banner
Home / News / Coupling experiment and theory to push the state-of-the-art in X-ray spectroscopy | Nature Reviews Chemistry
News

Coupling experiment and theory to push the state-of-the-art in X-ray spectroscopy | Nature Reviews Chemistry

Jun 04, 2025Jun 04, 2025

Nature Reviews Chemistry (2025)Cite this article

804 Accesses

8 Altmetric

Metrics details

X-ray spectroscopy plays a pivotal role in understanding the geometric and electronic structures of countless molecules and materials, from homogeneous and heterogeneous catalysts to biological active sites. The element-selectivity of X-ray spectroscopy allows for phenomena at specific photoabsorbers to be investigated. Since the early 2000s, experimental sophistication has progressed, with increasing applications of X-ray emission spectroscopy and two-dimensional photon-in-photon-out spectroscopies, such as resonant inelastic X-ray scattering. Although advanced X-ray spectroscopic methods increase selectivity and information content, the spectra obtained present major challenges for both qualitative and quantitative interpretation. To maximize the insight gained from X-ray spectroscopy, close coupling of experiment and theory is essential. Herein, we present the theoretical and experimental aspects of X-ray spectroscopy, with an emphasis on molecular systems and how an integrated approach with a solid foundation in molecular electronic structure theory enables new modes of inquiry into (bio)chemical catalysis.

This is a preview of subscription content, access via your institution

Access Nature and 54 other Nature Portfolio journals

Get Nature+, our best-value online-access subscription

$32.99 / 30 days

cancel any time

Subscribe to this journal

Receive 12 digital issues and online access to articles

$119.00 per year

only $9.92 per issue

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Lamberti, C. & Van Bokhoven, J. A. (eds) X-Ray Absorption and X-Ray Emission Spectroscopy: Theory and Applications (Wiley, 2016).

Bergmann, U. et al. Using X-ray free-electron lasers for spectroscopy of molecular catalysts and metalloenzymes. Nat. Rev. Phys. 3, 264–282 (2021).

Article CAS PubMed PubMed Central Google Scholar

Cutsail, G. E. III & DeBeer, S. Challenges and opportunities for applications of advanced X-ray spectroscopy in catalysis research. ACS Catal. 12, 5864–5886 (2022).

Article Google Scholar

Glatzel, P. & Bergmann, U. High resolution 1s core hole X-ray spectroscopy in 3d transition metal complexes — electronic and structural information. Coord. Chem. Rev. 249, 65–95 (2005).

Article CAS Google Scholar

Bergmann, U. & Glatzel, P. X-ray emission spectroscopy. Photosynth. Res. 102, 255–266 (2009).

Article CAS PubMed Google Scholar

R. Nascimento, D. & Govind, N. Computational approaches for XANES, VtC-XES, and RIXS using linear-response time-dependent density functional theory based methods. Phys. Chem. Chem. Phys. 24, 14680–14691 (2022).

Article Google Scholar

Pollock, C. J. & DeBeer, S. Insights into the geometric and electronic structure of transition metal centers from valence-to-core X-ray emission spectroscopy. Acc. Chem. Res. 48, 2967–2975 (2015).

Article CAS PubMed Google Scholar

Smith, J. W. & Saykally, R. J. Soft X-ray absorption spectroscopy of liquids and solutions. Chem. Rev. 117, 13909–13934 (2017).

Article CAS PubMed Google Scholar

Gel’mukhanov, F., Odelius, M., Polyutov, S. P., Föhlisch, A. & Kimberg, V. Dynamics of resonant x-ray and Auger scattering. Rev. Mod. Phys. 93, 035001 (2021).

Article Google Scholar

Eisebitt, S. & Eberhardt, W. Band structure information and resonant inelastic soft X-ray scattering in broad band solids. J. Electron. Spectrosc. Relat. Phenom. 110–111, 335–358 (2000).

Article Google Scholar

Kalha, C. et al. Hard x-ray photoelectron spectroscopy: a snapshot of the state-of-the-art in 2020. J. Phys. Condens. Matter 33, 233001 (2021).

Article CAS Google Scholar

de Groot, F. M. F. et al. Resonant inelastic X-ray scattering. Nat. Rev. Methods Primers 4, 45 (2024).

Article Google Scholar

Cramer, S. P. X-Ray Spectroscopy with Synchrotron Radiation: Fundamentals and Applications (Springer, 2020).

Raimondi, P. et al. The Extremely Brilliant Source storage ring of the European Synchrotron Radiation Facility. Commun. Phys. 6, 82 (2023).

Article CAS PubMed PubMed Central Google Scholar

Zimmermann, P. et al. Modern X-ray spectroscopy: XAS and XES in the laboratory. Coord. Chem. Rev. 423, 213466 (2020).

Article CAS Google Scholar

Malzer, W. et al. A laboratory spectrometer for high throughput X-ray emission spectroscopy in catalysis research. Rev. Sci. Instrum. 89, 113111 (2018).

Article PubMed Google Scholar

Mantouvalou, I. et al. High average power, highly brilliant laser-produced plasma source for soft X-ray spectroscopy. Rev. Sci. Instrum. 86, 035116 (2015).

Article PubMed Google Scholar

Miaja-Avila, L. et al. Laser plasma x-ray source for ultrafast time-resolved x-ray absorption spectroscopy. Struct. Dyn. 2, 024301 (2015).

Article CAS PubMed PubMed Central Google Scholar

Schoenlein, R. et al. Recent advances in ultrafast X-ray sources. Philos. Trans. R. Soc. A 377, 20180384 (2019).

Article CAS Google Scholar

Chergui, M. & Collet, E. Photoinduced structural dynamics of molecular systems mapped by time-resolved X-ray methods. Chem. Rev. 117, 11025–11065 (2017).

Article CAS PubMed Google Scholar

Principi, E. Preface to special topic: the advent of ultrafast X-ray absorption spectroscopy. Struct. Dyn. 11, 030401 (2024).

Article CAS PubMed PubMed Central Google Scholar

Reinhard, M. et al. Solution phase high repetition rate laser pump x-ray probe picosecond hard x-ray spectroscopy at the Stanford Synchrotron Radiation Lightsource. Struct. Dyn. 10, 054304 (2023).

Article CAS PubMed PubMed Central Google Scholar

Silatani, M. et al. NO binding kinetics in myoglobin investigated by picosecond Fe K-edge absorption spectroscopy. Proc. Natl Acad. Sci. USA 112, 12922–12927 (2015).

Article CAS PubMed PubMed Central Google Scholar

Reinhard, M. et al. Ferricyanide photo-aquation pathway revealed by combined femtosecond Kβ main line and valence-to-core x-ray emission spectroscopy. Nat. Commun. 14, 2443 (2023).

Article CAS PubMed PubMed Central Google Scholar

Milne, C. J. et al. Disentangling the evolution of electrons and holes in photoexcited ZnO nanoparticles. Struct. Dyn. 10, 064501 (2023).

Article CAS PubMed PubMed Central Google Scholar

Weakly, R. B. et al. Revealing core-valence interactions in solution with femtosecond X-ray pump X-ray probe spectroscopy. Nat. Commun. 14, 3384 (2023).

