# Revealed Preferential Short-Range Anion Ordering in Disordered RbM2O5F (M = Nb, Ta) Pyrochlore-Type Oxyfluorides

Ouail Zakary, Monique Body, Vincent Sarou-Kanian, Thibault Charpentier, Christophe Legein

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Ouail Zakary, Monique Body, Vincent Sarou-Kanian, Thibault Charpentier, Christophe Legein. Revealed Preferential Short-Range Anion Ordering in Disordered RbM2O5F (M = Nb, Ta) Pyrochlore-Type Oxyfluorides. Inorganic Chemistry, 2025, 64 (11), pp.6764-6777. hal-04992846

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Revealed Preferential Short-Range Anion Ordering in
Disordered RbM<sub>2</sub>O<sub>5</sub>F (M = Nb, Ta) Pyrochlore-Type
Oxyfluorides

<table><tr><td>Journal:</td><td>Inorganic Chemistry</td></tr><tr><td>Manuscript ID</td><td>ic-2025-00615g.R1</td></tr><tr><td>Manuscript Type:</td><td>Article</td></tr><tr><td>Date Submitted by the Author:</td><td>n/a</td></tr><tr><td>Complete List of Authors:</td><td>Zakary, Ouail; Le Mans Universite, Institut des Molécules et des Matériaux du Mans (IMMM). UMR CNRS 6283, Body, Monique; Institut des Molecules et Materiaux du Mans, IMMM UMR 6283 CNRS<br>SAROU-KANIAN, Vincent; CNRS, CEMHTI<br>Charpentier, Thibault; CEA Saclay, IRAMIS - SIS2M<br>Legein, Christophe; Le Mans Universite, Institut des Molécules et des Matériaux du Mans (IMMM), UMR CNRS 6283</td></tr></table>

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# Revealed Preferential Short-Range Anion Ordering in Disordered RbM₂O₅F (M = Nb, Ta) Pyrochlore-Type Oxyfluorides

Ouail Zakary,¹,²,* Monique Body,¹ Vincent Sarou-Kanian

D,³ Thibault Charpentier,⁴ and Christophe Legein ¹

¹Institut des Molécules et Matériaux du Mans (IMMM) – UMR 6283 CNRS, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France

²Present Address: NMR Research Unit, Faculty of Science, University of Oulu, FI-90014 Oulu, Finland

³Conditions Extrêmes et Matériaux, Haute Température et Irradiation (CEMHTI), UPR3079 CNRS Orléans, France

⁴Université Paris-Saclay, CEA, CNRS, NIMBE 91191, Gif-sur-Yvette cedex, France

(Dated: February 27, 2025)

**ABSTRACT:** Describing the crystal structure of disordered materials with mixed-occupancy crystallographic sites is essential for understanding their physicochemical properties and designing new materials tuned to targeted functionalities. Here, we investigate the structure of RbM₂O₅F (M = Nb, Ta) pyrochlore-type oxyfluorides using a multimodal approach that combines experimental and computational techniques. Rietveld structural refinement of PXRD data confirmed that these oxyfluorides are isostructural and their average crystal structure is disordered. The anionic site, 48f, is co-occupied by O and F, while the Rb site, 32e, is occupied at 25%. The shapes of the high-field solid-state ¹⁹F MAS, and ⁸⁷Rb and ⁹³Nb (CT)MAS and 3QMAS NMR spectra, indicate that the local environment of these nuclei is distributed. Using the "supercell" approach, models incorporating different anion arrangements and Rb atoms distributed in their crystallographic site, were built and relaxed using DFT, and NMR parameters for ¹⁹F, ⁸⁷Rb, and ⁹³Nb, were computed using the PAW and GIPAW approaches. The models showing the best agreement between computed and experimental NMR parameters are made up exclusively of [MO₅F]⁶⁻ octahedra, [RbO₁₅F₃]³²⁻, [RbO₁₆F₂]³³⁻, and [RbO₁₄F₄]³¹⁻ cages, indicating the existence of a preferential short-range anion ordering in these pyrochlores, instead of the expected random distribution.

**Keywords:** Pyrochlores, Preferential Anion Ordering, Multinuclear High-Field Solid-State NMR, Structural Modeling, First Principle Calculations

## I. INTRODUCTION

Pyrochlores are well-known for their highly "tai-lorable" structures, enabling the possibility to create materials with targeted physicochemical properties and functionalities.¹,² Having the ideal stoichiometric formula A₂M₂X₆Y (that of Ca₂Nb₂O₆F, i.e. the nominal pyrochlore mineral), the pyrochlore structure crystallizes in the isometric crystal system with centrosymmetric Fd₃m (no. 227) space-group. This structure incorporates four distinct crystallographic sites, two for the cations A (32e or 16c or 8b Wyckoff positions) and M (16d Wyckoff position) and two for the anions, noted X (48f Wyckoff position) and Y (8b Wyckoff position). The A cation, occupying the eightfold coordinated sites (AX₆Y₂ distorted cubes), is usually low valence with a larger ionic radius, such as alkali, alkaline-earth and rare-earth ions, whereas the M cation, occupying the sixfold coordinated sites (trigonal antiprisms MX₆), is usually high valence with a smaller ionic radius, like Ti⁴⁺, Ni²⁺, Zn²⁺, Nb⁵⁺, Ta⁵⁺, and W⁶⁺ transition metal ions. The 48f site is occupied by X anions that bond with both A and M cations, while the 8b site is occupied by Y anions, which are coordinated by four A cations. The structure incorporates large hexagonal-shaped tunnels

formed by corner-shared MX₆ octahedra and occupied by Y and A ions. These tunnels — intersecting [110], [101], and [011] — may form a three-dimensional ionic conducting path. The extensive flexibility observed in the composition of pyrochlores emanates from the wide variety of possible site substitutions that may occur on the cationic sites, but also on the anionic sites.³⁻⁶ Instead of the more commonly observed O²⁻ anion, these positions can be filled by anions such as OH⁻, F⁻ and S²⁻. For instance, as of the present date, there are at least 79 pyrochlore-type oxyfluorides whose structures are known, whether ordered or disordered (Tables S1 and S2), some of which possess intriguing properties. CsTi₂O₂.₈₅F₃.₁₅ is synthesized at relatively low temperatures and turns out to exhibit excellent thermal stability and acid/alkali resistance.⁷ The n-type semiconductors Na₂B₂O₅F₂ (B = Nb, Ta) have been shown to be photoactive.⁸ Similarly, pyrochlores such as Pb₂Ti₂O₅.₄F₁.₂,⁹ Sn₁.₀₆Nb₂O₅.₅₉F₀.₉₇,¹⁰ Sb₂TiNbO₆F,¹¹ and Na₂₋₂ₓSnₓM₂O₅F₂ (M = Nb, Ta and 0 ≤ x ≤ 1)¹² exhibit interesting photocatalytic properties. Moreover, in some cases, the structure of pyrochlore oxyfluorides enables dynamic processes, particularly ionic transport¹³ and conductivity.¹⁴ For instance, Li₂₋ₓLa(₁+x)/₃M₂O₆F (M = Nb, Ta), originally synthesized and the structure thoroughly characterized by Galven et al.,¹⁵ especially Li₁.₂₅La₀.₅₈Nb₂O₆F, exhibits a total Li-ion conductivity higher than any

<footnote>* ouail.zakary@oulu.fi</footnote>
reported oxide solid electrolytes.¹⁶

In oxide-derived heteroanionic pyrochlores, the coexistence in the host crystal structure of two (or more) anionic species with different charges, ionic radii, electronegativities, and polarizabilities allows for modifying stoichiometry and local structure, resulting in properties distinct from those of analogous pyrochlore oxides. These properties depend not only on the stoichiometry and identity of the constituent anions but also on their arrangement in the crystal structure. Therefore, understanding these anion arrangements is necessary not only to describe the properties exhibited by these materials but also to engineer new materials with targeted functionalities. Oxide-derived heteroanionic pyrochlores, such as oxyfluorides, are typically characterized with "long-length-scale" characterization techniques, such as X-ray and neutron diffractions, which, however, only provide a model of the average crystal structure, known as the "long-range structure".¹⁷ As O²⁻ and F⁻ have similar X-ray (or Neutron) scattering factors, relying solely on the diffraction data is insufficient to describe O/F ordering. In this context, solid-state NMR spectroscopy (ssNMR) — a "short-length-scale" characterization technique — combined with electronic structure calculation methods, including DFT, is regarded as a potent multimodal approach, as it can offer detailed insights into the local atomic environments. Indeed, over the past decade, multiple disordered oxyfluorides have been successfully described through the combination of powder X-ray powder diffraction (PXRD), ssNMR and DFT calculations.¹⁸⁻²²

The average structure of RbM₂O₅F (M = Nb, Ta) oxyfluorides, initially synthesized and characterized by Babel et al.,²³ was found to adopt the pyrochlore structure, wherein Rb and M cations are located in the 8b and 16c sites, respectively, while O and F co-occupy the 48f site with respective site occupancy factors (SOF) of 83.3% and 16.7%. However, follow-up investigations from Fourquet et al.²⁴ demonstrated that in RbNb₂O₅F, Rb atoms are statistically distributed in the 32e site, rather than fully occupying the 8b site. Later on, from single crystal data of RbTa₂O₅F and in accordance with the initial model given by Babel et al.,²³ Goodenough et al.¹³ conclude that the 32e site cannot be occupied and that Rb atoms indeed occupy the 8b site. From these studies, the positions of Rb atoms remain uncertain. Moreover, the co-occupation of the anionic site results in random configurations of [MO₆⁻ₓFₓ]ⁿ⁻ octahedra (x = 0, ..., 6, with x and n ∈ N) and [RbO₁₈⁻ᵧFᵧ]⁽ⁿ⁻⁾ polyhedra (y = 0, ..., 18, with y and m ∈ N), with possible homoleptic — one anionic species coordinates one specific cation — and heteroleptic — a cation is coordinated by more than one anionic species — polyhedral units.

Herein, we propose a set of models describing the structure of RbM₂O₅F pyrochlores. To achieve this, RbM₂O₅F compounds were prepared through solid-state synthesis and characterized by PXRD, and high field ss-

NMR of ¹⁹F, ⁸⁷Rb, and ⁹³Nb, with ⁹³Nb being probed at ultra-high MAS frequency. The average structure was obtained by refining the PXRD data. Using the "super-cell" approach, Ewald energy sorting, and cation environment probabilities as selective criteria, 20 structural configurations — with anions and Rb atoms distributed on the 48f and 32e sites, respectively — were selected for RbNb₂O₅F and 10 configurations for RbTa₂O₅F. Subsequently, DFT relaxation was performed on these 30 configurations, and NMR parameters were computed using the PAW and GIPAW approaches. These parameters were then compared to the experimental data. An overall agreement is reached for 5 configurations per RbM₂O₅F compound, exclusively featuring [MO₅F]⁶⁻ octahedra, identifying a strong short-range anion ordering in these pyrochlore-type oxyfluorides.

