## Introduction

The continuing growth of many modern technologies is driven by the development of functional solid-state materials, such as metal oxides, fluorides, and nitrides that adopt a range of structural types and compositions. The accumulation of knowledge based on experimental data (or at times “chemical intuition”) and computational modeling and validations has led to extensive knowledge of these “single-anion” materials and affords further prediction of properties. Most of these results derive from variations in metal cation chemistry, as opposed to the anion, when examining structure-property relationships.

A multiple or mixed-anion compound is a solid-state material containing more than one anionic species in a single phase, such as oxyfluorides (oxide-fluoride) and oxynitrides (oxide-nitride). Unlike oxides, which exhibit diverse chemistries and structures often known from mineralogy, the structures of most mixed-anion compounds, among other aspects, are less explored with much to learn. This is readily seen when looking at the local structure of these compounds where the metal cation is bonded to more than one anionic ligand to form a heteroleptic polyhedron (Box 1). The different anionic characteristics, such as charge, ionic radii, electronegativity, and polarizability (Table 1) add new dimensions to control and tune the electronic and atomic structure of materials, which may support phenomena inaccessible to a single-anion analog.

Such anion-centered chemistry and physics is still in its infancy; there is much unexplored space, making it perhaps the most untapped field of materials sciences and giving new challenges and opportunities. In this review, we aim to describe the current status and scope, as well as outline future prospects and challenges surrounding mixed-anion (mostly oxide based) compounds, in particular, focusing on crucial roles of multiple anions in synthesis, characterization, and chemical and physical properties. Note that we had to be selective in materials and references because of the limited space. We provided mainly reviews or selected references, which could be an entry point to the literature search for readers who need additional information.

## Mixed-anion directed strategies

Understanding of mixed-anion compounds is still growing, but recent studies have unveiled several key features that are otherwise inaccessible in traditional single-anion compounds, as summarized in Fig. 1. Replacing oxide ligands in coordination octahedra or tetrahedra with other anions can differentiate the binding energy (Fig. 1e), which may benefit chemical reaction and anionic diffusion (Fig. 1f). It might also cause a (local) symmetry breaking (Fig. 1d) or create a cis/trans degree of freedom (Fig. 1c). The latter is a familiar ingredient in coordination chemistry, but less so in solid-state chemistry. Additionally, the crystal field splitting (CFS) can be tuned to the extent that is only allowed in coordination complexes, while retaining the original polyhedral shape and connectivity (Fig. 1a). An extensive modification of band (electronic) structures is also noteworthy, leading to a reduced dimensionality (Fig. 1g) and an upward shift of valence band maximum (VBM) (Fig. 1b).

Oxyhydrides (oxide hydrides), containing oxide and negatively charged hydride (H) anions, are rare but can be remarkable materials. Several features specific to hydride are given in Fig. 2. Hydrogen is the simplest (and lightest) element with one electron and one proton, giving the hydride anion distinct characteristics that differentiate it from other anions. For example, its bipolar nature and moderate electronegativity allow covalent, metallic, and ionic bonding, depending on the electronegativity of the element with which hydrogen bonds. This is schematically represented by the unconventional periodic table of elements (Fig. 2b)1, where values of electronegativity, ionization potential, and electron affinity are shown in the upper left, lower left, and lower right corner of each box. Related to this, the extraordinary flexibility in size of hydride (Fig. 2a) and possible reactions involving the zwitterionic nature (Fig. 2d) may bring about unprecedented functions. The flexible nature of hydride is also evident in its polarizability, as the refractive index of LiH (1.985) is significantly larger than that of LiF (1.392) despite the fewer number of electrons. Finally, H is the only anion which does not possess p orbitals in the valence shell. The lack of p orbitals in the outermost shell (Fig. 2c) significantly distinguishes its chemical bonding nature and its magnetic interaction with other anions.

## Synthesis beyond heat and beat

Conventional inorganic materials are mostly oxides, due to the fact that the Earth’s atmosphere contains mainly reactive oxygen (and inert nitrogen). Thus, metal oxides are conventionally synthesized by high-temperature solid-state reactions, sometime called ‘heat and beat’ (or ‘shake and bake’) processing. A major difficulty in preparing mixed-anion compounds in the same way lies in the differing volatilities of precursors (oxides, chlorides, hydrides, and so on), so simple heating of mixed starting reagents often ends up with single-anion compounds, though some can be prepared in air (e.g., LaCl3 + 0.5O2 → LaOCl + Cl2). For this reason, the preparation of mixed anion compounds often requires controlled atmospheres, such as in vacuum or under various flowing gases (Cl2, F2, NH3, CS2, and so on) (Fig. 3a) or exploits alternative synthesis methods, including soft-chemistry (Fig. 3b), solvothermal synthesis, or thin-film growth techniques (Fig. 3c) and high-pressure synthesis (Fig. 3d).

