A cationic thorium–organic framework with triple single-crystal-to-single-crystal transformation peculiarities for ultrasensitive anion recognition

Single-crystal-to-single-crystal transformation of metal–organic frameworks has been met with great interest, as it allows for the creation of new materials in a stepwise manner and direct visualization of structural transitions when subjected to external stimuli. However, it remains a peculiarity among numerous metal–organic frameworks, particularly for the ones constructed from tetravalent metal cations. Herein, we present a cationic thorium–organic framework displaying unprecedented triple single-crystal-to-single-crystal transformations in organic solvents, water, and NaIO₃ solution. Notably, both the interpenetration conversion and topological change driven by the SC–SC transformation have remained elusive for thorium–organic frameworks. Moreover, the single-crystal-to-single-crystal transition in NaIO₃ solution can efficiently and selectively turn the ligand-based emission off, leading to the lowest limit of detection (0.107 μg kg⁻¹) of iodate, one of the primary species of long-lived fission product ¹²⁹I in aqueous medium, among all luminescent sensors.

A cationic thorium–organic framework displaying unprecedented triple single-crystal-to-single-crystal transformations has been developed, allowing for ultrasensitive and selective sensing of iodate.     

Backbonding contributions to small molecule chemisorption in a metal–organic framework with open copper(i) centers

Metal–organic frameworks are promising materials for applications such as gas capture, separation, and storage, due to their ability to selectively adsorb small molecules. The metal–organic framework Cu^I-MFU-4l, which contains coordinatively unsaturated copper(i) centers, can engage in backbonding interactions with various small molecule guests, motivating the design of frameworks that engage in backbonding and other electronic interactions for highly efficient and selective adsorption. Here, we examine several gases expected to bind to the open copper(i) sites in Cu^I-MFU-4l via different electronic interactions, including σ-donation, π-backbonding, and formal electron transfer. We show that in situ Cu L-edge near edge X-ray absorption fine structure (NEXAFS) spectroscopy can elucidate π-backbonding by directly probing excitations to unoccupied backbonding orbitals with Cu d-character, even for gases that participate in other dominant interactions, such as ligand-to-metal σ-donation. First-principles calculations based on density functional theory and time-dependent density functional theory additionally reveal the backbonding molecular orbitals associated with these spectroscopic transitions. The energies of the transitions correlate with the energy levels of the isolated small molecule adsorbates, and the transition intensities are proportional to the binding energies of the guest molecules within Cu^I-MFU-4l. By elucidating the molecular and electronic structure origins of backbonding interactions between electron rich metal centers in metal–organic frameworks and small molecule guests, it is possible to develop guidelines for further molecular-level design of solid-state adsorbents for energy-efficient separations of relevance to industry.

In situ near edge X-ray absorption fine structure spectroscopy directly probes unoccupied states associated with backbonding interactions between the open metal site in a metal–organic framework and various small molecule guests.     

Chemical principles underpinning the performance of the metal–organic framework HKUST-1

A common feature of multi-functional metal–organic frameworks is a metal dimer in the form of a paddlewheel, as found in the structure of Cu₃(btc)₂ (HKUST-1). The HKUST-1 framework demonstrates exceptional gas storage, sensing and separation, catalytic activity and, in recent studies, unprecedented ionic and electrical conductivity. These results are a promising step towards the real-world application of metal–organic materials. In this perspective, we discuss progress in the understanding of the electronic, magnetic and physical properties of HKUST-1, representative of the larger family of Cu···Cu containing metal–organic frameworks. We highlight the chemical interactions that give rise to its favourable properties, and which make this material well suited to a range of technological applications. From this analysis, we postulate key design principles for tailoring novel high-performance hybrid frameworks.     

