Main

One reason promethium (Pm) was so elusive for many years, despite a relatively low atomic number, is that it is the only element in the lanthanide (Ln) series (elements with atomic numbers 57–71) with no stable isotopes. Nowadays, mostly synthetic radioisotope 147Pm (with half-life τ1/2 = 2.62 years) is produced and isolated in small quantities through nuclear fission in reactors and subsequent tedious purification steps for many applications. Promethium uses range from long-life nuclear batteries used in space craft to radiation therapy7,8. A key obstacle impeding the efficient recovery of this critical element resides in our limited comprehension of the Pm coordination chemistry. In contrast to other lanthanides that favour the +3 oxidation state under ambient conditions, even the most fundamental characteristics of Pm in aqueous solution, including the bond distances and coordination number, remain unexplored. This valuable information is exceptionally challenging to obtain due to its radioactivity, synthetic nature and lack of availability. Only a few simple inorganic PmIII solids, such as halides17, oxide18, oxalate19, molybdate and tungstate20 have been prepared and characterized by X-ray powder diffraction to determine the lattice parameters. Furthermore, the absorption bands in the visible spectrum17,21,22, Raman spectra23 and magnetic susceptibility24 of the PmIII oxide and halides were reported. Beyond these examples, the fundamental chemistry of Pm is virtually unknown, and there are no experimental data to benchmark theoretical models for predicting Pm chemical bonding, structure and reactivity in solution. In addition, it is well known that the gradual population of the 4f electron shell in conjunction with relativistic effects cause a continuous decrease in the size of the ionic radii along the lanthanide series, leading to structural changes in Ln complexes. Whereas this lanthanide contraction phenomenon taught in general chemistry textbooks has been inferred mostly from theory25,26,27,28,29 and Shannon’s effective ionic radii database30, it still lacks experimental structural evidence for a complete set of lanthanides in solution that includes radioactive Pm31,32,33,34,35,36. Advancing our fundamental knowledge in this field is critical for rationalizing and predicting the structurally diverse coordination chemistry shown by lanthanides1,3,12.

Towards this goal, we report our experimental and computational efforts to investigate the Pm ion binding by a multidentate ligand in an aqueous solution, taking advantage of the recently enhanced isotope separation techniques (Methods), which have enabled the production of 147Pm in sufficient quantities and purity levels necessary for fundamental studies (Fig. 1a). A new, water-soluble complexing agent, bispyrrolidine diglycolamide (PyDGA) (Fig. 1b) was synthesized and used for Pm complexation. The DGA family of neutral ligands is well established for efficient lanthanide and actinide chelation and separation9,10, showing stable binding mode for LnIII ions37,38. These characteristics enabled the detection and characterization of the homoleptic [Pm(PyDGA)3]3+ complex by X-ray absorption spectroscopy (XAS) measurements at the National Synchrotron Light Source II (NSLS-II). The experimental results corroborated by the quantum chemical calculations provide the missing piece necessary for a comprehensive study of the impact of f-electron count on Ln contraction in the entire isostructural series of Ln complexes. This discovery reveals distinctive structural and electronic characteristics extending beyond the gradual ionic radii changes.

Fig. 1: Preparation of PmIII and its chelation by the multidentate ligand PyDGA in an aqueous solution.
figure 1

a, Photograph of purified PmIII compound prepared in this study. The depicted pink-coloured 147Pm(NO3)3·nH2O (n < 9) solid residue was obtained after several purification steps and used in a PmIII complexation. b, Each PyDGA ligand molecule consists of two amide carbonyl oxygen groups and one ether oxygen atom, enabling high aqueous solubility. This chelator coordinates with the promethium cation in a tridentate fashion to form the 1:3 complex by providing nine metal-binding O donor atoms in the first coordination sphere of PmIII.