Article CAS PubMed PubMed Central Google Scholar

Anwar, M. I. et al. Ultrafast x-ray absorption near edge spectroscopy of Fe3O4 using a laboratory based femtosecond x-ray source. Opt. Express 27, 6030–6036 (2019).

Article CAS PubMed Google Scholar

Lafuerza, S. et al. New reflections on hard X-ray photon-in/photon-out spectroscopy. Nanoscale 12, 16270–16284 (2020).

Article CAS PubMed PubMed Central Google Scholar

Capano, G. et al. Probing wavepacket dynamics using ultrafast x-ray spectroscopy. J. Phys. B 48, 214001 (2015).

Article Google Scholar

Kowalska, J. K., Lima, F. A., Pollock, C. J., Rees, J. A. & DeBeer, S. A practical guide to high-resolution X-ray spectroscopic measurements and their applications in bioinorganic chemistry. Isr. J. Chem. 56, 803–815 (2016).

Article CAS Google Scholar

Uhlig, J. et al. High-resolution X-ray emission spectroscopy with transition-edge sensors: present performance and future potential. J. Synchrotron Radiat. 22, 766–775 (2015).

Article CAS PubMed Google Scholar

Titus, C. J. et al. L-edge spectroscopy of dilute, radiation-sensitive systems using a transition-edge-sensor array. J. Chem. Phys. 147, 214201 (2017).

Article PubMed PubMed Central Google Scholar

Doronkin, D. E. et al. NH3-SCR over V–W/TiO2 investigated by operando X-ray absorption and emission spectroscopy. J. Phys. Chem. C 123, 14338–14349 (2019).

Article CAS Google Scholar

Black, A. P. et al. Synchrotron radiation based operando characterization of battery materials. Chem. Sci. 14, 1641–1665 (2023).

Article CAS PubMed Google Scholar

Kern, J. et al. Simultaneous femtosecond X-ray spectroscopy and diffraction of photosystem II at room temperature. Science 340, 491–495 (2013).

Article CAS PubMed PubMed Central Google Scholar

Rabeah, J. et al. Multivariate analysis of coupled operando EPR/XANES/EXAFS/UV–Vis/ATR-IR spectroscopy: a new dimension for mechanistic studies of catalytic gas-liquid phase reactions. Chem. Eur. J. 26, 7395–7404 (2020).

Article CAS PubMed Google Scholar

DiMucci, I. M. et al. The myth of d8 copper(III). J. Am. Chem. Soc. 141, 8508–18520 (2019).

Article Google Scholar

Vogt, L. I. et al. Sulfur X-ray absorption and emission spectroscopy of organic sulfones. J. Phys. Chem. A 127, 3692–3704 (2023).

Article CAS PubMed Google Scholar

Azzam, S. A. et al. Insights into copper sulfide formation from Cu and S K edge XAS and DFT studies. Inorg. Chem. 59, 15276–15288 (2020).

Article CAS PubMed Google Scholar

Liu, Y. et al. Cu4S cluster in “0-hole” and “1-hole” states: geometric and electronic structure variations for the active CuZ* site of N2O reductase. J. Am. Chem. Soc. 145, 18477–18486 (2023).

Article CAS PubMed PubMed Central Google Scholar

Maganas, D. et al. Combined experimental and ab initio multireference configuration interaction study of the resonant inelastic X-ray scattering spectrum of CO2. J. Phys. Chem. C 118, 20163–20175 (2014).

Article CAS Google Scholar

Atanasov, M., Ganyushin, D., Sivalingam, K. & Neese, F. in Molecular Electronic Structures of Transition Metal Complexes II. Structure and Bonding, Vol. 143 (eds Mingos, D. M. P., Day, P. & Dahl, J. P.) 149–220 (Springer, 2012).

Izsák, R., Ivanov, A. V., Blunt, N. S., Holzmann, N. & Neese, F. Measuring electron correlation: the impact of symmetry and orbital transformations. J. Chem. Theory Comput. 19, 2703–2720 (2023).

Article PubMed PubMed Central Google Scholar

de Groot, F. M. F. et al. 2p x-ray absorption spectroscopy of 3d transition metal systems. J. Electron. Spectrosc. Relat. Phenom. 249, 147061 (2021).

Article Google Scholar

Vinson, J. & Rehr, J. J. Ab initio Bethe-Salpeter calculations of the x-ray absorption spectra of transition metals at the L-shell edges. Phys. Rev. B 86, 195135 (2012).

Article Google Scholar

Krüger, P. Multichannel multiple scattering calculation of L2,3-edge spectra of TiO2 and SrTiO3: importance of multiplet coupling and band structure. Phys. Rev. B 81, 125121 (2010).

Article Google Scholar

Martin, R. L. Natural transition orbitals. J. Chem. Phys. 118, 4775–4777 (2003).

Article CAS Google Scholar

Maganas, D., DeBeer, S. & Neese, F. Pair natural orbital restricted open-shell configuration interaction (PNO-ROCIS) approach for calculating X-ray absorption spectra of large chemical systems. J. Phys. Chem. A 122, 1215–1227 (2018).

Article CAS PubMed Google Scholar

Neese, F. Software update: the ORCA program system — Version 5.0. Wiley Interdiscip. Rev. Comput. Mol. Sci. 12, e1606 (2022).

Article Google Scholar

Li Manni, G. et al. The OpenMolcas web: a community-driven approach to advancing computational chemistry. J. Chem. Theory Comput. 19, 6933–6991 (2023).

Article CAS PubMed PubMed Central Google Scholar

Delcey, M. G. MultiPsi: a python-driven MCSCF program for photochemistry and spectroscopy simulations on modern HPC environments. Wiley Interdiscip. Rev. Comput. Mol. Sci. 13, e1675 (2023).

Article CAS Google Scholar

te Velde, G. et al. Chemistry with ADF. J. Comput. Chem. 22, 931–967 (2001).

Article Google Scholar

Aprà, E. et al. NWChem: past, present, and future. J. Chem. Phys. 152, 184102 (2020).

Article PubMed Google Scholar

Shao, Y. et al. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package. Mol. Phys. 113, 184–215 (2015).

Article CAS Google Scholar

Kowalska, J. K. et al. Iron L2,3-edge X-ray absorption and X-ray magnetic circular dichroism studies of molecular iron complexes with relevance to the FeMoco and FeVco active sites of nitrogenase. Inorg. Chem. 56, 8147–8158 (2017).

Article CAS PubMed PubMed Central Google Scholar

Hocking, R. K. et al. Fe L-edge XAS studies of K4[Fe(CN)6] and K3[Fe(CN)6]:  a direct probe of back-bonding. J. Am. Chem. Soc. 128, 10442–10451 (2006).

Article CAS PubMed Google Scholar

Westre, T. E. et al. A multiplet analysis of Fe K-edge 1s → 3d pre-edge features of iron complexes. J. Am. Chem. Soc. 119, 6297–6314 (1997).