Influence of the primary and secondary coordination spheres on nitric oxide adsorption and reactivity in cobalt(ii)–triazolate frameworks

Nitric oxide (NO) is an important signaling molecule in biological systems, and as such, the ability of porous materials to reversibly adsorb NO is of interest for potential medical applications. Although certain metal–organic frameworks are known to bind NO reversibly at coordinatively unsaturated metal sites, the influence of the metal coordination environment on NO adsorption has not been studied in detail. Here, we examine NO adsorption in the frameworks Co₂Cl₂(bbta) (H₂bbta = 1H,5H-benzo(1,2-d:4,5-d′)bistriazole) and Co₂(OH)₂(bbta) using gas adsorption, infrared spectroscopy, powder X-ray diffraction, and magnetometry. At room temperature, NO adsorbs reversibly in Co₂Cl₂(bbta) without electron transfer, with low temperature data supporting spin-crossover of the NO-bound cobalt(ii) centers of the material. In contrast, adsorption of low pressures of NO in Co₂(OH)₂(bbta) is accompanied by charge transfer from the cobalt(ii) centers to form a cobalt(iii)–NO⁻ adduct, as supported by diffraction and infrared spectroscopy data. At higher pressures of NO, characterization data indicate additional uptake of the gas and disproportionation of the bound NO to form a cobalt(iii)–nitro (NO₂⁻) species and N₂O gas, a transformation that appears to be facilitated by secondary sphere hydrogen bonding interactions between the bound NO₂⁻ and framework hydroxo groups. These results provide a rare example of reductive NO binding in a cobalt-based metal–organic framework, and they demonstrate that NO uptake can be tuned by changing the primary and secondary coordination environment of the framework metal centers.

Nitric oxide (NO) shows differences in adsorption and reactivity in two related cobalt(ii)–triazolate frameworks, demonstrating how the primary and secondary coordination sphere of metal centers in adsorbents can be designed for targeted delivery.     

The structures of ordered defects in thiocyanate analogues of Prussian Blue

We report the structures of six new divalent transition metal hexathiocyanatobismuthate frameworks with the generic formula , M = Mn, Co, Ni and Zn. These frameworks are defective analogues of the perovskite-derived trivalent transition metal hexathiocyanatobismuthates M^III[Bi(SCN)₆]. The defects in these new thiocyanate frameworks order and produce complex superstructures due to the low symmetry of the parent structure, in contrast to the related and more well-studied cyanide Prussian Blue analogues. Despite the close similarities in the chemistries of these four transition metal cations, we find that each framework contains a different mechanism for accommodating the lowered transition metal charge, making use of some combination of Bi(SCN)₆³⁻ vacancies, M_Bi antisite defects, water substitution for thiocyanate, adventitious extra-framework cations and reduced metal coordination number. These materials provide an unusually clear view of defects in molecular framework materials and their variety suggests that similar richness may be waiting to be uncovered in other hybrid perovskite frameworks.

We report the structures of six new divalent transition metal hexathiocyanatobismuthate Prussian Blue analogues frameworks, which contain complex ordered defect structures.     

Engineering entangled photon pairs with metal–organic frameworks

The discovery and design of new materials with competitive optical frequency conversion efficiencies can accelerate the development of scalable photonic quantum technologies. Metal–organic framework (MOF) crystals without inversion symmetry have shown potential for these applications, given their nonlinear optical properties and the combinatorial number of possibilities for MOF self-assembly. In order to accelerate the discovery of MOF materials for quantum optical technologies, scalable computational assessment tools are needed. We develop a multi-scale methodology to study the wavefunction of entangled photon pairs generated by selected non-centrosymmetric MOF crystals via spontaneous parametric down-conversion (SPDC). Starting from an optimized crystal structure, we predict the shape of the G⁽²⁾ intensity correlation function for coincidence detection of the entangled pairs, produced under conditions of collinear type-I phase matching. The effective nonlinearities and photon pair correlation times obtained are comparable to those available with inorganic crystal standards. Our work thus provides fundamental insights into the structure–property relationships for entangled photon generation with metal–organic frameworks, paving the way for the automated discovery of molecular materials for optical quantum technology.

The discovery and design of new materials with competitive optical frequency conversion efficiencies can accelerate the development of scalable photonic quantum technologies.     