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Our motivation for probing the Pm complexation in the solution phase arises from the absence of crystal lattice effects that could affect the measured bond distances. Also, a dilute aqueous environment is generally free from the heat and damage inherent to radioactive materials, which are more pronounced in the solid state. Thus, for XAS investigations, the sample was prepared in 0.01 M HNO3 solution containing 147Pm (90 µl, 8.5 mM) complexed with PyDGA at a roughly 1 to 20 metal ion-to-ligand ratio to ensure the full ion chelation and formation of the [Pm(PyDGA)3]3+ complex (Fig. 1b). The solution was then triply contained and secured in a rigid aluminium sample holder (Extended Data Fig. 1). The L3- and L1-edge XAS spectra were acquired at room temperature in fluorescence mode using a Vortex four-element silicon-drift detector at beamline 6-BM of NSLS-II (Fig. 2; L1-edge XAS results are shown in Extended Data Fig. 2). The X-ray absorption near-edge structure (XANES) indicates that the Pm spectral features are consistent with the XANES data measured for other adjacent lanthanides having +3 oxidation state (Extended Data Fig. 3a). The position of the L3-absorption edge (the inflection point) was determined to be at 6,464.4 eV (calibrated to the K-edge of an Fe foil, 7,112.0 eV, and measured with an instrumental uncertainty below 0.1 eV). The XANES spectrum can be separated into four distinct regions (Fig. 2a). On the basis of our density functional theory (DFT) restricted open shell configuration interaction singles (DFT–ROCIS) and multiple scattering theory calculations (Extended Data Fig. 3b,c), region I corresponds to transitions from Pm 2p to 4f/5d orbitals, and the most intense peak II is dominated by 2p core electron excitations to 5d but with some PyDGA orbital contributions. Less visible peak III can be attributed to transitions involving Pm 4f/5d/ligand orbitals, whereas the origin of broad feature IV is complex with leading components from 2p to 5d/ligand and Pm 4f dz3 orbitals.

Fig. 2: The spectroscopic, structural and electronic characteristics of the observed [Pm(PyDGA)3]3+ coordination complex in aqueous environment revealed by synchrotron XAS and quantum chemical studies.
figure 2

a, Pm L3-edge XANES spectrum (black line) and its interpretation using DFT–ROCIS calculations (circles). E is the incident photon energy and the corresponding orbitals participating in the core electron excitations are shown in Extended Data Fig. 3b. b,c, Pm EXAFS data (squares), the fit (pink line) representing model scattering paths associated with the Pm complex and the AIMD simulated EXAFS (turquoise dashed line). b, L3-edge EXAFS spectrum of the Pm complex in solution where k is the energy of the photoelectron in wavenumbers and k3χ(k) is the k3-weighted EXAFS function. Data between 2.3 and 7.8 Å−1 were Fourier transformed using a Hanning window to obtain real-space information. c, Magnitude of the Fourier transform (FT) (black squares) and the real component of the Fourier transform (empty squares). The data were fit over the range from 1.4 to 3.2 Å. Spectra are not phase adjusted. d, Snapshot of the Pm complex surrounded by water molecules from the AIMD simulations. e, Formation of the dative Pm–O bond in the Pm complex in terms of overlapping amide carbonyl oxygen lone pair, on the right, with the Pm 5d acceptor orbital, on the left. Only the local Pm–ligand environment is visualized for clarity. f, The resulting Pm–O bonding NBO that includes roughly 4% Pm character. The Pm hybrid’s nodal character in the bond is not visible because its amplitude is below the 0.035 amplitude cut-off for the orbital visualization.

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To investigate the local coordination structure around the PmIII ion, we analysed the extended X-ray absorption fine structure (EXAFS) of the [Pm(PyDGA)3]3+ complex. The Pm EXAFS data in Fig. 2b show the expected sinusoidal-like behaviour; however, a sharp feature can be seen at 8.2 Å−1, which is attributed to the presence of a small amount of NdIII (L2-edge) and 147SmIII (L3-edge), a decay product of 147Pm. Hence real-space functions (Fig. 2c) were produced using a Fourier transform of the EXAFS data that contain only Pm information (2.3 ≤ k ≤ 7.8 Å−1), giving a physical description of the atomic arrangement around the Pm ion. The Fourier transform of the EXAFS reveals two intense features at 1.9 and 2.8 Å (non-phase corrected), presumably corresponding to the inner-sphere Pm–O and more distant Pm–C scattering correlations originating from PmIII complexation by PyDGA. A two-shell oxygen-carbon model based on the Pm surrogate crystal structure (Extended Data Fig. 4) was developed to fit the EXAFS data. According to this representation, the first shell comprised six amide carbonyl and three ether O donors, and the second shell at longer distances accounted for the six sp3-hybridized (ether moiety) and six sp2-hybridized (carbonyl moiety) C atoms from the PyDGA scaffold. However, given the limited k-space data, affecting the interatomic resolution, and the dynamic nature of the solution phase at room temperature, amido and ether O, as well as sp3- and sp2-C distances, could not be resolved and were each fitted in a conservative manner with the Ln–O and Ln–C single scattering paths. This resulted in an average Pm–O bond distance of 2.476(16) Å (Debye–Waller factor σ2 = 0.006(1) Å2) and an average Pm–C distance of 3.38(7) Å (σ2 = 0.02(1) Å2), consistent with PmIII chelation by three PyDGA ligands (Extended Data Table 1).