Article CAS Google Scholar

Pollock, C. J., Delgado-Jaime, M. U., Atanasov, M., Neese, F. & DeBeer, S. Kβ mainline X-ray emission spectroscopy as an experimental probe of metal–ligand covalency. J. Am. Chem. Soc. 136, 9453–9463 (2014).

Article CAS PubMed PubMed Central Google Scholar

Lee, N., Petrenko, T., Bergmann, U., Neese, F. & DeBeer, S. Probing valence orbital composition with iron Kβ X-ray emission spectroscopy. J. Am. Chem. Soc. 132, 9715–9727 (2010).

Article CAS PubMed Google Scholar

Geoghegan, B. L. et al. Combining valence-to-core X-ray emission and Cu K-edge X-ray absorption spectroscopies to experimentally assess oxidation state in organometallic Cu(I)/(II)/(III) complexes. J. Am. Chem. Soc. 144, 2520–2534 (2022).

Article CAS PubMed PubMed Central Google Scholar

McCubbin Stepanic, O. et al. Probing a silent metal: a combined X-ray absorption and emission spectroscopic study of biologically relevant zinc complexes. Inorg. Chem. 59, 13551–13560 (2020).

Article PubMed PubMed Central Google Scholar

Glatzel, P., Bergmann, U., de Groot, F. M. F. & Cramer, S. P. Multiple excitations in the K fluorescence emission of Mn, Fe and Ni compounds. AIP Conf. Proc. 652, 250–255 (2003).

Article CAS Google Scholar

Lim, H. et al. Kβ X-ray emission spectroscopy as a probe of Cu(I) sites: application to the Cu(I) site in preprocessed galactose oxidase. Inorg. Chem. 59, 16567–16581 (2020).

Article CAS PubMed PubMed Central Google Scholar

Woicik, J. C. et al. Charge-transfer satellites and chemical bonding in photoemission and x-ray absorption of SrTiO3 and rutile TiO2: experiment and first-principles theory with general application to spectroscopic analysis. Phys. Rev. B 101, 245119 (2020).

Article CAS Google Scholar

Ghiasi, M. et al. Charge-transfer effect in hard x-ray 1s and 2p photoemission spectra: LDA + MDFT and cluster-model analysis. Phys. Rev. B 100, 075146 (2019).

Article CAS Google Scholar

Safonov, V. A. et al. Valence-to-core X-ray emission spectroscopy identification of carbide compounds in nanocrystalline Cr coatings deposited from Cr(III) electrolytes containing organic substances. J. Phys. Chem. B 110, 23192–23196 (2006).

Article CAS PubMed Google Scholar

Lancaster, K. M. et al. X-ray emission spectroscopy evidences a central carbon in the nitrogenase iron-molybdenum cofactor. Science 334, 974–977 (2011).

Article CAS PubMed PubMed Central Google Scholar

Smolentsev, G. et al. X-ray emission spectroscopy to study ligand valence orbitals in Mn coordination complexes. J. Am. Chem. Soc. 131, 13161–13167 (2009).

Article CAS PubMed PubMed Central Google Scholar

Mijovilovich, A., Hamman, S., Thomas, F., de Groot, F. M. F. & Weckhuysen, B. M. Protonation of the oxygen axial ligand in galactose oxidase model compounds as seen with high resolution X-ray emission experiments and FEFF simulations. Phys. Chem. Chem. Phys. 13, 5600–5604 (2011).

Article CAS PubMed Google Scholar

Leidel, N. et al. Electronic structure of an [FeFe] hydrogenase model complex in solution revealed by X-ray absorption spectroscopy using narrow-band emission detection. J. Am. Chem. Soc. 134, 14142–14157 (2012).

Article CAS PubMed Google Scholar

Lassalle-Kaiser, B. et al. Experimental and computational X-ray emission spectroscopy as a direct probe of protonation states in oxo-bridged MnIV dimers relevant to redox-active metalloproteins. Inorg. Chem. 52, 12915–12922 (2013).

Article CAS PubMed Google Scholar

Mathe, Z. et al. Calcium valence-to-core X-ray emission spectroscopy: a sensitive probe of oxo protonation in structural models of the oxygen-evolving complex. Inorg. Chem. 58, 16292–16301 (2019).

Article CAS PubMed PubMed Central Google Scholar

Kositzki, R. et al. Protonation state of MnFe and FeFe cofactors in a ligand-binding oxidase revealed by X-ray absorption, emission, and vibrational spectroscopy and QM/MM calculations. Inorg. Chem. 55, 9869–9885 (2016).

Article CAS PubMed Google Scholar

Lancaster, K. M., Finkelstein, K. D. & DeBeer, S. Kβ X-ray emission spectroscopy offers unique chemical bonding insights: revisiting the electronic structure of ferrocene. Inorg. Chem. 50, 6767–6774 (2011).

Article CAS PubMed Google Scholar

Phu, P. N. et al. Quantification of Ni–N–O bond angles and NO activation by X-ray emission spectroscopy. Inorg. Chem. 60, 736–744 (2021).

Article CAS PubMed Google Scholar

Pollock, C. J., Grubel, K., Holland, P. L. & DeBeer, S. Experimentally quantifying small-molecule bond activation using valence-to-core X-ray emission spectroscopy. J. Am. Chem. Soc. 135, 11803–11808 (2013).

Article CAS PubMed Google Scholar

Zhang, Y., Mukamel, S., Khalil, M. & Govind, N. Simulating valence-to-core X-ray emission spectroscopy of transition metal complexes with time-dependent density functional theory. J. Chem. Theory Comput. 11, 5804–5809 (2015).

Article CAS PubMed Google Scholar

Hanson-Heine, M. W. D., George, M. W. & Besley, N. A. Kohn-Sham density functional theory calculations of non-resonant and resonant x-ray emission spectroscopy. J. Chem. Phys. 146, 094106 (2017).

Article Google Scholar

Samal, B. & Voora, V. K. Modeling nonresonant X-ray emission of second- and third-period elements without core-hole reference states and empirical parameters. J. Chem. Theory Comput. 18, 7272–7285 (2022).

Article CAS PubMed Google Scholar

Lim, H. et al. Kβ X-ray emission spectroscopy of Cu(I)-lytic polysaccharide monooxygenase: direct observation of the frontier molecular orbital for H2O2 activation. J. Am. Chem. Soc. 145, 16015–16025 (2023).

Article CAS PubMed PubMed Central Google Scholar

Mortensen, D. R. et al. Benchmark results and theoretical treatments for valence-to-core x-ray emission spectroscopy in transition metal compounds. Phys. Rev. B 96, 125136 (2017).

Article Google Scholar

Römelt, C., Peredkov, S., Neese, F., Roemelt, M. & DeBeer, S. Valence-to-core X-ray emission spectroscopy of transition metal tetrahalides: mechanisms governing intensities. Phys. Chem. Chem. Phys. 26, 19960–19975 (2024).

Article Google Scholar

Jahrman, E. P. et al. Valence-to-core X-ray emission spectroscopy of vanadium oxide and lithiated vanadyl phosphate materials. J. Mater. Chem. A 8, 16332–16344 (2020).