Single-step synthesis and interface tuning of core–shell metal–organic framework nanoparticles

Control over the spatial distribution of components in metal–organic frameworks has potential to unlock improved performance and new behaviour in separations, sensing and catalysis. We report an unprecedented single-step synthesis of multi-component metal–organic framework (MOF) nanoparticles based on the canonical ZIF-8 (Zn) system and its Cd analogue, which form with a core–shell structure whose internal interface can be systematically tuned. We use scanning transmission electron microscopy, X-ray energy dispersive spectroscopy and a new composition gradient model to fit high-resolution X-ray diffraction data to show how core–shell composition and interface characteristics are intricately controlled by synthesis temperature and reaction composition. Particle formation is investigated by in situ X-ray diffraction, which reveals that the spatial distribution of components evolves with time and is determined by the interplay of phase stability, crystallisation kinetics and diffusion. This work opens up new possibilities for the control and characterisation of functionality, component distribution and interfaces in MOF-based materials.

Core–shell metal–organic framework nanoparticles have been synthesised in which the internal interface and distribution of components is found to be highly tunable using simple variations in reaction conditions.     

How to not build a cage: endohedral functionalization of polyoxometalate-based metal–organic polyhedra

Introducing functionalities into the interior of metal–organic cage complexes can confer properties and utilities (e.g. catalysis, separation, drug delivery, and guest recognition) that are distinct from those of unfunctionalized cages. Endohedral functionalization of such cage molecules, for decades, has largely relied on modifying their organic linkers to covalently append targeted functional groups to the interior surface. We herein introduce an effective coordination method to bring in functionalities at the metal sites instead, for a set of polyhedral cages where the nodes are in situ formed polyoxovanadate clusters, [V^IV₆O₆(OCH₃)₉(μ₆-SO₄)(COO)₃]²⁻. Replacing the central sulfates of these hexavanadate clusters with more strongly coordinating phosphonate groups allows the installation of functionalities within the cage cavities. Organophosphonates with phenyl, biphenyl, and terphenyl tails were examined for internalization. Depending on the size/shape of the cavities, small phosphonates can fit into the molecular containers whereas larger ones inhibit or transform the framework architecture, whereby the first non-cage complex was isolated from a reaction that otherwise would lead to entropically favored regular polyhedra cages. The results highlight the complex and dynamic nature of the self-assembly process involving polyoxometalates and the scope of molecular variety accessible by the introduction of endo functional groups.

Installation of oversized functions within a metal–organic cage may “burst” or even transform the molecular cage itself.     

Thermodynamic consequences of Tyr to Trp mutations in the cation–π-mediated binding of trimethyllysine by the HP1 chromodomain

Evolution has converged on cation–π interactions for recognition of quaternary alkyl ammonium groups such as trimethyllysine (Kme3). While computational modelling indicates that Trp provides the strongest cation–π interaction of the native aromatic amino acids, there is limited corroborative data from measurements within proteins. Herein we investigate a Tyr to Trp mutation in the binding pocket of the HP1 chromodomain, a reader protein that recognizes Kme3. Binding studies demonstrate that the Trp-mediated cation–π interaction is about −5 kcal mol⁻¹ stronger, and the Y24W crystal structure shows that the mutation is not perturbing. Quantum mechanical calculations indicate that greater enthalpic binding is predominantly due to increased cation–π interactions. NMR studies indicate that differences in the unbound state of the Y24W mutation lead to enthalpy–entropy compensation. These results provide direct experimental quantification of Trp versus Tyr in a cation–π interaction and afford insight into the conservation of aromatic cage residues in Kme3 reader domains.

In this work, we experimentally validate that tryptophan provides the strongest cation–π binding interaction among aromatic amino acids and also lend insight into the importance of residue identity in trimethyllysine recognition by reader proteins.     

Linking metal–organic cages pairwise as a design approach for assembling multivariate crystalline materials

Using metal–organic cages (MOCs) as preformed supermolecular building-blocks (SBBs) is a powerful strategy to design functional metal–organic frameworks (MOFs) with control over the pore architecture and connectivity. However, introducing chemical complexity into the network via this route is limited as most methodologies focus on only one type of MOC as the building-block. Herein we present the pairwise linking of MOCs as a design approach to introduce defined chemical complexity into porous materials. Our methodology exploits preferential Rh-aniline coordination and stoichiometric control to rationally link Cu₄L₄ and Rh₄L₄ MOCs into chemically complex, yet extremely well-defined crystalline solids. This strategy is expected to open up significant new possibilities to design bespoke multi-functional materials with atomistic control over the location and ordering of chemical functionalities.

