 47, 4174 (1993).
  84. K. Lejaeghere et al., Reproducibility in density functional theory calculations of solids, Science 351, aad3000 (2016).
  85. D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
  86. P. R. T. Schipper, O. V. Gritsenko, and E. J. Baerends, Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities, Theor. Chem. Acc. 98, 16 (1997).
  87. K. Capelle and G. Vignale, Nonuniqueness of the potentials of spin-density-functional theory, Phys. Rev. Lett. 86, 5546 (2001).
  88. N. I. Gidopoulos, Potential in spin-density-functional theory of noncollinear magnetism determined by the many-electron ground state, Phys. Rev. B 75, 134408 (2007).
  89. M. Penz, E. I. Tellgren, M. A. Csirik, M. Ruggenthaler, and A. Laestadius, The structure of density-potential mapping. Part I: Standard density-functional theory, ACS Phys. Chem. Au 3, 334 (2023).
  90. M. Penz, E. I. Tellgren, M. A. Csirik, M. Ruggenthaler, and A. Laestadius, The structure of the density-potential mapping. Part II: Including magnetic fields, ACS Phys. Chem. Au 3, 492 (2023).
  91. A. Savin, F. Colonna, and M. Allavena, Analysis of the linear response function along the adiabatic connection from the Kohn-Sham to the correlated system, J. Chem. Phys. 115, 6827 (2001).
  92. A. Savin, F. Colonna, and R. Pollet, Adiabatic connection approach to density functional theory of electronic systems, Int. J. Quantum Chem. 93, 166 (2003).
  93. A. K. Theophilou, The energy density functional formalism for excited states, J. Phys. C: Solid State Phys. 12, 5419 (1979).
  94. M.-C. Kim, E. Sim, and K. Burke, Ions in solution: Density corrected density functional theory (DC-DFT), J. Chem. Phys. 140, 18A528 (2014).
  95. Y. Yang, V. Gorelov, C. Pierleoni, D. M. Ceperley, and M. Holzmann, Electronic band gaps from quantum Monte Carlo methods, Phys. Rev. B 101, 085115 (2020).
  96. A. Annaberdiyev, G. Wang, C. A. Melton, M. C. Bennett, and L. Mitas, Cohesion and excitations of diamond-structure silicon by quantum Monte Carlo: Benchmarks and control of systematic biases, Phys. Rev. B 103, 205206 (2021).
  97. V. Gorelov, Y. Yang, M. Ruggeri, D. M. Ceperley, C. Pierleoni, and M. Holzmann, Neutral band gap of carbon by quantum Monte Carlo methods, Condens. Matter Phys. 26, 33701 (2023).
  98. M. D. Towler, R. Q. Hood, and R. J. Needs, Minimum principles and level splitting in quantum Monte Carlo excitation energies: Application to diamond, Phys. Rev. B 62, 2330 (2000).
  99. S. H. Wemple, Polarization fluctuations and the optical-absorption edge in BaTiO3, Phys. Rev. B 2, 2679 (1970).
  100. K. van Benthem, C. Elsässer, and R. H. French, Bulk electronic structure of SrTiO3: Experiment and theory, J. Appl. Phys 90, 6156 (2001).
  101. J.-W. Lee, L. Mitas, and L. K. Wagner, Quantum Monte Carlo study of MnO solid, arXiv:cond-mat/0411247.
  102. R. Zimmermann et al., Electronic structure of 3d-transition-metal oxides: On-site Coulomb repulsion versus covalency, J. Phys.: Condens. Matter 11, 1657 (1999).
  103. J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Density-functional theory for fractional particle number: Derivative discontinuities of the energy, Phys. Rev. Lett. 49, 1691 (1982).
  104. J. P. Perdew and M. Levy, Comment on “Significance of the highest occupied Kohn-Sham eigenvalue”, Phys. Rev. B 56, 16021 (1997).
  105. L. J. Sham and M. Schlüter, Density-functional theory of the energy gap, Phys. Rev. Lett. 51, 1888 (1983).
  106. L. J. Sham and M. Schlüter, Density-functional theory of the band gap, Phys. Rev. B 32, 3883 (1985).
  107. W. Knorr and R. W. Godby, Investigating exact density-functional theory of a model semiconductor, Phys. Rev. Lett. 68, 639 (1992).
  108. W. Knorr and R. W. Godby, Quantum Monte Carlo study of density-functional theory for a semiconducting wire, Phys. Rev. B 50, 1779 (1994).
  109. N. A. Lima, L. N. Oliveira, and K. Capelle, Density-functional study of the Mott gap in the Hubbard model, Europhys. Lett. 60, 601 (2002).
  110. K. Capelle, N. A. Lima, M. F. Silva, and L. N. Oliveira, Density-functional theory for the Hubbard model: Numerical results for the Luttinger liquid and the Mott insulator, in The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State, edited by N. I. Gidopoulos and S. Wilson (Springer, Netherlands, Dordrecht, 2003), pp. 145-168.
  111. E. M. Stoudenmire, L. O. Wagner, S. R. White, and K. Burke, One-dimensional continuum electronic structure with the density-matrix renormalization group and its implications for density-functional theory, Phys. Rev. Lett. 109, 056402 (2012).
  112. K. Burke and J. Kozlowski, Lies my teacher told me about density functional theory: Seeing through them with the Hubbard dimer, in Simulating Correlations with Computers, Modeling and Simulation, edited by E. Pavarini and E. Koch (Verlag des Forschungszentrums, Jülich, 2021), Vol. 11, Chap. 3.
  113. A. I. Blair, A. Kroukis, and N. I. Gidopoulos, A correction for the Hartree-Fock density of states for jellium without screening, J. Chem. Phys. 142, 084116 (2015).
  114. L. K. Wagner, Transition metal oxides using quantum Monte Carlo, J. Phys.: Condens. Matter 19, 343201 (2007).
  115. L. Mitáš, Quantum Monte Carlo calculation of the Fe atom, Phys. Rev. A 49, 4411 (1994).
  116. These pseudopotentials are shipped with CASTEP as MnO_00.recpot and O_00.recpot for Mn and O, respectively.
  117. M.-H. Lee, Advanced pseudopotentials for large scale electronic structure calculations with application to a study of weakly ordered material - γ−Al2O3, Ph.D. thesis, Clare College, University of Cambridge, 1995.
  118. F. Giustino, S. G. Louie, and M. L. Cohen, Electron-phonon renormalization of the direct band gap of diamond, Phys. Rev. Lett. 105, 265501 (2010).
  119. F. Karsai, M. Engel, E. Flage-Larsen, and G. Kresse, Electron-phonon coupling in semiconductors within the gw approximation, New J. Phys. 20, 123008 (2018).
  120. I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, Ab initio density functional theory: OEP-MBPT(2). A new orbital-dependent correlation functional, J. Chem. Phys. 116, 4415 (2002).
  121. R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, The exchange-correlation potential in ab initio density functional theory, J. Chem. Phys. 122, 034104 (2005).
  122. R. J. Bartlett, Ab initio DFT and its role in electronic structure theory, Mol. Phys. 108, 3299 (2010).
  123. R. J. Bartlett, Adventures in DFT by a wavefunction theorist, J. Chem. Phys. 151, 160901 (2019), see also contained references for section IV.
  124. C. Filippi, X. Gonze, and C. Umrigar, Generalized gradient approximations to density functional theory: Comparison with exact results, in Recent Developments and Applications of Modern Density Functional Theory, Theoretical and Computational Chemistry, edited by J. Seminario (Elsevier, Amsterdam, 1996), Vol. 4, pp. 295–326.
  125. E. Trushin, S. Fauser, A. Mölkner, J. Erhard, and A. Görling, Accurate correlation potentials from the self-consistent random phase approximation, Phys. Rev. Lett. 134, 016402 (2025).
  126. V. Ravindran, C. Johnson, N. D. Drummond, S. J. Clark, and N. I. Gidopoulos, From densities to potentials: Benchmarking local exchange-correlation approximations [dataset], http://doi.org/10.15128/r2q811kj67b (2025).
  127. A. J. Morris, R. J. Nicholls, C. J. Pickard, and J. R. Yates, OptaDOS: A tool for obtaining density of states, core-level and optical spectra from electronic structure codes, Comput. Phys. Commun. 185, 1477 (2014).
  128. M. D. Segall, R. Shah, C. J. Pickard, and M. C. Payne, Population analysis of plane-wave electronic structure calculations of bulk materials, Phys. Rev. B 54, 16317 (1996).
  129. J. R. Yates, X. Wang, D. Vanderbilt, and I. Souza, Spectral and Fermi surface properties from Wannier interpolation, Phys. Rev. B 75, 195121 (2007).
  130. D. R. Hamann, M. Schlüter, and C. Chiang, Norm-conserving pseudopotentials, Phys. Rev. Lett. 43, 1494 (1979).
  131. S. G. Louie, S. Froyen, and M. L. Cohen, Nonlinear ionic pseudopotentials in spin-density-functional calculations, Phys. Rev. B 26, 1738 (1982).
  132. D. Porezag, M. R. Pederson, and A. Y. Liu, Importance of nonlinear core corrections for density-functional based pseudopotential calculations, Phys. Rev. B 60, 14132 (1999).
  133. Distributed with castep as Si_00.recpot.

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Phys. Rev. B 114, 125121– Published 21 August, 2026
  • Received 30 October 2025
  • Revised 17 June 2026
  • Accepted 13 July 2026
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