## II. METHODS

### A. Experimental

#### 1. Synthesis

Pure RbNb₂O₅F and RbTa₂O₅F compounds were prepared by direct solid-state synthesis from a stoichiometric mixture of RbF (Alfa Produkte, 99.9%) and M₂O₅ (M = Nb, Ta) (Alfa Aesar, 99.85% and 99.9% for Ta₂O₅ and Nb₂O₅, respectively). Prior to synthesis, M₂O₅ compounds were dried under a secondary vacuum at 150 °C for 9 hours, with heating and cooling occurring at a rate of 2 °C/minute, and then stored in a glove box under nitrogen atmosphere. With RbF being moisture sensitive, the weighing, mixing, and grinding steps were performed under nitrogen atmosphere in a glove box. The resulting mixtures were then placed inside platinum tubes, sealed, and heated to 750 °C for four days with a heating rate of 5 °C/minute, after which they were left to cool down naturally.

#### 2. X-ray powder diffraction

The PXRD diagrams were recorded using a PANalytical θ/θ Bragg-Brentano EMPYREAN diffractometer (CuKα₁+₂ radiations) equipped with a PIXcel¹⁵ detector. The patterns were measured in a 2θ range of 5° to ≈120° with a 0.0131° step size, the recording time was approximately 6 hours. The obtained data was refined employing the Rietveld structural refinement method²⁵ incorporated in the Fullprof software.²⁶ Alongside the usual refinement parameters, the preferred orientation parameter (G1) was refined. The background intensity was estimated from linear interpolation between points manually selected in regions free from Bragg reflections.

#### 3. Solid-state NMR spectroscopy

The ¹⁹F (I = 1/2) magic angle spinning (MAS) NMR spectra were recorded with a Bruker Avance III spectrometer functioning at 20.0 T (¹⁹F Larmor frequency of 800 MHz) using a 1.3 mm CP-MAS probe-head, the spinning frequency was set to 46 kHz. The Hahn echo sequence was used with an interpulse delay of one rotor period and a recycle delay of 30 s and 60 s for RbNb₂O₅F
and RbTa₂O₅F, respectively. The 90° pulse was set to 1.6 µs (RF field of 156 kHz) for both RbM₂O₅F compounds.

The ⁸⁷Rb ($I = 3/2$) and ⁹³Nb ($I = 9/2$) MAS and multiple-quantum MAS (MQMAS²⁷,²⁸) NMR spectra were acquired using a Bruker Avance III spectrometer operating at 20.0 T (⁸⁷Rb and ⁹³Nb Larmor frequencies of 278.2 and 208.1 MHz, respectively).

The ⁸⁷Rb MAS and MQMAS spectra were recorded using a 2.5 mm CP-MAS probe-head, at a 30 kHz spinning frequency. The ⁸⁷Rb one-pulse MAS NMR spectra were recorded with a recycle delay of 0.25 s and a pulse duration of 0.38 µs (RF field of 64 kHz), corresponding to a small flip angle of 10° to ensure a total excitation of the entire spin system. The ⁸⁷Rb two-dimensional z-filtered MQMAS spectra were recorded using an RF field strength of 64 kHz for the triple-quantum excitation and reconversion (3QMAS), with a z-filter duration of 33 µs, recycle delay of 0.33 s and 128 $t_1$ increments with 1152 transients each. The duration of the central transition (CT) 90° selective pulse was set to 9.8 µs (RF field of 13 kHz).

The ⁹³Nb MAS and MQMAS NMR spectra were recorded using a 0.7 mm CP-MAS probe-head, at an ultra-high spinning frequency of 100 kHz. The Hahn echo sequence was used for the ⁹³Nb one-dimensional CT MAS NMR spectrum (CTMAS), with a recycle delay of 1 s and duration of the CT 90° selective pulse of 2 µs (RF field of 25 kHz). The ⁹³Nb 3QMAS spectrum was acquired with an RF field strength of 350 kHz for the triple-quantum excitation and reconversion, a CT selective pulse of 2 µs (RF field of 25 kHz), a z-filter duration of one rotor period and a recycle delay of 0.5 s. 40 $t_1$ increments of 4800 transients each were accumulated.

The recorded spectra of ¹⁹F, ⁸⁷Rb and ⁹³Nb were referenced to CFCl₃,²⁹ 1 M aqueous solution of RbCl and KNbCl₆, respectively. All spectra were fitted using the DMFit software,³⁰ and the baseline intensities of the ⁸⁷Rb MAS and ⁹³Nb CTMAS spectra were estimated from linear interpolation between points manually selected in regions free from high-intensity resonances. The “Czjzek”³¹ and “CzSimple” models were used to fit the MAS, CTMAS and 3QMAS spectra, respectively. The “Czjzek” model considers a statistical distribution of the quadrupolar interaction (the quadrupolar coupling constant, $C_Q$, and the asymmetry parameter, $\eta_Q$) induced by the distribution of the local environment of the probed nuclei, whereas the “CzSimple” model includes a rapid version of the “Czjzek” model with an uncoupled Gaussian distribution of $\delta_{iso}$ values. Both models are used with $d = 5$ and enable the retrieval of the average $\delta_{iso}$ and $C_Q$ values, as well as the width of the Gaussian distribution of $\delta_{iso}$ values ($\Delta\delta_{iso}$). The average $\eta_Q$ parameter value is fixed at $\approx 0.61$ with an approximate standard deviation of $\sigma_\eta \approx 0.24$.³¹

## B. Computational

For the unit cells, the ground state electronic structure, the optimized geometries, the electric field gradient ten-

sor (EFG), and the magnetic shielding tensor ($\hat{\sigma}$) were all obtained using VASP (version 6.2.1).³²,³³ For the 2×2×2 supercells, the ground state electronic structure calculations and the geometry optimization were obtained using CP2K (version 8.2),³⁴ the EFG and $\hat{\sigma}$ tensors were computed using VASP (version 6.2.1).³²,³³

### 1. DFT relaxation

The electronic structure of the unit cell consisting of 72 atoms was computed through solid-state DFT with periodic boundary conditions (PBC). The conjugate-gradient algorithm was used in ionic relaxation. The Perdew-Burke-Ernzerhof functional including the generalized gradient approximation (PBE-GGA)³⁵ was employed to obtain the ground state electronic structure. The interactions between core and valence electrons were described using the projector augmented wave (PAW) method,³⁶ with core configurations of [He] for O and F, [Ar] 3d¹⁰ for Rb and Nb, and [Xe] 4f¹⁴ for Ta. The PAW potentials³⁷ used for O, F, Na, Nb and Ta are O_s_GW, F_GW, Rb_sv_GW, Nb_sv_GW and Ta_sv_GW, respectively. These potentials include six electrons for O (2s² 2p⁴), seven electrons for F (2s² 2p⁵), nine electrons for Rb (4s² 4p⁶ 4d¹), thirteen for Nb (4s² 4p⁶ 4d⁵), and Ta (5s² 5p⁶ 5d⁵). The wave functions were expanded on a plane-wave basis set with a 550 eV kinetic energy cut-off and a 3 × 3 × 3 shifted Monkhorst-Pack k-point mesh. The atomic positions were relaxed until all forces converged to less than 0.1 meV.Å⁻¹. The total energy was converged up to change below 10⁻⁸ eV. Similarly, the electronic structure of the 2×2×2 supercell consisting of 576 atoms was computed at the PBE-GGA³⁵ level with PBC. The core-valence electrons interactions were described using Goedecker-Teter-Hutter (GTH) pseudopotentials,³⁸ and the wave functions were expanded on a TZVP Gaussian basis sets (MOLOPT library), with a charge density plane-wave expansion energy cutoff of 720 Ry and a Γ-only k-point mesh.

### 2. NMR parameters calculations

The PAW³⁶,³⁹ and GIPAW⁴⁰,⁴¹ approaches were used to calculate the EFG and the $\hat{\sigma}$ tensors, respectively. For both the unit cells and 2×2×2 supercells, the PAW potentials, plane-wave energy cut-off, and the k-point mesh were set the same as the unit cells and 2×2×2 supercells DFT relaxation. The magnetic shielding and chemical shift parameters are defined using the Haeberlen convention.⁴² The isotropic magnetic shielding ($\sigma_{iso}$), the magnetic shielding anisotropy ($\sigma_{CSA}$) and the asymmetry ($\eta_{CSA}$) parameters are respectively defined as $\sigma_{iso} = (\sigma_{xx} + \sigma_{yy} + \sigma_{zz})/3$, $\sigma_{CSA} = \sigma_{zz} - \sigma_{iso}$, and $\eta_{CSA} = (\sigma_{yy} - \sigma_{xx})/\sigma_{CSA}$, with the magnetic shielding tensor components $\sigma_{ii}$ defined in the sequence $|\sigma_{zz} - \sigma_{iso}| \ge |\sigma_{xx} - \sigma_{iso}| \ge |\sigma_{yy} - \sigma_{iso}|$. Similarly, the isotropic chemical shift ($\delta_{iso}$), the chemical shift anisotropy ($\delta_{CSA}$) and the asymmetry ($\eta_{CSA}$) parameters are given by $\delta_{iso} = (\delta_{xx} + \delta_{yy} + \delta_{zz})/3$, $\delta_{CSA} = \delta_{zz} - \delta_{iso}$, and $\eta_{CSA} = (\delta_{yy} - \delta_{xx})/\delta_{CSA}$, with the chem-
ical shift tensor components $\delta_{ii}$ ordered in the sequence $|\delta_{zz} - \delta_{iso}| \ge |\delta_{xx} - \delta_{iso}| \ge |\delta_{yy} - \delta_{iso}|$. The relationship between $\sigma_{iso}$ and $\delta_{iso}$ is defined by the equation $\delta_{iso} \simeq \sigma_{iso}^{ref} - \sigma_{iso}$, where $\sigma_{iso}^{ref}$ represents the absolute isotropic magnetic shielding reference.

To simulate theoretical ¹⁹F MAS, and ⁸⁷Rb and ⁹³Nb (CT)MAS from DFT calculations, the computed $\sigma_{iso}$ and $\sigma_{CSA}$ should be converted to $\delta_{iso}$ and $\delta_{CSA}$, respectively. This process involves obtaining transformation functions by fitting models for $\sigma_{iso} \to \delta_{iso}$ and for $\sigma_{CSA} \to \delta_{CSA}$ using linear least-squares regression between computed magnetic shielding and experimental chemical shift values. For ¹⁹F, the transformation functions $\sigma_{iso} \to \delta_{iso}$ and $\sigma_{CSA} \to \delta_{CSA}$ were derived from combining RbF⁴³ and MF₅ (M = Nb, Ta)⁴⁴,⁴⁵ fluorides. Furthermore, computed ⁸⁷Rb $\delta_{iso}$ values were deduced from a new linear transformation function $\sigma_{iso} \to \delta_{iso}$ established in the present work. For ⁹³Nb, we used a relation from the literature.¹⁹ Further details of the derivation of these transformation functions are discussed in Section III C and the data are reported as supplementary information (Figures S1-S3 and Tables S7-S10).