For example, a high-temperature ammonolysis reaction (under NH3 flow) is employed2, instead of inert N2, to obtain many oxynitride semiconductors, including AMO2N (A = Ba, Sr, Ca; M = Ta, Nb) with a high dielectric constant due to the larger polarizability of nitrogen (Fig. 1e)3. However, the ammonolysis reaction involves the dissociation of NH3–N2 and H2 (Fig. 3a) and thus provides a highly reducing atmosphere, which gives a certain constraint on available metals. To increase the reactivity of ammonia, a microwave oven is used to generate an ammonia plasma2.

The high reactivity of the anionic species, often gaseous in elemental form, can conversely be an advantage in tailoring anions in extended solids at low temperature. Topochemical insertion and exchange reactions (Fig. 3b), which provide metastable mixed-anion phases from precursors (typically oxides) in a rational, chemically designed manner, have been developed over the last two decades4. A proper choice of reagents and host structures is essential in directing reactions in a desired way. Consider for example oxyfluorides: a F2 treatment can give an oxidative fluorination involving F-intercalation (e.g., LaSrMn3+O4 → LaSrMn5+O4F2), while poly(tetrafluoroethylene), known as Telfon, acts as a reductant and may lead to reductive fluorination involving O/F-exchange (e.g., RbLaNb5+2O7 → RbLaNb4.5+2O6F)5,6.

The hydride anion is strongly reductive in nature, with a large standard redox potential of −2.2 V (H/H2 vs. SHE), so a transition metal oxyhydride appears impossible to stabilize. However, topochemical reaction using metal hydrides, such as CaH2 has opened a new avenue, yielding as the first example LaSrCoO3H0.7 (Co1.7+, d7.3) in 20027. Density functional theory (DFT) calculations revealed the presence of fairly strong σ bonding between Co eg and H 1s orbitals8. On the other hand, the formation of BaTiO2.4H0.6 (Ti3.4+; d0.6), SrVO2H (V3+; d2), and SrCrO2H (Cr3+; d3) is not readily rationalized since Ti/V/Cr t2g and H 1s orbitals are orthogonal (Fig. 2c)9,10,11. Since all the known transition-metal oxyhydrides exist with alkali and alkaline earth elements12, inclusion of any highly electropositive cation appears to be needed to make hydrogen with its moderate electronegativity (Fig. 2b) become negatively charged. This may explain why TiO2 does not incorporate hydride.

The observation of H/D exchange in BaTiO2.4H0.6 when heated in deuterium gas at ~400 °C indicates the labile nature of H (Fig. 1f)10. The lability of hydride in BaTiO2.4H0.6 (and other oxyhydrides) enables further topochemical anion exchange reactions (Fig. 3b)11,13,14. When BaTiO2.4H0.6 is used as a precursor, the ammonolysis reaction temperature (>1000 °C) is remarkably lowered to 350 °C, yielding BaTiO2.4N0.413. Even N2 flow at 400 °C gave the same product, demonstrating the ability of H to activate the nitrogen molecule. This hydride exchange chemistry is general, yielding other mixed-anion compounds, such as oxide-hydride-hydroxide BaTiO2.5H0.25(OH)0.2514.

Solvothermal synthesis is a synthetic method in which reactions occur in solution (i.e., water in the case of hydrothermal synthesis) inside a sealed vessel at temperatures near the boiling point of the solvent and pressures greater than atmospheric pressure15. Liquid-phase transport of the reactants allows for rapid nucleation and subsequent growth of a crystalline product with controlled morphology. This method produces crystals at lower temperatures and on shorter timescales than typical solid-state reactions. It also increases the likelihood of formation of mixed-anion compounds (e.g., halide hydroxides, oxyhalides), which are often unfavored at higher temperatures. Solvothermal syntheses have been very successful in producing materials with acentric coordination environments that lead to noncentrosymmetric (NCS) structures having desirable properties, such as piezoelectricity, pyroelectricity, and nonlinear optical activity16.

Direct fluorination of oxides with F2(g) or HF(g) is quite effective with minimal risk of side products. The handling of caustic, reactive gases, however, requires particularly specialized gas-phase reactors. In contrast, hydrothermal synthesis in hydrofluoric acid, or solutions of alkali fluorides, may be the easiest and safest route. The Teflon pouch approach is an efficient process to allow for fast development of discovery–based syntheses of new materials because various reactions can be performed in separate, small Teflon reaction pouches under identical, autogeneous conditions in an autoclave (Fig. 3c). Up to six reactions can be run in a 125 mL vessel.