A new strategy to design atomically precise multivariate metal–organic frameworks is presented. This is achieved by linking two preformed metal–organic cages via a precisely tuned Rh–aniline interaction.     

Switchable electrical conductivity in a three-dimensional metal–organic framework via reversible ligand n-doping

Redox-active metal–organic frameworks (MOFs) are promising materials for a number of next-generation technologies, and recent work has shown that redox manipulation can dramatically enhance electrical conductivity in MOFs. However, ligand-based strategies for controlling conductivity remain under-developed, particularly those that make use of reversible redox processes. Here we report the first use of ligand n-doping to engender electrical conductivity in a porous 3D MOF, leading to tunable conductivity values that span over six orders of magnitude. Moreover, this work represents the first example of redox switching leading to reversible conductivity changes in a 3D MOF.

Redox-active ligands are used to reversibly tune electrical conductivity in a porous 3D metal–organic framework (MOF).     

A metal–organic framework/polymer derived catalyst containing single-atom nickel species for electrocatalysis

While metal–organic frameworks (MOF) alone offer a wide range of structural tunability, the formation of composites, through the introduction of other non-native species, like polymers, can further broaden their structure/property spectrum. Here we demonstrate that a polymer, placed inside the MOF pores, can support the collapsible MOF and help inhibit the aggregation of nickel during pyrolysis; this leads to the formation of single atom nickel species in the resulting nitrogen doped carbons, and dramatically improves the activity, CO selectivity and stability in electrochemical CO₂ reduction reaction. Considering the vast number of multifarious MOFs and polymers to choose from, we believe this strategy can open up more possibilities in the field of catalyst design, and further contribute to the already expansive set of MOF applications.

A metal–organic framework/polymer derived catalyst containing single-atom nickel species shows good performance for electroreduction of CO₂ to CO.     

Understanding the geometric diversity of inorganic and hybrid frameworks through structural coarse-graining

Much of our understanding of complex structures is based on simplification: for example, metal–organic frameworks are often discussed in the context of “nodes” and “linkers”, allowing for a qualitative comparison with simpler inorganic structures. Here we show how such an understanding can be obtained in a systematic and quantitative framework, combining atom-density based similarity (kernel) functions and unsupervised machine learning with the long-standing idea of “coarse-graining” atomic structure. We demonstrate how the latter enables a comparison of vastly different chemical systems, and we use it to create a unified, two-dimensional structure map of experimentally known tetrahedral AB₂ networks – including clathrate hydrates, zeolitic imidazolate frameworks (ZIFs), and diverse inorganic phases. The structural relationships that emerge can then be linked to microscopic properties of interest, which we exemplify for structural heterogeneity and tetrahedral density.

A coarse-graining approach enables structural comparisons across vastly different chemical spaces, from inorganic polymorphs to hybrid framework materials.     

A conductive metal–organic framework photoanode

We report the development of photosensitizing arrays based on conductive metal–organic frameworks (MOFs) that enable light harvesting and efficient charge separation. Zn₂TTFTB (TTFTB = tetrathiafulvalene tetrabenzoate) MOFs are deposited directly onto TiO₂ photoanodes and structurally characterized by pXRD and EXAFS measurements. Photoinduced interfacial charge transfer dynamics are investigated by combining time-resolved THz spectroscopy and quantum dynamics simulations. Sub-600 fs electron injection into TiO₂ is observed for Zn₂TTFTB–TiO₂ and is compared to the corresponding dynamics for TTFTB–TiO₂ analogues that lack the extended MOF architecture. Rapid electron injection from the MOF into TiO₂ is enhanced by facile migration of the hole away from the interfacial region. Holes migrate through strongly coupled HOMO orbitals localized on the tetrathiafulvalene cores of the columnar stacks of the MOF, whereas electrons are less easily transferred through the spiral staircase arrangement of phenyl substituents of the MOF. The reported findings suggest that conductive MOFs could be exploited as novel photosensitizing arrays in applications to slow, and thereby make difficult, photocatalytic reactions such as those required for water-splitting in artificial photosynthesis.