To further gain insights into the dynamic structural behaviour of PmIII complexation in an aqueous environment, we performed ab initio molecular dynamics (AIMD) simulations. The theoretical EXAFS spectrum and its Fourier transform (Fig. 2b,c) were simulated directly from the AIMD trajectory and show very good agreement with the experimental data, validating the formation of a homoleptic [Pm(PyDGA)3]3+ complex (Fig. 2d). Key structural parameters align well with those determined by the EXAFS experiments, as can be judged from the analyses of radial distribution functions (RDFs), with the AIMD predicted Pm–O bond length of 2.48 Å (Extended Data Fig. 5). Beyond the inner-sphere Pm–O correlations, the AIMD results also indicated some water structuring around the complex at 4.43 Å through transient hydrogen bond interactions with the O donor groups of the PyDGA ligands. It is also worth noting that, like in the experimental EXAFS data, the amide carbonyl and etheric Pm–O bonds could not be resolved in the AIMD and thus appeared as a single peak in the corresponding RDF, pointing to the dynamic nature of the first-sphere ligand-metal interactions in aqueous solution (Supplementary Video 1).

Next, we performed natural bond orbital (NBO) calculations to examine the nature of Pm–O bonding. Natural population analysis indicates that the promethium 5d and 6s orbitals are substantially populated (0.82 electrons |e| and 0.17 |e|, respectively), with a non-negligible population of the vacant 4f orbitals (0.07 |e|). The dative Pm–O bonds originate from a characteristic σ-type donation of electron density from O lone pairs to the Pm centre. Figure 2e shows the representative leading orbital interaction that stems from an overlap of the O lone pair with an acceptor orbital of primarily 5d character on Pm, resulting in the Pm–O NBO, which is predominantly localized on the oxygen atom (Fig. 2f). The strength of interactions involving amide carbonyl O groups was found to be only slightly higher than that involving ether oxygens. This was confirmed by the comparable calculated values of Wiberg bond indices for the amidic (0.12) and etheric (0.08) Pm–O bonds, pointing to their prevalent ionic nature and explaining their dynamic behaviour in aqueous solution. As a result, these bonding characteristics do not exert substantial ligand field effects, leading to the challenges that are frequently encountered in the selective recovery of Pm and other rare-earth elements1.

Having established promethium coordination and bond lengths, we studied the remaining lanthanide (LaIII, CeIII, PrIII, NdIII, SmIII, EuIII, GdIII, TbIII, DyIII, HoIII, ErIII, TmIII, YbIII, LuIII) complexes with PyDGA using XAS (Fig. 3 and Extended Data Fig. 6) to understand how the solution structure of the coordination complex transforms across the lanthanide series. The Fourier transform-EXAFS results in Fig. 3a,b show that the positions and intensities of the main features corresponding to the Ln–O distances vary slightly between the lanthanides. This is expected on the basis of the different harmonics generated from the shortening of the inner-sphere bonds caused by the Ln contraction. Furthermore, the shrinkage of the Ln–O bonds is corroborated by the trend in the relative energy positions of the Ln L3-edge XANES spectral features (Extended Data Fig. 3a), consistent with the results of a recent study39 on some isostructural Ln compounds using high-energy-resolution fluorescence-detected XANES40,41 measurements.