Article CAS Google Scholar

Valenza, R. A., Jahrman, E. P., Kas, J. J. & Seidler, G. T. Double-ionization satellites in the x-ray emission spectrum of Ni metal. Phys. Rev. A 96, 032504 (2017).

Article Google Scholar

Sternemann, C., Kaprolat, A., Krisch, M. H. & Schülke, W. Evolution of the germanium Kβ′′′ x-ray satellites from threshold to saturation. Phys. Rev. A 61, 020501 (2000).

Article Google Scholar

Zhang, Y., Bergmann, U., Schoenlein, R., Khalil, M. & Govind, N. Double core hole valence-to-core x-ray emission spectroscopy: a theoretical exploration using time-dependent density functional theory. J. Chem. Phys. 151, 144114 (2019).

Article PubMed Google Scholar

Rana, A., Peredkov, S., Behrens, M. & DeBeer, S. Probing the local environment in potassium salts and potassium-promoted catalysts by potassium valence-to-core X-ray emission spectroscopy. Inorg. Chem. 63, 16217–16223 (2024).

Article CAS PubMed PubMed Central Google Scholar

Gütlich, P., Bill, E. & Trautwein, A. X. Mössbauer Spectroscopy and Transition Metal Chemistry: Fundamentals and Applications (Springer, 2011).

Keilwerth, M. et al. The synthesis and characterization of an iron(VII) nitrido complex. Nat. Chem. 16, 514–520 (2024).

Article CAS PubMed PubMed Central Google Scholar

Wilson, D. W. N. et al. Three-coordinate nickel and metal–metal interactions in a heterometallic iron–sulfur cluster. J. Am. Chem. Soc. 146, 4013–4025 (2024).

Article CAS PubMed PubMed Central Google Scholar

Castillo, R. G. et al. High-energy-resolution fluorescence-detected X-ray absorption of the Q intermediate of soluble methane monooxygenase. J. Am. Chem. Soc. 139, 18024–18033 (2017).

Article CAS PubMed PubMed Central Google Scholar

Ledray, A. P., Krest, C. M., Yosca, T. H., Mittra, K. & Green, M. T. Ascorbate peroxidase compound II is an iron(IV) oxo species. J. Am. Chem. Soc. 142, 20419–20425 (2020).

Article CAS Google Scholar

Chrysina, M. et al. Nature of S-states in the oxygen-evolving complex resolved by high-energy resolution fluorescence detected X-ray absorption spectroscopy. J. Am. Chem. Soc. 145, 25579–25594 (2023).

Article CAS PubMed PubMed Central Google Scholar

Kutzler, F. W. et al. Single-crystal polarized x-ray absorption spectroscopy. Observation and theory for thiomolybdate(2-). J. Am. Chem. Soc. 103, 6083–6088 (1981).

Article CAS Google Scholar

Shadle, S. E. et al. X-ray absorption spectroscopic studies of the blue copper site: metal and ligand K-edge studies to probe the origin of the EPR hyperfine splitting in plastocyanin. J. Am. Chem. Soc. 115, 767–776 (1993).

Article CAS Google Scholar

Yano, J. et al. Polarized X-ray absorption spectroscopy of single-crystal Mn(V) complexes relevant to the oxygen-evolving complex of photosystem II. J. Am. Chem. Soc. 129, 12989–13000 (2007).

Article CAS PubMed PubMed Central Google Scholar

Martin-Diaconescu, V. et al. Ca K-edge XAS as a probe of calcium centers in complex systems. Inorg. Chem. 54, 1283–1292 (2015).

Article CAS PubMed Google Scholar

Gerz, I. et al. Structural elucidation, aggregation, and dynamic behaviour of N,N,N,N-copper(I) Schiff base complexes in solid and in solution: a combined NMR, X-ray spectroscopic and crystallographic investigation. Eur. J. Inorg. Chem. 2021, 4762–4775 (2021).

Article CAS PubMed PubMed Central Google Scholar

Guo, M., Sørensen, L. K., Delcey, M. G., Pinjari, R. V. & Lundberg, M. Simulations of iron K pre-edge X-ray absorption spectra using the restricted active space method. Phys. Chem. Chem. Phys. 18, 3250–3259 (2016).

Article CAS PubMed Google Scholar

Guo, M. et al. HERFD-XANES probes of electronic structures of ironII/III carbene complexes. Phys. Chem. Chem. Phys. 22, 9067–9073 (2020).

Article CAS PubMed Google Scholar

Ghosh, S., Mukamel, S. & Govind, N. A combined wave function and density functional approach for K-edge X-ray absorption near-edge spectroscopy: a case study of hydrated first-row transition metal ions. J. Phys. Chem. Lett. 14, 5203–5209 (2023).

Article CAS PubMed Google Scholar

Borfecchia, E. et al. Revisiting the nature of Cu sites in the activated Cu-SSZ-13 catalyst for SCR reaction. Chem. Sci. 6, 548–563 (2015).

Article CAS PubMed Google Scholar

Guda, A. et al. Excited-state structure of copper phenanthroline-based photosensitizers. Phys. Chem. Chem. Phys. 23, 26729–26736 (2021).

Article CAS PubMed Google Scholar

DeBeer George, S., Petrenko, T. & Neese, F. Time-dependent density functional calculations of ligand K-edge X-ray absorption spectra. Inorg. Chim. Acta 361, 965–972 (2008).

Article CAS Google Scholar

Foglia, N. O., Maganas, D. & Neese, F. Going beyond the electric-dipole approximation in the calculation of absorption and (magnetic) circular dichroism spectra including scalar relativistic and spin–orbit coupling effects. J. Chem. Phys. 157, 084120 (2022).

Article CAS PubMed Google Scholar

Sørensen, L. K., Kieri, E., Srivastav, S., Lundberg, M. & Lindh, R. Implementation of a semiclassical light-matter interaction using the Gauss-Hermite quadrature: a simple alternative to the multipole expansion. Phys. Rev. A 99, 013419 (2019).

Article Google Scholar

C. Tomson, N. et al. Re-evaluating the Cu K pre-edge XAS transition in complexes with covalent metal–ligand interactions. Chem. Sci. 6, 2474–2487 (2015).

Article PubMed Google Scholar

Desnoyer, A. N. et al. The importance of ligand-induced backdonation in the stabilization of square planar d10 nickel π-complexes. Chem. Eur. J. 25, 5259–5268 (2019).

Article CAS PubMed Google Scholar

Lewis, L. C., Sanabria-Gracia, J. A., Lee, Y., Jenkins, A. J. & Shafaat, H. S. Electronic isomerism in a heterometallic nickel–iron–sulfur cluster models substrate binding and cyanide inhibition of carbon monoxide dehydrogenase. Chem. Sci. 15, 5916–5928 (2024).

Article CAS PubMed PubMed Central Google Scholar

Penfold, T. J. et al. Solvent-induced luminescence quenching: static and time-resolved X-ray absorption spectroscopy of a copper(I) phenanthroline complex. J. Phys. Chem. A 117, 4591–4601 (2013).