Crystallographic long range ordering of oxide and fluoride anions has historically been a challenge, but materials based on anionic coordination polyhedra [MOmF6–m]n (where (m, n) = (1, 2) for M = V5+, Nb5+, Ta5+, (2, 2) for M = Mo6+, W6+, and (3, 3) for M = Mo6+)  have been solvothermally prepared without apparent anion-site disorder (Fig. 3c)16. In the ordered perovskite KNaNbOF5 and CsNaNbOF5 (with the general formula AM'MX(M' = alkali metal, M =  2nd order Jahn-Teller d0 metal)), the interactions of the [NbOF5]2– anion with the combination of Na/K or Na/Cs differ significantly. The NCS structure (KNaNbOF5) maintains a larger primary electronic distortion of the [NbOF5]2– anion along with a low coordination number of the K+ ion, consistent with the largest bond strain index. In contrast, the Cs+ ions of the centrosymmetric structure (CsNaNbOF5) can exhibit higher coordination numbers and the [NbOF5]2– anion exhibits a greatly reduced primary distortion. Theoretically, the group-theoretical method was applied to investigate anion ordering in the cubic perovskite, establishing 261 ordered low-symmetry structures, each with a unique space-group symmetry17. These idealized structures are considered as aristotypes with different derivatives formed by tilting of MO6 octahedra, providing a guide for designing NCS properties.

Thin film growth of oxides using pulsed laser deposition (PLD) or molecular beam epitaxy (MBE) is another useful bottom-up approach to construct desired artificial lattices, which has significantly contributed to the progress of condensed matter physics in the last two decades18. More rarely, thin film growth has been shown to be a promising method to prepare mixed-anion compounds, avoiding potential problems in anion diffusion. Oxynitrides films are fabricated by nitrogen plasma-assisted PLD, while polyvinylidene fluoride (PDVF) is used to topochemically convert oxide films to oxyfluoride ones. TaON films grown on a (LaAlO3)0.3(SrAl0.5Ta0.5O3)0.7 substrate adopt a metastable anatase structure with anion vacancies, leading to high-mobility electron transfer19. Tensile and compressive stresses from the substrate enables tailoring of the anion arrangement of a given structure. Compressively strained SrTaO2N films show a partial cis-to-trans conversion of TaO4N2 octahedra (Fig. 3c)20. An anion order/disorder transition can also be induced by strain engineering21. However, we note that there are still very few reports on mixed-anion films and most are thin film studies targeting optical (or surface) coating applications.

High pressure- and high-temperature conditions are typically used to stabilize dense materials through solid-state reactions or structural transformations. High-pressure reactions in sealed vessels prevent loss-of-volatile elements and so are particularly useful for anions, such as nitride to prevent loss-of-gaseous nitrogen (Fig. 3d). Autoclaves can be used for reactions under nitrogen up to kbar pressures, but many syntheses of oxynitrides have used direct reactions between solid oxides and nitrides (or oxynitrides) in multi-anvil presses where pressures can be extended to 10’s of kbar (GPa) values. The spinel Ga3O3N22 and AZrO2N perovskites (A = Pr, Nd, and Sm)23 were synthesized by direct solid-state reaction between oxides and nitrides or oxynitrides under GPa pressures. The use of solid reagents (instead of NH3) offers access to oxynitrides with middle-to-late transitions metals. A polar LiNbO3-type structure MnTaO2N with a helical spin order was recently synthesized at 6 GPa and 1400 °C24. A non-polar analog ZnTaO2N was also prepared25. New light atom materials have also been reported, such as the sphalerite-related boron oxynitride B6N4O3 synthesized from direct reaction between B2O3 and hexagonal-BN at 15 GPa and temperatures above 1900 °C26. Pressurization of baddeleyite-structured TaON drives a transition to a cotunnite-type structure with a very high-bulk modulus of 370 GPa (Fig. 3d)27.

## Chemical and structural analyses

Single crystal or powder diffraction methods are used to characterize many crystalline substances. A particular challenge for mixed-anion materials is to determine the distribution and degree of order-disorder of two or more anions. This complexity presents a challenge for both experiment and materials simulation (Fig. 3e), where equilibrium structures consisting of ordered or disordered anion configurations may be used for electronic structure calculations, e.g., those based on DFT or many-body methods. Ultimately to assess the properties of a mixed-anion material, the structure must be known. To that end, a number of structure-search algorithms, including cluster expansions28, special quasirandom structures29, and genetic algorithms30, frequently applied to multicomponent alloys and single-anion compounds, could be used to assess phase stability and solve structures in multi-anion compounds. In combination with experimental methods (below), a more complete description of the local and crystal structure can be obtained. These methods are also important for obtaining interaction energies for effective model Hamiltonians to describe ordering and ferroic transitions31.