Fig. 3: The lanthanide contraction phenomenon captured by the element-specific XAS for the entire isostructural series of the lanthanide complexes in solution.
figure 3

a,b, One-dimensional profiles (a) and 2D intensity map (b) of the real component of the Fourier transformed EXAFS data for the lanthanide complexes, visualizing the contraction of the first shell across the lanthanide series. Spectra are not phase adjusted. c, The dependence of the Ln–O bond distances on the number of 4f electrons, revealing accelerated contraction from LaIII to PmIII followed by a steadier Ln–O bond shortening for the heavier lanthanides (1σ error bars associated with each data point are based on EXAFS fitting uncertainty).

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Good fits to the Ln-PyDGA EXAFS data were obtained with the model used for promethium, giving physically sound parameters (Extended Data Table 2) and suggesting that the [Ln(PyDGA)3]3+ species prevail in the aqueous solution across the series. Figure 3c represents the most comprehensive view of the Ln contraction phenomenon obtained from experiments and shows how the inner-sphere Ln–O bond distances change depending on the number of 4f electrons in the electronic structure of LnIII. By monitoring the decrease of Ln–O bonds from La (2.560(21) Å) to Lu (2.329(12) Å), a quadratic dependence across the series was observed and fitted by a polynomial regression (Extended Data Fig. 7). Filling the 4f orbitals apparently influences shielding of the nuclear charge and according to our data this effect was most pronounced early in the series from La to Pm, accounting for as much as roughly 36% of the overall Ln contraction. After Pm, there was a steadier shortening of the Ln–O bonds. This behaviour is in line with Shannon’s effective ionic radii decrease (at coordination number of nine)30, which is larger at the beginning of the series than at the end. It is also worth mentioning that the observed accelerated contraction parallels well with the Ln extraction performance of lipophilic diglycolamides in a liquid–liquid extraction process, where better separation between adjacent lanthanides was achieved for the light (La–Nd) than for the heavy (Er–Lu) members of the series9,10. Moreover, by adapting the modified Slater theoretical model36 to our experimental dataset, we derived a value of the shielding constant for f electrons (s = 0.74), which is in good agreement with the previously reported and generally accepted value of 0.69 obtained from the Ln ionization energies42. We note, however, that accurate fully relativistic quantum mechanical calculations using a new generation of supercomputers will be important to further investigate the observed Ln contraction behaviour in future studies.

After almost eight decades since the discovery of the element Pm, its coordination complex has been synthesized and characterized in solution using modern synchrotron spectroscopy tools. The determined Pm–O bond distance of 2.476(16) Å is in line with quantum chemical investigations and originates from a σ-type donation of electron density from the ligands to the primarily 5d vacant orbitals of Pm. Finally, this previously inaccessible piece of information allowed us to complete structural studies of a full lanthanide set of isostructural complexes in solution, ultimately establishing and confirming the Ln contraction phenomenon solely based on the experimental structural data. These results are expected to contribute to our fundamental understanding and prediction of the coordination chemistry of lanthanides and scarce f-block elements43,44,45,46,47,48, with pertinence to emergent rare-earth separation and radiopharmaceutical technologies.

Methods

Materials synthesis

The PyDGA ligand was synthesized according to the following procedure. In a round-bottom flask equipped with a stir bar, pyrrolidine (11.68 ml, 2.5 equiv.) was combined with anhydrous CH2Cl2 (120 ml) and Et3N (19.58 ml, 2.5 equiv.). The reaction mixture was stirred for 15 min in an ice-water bath. Diglycolyl chloride (6.67 ml, 1.0 equiv.) was added dropwise under an inert atmosphere (Argon), and the reaction mixture was allowed to warm up to room temperature, followed by stirring for the next 12 h. Afterwards, CH2Cl2 was evaporated to dryness under reduced pressure, and the residue was dissolved in 100 ml of methanol and treated with K2CO3 (23.32 g, 3.0 equiv.) to convert Et3N·HCl to KCl and free triethylamine. The reaction mixture was filtrated through a short Celite plug and rinsed with excess methanol to separate the solid salt, and the filtrate was concentrated to yield a crude product. The crude product was purified on CombiFlash Rf automated flash chromatography system using normal phase silica gel as a stationary phase and gradient 0–20% MeOH in CH2Cl2 as an eluent to yield a white crystalline solid (12.00 g, 89%) (see Extended Data Fig. 8 for spectra from 1H nuclear magenetic resonance, 13C nuclear magenetic resonance, Fourier transform-infrared spectroscopy and electrospray ionization with mass spectrometry).