Article CAS PubMed Google Scholar

Roemelt, M. et al. Manganese K-edge X-ray absorption spectroscopy as a probe of the metal–ligand interactions in coordination compounds. Inorg. Chem. 51, 680–687 (2012).

Article CAS PubMed Google Scholar

Kowalska, J. K. et al. X-ray absorption and emission spectroscopic studies of [L2Fe2S2]n model complexes: implications for the experimental evaluation of redox states in iron–sulfur clusters. Inorg. Chem. 55, 4485–4497 (2016).

Article CAS PubMed PubMed Central Google Scholar

Abbehausen, C. et al. X-ray absorption spectroscopy combined with time-dependent density functional theory elucidates differential substitution pathways of Au(I) and Au(III) with zinc fingers. Inorg. Chem. 57, 218–230 (2018).

Article CAS PubMed Google Scholar

Martini, A. et al. Composition-driven Cu-speciation and reducibility in Cu-CHA zeolite catalysts: a multivariate XAS/FTIR approach to complexity. Chem. Sci. 8, 6836–6851 (2017).

Article CAS PubMed PubMed Central Google Scholar

Ross, M. et al. Comprehensive experimental and computational spectroscopic study of hexacyanoferrate complexes in water: from infrared to X-ray wavelengths. J. Phys. Chem. B 122, 5075–5086 (2018).

Article CAS PubMed Google Scholar

Groot, F. de & Kotani, A. Core Level Spectroscopy of Solids (CRC Press, 2008).

Jayarathne, U. et al. X-ray absorption spectroscopy systematics at the tungsten L-edge. Inorg. Chem. 53, 8230–8241 (2014).

Article CAS PubMed PubMed Central Google Scholar

Sarangi, R. et al. X-ray absorption edge spectroscopy and computational studies on LCuO2 species:  superoxide−CuII versus peroxide−CuIII bonding. J. Am. Chem. Soc. 128, 8286–8296 (2006).

Article CAS PubMed PubMed Central Google Scholar

Kubas, A., Verkamp, M., Vura-Weis, J., Neese, F. & Maganas, D. A restricted open configuration interaction singles study on M- and L-edge X-ray absorption spectroscopy of solid chemical systems. J. Chem. Theory Comput. 14, 4320–4334 (2018).

Article CAS PubMed Google Scholar

Roemelt, M., Maganas, D., DeBeer, S. & Neese, F. A combined DFT and restricted open-shell configuration interaction method including spin-orbit coupling: application to transition metal L-edge X-ray absorption spectroscopy. J. Chem. Phys. 138, 204101 (2013).

Article PubMed Google Scholar

Neese, F., Lang, L. & Chilkuri, V. G. in Topology, Entanglement, and Strong Correlations. Modeling and Simulation, Vol. 10 (eds Pavarini, E. & Koch, E.) Ch. 4 (Jülich, 2020).

Asada, S., Satoko, C. & Sugano, S. Multiplet structure in X-ray p-shell photoelectron and K-emission spectra of nickel compounds. J. Phys. Soc. Jpn. 38, 855–865 (1975).

Article CAS Google Scholar

Thole, B. T., Van Der Laan, G. & Butler, P. H. Spin-mixed ground state of Fe phthalocyanine and the temperature-dependent branching ratio in X-ray absorption spectroscopy. Chem. Phys. Lett. 149, 295–299 (1988).

Article CAS Google Scholar

Braun, A. et al. X-ray spectroscopic study of the electronic structure of a trigonal high-spin Fe(IV)═O complex modeling non-heme enzyme intermediates and their reactivity. J. Am. Chem. Soc. 145, 18977–18991 (2023).

Article CAS PubMed PubMed Central Google Scholar

Haverkort, M. W., Zwierzycki, M. & Andersen, O. K. Multiplet ligand-field theory using Wannier orbitals. Phys. Rev. B 85, 165113 (2012).

Article Google Scholar

Ramanantoanina, H. & Daul, C. A non-empirical calculation of 2p core-electron excitation in compounds with 3d transition metal ions using ligand-field and density functional theory (LFDFT). Phys. Chem. Chem. Phys. 19, 20919–20929 (2017).

Article CAS PubMed Google Scholar

Singh, S. K., Eng, J., Atanasov, M. & Neese, F. Covalency and chemical bonding in transition metal complexes: an ab initio based ligand field perspective. Coord. Chem. Rev. 344, 2–25 (2017).

Article CAS Google Scholar

Chantzis, A., Kowalska, J. K., Maganas, D., DeBeer, S. & Neese, F. Ab initio wave function-based determination of element specific shifts for the efficient calculation of X-ray absorption spectra of main group elements and first row transition metals. J. Chem. Theory Comput. 14, 3686–3702 (2018).

Article CAS PubMed Google Scholar

Maganas, D., Kowalska, J. K., Van Stappen, C., DeBeer, S. & Neese, F. Mechanism of L2,3-edge x-ray magnetic circular dichroism intensity from quantum chemical calculations and experiment — a case study on V(IV)/V(III) complexes. J. Chem. Phys. 152, 114107 (2020).

Article CAS PubMed Google Scholar

Van Stappen, C. et al. Correlating valence and 2p3d RIXS spectroscopies: a ligand-field study of spin-crossover iron(II). Inorg. Chem. 63, 7386–7400 (2024).

Article PubMed PubMed Central Google Scholar

Birsen Boydas, E. & Roemelt, M. The trials and triumphs of modelling X-ray absorption spectra of transition metal phthalocyanines. Phys. Chem. Chem. Phys. 26, 20376–20387 (2024).

Article Google Scholar

Malmqvist, P. A., Pierloot, K., Shahi, A. R. M., Cramer, C. J. & Gagliardi, L. The restricted active space followed by second-order perturbation theory method: theory and application to the study of CuO2 and Cu2O2 systems. J. Chem. Phys. 128, 204109 (2008).

Article PubMed Google Scholar

Pinjari, R. V., Delcey, M. G., Guo, M., Odelius, M. & Lundberg, M. Restricted active space calculations of L-edge X-ray absorption spectra: from molecular orbitals to multiplet states. J. Chem. Phys. 141, 124116 (2014).

Article PubMed Google Scholar

Josefsson, I. et al. Ab initio calculations of X-ray spectra: atomic multiplet and molecular orbital effects in a multiconfigurational SCF approach to the L-edge spectra of transition metal complexes. J. Phys. Chem. Lett. 3, 3565–3570 (2012).

Article CAS PubMed Google Scholar

Boydas, E. B., Winter, B., Batchelor, D. & Roemelt, M. Insight into the X-ray absorption spectra of Cu-porphyrazines from electronic structure theory. Int. J. Quantum Chem. 121, e26515 (2021).

Article CAS Google Scholar

Guo, Y., Sivalingam, K., Valeev, E. F. & Neese, F. SparseMaps — A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory. J. Chem. Phys. 144, 094111 (2016).

Article PubMed Google Scholar

Menezes, F., Kats, D. & Werner, H.-J. Local complete active space second-order perturbation theory using pair natural orbitals (PNO-CASPT2). J. Chem. Phys. 145, 124115 (2016).