Experimentally, the anion distribution may be studied directly using the scattering contrast between the anionic elements or indirectly through the different sizes or coordination environments of the anions in the structure. Direct X-ray scattering contrast is poor between elements from the same row of the periodic table, such as N/O/F or As/Se/Br, and neutron scattering may be useful in some cases, for example, to differentiate N and O which have respective neutron scattering lengths of 9.36 and 5.83 fm (Table 1) in oxynitrides. Neutron scattering also enables the positions of these light atoms to be determined more precisely in the presence of heavy metal atoms than is usually possible from X-ray refinements.

Anions that have very similar X-ray and neutron scattering factors, such as oxide and fluoride may be distinguished by their structural environments if well-ordered within a crystal structure. Differences in formal charge and size are captured by the popular bond valence sum (BVS) method32, but even a simple approach based on apportioning ideal bond valences from Pauling’s second crystal rule was found to account for anion orders in many oxyhalides and oxynitrides (Fig. 4a)33. Increasing the formal anion charge tends to promote more covalent bonding to the metal cations and this can also enable anions to be distinguished; for example, vanadium forms very short ‘vanadyl’ bonds to oxide but not fluoride in V4+ and V5+ oxyfluorides.

Between the limits of fully ordered and randomly disordered anions, there are many cases of intermediate anion orders with local clustering or extended correlations that may give rise to non-random site occupancies in the averaged crystal structure. A particularly widespread example of such correlated disorder is found in AMO2N and AMON2 perovskite oxynitrides where layers of zig–zag MN chains (Fig. 4c) result from strong-covalent interactions between high-valence transition metals M and nitride anions that promote local cis-MN2 (or MO4N2) configurations (Fig. 1c, e). This order has been deduced from powder neutron refinements of O/N site occupancies in materials, such as SrMO2N (M = Nb, Ta)34, LaTaON235, and AVO2N (A = Pr, Nd)36,37 perovskites. Local O/N correlations are also present in silicon oxynitrides where covalency tends to equalize the SiO4–nNn compositions of all nitridosilicate tetrahedra, for example, in melilite-type Y2Si3O3N438.

Analysis of total X-ray or neutron scattering data, including diffuse features from short-range correlations, as well as the Bragg scattering, has been used to construct the pair distribution function (PDF) of interatomic distances in many materials. Fitting of the PDF can be a powerful tool for revealing short range structural correlations in crystalline materials, as well as in amorphous substances39. Scattering or size contrast between anions can be used to determine their local order, for example, neutron PDF analysis revealed the prevalence of local cis-TaN2 configurations in the perovskite BaTaO2N (Fig. 4c)40.

Complementary information for analyzing the neutron- or X-ray-PDFs can be acquired by other techniques, such as electron energy loss spectroscopy (EELS) combined with scanning transmission electron microscopy (STEM), X-ray absorption near edge structure (XANES) of X-ray absorption spectroscopy (Fig. 4c), and magic angle-spinning (MAS) nuclear magnetic resonance (NMR) (Fig. 4b), which provide not only anion composition but also the local structures. As opposed to the above diffraction methods that may have difficulty in distinguishing among O, F, and N, state-of-the-art STEM-EELS can determine atomic occupancy with a resolution of each atomic column in a crystal lattice. This is particularly advantageous for thin film samples, in which crystal orientation is well controlled but precise structural analysis by diffraction methods is not as applicable. XANES is also effective for identifying the above elements and determining their chemical states. Perovskite (Ca1–xSrx)TaO2N epitaxial films with controlled strains were analyzed using XANES with a polarized light source41. From the intensity of π-bonded states of O or N with Ta-5d via excitation from O and N core levels, it was concluded that N preferably takes the trans configuration in the TaO4N2 octahedron for compressive strain states, which was also supported by STEM-EELS and DFT calculations (Fig. 4c).

NMR has also been effective for (local) structural determination of mixed-anion compounds42. Structural determination of industrially important Si–Al–O–N materials (SiAlON), which are solid solutions between Si3N4 and Al2O3, by X-ray diffractometry is insufficient because X-ray scattering factors within the Si–Al and O–N pairs are similar; however, the high-resolution MAS-NMR method overcomes this challenge. Local coordination around the 29Si and 27Al nuclei was determined by MAS-NMR and their integration gives a full structural model for such oxynitride materials43 and, coupled with ab initio calculations, preferential Al–O clustering44.

High sensitivity is a hallmark of 1H-NMR, enabling detection of H with a concentration as low as 0.1% of the total anions. Coexistence of H+ (or OH) and H ions in a single material is not trivial because their thermodynamic stability is different and depends on oxygen partial pressure, p(O2). However, these two species sometimes coexist due to non-equilibrium14 or high-temperature equilibrium45. Recent 1H-NMR has identified a ‘hidden’ hydride anion and its local environment in hydroxyl-oxides like apatite Ca10(PO4)6(OH)245. Here, the size flexibility of H (Fig. 2a) substantially changes the electron density (and relevant magnetic field shielding) at 1H nuclei and hence the isotropic chemical shift of 1H-NMR (Fig. 4b).