### 3. Theoretical NMR spectra

The theoretical ¹⁹F MAS NMR spectra were simulated for RbNb₂O₅F and RbTa₂O₅F using the Python package "mrsimulator".⁴⁶⁻⁴⁹ The simulation begins by reading the computed $\delta_{iso}$, $\delta_{CSA}$, and $\eta_{CSA}$ values for each F atom from the final configurations. These values are used to create "SpinSystem" objects, which form the basis for simulating the overall spectrum. The "BlochDecaySpecification" method is employed for generating the theoretical MAS NMR spectrum. The primary parameters for this method include (i) the channel set to ¹⁹F, (ii) the magnetic flux density set at 20 T, (iii) the rotor angle set to 54.735° (MAS), (iv) the rotor frequency set at 46 and 50 kHz for RbNb₂O₅F and RbTa₂O₅F, respectively, (v) the number of points set to 512 (ensuring sufficient resolution), and (vi) the spectral width set to 800 kHz (enabling coverage of the necessary chemical shift range). The raw spectrum underwent processing through Gaussian apodization using an 8 kHz FWHM to enhance spectral resolution and reduce noise. Inverse and Forward Fourier Transforms (IFFT and FFT) were employed to convert the time-domain signal into the frequency domain for visualization.

Similar to ¹⁹F, the Python package "mrsimulator"⁴⁶⁻⁴⁹ was used to simulate theoretical ⁸⁷Rb MAS and ⁹³Nb CTMAS NMR spectra for RbNb₂O₅F and RbTa₂O₅F. The simulation process begins by parsing the computed parameters, including $\delta_{iso}$, $\delta_{CSA}$, $\eta_{CSA}$, $C_Q$, and $\eta_Q$ for each atom Rb and Nb from the final configurations. These parameters are used to create "SpinSystem" objects, each of which defines the magnetic and quadrupolar properties of individual ⁸⁷Rb and ⁹³Nb nuclei. The "BlochDecayCTSpectrum" method was then applied to generate the theoretical MAS NMR spectra. Key parameters for this method include (i) the observation channel

set to ⁸⁷Rb and ⁹³Nb, (ii) a magnetic flux density of 20 T, (iii) a rotor angle set to MAS, (iv) a rotor frequency set at 30 and 100 kHz for ⁸⁷Rb and ⁹³Nb, respectively, (v) a count of 1000 points to ensure high spectral resolution, and (vi) a spectral width of 1.45 and 5 MHz for ⁸⁷Rb and ⁹³Nb, respectively, covering the necessary chemical shift range. The raw spectrum underwent processing through IFFT, exponential apodization with a 10 Hz FWHM, Gaussian apodization with a 2 and 10 kHz FWHM for ⁸⁷Rb and ⁹³Nb, respectively, and a final FFT to convert the processed signal back into the frequency domain.

## III. RESULTS AND DISCUSSION

### A. Characterization

#### 1. ¹⁹F MAS NMR spectra

The experimental ¹⁹F MAS NMR spectra with their fits are shown in Figure 1. They display a broad and asymmetric main line and are both fitted using two contributions, which is consistent with the disordered environment of the bridging fluorine site.¹³,²³,²⁴ The weighted average $\delta_{iso}$ values are estimated around -102.3 ppm and -111.4 ppm for RbNb₂O₅F and RbTa₂O₅F, respectively (Table I). The first value is within the $\delta_{iso}$ range of values identified for fluorine atoms surrounded by at least one alkaline and one niobium atom (from -85.1 to -119.2 ppm for equatorial F sites in both phases of KNaNbOF₅).⁵⁰

<table><caption>TABLE I. ¹⁹F $\delta_{iso}$ ($\delta_{iso}$, ppm), $\delta_{CSA}$ ($\delta_{CSA}$, ppm), full width at half maximum (FWHM, ppm), and the relative intensity ($I_R$, %) of the individual resonances used in the fits from RbNb₂O₅F and RbTa₂O₅F. The weighted average values of $\delta_{iso}$ and $\delta_{CSA}$ are given in bold italics. $\eta_{CSA}$ was set to 0 because it did not affect the spectra during the fitting process.</caption><thead><tr><th></th><th>δ<sub>iso</sub></th><th>δ<sub>CSA</sub></th><th>FWHM</th><th>I<sub>R</sub></th></tr></thead><tbody><tr><td colspan="5">RbNb<sub>2</sub>O<sub>5</sub>F</td></tr><tr><td>Line 1</td><td>-100.7</td><td>-40</td><td>10.2</td><td>80.9</td></tr><tr><td>Line 2</td><td>-109.2</td><td>-32.8</td><td>8.3</td><td>19.1</td></tr><tr><td>⟨⟩</td><td><b>-102.3</b></td><td><b>-38.7</b></td><td><b>n.a.</b></td><td><b>n.a.</b></td></tr><tr><td colspan="5">RbTa<sub>2</sub>O<sub>5</sub>F</td></tr><tr><td>Line 1</td><td>-110.2</td><td>-36</td><td>10.3</td><td>81.9</td></tr><tr><td>Line 2</td><td>-116.8</td><td>-23.3</td><td>9.9</td><td>18.1</td></tr><tr><td>⟨⟩</td><td><b>-111.4</b></td><td><b>-33.7</b></td><td><b>n.a.</b></td><td><b>n.a.</b></td></tr></tbody></table>

#### 2. ⁸⁷Rb and ⁹³Nb (CT)MAS and 3QMAS NMR spectra

Given that ⁸⁷Rb ($I = 3/2$) and ⁹³Nb ($I = 9/2$) nuclei are subject to the quadrupolar interaction, the use of ⁸⁷Rb and ⁹³Nb NMR enables insights on the distribution of their local environments. Figure 2 presents ⁸⁷Rb and ⁹³Nb (CT)MAS and 3QMAS NMR spectra from RbNb₂O₅F and RbTa₂O₅F. Both ⁸⁷Rb MAS NMR spectra (Figure 2 (a) and (b)) display a broad asymmetric CT shape and an absence of singularities in the ST patterns. These features are consistent with a disordered local environment for ⁸⁷Rb. The line shapes observed
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /><figcaption>FIG. 1. Experimental (dark blue) and fitted (dashed red) $^{19}$F MAS NMR (20 T) spectra of RbNb$_{2}$O$_{5}$F (46 kHz, a) and RbTa$_{2}$O$_{5}$F (50 kHz, b). The individual resonances used for the fit (teal and orange) and the difference (grey) are shown below. The asterisks refer to spinning sidebands.</figcaption></figure>

on $^{87}$Rb 3QMAS spectra (Figure 2 (d) and (e)) take the form of a ridge along the diagonal, confirming the presence of both chemical shift and quadrupolar interaction dispersions.⁵¹ For both compounds, an initial set of parameters was obtained by reconstructing the $^{87}$Rb MAS spectrum using Gaussian distributions for both the chemical shift and quadrupolar interactions. These parameters were then used to construct the $^{87}$Rb 3QMAS spectrum and were subsequently adjusted to achieve the best possible reconstruction of both 1D and 2D spectra. The parameters used for the fit are gathered in Table II. Similar $^{87}$Rb $\delta_{iso}$ and $\Delta\delta_{iso}$ values are obtained for both compounds, indicating similar environments. The $C_Q$ value is slightly higher for RbTa$_{2}$O$_{5}$F, which may be attributed to slightly more distorted environments.

$^{93}$Nb CTMAS and 3QMAS spectra were recorded for RbNb$_{2}$O$_{5}$F at an ultra-high MAS frequency of 100 kHz. They were fitted using the same approach used for the $^{87}$Rb spectra. The parameters used for the fit model are gathered in Table II. In comparison to $^{87}$Rb MAS NMR spectra, $^{93}$Nb CTMAS spectrum (Figure 2 (c)) exhibit broader asymmetric CT, indicating largely distributed $^{93}$Nb local environments. This distribution is further

<table><caption>TABLE II. $\delta_{iso}$ ($\delta_{iso}$, ppm), relative intensity ($I_R$, %), width of the distribution of $\delta_{iso}$ ($\Delta\delta_{iso}$, ppm), average quadrupolar coupling constant ($C_Q$, MHz), and width of the distribution of $C_Q$ ($\Delta C_Q$, MHz) of the resonances used in the fits of the spectra from RbNb$_{2}$O$_{5}$F and RbTa$_{2}$O$_{5}$F. The weighted average values of $\delta_{iso}$, $\Delta\delta_{iso}$, $C_Q$, and $\Delta C_Q$ are given in bold italics.</caption><thead><tr><th></th><th>Spectrum</th><th>δ<sub>iso</sub></th><th>I<sub>R</sub></th><th>Δδ<sub>iso</sub></th><th>C<sub>Q</sub></th><th>ΔC<sub>Q</sub></th></tr></thead><tbody><tr><td colspan="7">RbNb<sub>2</sub>O<sub>5</sub>F</td></tr><tr><td rowspan="3"><sup>87</sup>Rb</td><td>STSS (n = 0)</td><td>-77.5</td><td>2.5</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>MAS</td><td>-79.5</td><td>97.5</td><td>-13.3</td><td>1.7</td><td>0.8</td></tr><tr><td>3QMAS</td><td>-79.5</td><td>n.a.</td><td>-13.3</td><td>1.7</td><td>0.8</td></tr><tr><td rowspan="3"><sup>93</sup>Nb</td><td>⟨⟩</td><td><b>-79.4</b></td><td>n.a.</td><td><b>-13.3</b></td><td><b>1.7</b></td><td><b>0.8</b></td></tr><tr><td>CTMAS</td><td>-1048.8</td><td>n.a.</td><td>-86.3</td><td>55.1</td><td>27.5</td></tr><tr><td>3QMAS</td><td>-1060.5</td><td>n.a.</td><td>-86.3</td><td>55.1</td><td>27.5</td></tr><tr><td></td><td>⟨⟩</td><td><b>-1054.6</b></td><td>n.a.</td><td><b>-86.3</b></td><td><b>55.1</b></td><td><b>27.5</b></td></tr><tr><td colspan="7">RbTa<sub>2</sub>O<sub>5</sub>F</td></tr><tr><td rowspan="3"><sup>87</sup>Rb</td><td>STSS (n = 0)</td><td>-73.6</td><td>2.1</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>MAS</td><td>-76.5</td><td>97.9</td><td>-13.5</td><td>2.0</td><td>1.0</td></tr><tr><td>3QMAS</td><td>-76.5</td><td>n.a.</td><td>-13.5</td><td>2.0</td><td>1.0</td></tr><tr><td></td><td>⟨⟩</td><td><b>-76.5</b></td><td>n.a.</td><td><b>-13.5</b></td><td><b>2.0</b></td><td><b>1.0</b></td></tr></tbody></table>

confirmed by the $^{93}$Nb 3QMAS spectrum (Figure 2 (f)), which exhibits a combination of a horizontal ridge and a wide ridge along the diagonal indicating largely distributed $\delta_{iso}$ and $C_Q$.