147Pm experimental preparation

Caution! 147Pm (τ1/2 = 2.62 years) has potential health risks due to its β emission. Processing, preparation and handling were carefully performed in a radiological facility with gloveboxes and fume hoods equipped with HEPA (high-efficiency particulate absorbing) filters. The preparation of samples was carefully surveyed and monitored for contamination by trained radiological control technicians.

The promethium was harvested from the waste solutions generated by the production of 238Pu from irradiated 237Np targets. The concentration and initial crude separation of promethium was done using a separation column49 in the hot cell. This had the advantage of obtaining the Pm in a manageable volume and rejecting most other fission products. A careful gradient separation substantially decreased the amount of the high gamma-emitting lanthanide fission products, specifically 141,144Ce and 154,155,156Eu. The solution was further purified by repeating separation cycles in smaller columns within shielded caves or gloveboxes, leaving essentially a Pm solution still containing traces of curium as these two elements typically co-extract and costrip during this process. The separation between promethium and curium was accomplished using a TALSPEAK-based solvent extraction system50 with several scrubs to reach the desired purity.

A 70 mM 147PmIII stock solution in 0.01 M HNO3 was prepared for distribution into the XAS sample after the dilution. To ensure the complete complexation of promethium, a solution (roughly 90 µl) of 8.5 mM 147Pm(NO3)3 containing 180 mM PyDGA was prepared. The obtained solution was then loaded into a polyimide capillary (1.8 mm inner diameter by 5 cm long, 0.05 mm thickness, Cole-Parmer) using a Hamilton syringe and then sealed twice with Devcon 2 Ton epoxy (Extended Data Fig. 1). Once the epoxy had dried completely, the sample was transferred from a glovebox to a radiological fume hood for further decontamination. The sample was then surveyed and doubly contained for shipment to the XAS beamline.

The radiochemical purity of the recovered 147Pm(NO3)3 used for the [Pm(PyDGA)3]3+ sample preparation was more than 99.9%. The residual concentration of 151Sm was assessed at below the detection level. A small quantity of 146Nd was present in the sample due to challenging separations of the adjacent lanthanides using the aforementioned techniques. Traces of Sm present in the sample on the moment of XAS measurements originated from the radioactive decay of promethium to the daughter samarium according to the following process: 147Pm (β−→) 147Sm. Roughly 77 days had passed between the Pm purification and XAS data collection. On the basis of the τ1/2 = 2.62 years of the radioactive decay, up to 5.632% of the starting 147Pm had decayed into 147Sm at the time of the sample measurements at NSLS-II.

XAS data collection and analysis

XAS measurements were acquired at the Ln L3- and L1-edges at beamline 6-BM of the NSLS-II. For the dilute solution of Pm, measurements were performed in fluorescence mode using a four-element silicon-drift detector with no beam-induced changes to the sample being detected. This was checked by comparing individual XAS scans, which did not show any abnormal changes. For all other Ln (La–Nd, Sm–Lu), aqueous solutions of 0.1 M Ln(NO3)3 (prepared from commercial solid LnIII nitrate salts with 99.9% metal purity) and 0.4 M PyDGA were combined in 0.01 M HNO3, and then placed into polyether ether ketone (PEEK) liquid holders of varying thickness with polyimide windows and sealed with epoxy, affording XAS data collection in transmission mode. The data for Ln, except Pm, were energy-calibrated to the main edge from the spectra of Ln oxide standards. The Ln dataset consisted of three scans, which were averaged and background subtracted. For the Pm, 20 (L3-edge) and 30 (L1-edge) individual scans were merged with first derivative maxima at 6,464.4 and 7,441.4 eV, respectively (calibrated to the K-edge of an Fe foil, 7,112.0 eV). Data normalization was performed using the Athena software package51.

Ejected photoelectrons are defined by their wavenumber (k) in relation to the absorption edge energy (E0) through the equation

$$k=\sqrt{2{m}_{{\rm{e}}}(E-{E}_{0})/{\hbar }^{2}}$$
(1)

where me is the electron mass and ħ is the reduced Planck’s constant. The experimental EXAFS oscillations of each sample, χ(k), were extracted from the normalized XAS data using subtraction of a spline and a cut-off distance (RBKG) that varied between 1.2 and 1.0 Å. For analysis of the EXAFS region, we used the EXAFS relationship given by

$$\chi \left(k\right)=\sum _{i}\frac{{F}_{i}(k){S}_{0}^{2}{N}_{i}}{k{R}_{i}^{2}}{{\rm{e}}}^{-{2k}^{2}{\sigma }_{i}^{2}{{\rm{e}}}^{\frac{{-2R}_{i}}{\lambda (k)}}}\sin \left(2k{R}_{i}+{\delta }_{i}\left(k\right)-\frac{4}{3}{k}^{3}{C}_{3,i}\right)$$
(2)

where the index i is considered the path index and the χ(k) is calculated as the summation over all paths. For fitting of the EXAFS, FEFF6 within the Artemis software package51 was used considering the experimental χ(k) data weighted by k3. In equation (2), Fi(k), δi(k) and λ(k) represent the effective scattering amplitude, total phase shift and mean-free-path of the photoelectron and each are derived from the FEFF6 code. The many-body amplitude-reduction factor, S02, was fixed to 1. Furthermore, Ni values, the degeneracy of the path and therefore the coordination numbers for single scattering paths, were held constant (9 and 12 for the first and second coordination shells, respectively), as inferred from the stable 1:3 complexation and the respective Ln-DGA crystal structures37. Therefore, the parameters still to be fit included Ri, the half-path length; σ2i, the Debye–Waller factor; and C3,i, the asymmetry of the distribution. Variation of C3,i was found to provide negligible improvements on the single scattering paths and thus was not included in the fitting process. Furthermore, a single non-structural parameter for all paths, ΔE0, was varied to align the k = 0 point of the experimental data and theory. Fits were performed in R space using a Hanning window for k-space data. For the EXAFS fits, we focused on the Ln–O and Ln–C single scattering paths originating from the binding of three PyDGA ligands. For all lanthanides, both the L3- and L1-edge spectra were simultaneously fit with only the addition of a second ΔE0 variable for the L1-edge data. The L3-edge dataset included both the single scattering paths for Ln–O and Ln–C, whereas the L1-edge used a restricted R-window and only the Ln–O scattering path was fitted. This approach allowed the number of variables (six) per fit to stay below the number of independent data points (ten) available in the primary Pm data with kmax = 7.8 Å−1.

X-ray diffraction studies

Crystallization of [Sm(PyDGA)3][Sm(NO3)6]·3C2H5OH: a solution (1.0 ml) of Sm(NO3)3 (56 mg, 125 mM) was added to 1 ml of CH3OH:C2H5OH (1:1) solution of PyDGA (60 mg, 250 mM), followed by vapour diffusion under isopropyl ether inside a refrigerator at 5 °C. After 7 days, plate shape (monoclinic, P21/c) crystals were obtained. Crystallization of [Er(PyDGA)3]2[Er(NO3)5]3·2H2O: a solution (1.0 ml) of Er(NO3)3 (110 mg, 250 mM) was added to a 1 ml of CH3OH:H2O (9:1) solution of PyDGA (120 mg, 500 mM), followed by vapour diffusion under diethyl ether at room temperature. After 3 days, triclinic (P–1) crystals were obtained. X-ray diffraction data were collected at 100 K on a Bruker D8 Advance Quest diffractometer equipped with a graphite monochromator using Mo Kα radiation (λ = 0.71073 Å). The frames were integrated with the Bruker SAINT software package using a narrow-frame algorithm. An empirical absorption correction using the multi-Scan method SADABS was applied to the data. The structure was solved by direct methods using the Bruker SHELXTL Software Package, v.2018/3. Non-hydrogen atoms were refined anisotropically. Hydrogen atoms were calculated and placed in idealized positions. The CIF files within this report were archived in the Cambridge Crystallographic Data Centre (CCDC) under CCDC depositions 2279633 and 2279634.

Computational details

The Vienna ab initio simulation package (VASP)52,53 was used to conduct AIMD simulations using spin-polarized DFT. The valence electronic states were expanded on a basis of plane waves, whereas the core valence interactions were described using the projector augmented wave approach and standard f-in-valence projector augmented wave potential was used for Pm54,55. The plane-wave kinetic energy cut-off was set to 650 eV and the Perdew–Burke–Ernzerhof (PBE) GGA functional56 was used to describe the exchange-correlation interactions. The Brillouin zone was sampled using the gamma point approximation. The DFT-D3 approach of Grimme57 was used to account for the van der Waals interactions. The initial structure of the Pm complex–water system (a periodic cubic box of 18 Å length containing one complex and 144 water molecules) was pre-equilibrated for 5 ns in a canonical ensemble at a temperature of 300 K using the extended polymer consistent force field (PCFF+)58 supported in MedeA-LAMMPS59,60. As the nitrate counterions are expected to be completely dissociated and/or screened from [Pm(PyDGA)3]3+ in a dilute aqueous environment38, they were not explicitly introduced in the molecular dynamics simulations and the +3 charge on the Pm complex was instead compensated by a uniform background charge. AIMD simulations at 300 K were performed using the Nosé–Hoover thermostat61,62 with a time step of 1 femtosecond (fs). After equilibrating for 10 picoseconds (ps), the AIMD trajectory was collected for 50 ps and used for the RDF analysis. Furthermore, the evenly spaced 1,000 configurations from the last 10 ps of the AIMD trajectory were used to compute and simulate AIMD-EXAFS spectra using the Green’s function-based approach implemented in the FEFF9 package63. Before running the FEFF9 code, a coordinate transformation procedure was performed to ensure that the absorbing ion, Pm, was at the centre of the simulation box and the other atoms were arranged according to their distances from Pm in the ascending order. The multiple scattering path expansion within 8.5 Å of Pm was used during the self-consistent cycle. All multiple scattering paths were included within the plane-wave approximation except the ones with the mean amplitude below 0.01%. XANES and projected density of states calculations of the Pm complex were also performed using FEFF9 (ref. 63). The XANES spectrum was computed using the full multiple scattering, self-consistent field and Hedin–Lundqvist energy-dependent exchange-correlation potential, considering both dipolar and quadrupolar transitions. The ground state potential was used for the background function. For the projected density of states calculations, a Lorentzian broadening parameter of 0.05 eV was applied.

Cluster model calculations in the gas phase were performed with the Gaussian v.16, Revision A.03 program package64. Geometry optimizations enlisted unrestricted Kohn–Sham methods, with the aug-cc-pVTZ basis set for the light atoms65. The small-core f-in-valence quasi-relativistic ECP28MWB/ECP28MWB_ANO effective-core-potential/basis-set66 was used for Pm and the complex was treated as a triply charged quintet with four unpaired f electrons. The optimized structure at the PBE0-D3 level of theory67 was confirmed as a true minimum by analytical frequency calculations. The Pm first- and second-sphere bond distances agreed well with the EXAFS (Extended Data Table 1) and AIMD data (Extended Data Fig. 5), and this structure was used for our subsequent analysis. The Pm L3-edge XANES calculations were performed with the ORCA v.5.0 program68. The ROCIS method was used on top of the DFT wave function (DFT–ROCIS)69,70. The B3LYP functional71 was deployed together with Douglas–Kroll–Hess (DKH) Hamiltonian to account for relativistic effects. The DKH-optimized all-electron TZ-quality basis set was applied to all elements except for Pm, in which segmented all-electron relativistically contracted basis was used (the dkh-def2-tzvp and sarc-dkh-tzvp in ORCA notation, correspondently). Spin–orbit coupling as well as lower and higher multiplets were accounted for. The analysis was done using the natural difference orbitals72. To account for systematic errors in the calculation of transition energies, the simulated spectrum was uniformly shifted by 175 eV to match the experimental absorption edge energy. The bonding in the Pm complex was examined by using the NBO methodology73, as implemented in the NBO7 program74,75. Molecular orbital diagrams were drawn with an isovalue of 0.035 a.u. Model representations in the figures were prepared using the UCSF Chimera software76. The Slater shielding constant for 4f electrons was derived based on the methodology described by Seitz et al.36.