Cage structures can incorporate various anionic species. Mayenite 12CaO·7Al2O3 with a positively charged cage structure is shown to host many mono- or divalent guest anions (F, Cl, S2–, O, O2–, O22–, C22–, NH2–, CN, O2–, OH, and H) (Fig. 1h)46. Raman and electron paramagnetic spin resonance (EPR) measurements show that active oxygen species of O, O2, and O22–, less stable than O2– in oxide crystals and usually formed on surfaces transiently47, can stably exist in the cage. In a lightly hydride-doped mayenite, an irradiation of UV light induces a chemical reaction in the cage: H + O2– 2e + OH (Fig. 2d). Here, the e is confined within the cage, like F+ centers in alkali halides, and is responsible for a ‘permanent’ electrical conductivity as the reverse of the above reaction proceeds with a timescale of 10,000 years at room temperature48. Formation of transient atomic hydrogen during the photo-dissociation of H is monitored by EPR, revealing that its lifetime of the atomic hydrogen is a few minutes at 40 K49.

## Chemical properties

### Optical applications

Many oxides have a wide band gap and so are transparent. Valence band engineering according to Fig. 1b is useful to make them responsive to visible light, the main component of solar spectrum. When the oxide anion is substituted by other anions with less electronegativity like nitride (Table 1), the non-oxide p orbitals having high-potential energy extend the valence band and allow for visible-light absorption. Solid solutions of CaTaO2N and LaTaON2 perovskites have tuneable colors that range from yellow to red via orange (500–600 nm in wavelengths), depending on the composition of the solid solutions50. These oxynitrides are potential non-toxic alternatives to chalcogenide-based inorganic pigments.

This strategy may be of particular importance for finding a photocatalyst which can split water to produce H2 and O2 under visible light. Otherwise, if oxides with a small band gap of < 3 eV (corresponding to λ > 400 nm) are used, the conduction band minimum (CBM, or flat-band potential) becomes more positive than the water reduction potential (0 V vs. NHE (normal hydrogen electrode) at pH 0), a limitation shown by Scaife50 (Fig. 5a). So far, various oxynitrides and oxysulfides that overcome this limitation have shown water splitting performance51,52,54. Some of them (e.g., ZrO2-grafted TaON) were found to be a useful component for Z-scheme type water splitting55 and CO2 reduction with the aid of a functional metal complex56.

Unexpected changes in electronic structure are often found in mixed-anion compounds, which presents a challenge to predictive materials theory. Methods based on DFT require appropriate exchange-correlation functionals57,58 to accurately describe the mixed bonding character presented in these materials. Alloying wide-gap semiconductors, GaN and ZnO, results in an unprecedented yellowish powder (Fig. 5a), and this provides the first reproducible example of visible-light-driven overall water splitting59. Loaded with nanoparticulate Rh2O3–Cr2O3 that works as an active site for H2 evolution, (Ga1–xZnx)(N1–xOx) exhibited H2 and O2 evolution for >3 months60. One of the drawbacks of mixed anion photocatalysts in general is their instability against photo-induced holes. This is seen even in (Ga1–xZnx)(N1–xOx), where the photo-induced holes oxidize the N3– anion, degrading its photocatalytic activity by self-decomposition60. Bi4NbO8Cl, a Sillen–Aurivillius layered perovskite, was recently shown to stably oxidize water without any surface modifications. The observed stability is attributed to highly dispersive O-2p orbitals (dominating the VBM instead of Cl-3p)61. A recent study on a series of layered bismuth oxyhalides has revealed that Madelung site potentials of anions capture essential features of the valence band structures of these materials, enabling prediction and design of the valence band structures by manipulating the stacking sequence of layers (Fig. 1g)62.

Oxynitrides doped with rare earth elements show photoluminescence. Here, substitution of O2– for N3– gives a greater CFS of the 5d levels of rare earth elements, such as Eu2+ (Fig. 1a), extending the excitation and emission peaks to longer wavelengths. SiAlON, (Si3–xAlx)(N4–xOx):Eu2+, and related phosphors undergo photoexcitation by absorbing blue light, and emitting yellow light, and hence are used in phosphor-converted white-light emitting LED lamps (WLEDs)63. Other important SiAlON-related phosphors used in WLEDs are the ASi2O2N2:Eu2+ and A2Si5N8:Eu2+ families (A = Ca, Sr, and Ba)64, the latter can be oxide-doped with Al3+ providing charge compensation in A2Si5−xAlxN8−xOx:Eu2+ (x = 0–1)65. The high thermal and chemical stability arising from covalent M−N bonding (Fig. 1e) leads to practical applications. Similar chemical tuning has been applied for oxyfluoride type solid solutions, such as AII3–xAIIIxMO4F family with A = Sr, Ca, Ba and M = Al, Ga (e.g., (Sr,Ba)2.975Ce0.025AlO4F) 66,67.