### 3. Crystal structures

The experimental structure (ES) was derived by refining the PXRD patterns using the Rietveld refinement method. Two structural solutions were tested, the first solution involves considering Rb atoms totally occupying the 8b site, while the second solution considers Rb atoms occupying 25% of the 32e site. Lower reliability refinement parameters were obtained with the latter structural solution, considering isotropic displacement parameters (IDPs) for all atoms and constraining these IDPs for cations to $U_{iso}(Nb) = U_{iso}(Rb)$ and anions to $U_{iso}(O) = U_{iso}(F)$. Due to the Rb site symmetry 3m, the coordinates of this site were constrained to $x(Rb) = y(Rb) = z(Rb)$. As the anionic site is co-occupied by O and F, the coordinate $x$ was contained to $x(O) = x(F)$. The ES crystallographic features are gathered in Table III. The experimental and calculated PXRD patterns, as well as their refinement reliability parameters, are gathered in Figure 3. Crystal structures have been deposited via the joint CCDC/FIZ Karlsruhe deposition service. CSD⁵² 2401963 and 2401964 (deposit number) contain the supplementary crystallographic data for RbNb$_{2}$O$_{5}$F and RbTa$_{2}$O$_{5}$F, respectively. These data can be found free of charge from FIZ Karlsruhe via https://www.ccdc.cam.ac.uk/structures. The obtained ES fits the model proposed by Fourquet et al.²⁴ The structure consists of a 3D network of corner-shared $[MO_{6-x}F_x]^{n-}$ octahedra, forming ring-like hexagonal-shaped tunnels referred to hereafter as the subarray sub-{MX$_{3}$} ($X$ = O, F), which collectively constitute
<figure><img src="image_4.png" /><figcaption>FIG. 2. Experimental (dark blue) and fitted (dashed red) $^{87}$Rb MAS (30 kHz), $^{93}$Nb CTMAS (100 kHz), and 3QMAS (30 and 100 kHz for $^{87}$Rb and $^{93}$Nb, respectively) NMR (20 T) spectra of RbNb$_{2}$O$_{5}$F (a, c, d, and f) and RbTa$_{2}$O$_{5}$F (b and e). The insets represent zooms of the central transition (top-left of a, b, and c) and the three first-order satellite transitions (top-right of a and b). The individual resonance used for the fit (teal), the zeroth-order satellite transition spinning sidebands (orange), and the model difference (grey) are shown below the spectra. For each 3QMAS spectrum, the diagonal with a unity slope (light orange) and projections along (MAS, Intensity) and (Isotropic, Intensity) are presented.</figcaption></figure>

the tridimensional framework. A large polyhedral cage, whose center hosts the 32e site — partially occupied by Rb atoms — is formed by four $sub-\{MX_{3}\}$ (Figure 4).

## B. Modeling approach and DFT relaxation

Constructing structural models that describe disordered crystals, i.e. crystals with mixed-occupancy sites requires, (i) generating all possible structural configurations by distributing atoms within their respective mixed-occupancy sites, (ii) filtering out the configurations equivalent by symmetry operations, and (iii) sorting out configurations with highest Ewald energy ($E_{Ewald}$, in eV). Using the program "Supercell",$^{54}$ the random distribution within the unit cell of 40 O and 8 F in 48 positions, and 8 Rb in 32 positions, results in a considerable number of possible configurations equivalent by symmetry operations $N_{eq} \simeq 4 \times 10^{15}$ ("initial dist. 32e + 48f" step in Figure 5). As a result, atoms were distributed following two steps, the first step involves distributing 8 Rb atoms in the 32 positions. As this step results in a significant number of configurations inequivalent by symmetry operations $N_{ineq} \simeq 5.6 \times 10^{4}$, only five

configurations with the lowest $E_{Ewald}$ were taken for the next step ("1st dist. 32e" step in Figure 5). The second step involves distributing 40 O and 8 F in the 48 positions from the selected five configurations, resulting in $N_{ineq} \simeq 1.9 \times 10^{8}$ configurations, out of which 0.05% was selected for subsequent analysis ($N_{tot} = 1 \times 10^{5}$). These $N_{tot}$ configurations compose $N_{select}\{E_{Ewald}^{(\lambda)}\} = 0.5 \times 10^{5}$ and $N_{select}\{E_{Ewald}^{(\nabla)}\} = 0.5 \times 10^{5}$, referring to the lowest and highest $E_{Ewald}$ configurations, respectively ("2nd dist. 48f" step in Figure 5). The distribution of $E_{Ewald}$ values is illustrated in Figure 5 showcasing an energy difference of $\simeq 42$ eV between $N_{select}\{E_{Ewald}^{(\lambda)}\}$ and $N_{select}\{E_{Ewald}^{(\nabla)}\}$.

To investigate anion ordering in this pyrochlore-type structure and showcase whether it follows a random (maximum entropy state) or a non-random (preferential anion ordering) arrangement, the populations of $[NbO_{6-x}F_{x}]^{n-}$ octahedra and $[RbO_{18-y}F_{y}]^{m-}$ cages from the $N_{total}$ configurations (Figure 5) were thoroughly analyzed, and then compared to those computed considering a random distribution. Given this
<table><caption>TABLE III. Atom, Wyckoff multiplicity (Wyck.), site symmetry (Sym.), atomic coordinates (x, y, z), site occupancy factor (SOF) and IDPs ($U_{iso}$, Å²) for RbNb₂O₅F and RbTa₂O₅F. Uncertainties are indicated between brackets.</caption><thead><tr><th>Atom</th><th>Wyck.</th><th>Sym.</th><th>x</th><th>y</th><th>z</th><th>SOF</th><th>U<sub>iso</sub></th></tr></thead><tbody><tr><td colspan="8">RbNb<sub>2</sub>O<sub>5</sub>F (SG: Fd<sub>3</sub>m, no. 227, a = b = c = 10.4956(1)Å, V = 1156.18(1)Å<sup>3</sup>)</td></tr><tr><td>Rb</td><td>32e</td><td>3m</td><td>0.3960(1)</td><td>0.3960(1)</td><td>0.3960(1)</td><td>0.25</td><td>0.0228(2)</td></tr><tr><td>Nb</td><td>16c</td><td>3&#773;m</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0.0228(2)</td></tr><tr><td>O</td><td>48f</td><td>2mm</td><td>0.3194(2)</td><td>0.125</td><td>0.125</td><td>0.833</td><td>0.026(1)</td></tr><tr><td>F</td><td>48f</td><td>2mm</td><td>0.3194(2)</td><td>0.125</td><td>0.125</td><td>0.167</td><td>0.026(1)</td></tr><tr><td colspan="8">RbTa<sub>2</sub>O<sub>5</sub>F (SG: Fd<sub>3</sub>m, no. 227, a = b = c = 10.4774(1)Å, V = 1150.17(2)Å<sup>3</sup>)</td></tr><tr><td>Rb</td><td>32e</td><td>3m</td><td>0.3961(1)</td><td>0.3961(1)</td><td>0.3961(1)</td><td>0.25</td><td>0.0162(2)</td></tr><tr><td>Ta</td><td>16c</td><td>3&#773;m</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0.0162(2)</td></tr><tr><td>O</td><td>48f</td><td>2mm</td><td>0.3362(4)</td><td>0.125</td><td>0.125</td><td>0.833</td><td>0.058(2)</td></tr><tr><td>F</td><td>48f</td><td>2mm</td><td>0.3362(4)</td><td>0.125</td><td>0.125</td><td>0.167</td><td>0.058(2)</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>FIG. 3. Experimental (red), calculated (dark blue), and difference (grey) diffraction patterns of both compounds. The teal vertical markers refer to the Bragg positions. The obtained refinement reliability factors of RbNb₂O₅F (RbTa₂O₅F) are $R_p$ = 10.8 (10.8) %, $R_{wp}$ = 8.7 (10.1) %, $R_{exp}$ = 2.3 (2.1) %, $R_B$ = 4.3 (4.8) %, and $R_F$ = 3.9 (3.6) %.</figcaption></figure>

distribution, [NbO₆]⁷⁻, [NbO₅F]⁶⁻ and [NbO₄F₂]⁵⁻ octahedra present the highest probabilities (Random in **Figure 6 (a)** and **Table S3**). As Rb atoms are coordinated by 18 anions, various polyhedral configurations are possible, with the most likely ones being [RbO₁₇F]³⁴⁻, [RbO₁₆F₂]³³⁻, [RbO₁₅F₃]³²⁻, [RbO₁₄F₄]³¹⁻, and [RbO₁₃F₅]³⁰⁻ (Random in **Figure 6 (b)** and **Table S3**). $N_{select}\{E_{Ewald}^{(\uparrow)}\}$ present larger proportions of the most probable configurations and, therefore, fewer configurations than assuming a random distribution, whereas $N_{select}\{E_{Ewald}^{(\downarrow)}\}$ present smaller proportions of the most probable configurations and, therefore, more configurations (**Figure 6** and **Table S3**).

Considering $E_{Ewald}$ as the sole criterion is insufficient to sort configurations. Therefore, 10 configura-

<figure><img src="image_6.png" /><figcaption>FIG. 4. Perspective view of the average crystal structure of RbNb₂O₅F (a), first coordination sphere of A (A = □⁺, Rb⁺), Nb⁵⁺ cations, and X anions (b), and an illustrative view of the subarray sub-{NbX₃} (left c) rotated 90° around the ⃗r axis (right c). The drawings were created using VESTA.⁵³</figcaption></figure>

tions from $N_{select}\{E_{Ewald}^{(\uparrow)}\}$ and 10 from $N_{select}\{E_{Ewald}^{(\downarrow)}\}$, with the proportions of [NbO₆⁻Fₓ]ⁿ⁻ octahedra and [RbO₁₈⁻Fᵧ]ⁿ⁻ cages close to those computed considering a random distribution, were selected for DFT relaxation (Selected in **Figure 6** and **Table S3**). Ultimately, the most favored polyhedra in these configurations were [NbO₅F]⁶⁻ and [RbO₁₅F₃]³²⁻ polyhedra, comprising ≈56 and ≈44 %, respectively.