Article PubMed Google Scholar

Maganas, D., Kowalska, J. K., Nooijen, M., DeBeer, S. & Neese, F. Comparison of multireference ab initio wavefunction methodologies for X-ray absorption edges: a case study on [Fe(II/III)Cl4]2−/1− molecules. J. Chem. Phys. 150, 104106 (2019).

Article PubMed Google Scholar

Helmich-Paris, B. Simulating X-ray absorption spectra with complete active space self-consistent field linear response methods. Int. J. Quantum Chem. 121, e26559 (2021).

Article CAS Google Scholar

Bagus, P. S., Nelin, C. J., Ilton, E. S., Sassi, M. J. & Rosso, K. M. Analysis of X-ray adsorption edges: L2,3 edge of FeCl4−. J. Chem. Phys. 147, 224306 (2017).

Article PubMed Google Scholar

Ganyushin, D. & Neese, F. A fully variational spin-orbit coupled complete active space self-consistent field approach: application to electron paramagnetic resonance g-tensors. J. Chem. Phys. 138, 104113 (2013).

Article PubMed Google Scholar

Brik, M. G., Ogasawara, K., Ikeno, H. & Tanaka, I. Fully relativistic calculations of the L2,3-edge XANES spectra for vanadium oxides. Eur. Phys. J. B 51, 345–355 (2006).

Article CAS Google Scholar

Bagus, P. S., Freund, H., Kuhlenbeck, H. & Ilton, E. S. A new analysis of X-ray adsorption branching ratios: use of Russell–Saunders coupling. Chem. Phys. Lett. 455, 331–334 (2008).

Article CAS Google Scholar

Bjornsson, R. et al. Molybdenum L-Edge XAS spectra of MoFe nitrogenase. Z. Anorg. Allg. Chem. 641, 65–71 (2015).

Article CAS PubMed Google Scholar

Jay, R. M. et al. Tracking C–H activation with orbital resolution. Science 380, 955–960 (2023).

Article CAS PubMed Google Scholar

Van Kuiken, B. E. et al. Simulating Ru L3-Edge X-ray absorption spectroscopy with time-dependent density functional theory: model complexes and electron localization in mixed-valence metal dimers. J. Phys. Chem. A 117, 4444–4454 (2013).

Article PubMed Google Scholar

Alperovich, I. et al. Understanding the electronic structure of 4d metal complexes: from molecular spinors to L-edge spectra of a di-Ru catalyst. J. Am. Chem. Soc. 133, 15786–15794 (2011).

Article CAS PubMed Google Scholar

Carra, P., Thole, B. T., Altarelli, M. & Wang, X. X-ray circular dichroism and local magnetic fields. Phys. Rev. Lett. 70, 694–697 (1993).

Article CAS PubMed Google Scholar

Funk, T., Deb, A., George, S. J., Wang, H. & Cramer, S. P. X-ray magnetic circular dichroism — a high energy probe of magnetic properties. Coord. Chem. Rev. 249, 3–30 (2005).

Article CAS Google Scholar

Piamonteze, C., Miedema, P. & de Groot, F. M. F. Accuracy of the spin sum rule in XMCD for the transition-metal L edges from manganese to copper. Phys. Rev. B 80, 184410 (2009).

Article Google Scholar

Guo, M., Braun, A., Sokaras, D. & Kroll, T. Iron Kβ X-ray emission spectroscopy: the origin of spectral features from atomic to molecular systems using multi-configurational calculations. J. Phys. Chem. A 128, 1260–1273 (2024).

Article CAS PubMed Google Scholar

Ito, Y. et al. Structure of high-resolution Kβ1,3 x-ray emission spectra for the elements from Ca to Ge. Phys. Rev. A 97, 052505 (2018).

Article CAS Google Scholar

Nguyen, T. V. B., Melia, H. A., Janssens, F. I. & Chantler, C. T. Multiconfiguration Dirac-Hartree-Fock theory for copper Kα and Kβ diagram lines, satellite spectra, and ab initio determination of single and double shake probabilities. Phys. Rev. A 105, 022811 (2022).

Article CAS Google Scholar

Glatzel, P. et al. The electronic structure of Mn in oxides, coordination complexes, and the oxygen-evolving complex of photosystem II studied by resonant inelastic X-ray scattering. J. Am. Chem. Soc. 126, 9946–9959 (2004).

Article CAS PubMed PubMed Central Google Scholar

Peng, G. et al. High-resolution manganese x-ray fluorescence spectroscopy. Oxidation-state and spin-state sensitivity. J. Am. Chem. Soc. 116, 2914–2920 (1994).

Article CAS Google Scholar

Glatzel, P., Jacquamet, L., Bergmann, U., de Groot, F. M. F. & Cramer, S. P. Site-selective EXAFS in mixed-valence compounds using high-resolution fluorescence detection: a study of iron in Prussian Blue. Inorg. Chem. 41, 3121–3127 (2002).

Article CAS PubMed Google Scholar

Norman, P. & Dreuw, A. Simulating X-ray spectroscopies and calculating core-excited states of molecules. Chem. Rev. 118, 7208–7248 (2018).

Article CAS PubMed Google Scholar

Maganas, D., DeBeer, S. & Neese, F. A restricted open configuration interaction with singles method to calculate valence-to-core resonant X-ray emission spectra: a case study. Inorg. Chem. 56, 11819–11836 (2017).

Article CAS PubMed PubMed Central Google Scholar

Eisenberger, P., Platzman, P. M. & Winick, H. X-ray resonant Raman scattering: observation of characteristic radiation narrower than the lifetime width. Phys. Rev. Lett. 36, 623–626 (1976).

Article CAS Google Scholar

Hämäläinen, K., Siddons, D. P., Hastings, J. B. & Berman, L. E. Elimination of the inner-shell lifetime broadening in x-ray-absorption spectroscopy. Phys. Rev. Lett. 67, 2850–2853 (1991).

Article PubMed Google Scholar

Hayashi, H., Udagawa, Y., Caliebe, W. A. & Kao, C.-C. Lifetime-broadening removed X-ray absorption near edge structure by resonant inelastic X-ray scattering spectroscopy. Chem. Phys. Lett. 371, 125–130 (2003).

Article CAS Google Scholar

de Groot, F. M. F., Krisch, M. H. & Vogel, J. Spectral sharpening of the Pt L edges by high-resolution x-ray emission. Phys. Rev. B 66, 195112 (2002).

Article Google Scholar

Carra, P., Fabrizio, M. & Thole, B. T. High resolution X-ray resonant Raman scattering. Phys. Rev. Lett. 74, 3700–3703 (1995).

Article CAS PubMed Google Scholar

Chernev, P. et al. Hydride binding to the active site of [FeFe]-hydrogenase. Inorg. Chem. 53, 12164–12177 (2014).

Article CAS PubMed Google Scholar

Castillo, R. G. et al. Probing physical oxidation state by resonant X-ray emission spectroscopy: applications to iron model complexes and nitrogenase. Angew. Chem. Int. Ed. 60, 10112–10121 (2021).