Another interesting feature from the mixed-anion system is pleochroism, recently found in Ca3ReO5Cl2 with the Re6+ ion in a 5d1 configuration (Fig. 5b)68. The heavily distorted octahedral coordination of Re6+ by one Cl and five O2– anions along with the spatially extended 5d orbitals gives rise to unique CFS energy levels (Fig. 1a), much greater than for 3d orbitals owing to stronger electrostatic interactions exerted from the ligands. The uni-directional alignment of these octahedra along the c-axis makes the d–d transitions highly anisotropic. As a result, this compound exhibits very different colors depending on the viewing direction, i.e., distinct pleochroism.

### Anion conductors

Certain anions are mobile in solids. The merit of a mixed-anion material is that it allows for anion diffusion by one (more ionic, less highly charged) anion and structural stability by the other (more covalent, more highly charged) anion (Fig. 1e, f). This concept can be directly assessed using electronic structure methods, where calculations of intrinsic defect levels and diffusion barriers69 can be correlated with changes in the anion lattice. A layered lanthanum oxychloride LaOCl is a Cl-ion conductor70. While La2O3 and LaCl3 are both sensitive to moisture, a critical disadvantage for practical applications, LaOCl is water-insoluble and exhibits Cl conductivity. An aliovalent Ca–for–La substitution generates vacancies at the chloride site and hence the Cl conductivity is improved.

H anion conductors are expected to provide high-energy storage and conversion devices because H has an appropriate ionic size for fast diffusion (Fig. 2a), a low electronegativity (Fig. 2b) and a high-standard redox potential of H/H2 (−2.3 V), close to that of Mg/Mg2+ (−2.4 V). A pure H conduction in K2NiF4-type La2LiHO3 has recently been demonstrated, using an all-solid-state TiH2/La2LiHO3/Ti cell (Fig. 5c)71. The two-dimensional (2D) H diffusion is further facilitated by introducing H vacancies, leading to the activation energy of 68.4 kJ mol−1 for La0.6Sr1.4LiH1.6O2.

### Battery electrodes

Mixed-anion chemistry of oxyfluorides offers a new handle to tune the redox potential of battery electrodes. Here, instead of ‘direct’ valence (anion) band control described in Fig. 1b, anion substitution enables an ‘indirect’ manipulation of the cation band. The redox potential of the LiFeSO4F phase (tavorite) is higher than the LiFePO4 phase (olivine) by 750 mV72. This primarily results from the weaker (more ionic) Fe–F bond as compared with the Fe–O bond (Fig. 1e), which stabilizes the anti-bonding band of Fe eg orbitals (Fig. 5c). Furthermore, Ag2V2O6F2 (SVOF) is a battery material potentially used in cardiac defibrillators owing to a fast discharge rate and high-current density73. The silver density in SVOF is greater than that of the currently used industry standard cathode material Ag2V4O11 (SVO)74 and thus the current density above 3 V for SVOF (148 mAh/g) is greater than that for SVO (100 mAh/g). The current density above 3 V is sufficient and the potential at which it is delivered (3.52 V) is 300 mV greater than SVO owing to the fluoride incorporation (Fig. 1b).

Multivalent batteries exhibit a number of potentially valuable advantages compared to current lithium technology. The first functional multivalent battery was constructed in 2000; this prototype used a magnesium metal anode against a low-voltage Chevrel phase cathode75. A significant barrier to the adoption of magnesium batteries is the lack of an available high-voltage cathode that can reversibly intercalate magnesium. Cathodes composed of layered molybdenum fluoro-bronze are found to reversibly intercalate magnesium76. MoO2.8F0.2, combined with a Mg-based electrolyte, gave a reversible capacity of nearly 80 mAh/g, an order of magnitude higher than isostructural α-MoO3 with a similar particle size (Fig. 5c). First-principles calculations revealed that the incorporation of fluoride within the crystal lattice reduces nearby molybdenum ions, enhancing in-plane electronic conductivity77. The associated increase in electronic screening reduces the activation barrier for Mg ion diffusion but yet does not significantly lower the voltage.

### Thermoelectric materials

Thermoelectric materials enable direct conversion between thermal and electrical energy. Optimal materials with a high figure of merit ZT have a high Seebeck coefficient and electronic conductivity in combination with a low-thermal conductivity. BiCuSeO with (Cu2Se2)2− layers alternately stacked with (Bi2O2)2+ layers (Fig. 1g), is a promising thermoelectric material, where one layer is responsible for electric conduction, while another lowers thermal conductivity78.

