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Multichannel active-space embedding of atomic multiplets in plane-wave density functional theory/projector augmented-wave for core-level spectroscopies

Alessandro Mirone1,*, Mauro Rovezzi2, Christoph J. Sahle1, and Alessandro Longo2,3

  • *Contact author: mirone@esrf.fr
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Phys. Rev. Research 8, 023056 – Published 16 April, 2026

DOI: https://doi.org/10.1103/gnd5-sxl2

Abstract

We introduce an active-space embedding framework for core-level spectroscopies that connects localized atomic multiplets to continuum resonances within a plane-wave density functional theory/projector augmented-wave description. The approach is complementary to widely used core-level Bethe-Salpeter implementations based on a two-particle (core-exciton) picture with typically static screening: Here, a correlated multiplet manifold of the absorber (including the core hole and open-shell configurations) is coherently coupled to a plane-wave photoelectron, enabling a unified treatment of localized multiplet structure and continuum lineshapes. Spectra are computed in a general time-domain formulation equivalent to Fermi's golden rule: A transition operator tailored to the specific spectroscopy technique is applied to the correlated ground state to generate an excited wave packet, and the corresponding wave packet autocorrelation function is evaluated without explicit real-time propagation, using Lanczos tridiagonalization or the kernel polynomial method; the spectral intensity follows from its Fourier representation. We validate the method at the Ce N4,5 edges, reproducing in quantitative agreement with experiment both high-Q multiplet features and the low-Q giant dipole resonance continuum, including a characteristic low-energy shoulder relevant for robust Ce valence assignments. The implementation is available open source within the quantum espresso xspectra package (xspectruplet mode), together with reproducible inputs and scripts.

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References (38)

  1. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  2. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  3. A. J. Cohen, P. Mori-Sánchez, and W. Yang, Challenges for density functional theory, Chem. Rev. 112, 289 (2012).
  4. F. Aryasetiawan and O. Gunnarsson, The GW method, Rep. Prog. Phys. 61, 237 (1998).
  5. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated Fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996).
  6. B. T. Thole, G. van der Laan, J. C. Fuggle, G. A. Sawatzky, R. C. Karnatak, and J.-M. Esteva, 3d x-ray-absorption lines and the 3d94fn+1 multiplets of the lanthanides, Phys. Rev. B 32, 5107 (1985).
  7. F. de Groot and A. Kotani, Core Level Spectroscopy of Solids (CRC Press, Boca Raton, FL, 2008).
  8. A. Mirone, M. Sacchi, and S. Gota, Ligand-field atomic-multiplet calculations for arbitrary symmetry, Phys. Rev. B 61, 13540 (2000).
  9. M. W. Haverkort, M. Zwierzycki, and O. K. Andersen, Multiplet ligand-field theory using Wannier orbitals, Phys. Rev. B 85, 165113 (2012).
  10. A. Longo, R. Wernert, A. Iadecola, C. J. Sahle, L. Stievano, L. Croguennec, D. Carlier, and A. Mirone, An original empirical method for simulating V L2,3 edges: The example of KVPO4F and KVOPO4 cathode materials, J. Phys. Chem. C 126, 19782 (2022).
  11. A. A. Mostofi, J. R. Yates, G. Pizzi, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, An updated version of wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 185, 2309 (2014).
  12. J. Vinson, J. J. Rehr, J. J. Kas, and E. L. Shirley, Bethe-Salpeter equation calculations of core excitation spectra, Phys. Rev. B 83, 115106 (2011).
  13. D. Prendergast and G. Galli, X-ray absorption spectra of water from first principles calculations, Phys. Rev. Lett. 96, 215502 (2006).
  14. C. Vorwerk, C. Cocchi, and C. Draxl, Addressing electron-hole correlation in core excitations of solids: An all-electron many-body approach, Phys. Rev. B 95, 155121 (2017).
  15. K. Gilmore, J. Vinson, E. Shirley, D. Prendergast, C. Pemmaraju, J. Kas, F. Vila, and J. Rehr, Efficient implementation of core-excitation Bethe–Salpeter equation calculations, Comput. Phys. Commun. 197, 109 (2015).
  16. G. Onida, L. Reining, and A. Rubio, Electronic excitations: Density-functional versus many-body Green's-function approaches, Rev. Mod. Phys. 74, 601 (2002).
  17. P. Cudazzo and L. Reining, Correlation satellites in optical and loss spectra, Phys. Rev. Res. 2, 012032(R) (2020).
  18. J. Authier and P.-F. Loos, Dynamical kernels for optical excitations, J. Chem. Phys. 153, 184105 (2020).
  19. O. Bunău and M. Calandra, Projector augmented wave calculation of x-ray absorption spectra at the L2,3 edges, Phys. Rev. B 87, 205105 (2013).
  20. M. Taillefumier, D. Cabaret, A.-M. Flank, and F. Mauri, X-ray absorption near-edge structure calculations with the pseudopotentials: Application to the K edge in diamond and α-quartz, Phys. Rev. B 66, 195107 (2002).
  21. C. Gougoussis, M. Calandra, A. P. Seitsonen, and F. Mauri, First-principles calculations of x-ray absorption in a scheme based on ultrasoft pseudopotentials: From α-quartz to high-Tc compounds, Phys. Rev. B 80, 075102 (2009).
  22. P. Giannozzi Jr et al., Advanced capabilities for materials modelling with Quantum ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017).
  23. P. Giannozzi et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
  24. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  25. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  26. G. C. Baldwin and G. S. Klaiber, Photo-fission in heavy elements, Phys. Rev. 71, 3 (1947).
  27. J. S. Levinger and H. A. Bethe, Dipole transitions in the nuclear photo-effect, Phys. Rev. 78, 115 (1950).
  28. A. P. Yutsis, I. B. Levinson, and V. V. Vanagas, Mathematical Apparatus of the Theory of Angular Momentum (Academy of Sciences of the Lithuanian SSR, Vilnius, 1962).
  29. R. A. Gordon, G. T. Seidler, T. T. Fister, M. W. Haverkort, G. A. Sawatzky, A. Tanaka, and T. K. Sham, High multipole transitions in NIXS: Valence and hybridization in 4f systems, Europhys. Lett. 81, 26004 (2008).
  30. A. Longo, A. Mirone, E. De Clermont Gallerande, C. J. Sahle, M. P. Casaletto, L. Amidani, S. A. Theofanidis, and F. Giannici, Oxygen vacancy clusters in bulk cerium oxide and the impact of gold atoms, Cell Rep. Phys. Sci. 4, 101699 (2023).
  31. S. K. Das, A. Longo, E. Bianchi, C. V. Bordenca, C. J. Sahle, M. P. Casaletto, A. Mirone, and F. Giannici, Deciphering the Ce3+ to Ce4+ evolution: Insight from x‐ray Raman scattering spectroscopy at CeN4,5 edges, ChemPhysChem 26, e202400742 (2025).
  32. A. Weiße, G. Wellein, A. Alvermann, and H. Fehske, The kernel polynomial method, Rev. Mod. Phys. 78, 275 (2006).
  33. E. Dagotto, Correlated Electrons in High-Temperature Superconductors (Springer, Berlin, 1994).
  34. The spin of on-site (ionic) electrons is part of |ai〉; The spin of the photoelectron is carried by the channel index i in the PW factor, as discussed below.
  35. Xspectruplet project, GitLab (2025), https://gitlab.com/xspectruplet/xspectruplet.
  36. D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41, 7892 (1990).
  37. A. Pieper, M. Kreutzer, A. Alvermann, M. Galgon, H. Fehske, G. Hager, B. Lang, and G. Wellein, High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations, J. Comput. Phys. 325, 226 (2016).
  38. S. Sen Gupta, J. A. Bradley, M. W. Haverkort, G. T. Seidler, A. Tanaka, and G. A. Sawatzky, Coexistence of bound and virtual-bound states in shallow-core to valence x-ray spectroscopies, Phys. Rev. B 84, 075134 (2011).

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Phys. Rev. Research 8, 023056– Published 16 April, 2026
  • Received 6 February 2025
  • Accepted 6 March 2026
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