Article CAS Google Scholar

Hall, E. R. et al. Valence-to-core-detected X-ray absorption spectroscopy: targeting ligand selectivity. J. Am. Chem. Soc. 136, 10076–10084 (2014).

Article CAS PubMed Google Scholar

Biasin, E. et al. Revealing the bonding of solvated Ru complexes with valence-to-core resonant inelastic X-ray scattering. Chem. Sci. 12, 3713–3725 (2021).

Article CAS PubMed PubMed Central Google Scholar

Banerjee, A. et al. Accessing metal-specific orbital interactions in C–H activation with resonant inelastic X-ray scattering. Chem. Sci. 15, 2398–2409 (2024).

Article CAS PubMed PubMed Central Google Scholar

Van Kuiken, B. E., Hahn, A. W., Maganas, D. & DeBeer, S. Measuring spin-allowed and spin-forbidden d–d excitations in vanadium complexes with 2p3d resonant inelastic X-ray Scattering. Inorg. Chem. 55, 11497–11501 (2016).

Article PubMed Google Scholar

Hunault, M. O. J. Y. et al. Direct observation of Cr3+ 3d states in ruby: toward experimental mechanistic evidence of metal chemistry. J. Phys. Chem. A 122, 4399–4413 (2018).

Article CAS PubMed PubMed Central Google Scholar

Hahn, A. W. et al. Measurement of the ligand field spectra of ferrous and ferric iron chlorides using 2p3d RIXS. Inorg. Chem. 56, 8203–8211 (2017).

Article CAS PubMed Google Scholar

Hahn, A. W. et al. Probing the valence electronic structure of low-spin ferrous and ferric complexes using 2p3d resonant inelastic X-ray scattering (RIXS). Inorg. Chem. 57, 9515–9530 (2018).

Article CAS PubMed Google Scholar

Jay, R. M. et al. Disentangling transient charge density and metal–ligand covalency in photoexcited ferricyanide with femtosecond resonant inelastic soft X-ray scattering. J. Phys. Chem. Lett. 9, 3538–3543 (2018).

Article CAS PubMed Google Scholar

Kunnus, K. et al. Viewing the valence electronic structure of ferric and ferrous hexacyanide in solution from the Fe and cyanide perspectives. J. Phys. Chem. B 120, 7182–7194 (2016).

Article CAS PubMed Google Scholar

Cutsail, G. E. et al. High-resolution iron X-ray absorption spectroscopic and computational studies of non-heme diiron peroxo intermediates. J. Inorg. Biochem. 203, 110877 (2020).

Article CAS PubMed Google Scholar

Henthorn, J. T. et al. Localized electronic structure of nitrogenase FeMoco revealed by selenium K-edge high resolution X-ray absorption spectroscopy. J. Am. Chem. Soc. 141, 13676–13688 (2019).

Article CAS PubMed PubMed Central Google Scholar

Fransson, T. et al. Effects of x-ray free-electron laser pulse intensity on the Mn Kβ1,3 x-ray emission spectrum in photosystem II — a case study for metalloprotein crystals and solutions. Struct. Dyn. 8, 064302 (2021).

Article CAS PubMed PubMed Central Google Scholar

Drosou, M., Comas-Vilà, G., Neese, F., Salvador, P. & Pantazis, D. A. Does serial femtosecond crystallography depict state-specific catalytic intermediates of the oxygen-evolving complex? J. Am. Chem. Soc. 145, 10604–10621 (2023).

Article CAS PubMed PubMed Central Google Scholar

Zaharieva, I. et al. Room-temperature energy-sampling Kβ X-ray emission spectroscopy of the Mn4Ca complex of photosynthesis reveals three manganese-centered oxidation steps and suggests a coordination change prior to O2 formation. Biochemistry 55, 4197–4211 (2016).

Article CAS PubMed Google Scholar

Glatzel, P. et al. Electronic structural changes of Mn in the oxygen-evolving complex of photosystem II during the catalytic cycle. Inorg. Chem. 52, 5642–5644 (2013).

Article CAS PubMed PubMed Central Google Scholar

Einsle, O. et al. Nitrogenase MoFe-protein at 1.16 Å resolution: a central ligand in the FeMo-cofactor. Science 297, 1696–1700 (2002).

Article CAS PubMed Google Scholar

Rees, J. A. et al. The Fe–V cofactor of vanadium nitrogenase contains an interstitial carbon atom. Angew. Chem. Int. Ed. 54, 13249–13252 (2015).

Article CAS Google Scholar

Decamps, L., Rice, D. & DeBeer, S. An Fe6C core in all nitrogenase cofactors. Angew. Chem. Int. Ed. 61, e202209190 (2022).

Article CAS Google Scholar

Bjornsson, R. et al. Identification of a spin-coupled Mo(III) in the nitrogenase iron–molybdenum cofactor. Chem. Sci. 5, 3096–3103 (2014).

Article CAS Google Scholar

Kowalska, J. K. et al. X-ray magnetic circular dichroism spectroscopy applied to nitrogenase and related models: experimental evidence for a spin-coupled molybdenum(III) center. Angew. Chem. Int. Ed. 58, 9373–9377 (2019).

Article CAS Google Scholar

Spatzal, T., Perez, K. A., Howard, J. B. & Rees, D. C. Catalysis-dependent selenium incorporation and migration in the nitrogenase active site iron-molybdenum cofactor. eLife 4, e11620 (2015).

Article PubMed PubMed Central Google Scholar

Mebs, S., Braun, B., Kositzki, R., Limberg, C. & Haumann, M. Abrupt versus gradual spin-crossover in FeII(phen)2(NCS)2 and FeIII(dedtc)3 compared by X-ray absorption and emission spectroscopy and quantum-chemical calculations. Inorg. Chem. 54, 11606–11624 (2015).

Article CAS PubMed Google Scholar

Smolentsev, G., Soldatov, A. V. & Chen, L. X. Three-dimensional local structure of photoexcited Cu diimine complex refined by quantitative XANES analysis. J. Phys. Chem. A 112, 5363–5367 (2008).

Article CAS PubMed Google Scholar

Velasco, L. et al. Mapping the ultrafast mechanistic pathways of Co photocatalysts in pure water through time-resolved X-ray spectroscopy. ChemSusChem 16, e202300719 (2023).

Article CAS PubMed Google Scholar

Moonshiram, D. et al. Tracking the structural and electronic configurations of a cobalt proton reduction catalyst in water. J. Am. Chem. Soc. 138, 10586–10596 (2016).

Article CAS PubMed Google Scholar

Li, Z.-J. et al. Tracking Co(I) intermediate in operando in photocatalytic hydrogen evolution by X-ray transient absorption spectroscopy and DFT calculation. J. Phys. Chem. Lett. 7, 5253–5258 (2016).

Article CAS PubMed Google Scholar

Smolentsev, G. et al. Structure of the CoI intermediate of a cobalt pentapyridyl catalyst for hydrogen evolution revealed by time-resolved X-ray spectroscopy. ChemSusChem 11, 3087–3091 (2018).