Nanostructuring which may be based on local segregation of anions is another effective means to reduce phonon thermal conductivity. The PbTe–PbS system exhibits phase separation (spinodal decomposition), owing to a large difference in the anion sizes (Hume-Rothery rules)79. The resultant PbTe-rich and PbS-rich regions form dissimilar nanostructures with interphase boundaries that act as effective scattering centers for short-wavelength phonons (Fig. 5d). A nominal composition of PbTe0.7S0.3 doped with 2.5% K achieved a figure-of-merit ZT of > 2 over a wide temperature range from 400 to 650 °C80. On contrary, a complete solid solution is formed in the PbTe–PbSe system. By tuning the anionic composition in Pb(Te1–xSex), the electronic band structure exhibits high-valley degeneracy (Fig. 5d), leading to an optimized ZT value of 1.8 at 577 °C81.

## Physical properties

Ordering of two anions within a material often leads to low dimensionality in structural and physical properties. Layering of different anion types (Fig. 1g) is common and leads to 2D conductivity or magnetic correlations when cations with unpaired electrons are present. The ZrCuSiAs structure type is a flexible arrangement that allows two different anions and cations to segregate into distinct layers according to HSAB (hard and soft acids and bases) principles. Many mixed-anion materials adopt the ZrCuSiAs type, notably the LnFeAsO family of layered magnetic conductors and (when suitably doped) high-Tc superconductors (Fig. 6a), the p-type semiconductor LaCuSO, the ferromagnetic Kondo material CeRuPO, and the Ag-ion conductor LaAgSO82. Layered order of nitride and halide anions in MNX materials (M = Ti, Zr, and Hf; X = Cl, Br, and I) results in X-M-N-N-M-X slabs separated by van der Waals gaps (Fig. 6a) into which cations such as lithium are intercalated, leading to conductivity and superconductivity83.

Multiple anions and their ratios may be used to control dimensionality and connectivity of magnetic interactions. V4+ and Cu2+ both have spin S = 1/2 and so are of interest for quantum magnetic and superconducting properties, especially in low-dimensional structures that are often found in mixed-anion materials. In the early copper oxide superconductor studies, two copper oxyhalides, Sr2CuO2F2+δ84 and (Ca,Na)2CuO2Cl285, played a role in understanding the superconducting mechanism (Fig. 6a). Although, these compounds possess F and Cl ions instead of O2– ions at the apical site above and below the Cu2+ ions, they are superconducting with Tc = 46 and 26 K, respectively. This fact challenged the theoretical models proposing a vital role of the apical oxygen in the superconducting mechanism. Now it is well established that the high-Tc superconductivity occurs within the CuO2 sheet having a strong covalency between the Cu $$d_{x^2 - y^2}$$ and O 2pσ states, while the apical-site anions (oxide ions) are more ionic (Fig. 1e), resulting in the 2D electronic state. In V4+ oxyfluorides, the V = O vanadyl oxide anions do not link to other cations whereas fluorides readily form V–F–V bridges, enabling many structural topologies to be achieved. DQVOF (Diammonium Quinuclidinium Vanadium OxyFluoride; [NH4]2[C7H14N][V7O6F18]) is notable as a geometrically frustrated kagomé bilayer material with a gapless spin liquid ground state, instead of the conventional Néel order (Fig. 6b)86. Various synthetic copper minerals with Cu2+ (S = 1/2 ion) and mixed anions have been studied as geometrically frustrated quantum magnets that can also show exotic ground states. A good example is herbertsmithite, ZnCu3(OH)6Cl2 (Fig. 6b), in which the Cu2+ ion is coordinated by two axial Cl ions and four equatorial OH ions with its spin residing on the $$d_{x^2 - y^2}$$ orbital87. The Cu2+ spins form a 2D kagomé lattice and are coupled to each other by strong superexchange interactions only via the OH ions. The compound exhibits no long-range order down to 50 mK with fractionalized excitations (Fig. 6b)88, owing to the strong frustration on the kagomé lattice. Volborthite Cu3V2O7(OH)2·2H2O and vesignieite BaCu3V2O8(OH)2 with trans-CuO4(OH)2 octahedra having different orbital arrangements composed of $$d_{x^2 - y^2}$$/$$d_{z^2}$$ and $$d_{z^2}$$ orbitals, respectively, enrich the phase diagram of the kagomé antiferromagnet89.

The lack of p orbitals in the valence shell of H (1s) effectively blocks the π-symmetry exchange pathways (Fig. 2c), a situation occurring in SrVIIIO2H with (t2g)2, where the in-plane exchange via V–O–V is much greater than the out-of-plane one via V–H1s–V interactions (Fig. 6c)9. The application of pressure to the Mott insulator drives a transition to a metal at ~50 GPa. Interestingly, despite the enormous compressibility of hydride (Fig. 2a), which is twice as compressible as oxide (Fig. 2a), the electronic structure of the metallic phase is quasi-2D, meaning that the hydride ligand acts as a ‘π-blocker’. The dimensional control from 2D to 1D is possible in the n-legged spin ladder oxyhydrides Srn+1VnO2n+1Hn (n = 1, 2,.., ∞) (Fig. 1g)90.

During the last decade, there has been remarkable progress in physics involving topological phases of matter, for which mixed-anion compounds play crucial roles in advancing this field. Binary chalcogenides Bi2Se3 and Bi2Te3 were thought to be potential three-dimensional topological insulators, but both suffered from native point defects and unintentional carrier doping. Alloying with these two compounds along with Sb-for-Bi substitution has established a highly insulating bulk and accessible Dirac carriers, accompanied by the observation of a sign change of the Dirac carriers (holes vs electrons) with chemical potential (Fig. 6d)91. The precise carrier control has been also utilized to achieve a topological surface state quantum Hall effect (Fig. 6d)92.

The layered polar semiconductor BiTeI shows a huge bulk Rashba-type spin splitting (Fig. 6d) that arises from the strong inversion asymmetry along the trigonal c-axis induced by distinct covalent Bi-Te and ionic Bi-I bonds in the facial-BiTe3I3 coordination (Fig. 1d)93. This built-in bulk polarity induces 2D electronic surface structures with heavy depleted (I-termination) and accumulated (Te-termination) electrons forming pn junctions (Fig. 6d)94. Although BiTeI is a nontopological insulator at ambient pressure, it is proposed that the strong spin-orbit interaction allows a pressure-induced transition to a strong topological insulator, where, due to the broken inversion symmetry, a Weyl semimetal emerges between the two insulating phases95.

## Outlook

Increasing interest in solids based on mixed anions is expected to lead to new materials, some of which will make significant contributions to catalysis, energy conversion, and electronic devices, and will ultimately benefit industry in the coming decades. Functionality based on the earth-abundant, light elements usually present as anionic species (O, N, H, S, Cl, and so on) also offers the advantage of avoiding the inherent scarcity problems of metals, such as lanthanides. The metastability of mixed-anion compounds increases the complexity of synthesis and can limit the ways in which these materials can be used in devices. Therefore, chemically stabilizing these phases has to be considered when they are adapted for applications.

Synthetically, there will still be much room to develop methodologies. For example, multiple synthetic tools are used together (e.g., topochemical reaction under high pressure) or in a multistep process (e.g., solvothermal reaction followed by electrochemical reaction), both providing further platforms to manipulate multiple anions in extended solids. One of the important challenges is how to control anion order/disorder—one idea may be to utilize the size flexibility of hydride (Fig. 2a) to induce an order-disorder transition by (chemical) pressure. Furthermore, exploratory synthesis can be joined with computational tools ranging from DFT calculations to machine learning to expedite the screening process.

Regarding catalysis, this review has focused on visible-light-driven water splitting, but we believe that mixed-anion compounds can offer a variety of new possibilities, which would provide a large impact on chemical industry. In fact, an oxyhydride BaTiO2.5H0.5 has been very recently found to be an active catalyst for ammonia synthesis, which is remarkable given that Ti has been regarded as a ‘dead’ element in terms of heterogeneous catalysis96. The lability of hydride (Fig. 1f) may be responsible for this catalytic activity. Introduction of a new anion, not limited to hydride, into oxides will therefore be a useful strategy to explore a new catalytic function of ‘inert’ oxides. In situ and in operando analytic techniques will benefit and improve our understanding of these functions arising from mixed anion materials. The integration of DFT and machine learning and experiment can lead to the most likely reaction mechanism, and also provide new concepts or guiding principles to be added in Figs. 1 and 2.

Most functional mixed-anion materials known to date, and providing the focus of this review, are oxide based, although non-oxide mixed-anion systems may also provide novel phases and phenomena83,97,98,99. The additional inclusion of molecular anions (e.g., O2, BH4) can give rise to new aspects of anion-based materials (Fig. 1h)100,101,102. For instance, the use of anisotropic anions, such as O22– or S22– will result in local symmetry breaking and alter the hybridization with coordinating cations. Furthermore, mixed anions in surface, 2D-sheet materials99, interfaces, porous and nano materials, and amorphous systems are an important area for both fundamental and applied research.

There is still much to discover about the scientific principles and technological applications of mixed-anion materials. It means that the future prospects of mixed-anion materials are largely unknown at this time and this is what precisely makes the field so interesting moving forward. P. W. Anderson famously proposed that ‘More is Different’; in the world of anion-based materials we analogously conclude that ‘Mixed is Different’.