DFT relaxation of the selected configurations results in increased coordination number and highly distorted envi-
<figure><img src="image_7.png" /><figcaption>FIG. 5. Diagrammatic presentation showcasing, (i) the simultaneous distribution (Group n°1 and n°2) of the Rb and O/F in 32e and 48f, respectively, and (ii) the two-step distribution, with first, distributing Rb in 32e (Group n°1), and second, distributing O/F in 48f (Group n°2). N<sub>eq</sub> and N<sub>ineq</sub> refer to the number of configurations equivalent and inequivalent by symmetry operations, respectively. The selected configurations with the lowest and highest E<sub>Ewald</sub> energies are labeled as N<sub>select</sub>{E<sub>Ewald</sub><sup>(\gamma)</sup>} and N<sub>select</sub>{E<sub>Ewald</sub><sup>(\gamma)</sup>}, respectively. N<sub>tot</sub> refers to the total selected number of configurations for subsequent analysis of [NbO<sub>6-x</sub>F<sub>x</sub>]<sup>n-</sup> octahedra and [RbO<sub>18-y</sub>F<sub>y</sub>]<sup>m-</sup> cages from RbNb<sub>2</sub>O<sub>5</sub>F.</figcaption></figure>

onments for the Nb initially at the center of [NbOF<sub>5</sub>]<sup>2-</sup> and [NbF<sub>6</sub>]<sup>-</sup> octahedra, leading to unlikely and unusual distorted [NbO<sub>2</sub>F<sub>5</sub>]<sup>4-</sup>, [NbOF<sub>6</sub>]<sup>3-</sup> or [NbO<sub>2</sub>F<sub>6</sub>]<sup>5-</sup> polyhedra formed after one and/or two oxygen atoms from neighboring oxygen-rich octahedra relaxed toward fluorine-rich octahedra (Table S4). Only two out of the four configurations presenting [NbO<sub>2</sub>F<sub>4</sub>]<sup>3-</sup> octahedra experienced this effect, specifically, two out of the three initially present [NbO<sub>2</sub>F<sub>4</sub>]<sup>3-</sup> octahedra in these two configurations changed after relaxation to [NbO<sub>3</sub>F<sub>4</sub>]<sup>5-</sup> polyhedra (Table S4). In contrast, [RbO<sub>18-y</sub>F<sub>y</sub>]<sup>m-</sup> cages experienced no change (Table S5). The DFT energy (E<sub>DFT</sub>, in eV) values for each configuration are gathered in Table S6. Unsurprisingly, configurations in which their fluorine-rich Nb octahedra experienced com-

positional changes exhibit the highest E<sub>DFT</sub> values. As both compounds are isostructural, the same configuration construction and sorting processes were applied to RbTa<sub>2</sub>O<sub>5</sub>F. As a result, 10 configurations were selected for this compound. Furthermore, similar DFT relaxation effects observed for RbNb<sub>2</sub>O<sub>5</sub>F are expected for RbTa<sub>2</sub>O<sub>5</sub>F.

### C. NMR parameters calculation

To verify whether the selected configurations describe the structure of these pyrochlores, NMR parameters, including δ<sub>iso</sub>, δ<sub>CSA</sub>, C<sub>Q</sub>, and η<sub>Q</sub>, were computed and compared to the experimental data. The parameter η<sub>CSA</sub> was not considered for this comparison since it did not show any effect on the <sup>19</sup>F MAS NMR spectra during
<figure><img src="image_8.png" /><figcaption>FIG. 6. Population distribution of [MO<sub>6-x</sub>F<sub>x</sub>]<sup>n-</sup> (a) and [RbO<sub>18-y</sub>F<sub>y</sub>]<sup>m-</sup> (b) from the $N_{select}\{E_{Ewald}^{(\lambda)}\}$ configurations (dark blue), $N_{select}\{E_{Ewald}^{(\lambda)}\}$ configurations (teal), random distribution (dark orange), and selected configurations for DFT relaxation (light orange).</figcaption></figure>

the fitting process. Except for $C_Q$ and $\eta_Q$, $\delta_{iso}$ and $\delta_{CSA}$ values are obtained from $\sigma_{iso}$ and $\sigma_{CSA}$, respectively, following linear transformation functions noted as $\sigma_{iso} \rightarrow \delta_{iso}$ and $\sigma_{CSA} \rightarrow \delta_{CSA}$. A conventional method to determine these functions involves using the relations $\delta_{iso} = a_1\sigma_{iso} + b_1$ and $\delta_{CSA} = a_2\sigma_{CSA}$, where the parameters $a_1$ ($a_2$) and $b_1$ represent the slope and $\sigma_{iso}^{ref}$, respectively, and are derived from a linear regression between experimental $\delta_{iso}$ ($\delta_{CSA}$) and computed $\sigma_{iso}$ ($\sigma_{CSA}$) data. For instance, many linear regression equations were established for <sup>19</sup>F from a wide range of fluorine-bonded cations.<sup>21,29,55-69</sup> A method for quantitatively predicting values in a disordered system with two metal cations involves developing a suitable linear transformation function. This function is derived using data from a reference ordered (oxy)fluoride, which contains the same cations as the target system and has fluoride ions distributed across multiple crystallographic sites. This method was previously used to simulate <sup>19</sup>F MAS NMR spectra from oxyfluorides with correlated anion disorder, including MO<sub>2</sub>F<sup>19</sup> and MOF<sub>3</sub><sup>21</sup> (M = Nb<sup>5+</sup>, Ta<sup>5+</sup>), as well as ReO<sub>3</sub>-type TiOF<sub>2</sub>.<sup>22</sup> The corresponding transformation functions were derived by fitting data from MF<sub>5</sub><sup>59</sup> fluorides for MO<sub>2</sub>F and MOF<sub>3</sub>, and from TiF<sub>4</sub><sup>67,70</sup> for the ReO<sub>3</sub>-type TiOF<sub>2</sub>.

To obtain linear transformation functions for RbM<sub>2</sub>O<sub>5</sub>F, a suitable reference system is RbF<sup>43</sup> and MF<sub>5</sub><sup>44,45</sup> fluorides. The experimental $\delta_{iso}$ ($\delta_{CSA}$) value of MF<sub>5</sub> and RbF, required to obtain $\sigma_{iso} \rightarrow \delta_{iso}$ ($\sigma_{CSA} \rightarrow \delta_{CSA}$) functions, are gathered from<sup>59</sup> and<sup>29</sup>, respectively. The computed $\sigma_{iso}$ ($\sigma_{CSA}$) data for MF<sub>5</sub> was gathered from<sup>21</sup>, and for RbF this data was collected in the present work (Table S7). The obtained best-fit $\sigma_{iso} \rightarrow \delta_{iso}$ ($\sigma_{CSA} \rightarrow \delta_{CSA}$) functions are $\delta_{iso}(ppm) = -0.959(29)\sigma_{iso} + 106.1(4.3)$ ($\delta_{CSA}(ppm) = -0.556(34)\sigma_{CSA}$) and $\delta_{iso}(ppm) =$

$-0.935(16)\sigma_{iso} + 108.9(1.8) \quad (\delta_{CSA}(ppm) = -0.628(30)\sigma_{CSA})$, for RbNb<sub>2</sub>O<sub>5</sub>F and RbTa<sub>2</sub>O<sub>5</sub>F, respectively (Figure S1).

For <sup>87</sup>Rb, a new linear transformation function $\sigma_{iso} \rightarrow \delta_{iso}$ was established from the compounds RbF,<sup>43</sup> RbNO<sub>3</sub>,<sup>71</sup> RbVO<sub>3</sub>,<sup>72</sup> RbClO<sub>4</sub>,<sup>73</sup> RbLaF<sub>4</sub>,<sup>74</sup> Rb<sub>2</sub>SO<sub>4</sub>,<sup>75</sup> and RbSr<sub>2</sub>Nb<sub>3</sub>O<sub>10</sub>.<sup>76</sup> Since the experimental <sup>87</sup>Rb $\delta_{iso}$ value for RbF fluoride is not reported in the literature, an <sup>87</sup>Rb MAS NMR spectrum of this fluoride was recorded and fitted. The fitting data and spectrum are given in Table S8 and Figure S2, respectively. The obtained best-fit $\sigma_{iso} \rightarrow \delta_{iso}$ function is $\delta_{iso}(ppm) = -0.722(32)\sigma_{iso} + 2297(103)$, with the data gathered in Tables S9 and S10 and the plot illustrated in Figure S3. For <sup>93</sup>Nb, the computed $\delta_{iso}$ values were deduced using the previously established $\sigma_{iso} \rightarrow \delta_{iso}$ function $\delta_{iso}(ppm) = -586.9 - \sigma_{iso}$.<sup>19</sup>

The <sup>87</sup>Rb and <sup>93</sup>Nb (CT)MAS and 3QMAS NMR spectra were fitted using "Czjzek" (GIM, $d = 5$)<sup>31</sup> and "CzSimple" models, which do not require fitting the parameter $\delta_{CSA}$, as a result, the linear transformation function $\sigma_{CSA} \rightarrow \delta_{CSA}$ was not established for these nuclei. These fits consider a statistical distribution of the pair ($C_Q$, $\eta_Q$), described by the following probability distribution $P(C_Q, \eta_Q)$:

$$P(C_Q, \eta_Q) = \frac{C_Q^4 \eta_Q}{\sqrt{2\pi}\sigma^5} \left(1 - \frac{\eta_Q^2}{9}\right) \exp\left(-\frac{C_Q^2}{2\sigma^2}\left(1 + \frac{\eta_Q^2}{3}\right)\right)$$

where $\sigma$ is related to the strength of average experimental $C_Q$ value ($\langle C_Q \rangle$) and is given by $\sigma = \langle C_Q \rangle/2$. This probability was computed using the experimental average values of $C_Q$ and $\eta_Q$ (Table II), and then plotted in the form of 3D charts as illustrated in Figure 7 (a), (b), and (c). These charts show the probability of occurrence of the pair ($C_Q$, $\eta_Q$). As shown for <sup>87</sup>Rb, this pair occurs in the range ([0.5:3.5] MHz, [0:1]) and ([0.6:3.8] MHz, [0:1]) for RbNb<sub>2</sub>O<sub>5</sub>F (Figure 7 (a)) and RbTa<sub>2</sub>O<sub>5</sub>F (Figure 7 (c)), respectively. The highest probabilities are located within the approximate range of ([1.1:1.8] MHz, [0.5:1]) and ([1.4:2.2] MHz, [0.5:1]) for RbNb<sub>2</sub>O<sub>5</sub>F (Figure 7 (a)) and RbTa<sub>2</sub>O<sub>5</sub>F (Figure 7 (c)), respectively. Similarly, the range of possible ($C_Q$, $\eta_Q$) values for <sup>93</sup>Nb (Figure 7 (b)) extends approximately in the range ([19:115] MHz, [0:1]), with the highest probabilities located within the approximate range ([37:65] MHz, [0.5:1]).

The selection of the best RbNb<sub>2</sub>O<sub>5</sub>F and RbTa<sub>2</sub>O<sub>5</sub>F configurations describing the short-range structure of these compounds is based on the overall agreement between the experimental and computed NMR parameters, including <sup>19</sup>F $\delta_{iso}$, <sup>19</sup>F $\delta_{CSA}$, <sup>87</sup>Rb $\delta_{iso}$, <sup>87</sup>Rb $C_Q$, <sup>87</sup>Rb $\eta_Q$, <sup>93</sup>Nb $\delta_{iso}$, <sup>93</sup>Nb $C_Q$, and <sup>93</sup>Nb $\eta_Q$. Particular emphasis is placed on the $C_Q$ parameters for <sup>87</sup>Rb and <sup>93</sup>Nb nuclei. Indeed, a small discrepancy between experimental and computed $\delta_{iso}$ and $\delta_{CSA}$ values may not be significant as it could be due to inaccurate linear transformation functions $\sigma_{iso} \rightarrow \delta_{iso}$ and $\sigma_{CSA} \rightarrow \delta_{CSA}$. Configurations with such discrepancies but with good agree-
<table><caption>TABLE IV. Configuration, average $\delta_{iso}$ (⟨$\delta_{iso}$⟩, ppm), average $\delta_{CSA}$ (⟨$\delta_{CSA}$⟩, ppm), standard deviation of $\delta_{iso}$ ($\hat{\sigma}$[$\delta_{iso}$], ppm) for $^{19}$F, and ⟨$\delta_{iso}$⟩, $\hat{\sigma}$[$\delta_{iso}$], average $C_Q$ (⟨$C_Q$⟩, MHz), standard deviation of $C_Q$ ($\hat{\sigma}$[$C_Q$], ppm), average $\eta_Q$ (⟨$\eta_Q$⟩, MHz), standard deviation of $\eta_Q$ ($\hat{\sigma}$[$\eta_Q$], ppm) for $^{87}$Rb and $^{93}$Nb, from the unit cell and 2 × 2 × 2 supercells final configurations of RbNb$_2$O$_5$F and RbTa$_2$O$_5$F. The average values from all of these configurations are given in bold italic for each compound.</caption><thead><tr><th colspan="2">Config. <sup>19</sup>F</th><th colspan="6"><sup>87</sup>Rb</th><th colspan="6"><sup>93</sup>Nb</th></tr><tr><th></th><th>⟨δ<sub>iso</sub>⟩</th><th>⟨δ<sub>CSA</sub>⟩</th><th>σ̂[δ<sub>iso</sub>]</th><th>⟨δ<sub>iso</sub>⟩</th><th>σ̂[δ<sub>iso</sub>]</th><th>C<sub>Q</sub></th><th>σ̂[C<sub>Q</sub>]</th><th>⟨η<sub>Q</sub>⟩</th><th>σ̂[η<sub>Q</sub>]</th><th>⟨δ<sub>iso</sub>⟩</th><th>σ̂[δ<sub>iso</sub>]</th><th>C<sub>Q</sub></th><th>σ̂[C<sub>Q</sub>]</th><th>⟨η<sub>Q</sub>⟩</th><th>σ̂[η<sub>Q</sub>]</th></tr></thead><tbody><tr><td colspan="16">RbNb<sub>2</sub>O<sub>5</sub>F (unit cells)</td></tr><tr><td>2</td><td>-92.9</td><td>-22.3</td><td>6.3</td><td>-77.8</td><td>1.5</td><td>2.4</td><td>0.5</td><td>0.54</td><td>0.2</td><td>-1012</td><td>8.1</td><td>66.4</td><td>14.6</td><td>0.51</td><td>0.22</td></tr><tr><td>3</td><td>-90.3</td><td>-27.8</td><td>8.0</td><td>-80.3</td><td>4.1</td><td>2.5</td><td>0.7</td><td>0.63</td><td>0.31</td><td>-997.8</td><td>24.3</td><td>89.6</td><td>14.9</td><td>0.49</td><td>0.26</td></tr><tr><td>4</td><td>-99.3</td><td>-26.4</td><td>0.2</td><td>-78.1</td><td>0.1</td><td>1.7</td><td>0</td><td>0.83</td><td>0.05</td><td>-1008.3</td><td>6.5</td><td>60.5</td><td>1.6</td><td>0.74</td><td>0.25</td></tr><tr><td>8</td><td>-96.9</td><td>-27.2</td><td>10.2</td><td>-79.9</td><td>2.4</td><td>1.8</td><td>0.8</td><td>0.58</td><td>0.18</td><td>-1017.9</td><td>8.5</td><td>65.1</td><td>6.3</td><td>0.66</td><td>0.14</td></tr><tr><td>9</td><td>-89.7</td><td>-27</td><td>12.5</td><td>-81.3</td><td>4.5</td><td>1.7</td><td>0.4</td><td>0.67</td><td>0.29</td><td>-992.2</td><td>5</td><td>90.8</td><td>10.8</td><td>0.5</td><td>0.17</td></tr><tr><td>⟨⟩</td><td><b>-93.8</b></td><td><b>-26.1</b></td><td><b>7.4</b></td><td><b>-79.5</b></td><td><b>2.5</b></td><td>2</td><td><b>0.5</b></td><td><b>0.65</b></td><td><b>0.21</b></td><td><b>-1005.6</b></td><td><b>10.5</b></td><td><b>74.5</b></td><td><b>9.6</b></td><td><b>0.58</b></td><td><b>0.21</b></td></tr><tr><td colspan="16">RbNb<sub>2</sub>O<sub>5</sub>F (2 × 2 × 2 supercells)</td></tr><tr><td>2</td><td>-97.6</td><td>-22.1</td><td>1.9</td><td>-87.7</td><td>2.6</td><td>1.6</td><td>0.2</td><td>0.69</td><td>0.19</td><td>-1008.2</td><td>9.1</td><td>67.4</td><td>11.3</td><td>0.52</td><td>0.3</td></tr><tr><td>3</td><td>-99.9</td><td>-14.9</td><td>5.4</td><td>-90.3</td><td>1.6</td><td>3</td><td>0.7</td><td>0.53</td><td>0.21</td><td>-994.3</td><td>29.6</td><td>94.5</td><td>15.3</td><td>0.43</td><td>0.2</td></tr><tr><td>4</td><td>-97.8</td><td>-27.7</td><td>0.9</td><td>-81.9</td><td>0.4</td><td>1.6</td><td>0.1</td><td>0.77</td><td>0.15</td><td>-1006.8</td><td>4.6</td><td>59.6</td><td>1.8</td><td>0.72</td><td>0.22</td></tr><tr><td>8</td><td>-97.9</td><td>-23.9</td><td>1.1</td><td>-84.2</td><td>4.3</td><td>1.3</td><td>0.5</td><td>0.53</td><td>0.32</td><td>-1028.4</td><td>2.7</td><td>65.9</td><td>1.4</td><td>0.6</td><td>0.05</td></tr><tr><td>9</td><td>-91.1</td><td>-27.4</td><td>11.1</td><td>-83.2</td><td>3</td><td>1.7</td><td>0.1</td><td>0.55</td><td>0.19</td><td>-991.5</td><td>6</td><td>90.5</td><td>9.4</td><td>0.49</td><td>0.16</td></tr><tr><td>⟨⟩</td><td><b>-96.9</b></td><td><b>-23</b></td><td><b>4.1</b></td><td><b>-85.5</b></td><td><b>2.4</b></td><td><b>1.8</b></td><td><b>0.3</b></td><td><b>0.62</b></td><td><b>0.21</b></td><td><b>-1005.8</b></td><td><b>10.4</b></td><td><b>75.6</b></td><td><b>7.8</b></td><td><b>0.55</b></td><td><b>0.19</b></td></tr><tr><td colspan="16">RbTa<sub>2</sub>O<sub>5</sub>F (unit cells)</td></tr><tr><td>2</td><td>-106.1</td><td>-23.8</td><td>2.1</td><td>-75.9</td><td>3.3</td><td>2.4</td><td>0.4</td><td>0.48</td><td>0.38</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>4</td><td>-108.1</td><td>-30.6</td><td>0.1</td><td>-77.4</td><td>0.1</td><td>2.6</td><td>0</td><td>0.74</td><td>0.01</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>7</td><td>-99.3</td><td>-30.9</td><td>8.4</td><td>-75.3</td><td>4.7</td><td>2.7</td><td>0.6</td><td>0.59</td><td>0.31</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>8</td><td>-109.7</td><td>-26.2</td><td>7.3</td><td>-79.2</td><td>4.2</td><td>1.7</td><td>1</td><td>0.83</td><td>0.06</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>9</td><td>-101.1</td><td>-24</td><td>8.4</td><td>-79.3</td><td>3.4</td><td>1.2</td><td>0.5</td><td>0.28</td><td>0.15</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>⟨⟩</td><td><b>-104.9</b></td><td><b>-27.1</b></td><td><b>5.2</b></td><td><b>-77.4</b></td><td><b>3.1</b></td><td><b>2.1</b></td><td><b>0.5</b></td><td><b>0.58</b></td><td><b>0.18</b></td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td colspan="16">RbTa<sub>2</sub>O<sub>5</sub>F (2 × 2 × 2 supercells)</td></tr><tr><td>2</td><td>-116.2</td><td>-19.1</td><td>1.3</td><td>-82.4</td><td>3.9</td><td>2.2</td><td>0.4</td><td>0.52</td><td>0.22</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>4</td><td>-115.9</td><td>-18.7</td><td>0.3</td><td>-84.8</td><td>0.3</td><td>1.7</td><td>0.04</td><td>0.71</td><td>0.1</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>7</td><td>-108.9</td><td>-25.4</td><td>6</td><td>-76</td><td>3.9</td><td>3.4</td><td>1</td><td>0.48</td><td>0.26</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>8</td><td>-114.5</td><td>-21.3</td><td>0.3</td><td>-83.8</td><td>4.9</td><td>1.9</td><td>0.8</td><td>0.13</td><td>0.07</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>9</td><td>-116</td><td>-15.2</td><td>5.8</td><td>-83.8</td><td>2.8</td><td>0.8</td><td>0.1</td><td>0.51</td><td>0.27</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr><tr><td>⟨⟩</td><td><b>-114.3</b></td><td><b>-20</b></td><td><b>2.7</b></td><td><b>-82.2</b></td><td><b>3.2</b></td><td>2</td><td><b>0.5</b></td><td><b>0.47</b></td><td><b>0.18</b></td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td><td>n.a.</td></tr></tbody></table>

ment between experimental and computed $C_Q$ values are retained. Conversely, configurations that show excellent agreement between experimental and computed $\delta_{iso}$ values, but significant discrepancies between computed and experimental $C_Q$ values for $^{87}$Rb and/or $^{93}$Nb are excluded. In addition, as the parameter $\eta_Q$ shows a non-zero probability of occurrence in the full range [0:1] (Figure 7 (a), (b), and (c)), it was not included in the selection process. Furthermore, since the experimental $^{87}$Rb and $^{93}$Nb (CT)MAS and 3QMAS NMR spectra present distribution of $C_Q$ and $\delta_{iso}$ parameters, configurations that do not exhibit a distribution of these parameters — configurations in which all Rb and/or Nb atoms exhibit a unique value of $C_Q$ and $\delta_{iso}$ — are excluded.

The computed NMR parameters relevant to the discussion are summarized in Table IV. Additional details on these parameters for each tested configuration are gathered in Table S11-S22. A first selection of configurations is made by directly comparing experimental and computed $C_Q$ values. For RbNb$_2$O$_5$F, one or more Rb atoms in configurations n°5, 6, and 10-20 present $C_Q$ values outside the range [0.5:3.5] MHz, outside which, there is zero probability of occurrence of the pair ($C_Q$, $\eta_Q$)

(Tables S11 and S12). Configurations n°5-7, and 10-20 present one or more Nb atoms with $C_Q$ values above the upper limit value of 115 MHz (Tables S11 and S12). In addition, all Rb atoms in configuration n°1 exhibit a unique $C_Q$ value (2.5 MHz) (Table S11). These fifteen configurations were, therefore, excluded. Considering that RbTa$_2$O$_5$F is isostructural to RbNb$_2$O$_5$F, the DFT relaxation and NMR parameters were only computed for the configurations n°1-10. For this tantalum pyrochlore-type oxyfluoride, one or more Rb atoms in configurations n°3, 5, 6, and 10, exhibit $C_Q$ values that are outside the range [0.6:3.8] MHz, outside which, the probability of occurrence of the pair ($C_Q$, $\eta_Q$) is zero (Table S19). Furthermore, in configuration n°1, 7 out of 8 Rb atoms exhibit a unique $C_Q$ value (2.7 MHz, Table S19). these five configurations were, therefore, excluded.

Almost all discarded configurations contain octahedra with compositions other than [NbO$_5$F]$^{6-}$ (Table S4). For instance, configurations n°5 contain [MO$_6$]$^{7-}$ and [MO$_4$F$_2$]$^{5-}$ octahedra, and both $^{87}$Rb and $^{93}$Nb $C_Q$ values are outside the ranges of ($C_Q$, $\eta_Q$) pair probability of occurrence (Tables S4 and S11). For the remaining configurations, i.e. configuration n°2-4, 8, and 9 for
<figure><img src="image_9.png" /><figcaption>FIG. 7. 3D charts representing the GIM distribution $P(C_Q, \eta_Q)$ constructed from the average $C_Q$ and $\eta_Q$ values that were used to fit the experimental (CT)MAS and 3QMAS spectra from $RbNb_2O_5F$ (a and b for $^{87}$Rb and $^{93}$Nb, respectively) and $RbTa_2O_5F$ (c for $^{87}$Rb). Similar charts were constructed using the computed $C_Q$ and $\eta_Q$ values from the final configurations for $RbNb_2O_5F$ (d and e for $^{87}$Rb and $^{93}$Nb, respectively) and $RbTa_2O_5F$ (f for $^{87}$Rb). Each point in these charts represents one $C_Q$ and one $\eta_Q$ value from one Rb/Nb atom.</figcaption></figure>

$RbNb_2O_5F$, and n°2, 4, and 7-9 for $RbTa_2O_5F$, all computed $C_Q$ and $\eta_Q$ values are within the range of ($C_Q, \eta_Q$) pair probability of occurrence for both $^{93}$Nb and $^{87}$Rb nuclei (Tables S11-S14, S19, and S20). Analysis of the computed $\sigma_{iso}$ (Tables S15, S16, and S21) and $\sigma_{CSA}$ (Tables S17, S18, and S22) values from these remaining configurations does not present clear distinctions to allow selecting one configuration over another. For $^{19}$F, the computed average $\delta_{iso}$ ($\delta_{CSA}$) values from all final configurations are different than the experimental values by 8.5 ppm (17.1 ppm) and 6.5 ppm (0 ppm) for $RbNb_2O_5F$ and $RbTa_2O_5F$, respectively (Tables I and IV). Furthermore, for $^{93}$Nb, the computed average $\delta_{iso}$ value from all final configurations is higher than the experimental value by 49 ppm (Tables II and IV). For $^{87}$Rb, the computed average $\delta_{iso}$ from all configurations are close to the experimental value with a difference

of 0.1 and 0.9 ppm for $RbNb_2O_5F$ and $RbTa_2O_5F$, respectively (Tables II and IV). For all three nuclei, the $\delta_{iso}$ range remains also compatible with the width of the distributions used to reconstruct the NMR spectra (FWHM in Table I and $\Delta\delta_{iso}$ in Table II).

The discrepancy between the average computed $^{19}$F $\delta_{iso}$, $^{19}$F $\delta_{CSA}$, and $^{19}$Nb $\delta_{CSA}$ and experimental values could be, however, due to either the inaccuracy of the linear transformation functions $\sigma_{iso} \to \delta_{iso}$ and $\sigma_{CSA} \to \delta_{CSA}$ or the size of the cell. For $^{19}$F, using linear transformation functions derived solely from $MF_5$ fluorides$^{21}$ will result in an increase of this discrepancy, indicating that the linear transformation functions derived from combining $MF_5$ and RbF fluorides are the most suitable to $RbNb_2O_5F$ and $RbTa_2O_5F$. As a result, the configurations n°1-10 were expanded into 2×2×2 supercells and then relaxed using DFT, the NMR parameters, including $\delta_{iso}$, $\delta_{CSA}$, $C_Q$, and $\eta_Q$, were computed. Concise representations of the relative differences between the computed and experimental NMR parameters are given as radar charts in Figure 8. The relative difference, denoted as $f\{G; N\}$, is expressed as a percentage and defined as follows:

$$f\{G; N\} = 100 - \frac{|G_{exp} - G_{cal}|}{|G_{exp}|} \times 100$$

where G represents an average NMR parameter value (either $\delta_{iso}$, or $C_Q$, or $\eta_Q$) from all final configurations (values in bold italics in Tables IV), and N is one of the nuclei ($^{19}$F, or $^{87}$Rb, or $^{93}$Nb). The computed and experimental values are denoted as $G_{cal}$ and $G_{exp}$, respectively. The percentage score indicates the closeness of the computed values to the experimental values, with higher percentages representing a better match.

As illustrated by each of these radar charts, the NMR parameters from the 2×2×2 supercells (teal surfaces in Figure 8) were compared to those from the unit cells (orange surfaces in Figure 8) for the final configurations, i.e. n°2-4, 8, and 9 for $RbNb_2O_5F$ (Figure 8 (a)), and n°2, 4, and 7-9 for $RbTa_2O_5F$ (Figure 8 (b)). These charts show that the 2×2×2 supercells result in a slightly improved agreement between the experimental and computed $^{93}$Nb $C_Q$ for $RbNb_2O_5F$, and $^{87}$Rb $C_Q$ for $RbTa_2O_5F$. However, for $^{19}$F $\delta_{CSA}$, $^{87}$Rb $\eta_Q$, $^{87}$Rb $C_Q$, and $^{93}$Nb $\delta_{iso}$ for $RbNb_2O_5F$, and $^{19}$F $\delta_{CSA}$, $^{87}$Rb $\delta_{iso}$, and $^{87}$Rb $\eta_Q$ for $RbTa_2O_5F$, the unit cells, clearly, show a better match to the experimental data than the 2×2×2 supercells.

The computed $C_Q$ and $\eta_Q$ values of each Rb and Nb atom from the final 2×2×2 supercell configurations n°2-4, 8, and 9 for $RbNb_2O_5F$ (corresponding to 384 Rb and 640 Nb atoms) and n°2, 4, and 7-9 (corresponding to 384 Rb atoms) were gathered into ($C_Q, \eta_Q$) pairs with their frequency noted as $M(C_Q, \eta_Q)$. This frequency is plotted in the form of 3D charts (Figure 7 (d), (e), and (f)). For $RbNb_2O_5F$, $M(C_Q, \eta_Q)$ represents a distribution range of ([0.8:3.8] MHz, [0.17:0.99]) with $max\{M(C_Q, \eta_Q)\} = (1.9$ MHz, 0.9), and ([50.7:111.1] MHz, [0.14:0.99]) with
<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

FIG. 8. Radar charts illustrating the relative differences between the average experimental and computed NMR parameters values for RbNb$_2$O$_5$F (a) and RbTa$_2$O$_5$F (b). The average NMR parameter values are those in bold italic from Table IV. The axes are scaled in % and features the scoring functions $f\{(\delta_{iso})$; $^{19}$F\}$, $f\{(\delta_{CSA})$; $^{19}$F\}$, $f\{(\delta_{iso})$; $^{87}$Rb\}$, $f\{(C_Q)$; $^{87}$Rb\}$, $f\{(\eta_Q)$; $^{87}$Rb\}$, $f\{(\delta_{iso})$; $^{93}$Nb\}$, $f\{(C_Q)$; $^{93}$Nb\}$, and $f\{(\eta_Q)$; $^{93}$Nb\}$. The unit cell and 2×2×2 supercell charts are colored orange and teal, respectively.

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

FIG. 9. Experimental (solid line) and theoretical (dashed line) $^{19}$F MAS (46 and 50 kHz for a and b, respectively) NMR spectra of RbNb$_2$O$_5$F (a) and RbTa$_2$O$_5$F (b). Both theoretical spectra correspond to the 2×2×2 supercell final configurations, and they were simulated using the *Python* package "mrsimulator".46–49 The asterisks refer to spinning sidebands. The top-left insets present zooms of the main resonance lines.

$max\{M(C_Q, \eta_Q)\} = (66.1$ MHz, 0.7) for $^{87}$Rb and $^{93}$Nb, respectively. This distribution range is close to that of $P(C_Q, \eta_Q)$, i.e. ([0.5:3.5]MHz, [0:1]) with $max\{P(C_Q, \eta_Q)\} = (1.3$ MHz, 1), and ([19:115]MHz, [0:1]) with $max\{P(C_Q, \eta_Q)\} = (48$ MHz, 1) for $^{87}$Rb and $^{93}$Nb, respectively (**Figure 7 (a) vs. (d)**, and **(b) vs. (e)**). Similarly, for RbTa$_2$O$_5$F, the distribution range of $^{87}$Rb $M(C_Q, \eta_Q)$ is ([0.7:4.6] MHz, [0.01:0.89]) with $max\{M(C_Q, \eta_Q)\} = (2$ MHz, 0.8), which is close to that of $^{87}$Rb $P(C_Q, \eta_Q)$, i.e. ([0.7:3.5]MHz, [0.1:1]) with $max\{P(C_Q, \eta_Q)\} = (2$ MHz, 1) (**Figure 7 (c) vs. (f)**). The computed $^{93}$Nb $C_Q$ values, in both the unit cell and 2×2×2 supercell final configurations, appear to be overestimated compared with the experimental values (**Tables II and IV**, and **Figure 8 (a)**), even though the latter may be underestimated by temperature-induced averaging (experiments conducted at RT or higher versus DFT calculations at 0 K). The [NbO$_5$F]$^{6-}$ octahedra in the final configurations are therefore slightly overdistorted. The inconsistent agreement patterns between

our unit cell and supercell geometry optimizations are attributed to using VASP for the former and CP2K for the latter because of accuracy-efficiency trade-offs.

## D. Theoretical NMR spectra

The simulated $^{19}$F MAS NMR spectra show a good agreement compared to the experimental ones (**Figure 9**) with 5.4 and 2.9 ppm absolute average difference ($\Delta_{iso}^{exp-th}$) for RbNb$_2$O$_5$F and RbTa$_2$O$_5$F, respectively. However, the spinning sidebands are slightly underestimated for RbNb$_2$O$_5$F. Furthermore, for RbNb$_2$O$_5$F, there is a small resonance line around -73 ppm which is due to 16 fluorine atoms in configuration n° 9 for which we did not detect any particular environment.

The resulting simulated $^{87}$Rb MAS and $^{93}$Nb CT-MAS NMR spectra align well with the experimental ones (**Figure 10**), with a $^{87}$Rb $\Delta_{iso}^{exp-th}$ of 6.1 and 5.7 ppm for RbNb$_2$O$_5$F and RbTa$_2$O$_5$F, respectively, and a $^{93}$Nb $\Delta_{iso}^{exp-th}$ of 48.8 ppm. As there is no known linear transformation function $\sigma_{CSA} \rightarrow \delta_{CSA}$ for $^{87}$Rb and $^{93}$Nb,
<figure><img src="image_14.png" /><figcaption>FIG. 10. Experimental (solid line) and theoretical (dashed line) MAS (30 kHz for $^{87}$Rb) and CTMAS (100 kHz for $^{93}$Nb) NMR (20 T) spectra of RbNb$_2$O$_5$F (a and c) and RbTa$_2$O$_5$F (b). The insets represent zooms of the central transition (top-left of a, b, and c) and the first-order satellite transitions (top-right of a and b). All theoretical spectra correspond to the final configurations, and they were simulated using the Python package "mrsimulator".$^{46-49}$</figcaption></figure>

we reversed the sign of the computed $\sigma_{CSA}$ values for comparison with the experimental spectra. Additionally, the $^{87}$Rb $\sigma_{CSA}$ values were multiplied by a factor of 3 to show the position of the first-order satellite transition, as the package "mrsimulator" does not generate satellite transition beyond the second order.

### E. Short-Range Anion Ordering

The final configurations, corresponding to the satisfying agreement between the computed and experimental high-field $^{19}$F MAS, $^{87}$Rb MAS, and $^{93}$Nb CTMAS NMR spectra, exclusively incorporate $[MO_5F]^{6-}$ octahedra. Excluding the rest of $[MO_{6-x}F_x]^{n-}$ octahedra highlights a short-range preferential arrangement of anions in RbM$_2$O$_5$F pyrochlore-type oxyfluorides. After DFT-relaxation, M atoms in the unit cell displace towards oxygens, away from the more electronegative, fluorine. Consequently, within each $[MO_5F]^{6-}$ octahedron, the initially equal metal-to-anion bond lengths in the ES models (1.993Å and 2.061Å for Nb-X and Ta-X, respectively), are distinguished, with Nb-O (Ta-O) bonds shorter than Nb-F (Ta-F) bonds, i.e. average lengths of 1.959Å (1.955Å) and 2.163Å (2.149Å), respectively (Tables S23 and S26). This displacement of the metal from its ideal centered position towards the polyhedral corners, edges, or faces occupied by oxygen atoms is well known in other metal transition oxyfluorides, including MO$_2$F,¹⁹ MOF$_3$,²¹ and ReO$_3$-type TiOF$_2$.²² In the ES models, the adjacent Nb-X (Ta-X) bonds form two distinct X-Nb-X (X-Ta-X) angles: 92.73° (98.81°) and 87.27° (81.19°), resulting in the same angular distortion $|X-Nb-X - 90°| = 2.73°$ ($|X-Ta-X - 90°| = 8.81°$). In contrast, the opposite Nb-X (Ta-X) bonds are perfectly aligned, corresponding to an angular distortion $|X-Nb-X - 180°| = 0$ ($|X-Ta-X - 180°| = 0$). After DFT-relaxation, these angles are distributed with average angular distortions of 4.94° (4.17°) for $|X-Nb-X - 90°|$ ($|X-Ta-X - 90°| = 10.64°$ (8.47°) for $|X-Nb-X - 180°|$ ($|X-Ta-X - 180°| = 10.64°$) (Tables S24 and S27)). Regarding Rb environments, the final configurations incorporate either exclusively $[RbO_{15}F_3]^{32-}$ cages, or an equal proportion of $[RbO_{16}F_2]^{33-}$ and $[RbO_{14}F_4]^{31-}$ cages, or a mixture of these three cage types. Similar to $[MO_{6-x}F_x]^{n-}$ octahedra, a deviation from the random distribution of the $[RbO_{18-y}F_y]^{m-}$ population, is observed. In the unit cell, the average Rb-O bond is slightly longer than the Rb-F bond, which is consistent with the strong affinity between the electropositive rubidium and the most electronegative fluorine (Tables S25 and S28). This highlights the displacement of Rb atoms to less symmetrical positions, facilitated by the wide dimensions of $[RbO_{18-y}F_y]^{m-}$ cages.

### IV. CONCLUSION

Here, we have presented a study of the structure of RbNb$_2$O$_5$F and RbTa$_2$O$_5$F pyrochlore-type oxyfluorides, combining $^{19}$F MAS, $^{87}$Rb and $^{93}$Nb (CT)MAS and 3QMAS NMR spectroscopy, PXRD, the "supercell" approach, and DFT calculations. The NMR spectra all indicate that the local environments of the probed nuclei are distributed. For both compounds, average structures were determined by refining the PXRD patterns using the Rietveld structural refinement method, resulting in an average structure where O and F atoms occupy the 48f site with site occupancy factors (SOFs) of 83.3% and 16.7%, respectively, and Rb atoms occupy the 32e site with an SOF of 25%, highlighting disorder in this structure. Using the "supercell" approach, 20 configurations were considered, with a population of $[NbO_{6-x}F_x]^{n-}$ ($x = 0, ..., 6$, with $x$ and $n \in N$) octahedra and $[RbO_{18-y}F_y]^{m-}$ ($y = 0, ..., 18$, with $y$ and $m \in N$) polyhedra close to that obtained assuming a random distribution. After DFT relaxation, one to two oxygen atoms are added to the fluorine-rich $[NbO_{6-x}F_x]^{n-}$ cages.
octahedra, such as $[NbOF_5]^{2-}$ and $[NbF_6]^{-}$, leading to either $[NbO_2F_5]^{4-}$, $[NbOF_6]^{3-}$, or $[NbO_2F_6]^{5-}$ polyhedra, underlining the preference of Nb atoms for less electronegative atoms. Out of the 20 configurations tested for $RbNb_2O_5F$ and 10 for $RbTa_2O_5F$, 5 configurations per compound present $C_Q$ values in good agreement with the $^{87}$Rb and $^{93}$Nb $C_Q$ values extracted from NMR spectra. These models present also a satisfactory agreement between the computed and experimental $\delta_{iso}$ values for $^{19}$F, $^{87}$Rb and $^{93}$Nb, and $\delta_{CSA}$ for $^{19}$F. Instead of a statistical distribution of $[MO_{6-x}F_x]^{n-}$ octahedra, the pyrochlore-type structure of $RbM_2O_5F$ presents a preferential anion ordering, defined by the exclusive presence of $[MO_5F]^{6-}$ octahedra, and $[RbO_{15}F_3]^{32-}$ cages and/or an equal proportion of $[RbO_{16}F_2]^{33-}$ and $[RbO_{14}F_4]^{31-}$ ones.

# V. ASSOCIATED CONTENT

## A. Author Contribution Statement

**Ouail Zakary:** Conceptualization, Formal analysis, Investigation, Validation, Data Curation, Writing - Original Draft, Writing - Review & Editing, Visualization. **Monique Body:** Conceptualization, Writing - Review & Editing, Supervision. **Vincent Sarou-Kanian:** Investigation. **Thibault Charpentier:** Investigation. **Christophe Legein:** Conceptualization, Writing - Review & Editing, Supervision, Project administration, Funding acquisition.

## B. Notes

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

# VI. ACKNOWLEDGEMENT

The authors are indebted to Le Mans Université for doctoral grant of O. Zakary and the platforms "Diffusion et Diffraction des rayons X" and "Résonances (RMN du Liquide et du Solide, RPE)" of IMMM. Financial support from the TGIR-RMN-THC FR3050 CNRS for conducting the solid-state NMR experiments is gratefully acknowledged. The authors would like to thank Franck Fayon (CEMHTI) and Aydar Rakhmatullin (CEMHTI) for their support with the $^{87}$Rb NMR experiments. T.C. acknowledges support from the TGCC (CP2K and VASP NMR calculations) with access to the HPC resources of under the allocation DARI-A0150906303 (2023) attributed by GENCI (Grand Equipement National de Calcul Intensif).

## A. Accession Codes

CCDC 2401963 and 2401964 contain the supplementary crystallographic data of the structures for $RbNb_2O_5F$ and $RbTa_2O_5F$, respectively. These data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures, or by emailing data.request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Center, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223336033.

# B. Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: **To Be Announced**

The reported pyrochlore-type oxyfluorides (ordered and disordered) from the literature; new $^{19}$F $\sigma_{iso} \rightarrow \delta_{iso}$ and $\sigma_{CSA} \rightarrow \delta_{CSA}$ linear transformation functions; generated configurations; new $^{87}$Rb $\sigma_{iso} \rightarrow \delta_{iso}$ linear transformation function; $RbNb_2O_5F$ and $RbTa_2O_5F$ NMR parameters, including $^{19}$F $\sigma_{iso}$, $^{19}$F $\sigma_{CSA}$, $^{87}$Rb $\sigma_{iso}$, $^{87}$Rb $\sigma_{CSA}$, $^{87}$Rb $C_Q$, $^{87}$Rb $\eta_Q$, $^{93}$Nb $\sigma_{iso}$, $^{93}$Nb $\sigma_{CSA}$, $^{93}$Nb $C_Q$, and $^{93}$Nb $\eta_Q$ values; $RbNb_2O_5F$ and $RbTa_2O_5F$ structural features. (SI.pdf)

# C. Data Availability

All datasets, and plotting scripts created in this paper are publicly available in the GitHub repository: https://github.com/ozakary/data-RbM2O5F. The repository includes (i) experimental and Rietveld refinement data for the PXRD diagrams, (ii) both experimental and fitted data of solid-state NMR spectra of $^{19}$F, $^{87}$Rb, and $^{93}$Nb nuclei, (iii) the steps of generating the different configurations, (iv) input and output VASP and CP2K files for DFT calculations (including geometry optimization and NMR parameter calculations), (v) code used to simulate the theoretical NMR spectra, and (vi) Python scripts and raw numerical data for all figures used in the manuscript and supplementary materials.

# VII. AUTHOR INFORMATION

## A. Corresponding Author

**Ouail Zakary** – Institut des Molécules et Matériaux du Mans (IMMM) – UMR 6283 CNRS, Le Mans Université avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France; Present Address: NMR Research Unit, Faculty of Science, University of Oulu, FI-90014 Oulu, Finland; Email: Ouail.Zakary@oulu.fi

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