Article CAS PubMed Google Scholar

Kunnus, K. et al. Vibrational wavepacket dynamics in Fe carbene photosensitizer determined with femtosecond X-ray emission and scattering. Nat. Commun. 11, 634 (2020).

Article CAS PubMed PubMed Central Google Scholar

Katayama, T. et al. Tracking multiple components of a nuclear wavepacket in photoexcited Cu(I)-phenanthroline complex using ultrafast X-ray spectroscopy. Nat. Commun. 10, 3606 (2019).

Article PubMed PubMed Central Google Scholar

Rogvall, J., Singh, R., Vacher, M. & Lundberg, M. Sensitivity of Kβ mainline X-ray emission to structural dynamics in iron photosensitizer. Phys. Chem. Chem. Phys. 25, 10447–10459 (2023).

Article CAS PubMed PubMed Central Google Scholar

Liekhus-Schmaltz, C. et al. Femtosecond X-ray spectroscopy directly quantifies transient excited-state mixed valency. J. Phys. Chem. Lett. 13, 378–386 (2022).

Article CAS PubMed Google Scholar

Capano, G., Chergui, M., Rothlisberger, U., Tavernelli, I. & Penfold, T. J. A quantum dynamics study of the ultrafast relaxation in a prototypical Cu(I)–phenanthroline. J. Phys. Chem. A 118, 9861–9869 (2014).

Article CAS PubMed Google Scholar

Rankine, C. D. & Penfold, T. J. Progress in the theory of X-ray spectroscopy: from quantum chemistry to machine learning and ultrafast dynamics. J. Phys. Chem. A 125, 4276–4293 (2021).

Article CAS PubMed Google Scholar

Shaik, S. Two-state reactivity: personal recounting of its conception and future prospects. Isr. J. Chem. 60, 938–956 (2020).

Article CAS Google Scholar

Rice, D. B., Wong, D., Weyhermüller, T., Neese, F. & DeBeer, S. The spin-forbidden transition in iron(IV)-oxo catalysts relevant to two-state reactivity. Sci. Adv. 10, eado1603 (2024).

Article CAS PubMed PubMed Central Google Scholar

Liao, J., Yang, J., Wang, D. & Dong, J. Combining experiment and theory for precise structure identification of single-atom catalysts. Chem Catal. 2, 2114–2117 (2022).

Article CAS Google Scholar

Lomachenko, K. A. et al. The Cu-CHA deNOx catalyst in action: temperature-dependent NH3-assisted selective catalytic reduction monitored by operando XAS and XES. J. Am. Chem. Soc. 138, 12025–12028 (2016).

Article CAS PubMed Google Scholar

Lätsch, L. et al. Tracking coordination environment and reaction intermediates in homogeneous and heterogeneous epoxidation catalysts via Ti L2,3-edge near-edge X-ray absorption fine structures. J. Am. Chem. Soc. 146, 7456–7466 (2024).

Article PubMed Google Scholar

Schoonjans, T. et al. The xraylib library for X-ray–matter interactions. Recent developments. Spectrochim. Acta B 66, 776–784 (2011).

Article CAS Google Scholar

Dittmer, A. Exploring Problems in Inorganic Solid-state Systems with Wavefunction-based Molecular Spectroscopy Methods. PhD thesis, Rheinischen Friedrich-Wilhelms-Universität Bonn (2024).

Jannuzzi, S. A. V., Peredkov, S., Mathe, Z. S. & DeBeer, S. Fe valence-to-core X-ray emission spectra of iron tetrachloride salts. Edmond Open Research Data Repository https://doi.org/10.17617/3.NMPS8V (2025).

Becke, A. D. Density‐functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648–5652 (1993).

Article CAS Google Scholar

Stephens, P. J., Devlin, F. J., Chabalowski, C. F. & Frisch, M. J. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J. Phys. Chem. 98, 11623–11627 (1994).

Article CAS Google Scholar

Weigend, F. & Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys. Chem. Chem. Phys. 7, 3297–3305 (2005).

Article CAS PubMed Google Scholar

Pantazis, D. A., Chen, X. Y., Landis, C. R. & Neese, F. All-electron scalar relativistic basis sets for third-row transition metal atoms. J. Chem. Theory Comput. 4, 908–919 (2008).

Article CAS PubMed Google Scholar

March, A. M. et al. Feasibility of valence-to-core X-ray emission spectroscopy for tracking transient species. J. Phys. Chem. C 119, 14571–14578 (2015).

Article CAS Google Scholar

Maganas, D. et al. First principles calculations of the structure and V L-edge X-ray absorption spectra of V2O5 using local pair natural orbital coupled cluster theory and spin–orbit coupled configuration interaction approaches. Phys. Chem. Chem. Phys. 15, 7260 (2013).

Article CAS PubMed Google Scholar

Staemmler, V. in Theoretical Aspects of Transition Metal Catalysis. Topics in Organometallic Chemistry, Vol. 12 (ed. Frenking, G.) 219–256 (Springer, 2005).

Hahn, A. W. Development and Application of Resonant Inelastic X-ray Scattering Spectroscopy in Inorganic Chemistry. PhD thesis, Ruhr-Universität Bochum (2018).

Grabenstetter, J. E., Tseng, T. J. & Grein, F. Generation of genealogical spin eigenfunctions. Int. J. Quantum Chem. 10, 143–149 (1976).

Article CAS Google Scholar

Chilkuri, V. G. & Neese, F. Comparison of many-particle representations for selected-CI I: a tree based approach. J. Comput. Chem. 42, 982–1005 (2021).

Article CAS PubMed Google Scholar

Neese, F. Prediction of molecular properties and molecular spectroscopy with density functional theory: from fundamental theory to exchange-coupling. Coord. Chem. Rev. 253, 526–563 (2009).

Article CAS Google Scholar

Download references

The authors thank the Max Planck Society for funding. The authors thank R. Shafei for assistance with L-edge calculations.

Department of Inorganic Spectroscopy, Max Planck Institute for Chemical Energy Conversion, Mülheim an der Ruhr, Germany

Zachary Mathe & Serena DeBeer

Department of Molecular Theory and Spectroscopy, Max-Planck-Institut für Kohlenforschung, Mülheim an der Ruhr, Germany

Dimitrios Maganas & Frank Neese

You can also search for this author inPubMed Google Scholar

You can also search for this author inPubMed Google Scholar

You can also search for this author inPubMed Google Scholar

You can also search for this author inPubMed Google Scholar

S.D. and F.N. conceived the idea. Z.M. wrote the original draft. All authors contributed substantially to the discussion and revision of the manuscript.

Correspondence to Frank Neese or Serena DeBeer.

The authors declare no competing interests.

Nature Reviews Chemistry thanks Frank de Groot and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

Mathe, Z., Maganas, D., Neese, F. et al. Coupling experiment and theory to push the state-of-the-art in X-ray spectroscopy. Nat Rev Chem (2025). https://doi.org/10.1038/s41570-025-00718-2

Download citation

Accepted: 08 April 2025

Published: 30 May 2025

DOI: https://doi.org/10.1038/s41570-025-00718-2

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative