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Exploring the accuracy of the equation-of-motion coupled-cluster band gap of solids

Evgeny Moerman1,*, Henrique Miranda2, Alejandro Gallo3, Andreas Irmler3, Tobias Schäfer3, Felix Hummel3, Manuel Engel2, Georg Kresse2,4, Matthias Scheffler1 et al.

Andreas Grüneis3,†

  • *Contact author: moerman@fhi-berlin.mpg.de
  • †Contact author: andreas.grueneis@tuwien.ac.at
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Phys. Rev. B 111, L121202 – Published 26 March, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L121202

Abstract

While the periodic equation-of-motion coupled-cluster (EOM-CC) method promises systematic improvement of electronic band gap calculations in solids, its practical application at the singles and doubles level (EOM-CCSD) is hindered by severe finite-size errors in feasible simulation cells. We present a hybrid approach combining EOM-CCSD with the computationally less demanding GW approximation to estimate thermodynamic limit band gaps for several insulators and semiconductors. Our method substantially reduces required cell sizes while maintaining accuracy. Comparisons with experimental gaps and self-consistent GW calculations reveal that deviations in EOM-CCSD predictions correlate with reduced single excitation character of the excited many-electron states. Our work not only provides a computationally tractable approach to EOM-CC calculations in solids but also reveals fundamental insights into the role of single excitations in electronic-structure theory.

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References (53)

  1. J. P. Perdew, W. Yang, K. Burke, Z. Yang, E. K. Gross, M. Scheffler, G. E. Scuseria, T. M. Henderson, I. Y. Zhang, A. Ruzsinszky et al., Understanding band gaps of solids in generalized Kohn–Sham theory, Proc. Natl. Acad. Sci. USA 114, 2801 (2017).
  2. L. Hedin, New method for calculating the one-particle Green's function with application to the electron-gas problem, Phys. Rev. 139, A796 (1965).
  3. D. Golze, M. Dvorak, and P. Rinke, The GW compendium: A practical guide to theoretical photoemission spectroscopy, Front. Chem. 7, 377 (2019).
  4. P. Rinke, A. Qteish, J. Neugebauer, C. Freysoldt, and M. Scheffler, Combining GW calculations with exact-exchange density-functional theory: an analysis of valence-band photoemission for compound semiconductors, New J. Phys. 7, 126 (2005).
  5. F. Fuchs, J. Furthmüller, F. Bechstedt, M. Shishkin, and G. Kresse, Quasiparticle band structure based on a generalized Kohn-Sham scheme, Phys. Rev. B 76, 115109 (2007).
  6. M. Shishkin, M. Marsman, and G. Kresse, Accurate quasiparticle spectra from self-consistent GW calculations with vertex corrections, Phys. Rev. Lett. 99, 246403 (2007).
  7. A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, Influence of the exchange screening parameter on the performance of screened hybrid functionals, J. Chem. Phys. 125, 224106 (2006).
  8. A. Miglio, V. Brousseau-Couture, E. Godbout, G. Antonius, Y.-H. Chan, S. G. Louie, M. Côté, M. Giantomassi, and X. Gonze, Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap, npj Comput. Mater. 6, 167 (2020).
  9. M. Engel, H. Miranda, L. Chaput, A. Togo, C. Verdi, M. Marsman, and G. Kresse, Zero-point renormalization of the band gap of semiconductors and insulators using the projector augmented wave method, Phys. Rev. B 106, 094316 (2022).
  10. M. Zacharias, M. Scheffler, and C. Carbogno, Fully anharmonic nonperturbative theory of vibronically renormalized electronic band structures, Phys. Rev. B 102, 045126 (2020).
  11. R. J. Hunt, M. Szyniszewski, G. I. Prayogo, R. Maezono, and N. D. Drummond, Quantum Monte Carlo calculations of energy gaps from first principles, Phys. Rev. B 98, 075122 (2018).
  12. R. J. Hunt, B. Monserrat, V. Zólyomi, and N. D. Drummond, Diffusion quantum Monte Carlo and GW study of the electronic properties of monolayer and bulk hexagonal boron nitride, Phys. Rev. B 101, 205115 (2020).
  13. J. F. Stanton and R. J. Bartlett, The equation of motion coupled-cluster method. a systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties, J. Chem. Phys. 98, 7029 (1993).
  14. X. Wang and T. C. Berkelbach, Excitons in solids from periodic equation-of-motion coupled-cluster theory, J. Chem. Theory Comput. 16, 3095 (2020).
  15. A. M. Lewis and T. C. Berkelbach, Ab initio linear and pump–probe spectroscopy of excitons in molecular crystals, J. Phys. Chem. Lett. 11, 2241 (2020).
  16. A. Gallo, F. Hummel, A. Irmler, and A. Grüneis, A periodic equation-of-motion coupled-cluster implementation applied to F-centers in alkaline earth oxides, J. Chem. Phys. 154, 064106 (2021).
  17. J. McClain, Q. Sun, G. K.-L. Chan, and T. C. Berkelbach, Gaussian-based coupled-cluster theory for the ground-state and band structure of solids, J. Chem. Theory Comput. 13, 1209 (2017).
  18. E. A. Vo, X. Wang, and T. C. Berkelbach, Performance of periodic EOM-CCSD for bandgaps of inorganic semiconductors and insulators, J. Chem. Phys. 160, 044106 (2024).
  19. E. Moerman, A. Gallo, A. Irmler, T. Schäfer, F. Hummel, A. Grüneis, and M. Scheffler, Finite-size effects in periodic EOM-CCSD for ionization energies and electron affinities: Convergence rate and extrapolation to the thermodynamic limit, J. Chem. Theory Comput. 21, 1865 (2025).
  20. D. S. Ranasinghe, J. T. Margraf, A. Perera, and R. J. Bartlett, Vertical valence ionization potential benchmarks from equation-of-motion coupled cluster theory and QTP functionals, J. Chem. Phys. 150, 074108 (2019).
  21. M. F. Lange and T. C. Berkelbach, On the relation between equation-of-motion coupled-cluster theory and the GW approximation, J. Chem. Theory Comput. 14, 4224 (2018).
  22. J. Tölle and G. K.-L. Chan, Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism, J. Chem. Phys. 158, 124123 (2023).
  23. M. S. Hybertsen and S. G. Louie, Ab initio static dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators, Phys. Rev. B 35, 5585 (1987).
  24. R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem, 2nd ed., Dover Books on Physics and Chemistry (Dover Publications, New York, 1992).
  25. T. Gruber, K. Liao, T. Tsatsoulis, F. Hummel, and A. Grüneis, Applying the coupled-cluster Ansatz to solids and surfaces in the thermodynamic limit, Phys. Rev. X 8, 021043 (2018).
  26. X. Xing and L. Lin, Inverse volume scaling of finite-size error in periodic coupled cluster theory, Phys. Rev. X 14, 011059 (2024).
  27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.111.L121202 for computational details including structural parameters of the studied materials, positions of the band edges, calculation settings chosen for the electronic structure calculations of quasiparticle energies and the ZPR, details on the evaluation of the basis set incompleteness error, the G0W0 convergence and EOM-CC vs G0W0 parity plots for the VASP calculations, additional EOM-CC convergence results, the system size-dependent change of the single-excitation character, and a benchmark of the implemented EOM-CCSD method for a set of small molecules.
  28. A. Grüneis, M. Marsman, and G. Kresse, Second-order Møller–Plesset perturbation theory applied to extended systems. II. Structural and energetic properties, J. Chem. Phys. 133, 074107 (2010).
  29. I. Y. Zhang, A. J. Logsdail, X. Ren, S. V. Levchenko, L. Ghiringhelli, and M. Scheffler, Main-group test set for materials science and engineering with user-friendly graphical tools for error analysis: Systematic benchmark of the numerical and intrinsic errors in state-of-the-art electronic-structure approximations, New J. Phys. 21, 013025 (2019).
  30. E. Moerman, F. Hummel, A. Grüneis, A. Irmler, and M. Scheffler, Interface to high-performance periodic coupled-cluster theory calculations with atom-centered, localized basis functions, J. Open Source Softw. 7, 4040 (2022).
  31. S. V. Levchenko, X. Ren, J. Wieferink, R. Johanni, P. Rinke, V. Blum, and M. Scheffler, Hybrid functionals for large periodic systems in an all-electron, numeric atom-centered basis framework, Comput. Phys. Commun. 192, 60 (2015).
  32. cc4s; available from https://manuals.cc4s.org. Accessed on 01.05.2025.
  33. M. Musiał, S. A. Kucharski, and R. J. Bartlett, Equation-of-motion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IP-EOM-CCSDT, J. Chem. Phys. 118, 1128 (2003).
  34. M. Musiał and R. J. Bartlett, Equation-of-motion coupled cluster method with full inclusion of connected triple excitations for electron-attached states: EA-EOM-CCSDT, J. Chem. Phys. 119, 1901 (2003).
  35. T. Chiang, Electronic Structure of Solids: Photoemission Spectra and Related Data (Springer, Berlin, 1989).
  36. O. Madelung, Semiconductors: Data Handbook (Springer Science & Business Media, Springer, Berlin, 2004).
  37. M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, Properties of Advanced Semiconductor Materials: GaN, AIN, InN, BN, SiC, SiGe (John Wiley & Sons, New York, 2001).
  38. K. Woo, K. Lee, and K. Kovnir, BP: Synthesis and properties of boron phosphide, Mater. Res. Express 3, 074003 (2016).
  39. S. Baroni, G. P. Parravicini, and G. Pezzica, Quasiparticle band structure of lithium hydride, Phys. Rev. B 32, 4077 (1985).
  40. M. Piacentini, D. W. Lynch, and C. G. Olson, Thermoreflectance of LiF between 12 and 30 eV, Phys. Rev. B 13, 5530 (1976).
  41. G. Baldini and B. Bosacchi, Optical properties of Na and Li halide crystals at 55 °K, physica status solidi (b) 38, 325 (1970).
  42. R. Whited, C. J. Flaten, and W. Walker, Exciton thermoreflectance of MgO and CaO, Solid State Commun. 13, 1903 (1973).
  43. F. Hummel, T. Tsatsoulis, and A. Grüneis, Low rank factorization of the Coulomb integrals for periodic coupled cluster theory, J. Chem. Phys. 146, 124105 (2017).
  44. J. Paier, R. Hirschl, M. Marsman, and G. Kresse, The Perdew–Burke–Ernzerhof exchange-correlation functional applied to the G2-1 test set using a plane-wave basis set, J. Chem. Phys. 122, 234102 (2005).
  45. R. Sundararaman and T. A. Arias, Regularization of the Coulomb singularity in exact exchange by Wigner-Seitz truncated interactions: Towards chemical accuracy in nontrivial systems, Phys. Rev. B 87, 165122 (2013).
  46. S. Massidda, M. Posternak, and A. Baldereschi, Hartree-Fock LAPW approach to the electronic properties of periodic systems, Phys. Rev. B 48, 5058 (1993).
  47. B. Monserrat, N. Drummond, and R. J. Needs, Anharmonic vibrational properties in periodic systems: energy, electron-phonon coupling, and stress, Phys. Rev. B 87, 144302 (2013).
  48. V. G. Plekhanov, Isotopic and disorder effects in large exciton spectroscopy, Phys. Usp. 40, 553 (1997).
  49. A. S. Alag, D. P. Jelenfi, A. Tajti, and P. G. Szalay, Accurate prediction of vertical ionization potentials and electron affinities from spin-component scaled CC2 and ADC(2) models, J. Chem. Theory Comput. 18, 6794 (2022).
  50. A. Marie and P.-F. Loos, Reference energies for valence ionizations and satellite transitions, J. Chem. Theory Comput. 20, 4751 (2024).
  51. J. F. Stanton and J. Gauss, A simple scheme for the direct calculation of ionization potentials with coupled-cluster theory that exploits established excitation energy methods, J. Chem. Phys. 111, 8785 (1999).
  52. F. Kossoski, M. Boggio-Pasqua, P.-F. Loos, and D. Jacquemin, Reference energies for double excitations: Improvement and extension, J. Chem. Theory Comput. 20, 5655 (2024).
  53. K. Krause, M. E. Harding, and W. Klopper, Coupled-cluster reference values for the GW27 and GW100 test sets for the assessment of GW methods, Mol. Phys. 113, 1952 (2015).

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Phys. Rev. B 111, L121202– Published 26 March, 2025
  • Received 22 January 2025
  • Accepted 27 February 2025
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