We report the development of photosensitizing arrays based on conductive metal–organic frameworks (MOFs) that enable light harvesting and efficient charge separation.     

Proton-conductive coordination polymer glass for solid-state anhydrous proton batteries

Designing solid-state electrolytes for proton batteries at moderate temperatures is challenging as most solid-state proton conductors suffer from poor moldability and thermal stability. Crystal–glass transformation of coordination polymers (CPs) and metal–organic frameworks (MOFs) via melt-quenching offers diverse accessibility to unique properties as well as processing abilities. Here, we synthesized a glassy-state CP, [Zn₃(H₂PO₄)₆(H₂O)₃](1,2,3-benzotriazole), that exhibited a low melting temperature (114 °C) and a high anhydrous single-ion proton conductivity (8.0 × 10⁻³ S cm⁻¹ at 120 °C). Converting crystalline CPs to their glassy-state counterparts via melt-quenching not only initiated an isotropic disordered domain that enhanced H⁺ dynamics, but also generated an immersive interface that was beneficial for solid electrolyte applications. Finally, we demonstrated the first example of a rechargeable all-solid-state H⁺ battery utilizing the new glassy-state CP, which exhibited a wide operating-temperature range of 25 to 110 °C.

Melt-quenched coordination polymer glass shows exclusive H⁺ conductivity (8.0 × 10⁻³ S cm⁻¹ at 120 °C, anhydrous) and optimal mechanical properties (42.8 Pa s at 120 °C), enables the operation of an all-solid-state proton battery from RT to 110 °C.     

Synthetic and computational assessment of a chiral metal–organic framework catalyst for predictive asymmetric transformation

Understanding and controlling molecular recognition mechanisms at a chiral solid interface is a continuously addressed challenge in heterogeneous catalysis. Here, the molecular recognition of a chiral peptide-functionalized metal–organic framework (MOF) catalyst towards a pro-chiral substrate is evaluated experimentally and in silico. The MIL-101 metal–organic framework is used as a macroligand for hosting a Noyori-type chiral ruthenium molecular catalyst, namely (benzene)Ru@MIL-101-NH-Gly-Pro. Its catalytic perfomance toward the asymmetric transfer hydrogenation (ATH) of acetophenone into R- and S-phenylethanol are assessed. The excellent match between the experimentally obtained enantiomeric excesses and the computational outcomes provides a robust atomic-level rationale for the observed product selectivities. The unprecedented role of the MOF in confining the molecular Ru-catalyst and in determining the access of the prochiral substrate to the active site is revealed in terms of highly face-specific host–guest interactions. The predicted surface-specific face differentiation of the prochiral substrate is experimentally corroborated since a three-fold increase in enantiomeric excess is obtained with the heterogeneous MOF-based catalyst when compared to its homogeneous molecular counterpart.

Understanding and controlling molecular recognition mechanisms at a chiral solid interface has been addressed in metal–organic framework catalysts for the asymmetric transfer hydrogenation reaction.     

Alloying a single and a double perovskite: a Cu+/2+ mixed-valence layered halide perovskite with strong optical absorption

Introducing heterovalent cations at the octahedral sites of halide perovskites can substantially change their optoelectronic properties. Yet, in most cases, only small amounts of such metals can be incorporated as impurities into the three-dimensional lattice. Here, we exploit the greater structural flexibility of the two-dimensional (2D) perovskite framework to place three distinct stoichiometric cations in the octahedral sites. The new layered perovskites A^I₄[Cu^II(Cu^IIn^III)_0.5Cl₈] (1, A = organic cation) may be derived from a Cu^I–In^III double perovskite by replacing half of the octahedral metal sites with Cu²⁺. Electron paramagnetic resonance and X-ray absorption spectroscopy confirm the presence of Cu²⁺ in 1. Crystallographic studies demonstrate that 1 represents an averaging of the Cu^I–In^III double perovskite and Cu^II single perovskite structures. However, whereas the highly insulating Cu^I–In^III and Cu^II perovskites are colorless and yellow, respectively, 1 is black, with substantially higher electronic conductivity than that of either endmember. We trace these emergent properties in 1 to intervalence charge transfer between the mixed-valence Cu centers. We further propose a tiling model to describe how the Cu⁺, Cu²⁺, and In³⁺ coordination spheres can pack most favorably into a 2D perovskite lattice, which explains the unusual 1 : 2 : 1 ratio of these cations found in 1. Magnetic susceptibility data of 1 further corroborate this packing model. The emergence of enhanced visible light absorption and electronic conductivity in 1 demonstrates the importance of devising strategies for increasing the compositional complexity of halide perovskites.

A novel 2D halide perovskite with stoichiometric quantities of Cu⁺, Cu²⁺, and In³⁺ in the inorganic slabs shows emergent properties not seen in Cu^II or Cu^I–In^III perovskites, including enhanced visible-light absorption and electronic conductivity.     

Cinnamal Sensing and Luminescence Color Tuning in a Series of Rare-Earth Metal−Organic Frameworks with Trans-1,4-cyclohexanedicarboxylate

Three isostructural metal–organic frameworks ([Ln₂(phen)₂(NO₃)₂(chdc)₂]·2DMF (Ln³⁺ = Y³⁺ for 1, Eu³⁺ for 2 or Tb³⁺ for 3; phen = 1,10-phenanthroline; H₂chdc = trans-1,4-cyclohexanedicarboxylic acid) were synthesized and characterized. The compounds are based on a binuclear block {M₂(phen)₂(NO₃)₂(OOCR)₄} assembled into a two-dime nsional square-grid network containing tetragonal channels with 26% total solvent-accessible volume. Yttrium (1)-, europium (2)- and terbium (3)-based structures emit in the blue, red and green regions, respectively, representing the basic colors of the standard RGB matrix. A doping of Eu³⁺ and/or Tb³⁺ centers into the Y³⁺-based phase led to mixed-metal compositions with tunable emission color and high quantum yields (QY) up to 84%. The bright luminescence of a suspension of microcrystalline 3 in DMF (QY = 78%) is effectively quenched by diluted cinnamaldehyde (cinnamal) solutions at millimolar concentrations, suggesting a convenient and analytically viable sensing method for this important chemical.     

Guest induced reversible on–off switching of elastic frustration in a 3D spin crossover coordination polymer with room temperature hysteretic behaviour

A binary reversible switch between low-temperature multi-step spin crossover (SCO), through the evolution of the population γ_HS(T) with high-spin (HS)-low-spin (LS) sequence: HS₁LS₀ (state 1) ↔ HS_2/3LS_1/3 (state 2) ↔ HS_1/2LS_1/2 (state 3) ↔ HS_1/3LS_2/3 (state 4) ↔ HS₀LS₁ (state 5), and complete one step hysteretic spin transition featuring 20 K wide thermal hysteresis centred at 290 K occurs in the three-dimensional (3D) Hofmann-type porous coordination polymer {Fe^II(3,8phen)[Au(CN)₂]₂}·xPhNO₂ (3,8phen = 3,8-phenanthroline, PhNO₂ = nitrobenzene), made up of two identical interpenetrated pcu-type frameworks. The included PhNO₂ guest (x = 1, 1·PhNO₂) acts as a molecular wedge between the interpenetrated 3D frameworks via PhNO₂-3,8phen intermolecular recognition and is the source of the strong elastic frustration responsible for the multi-step regime. Detailed X-ray single crystal analysis reflects competition between spatial periodicities of structurally inequivalent HS and LS SCO centres featuring: (i) symmetry breaking (state 3) with ⋯HS–LS⋯ ordering with γ_HS = 1/2; and (ii) occurrence of spatial modulation of the structure providing evidence for stabilization of local or aperiodic ordered mixed spin states for states 2 and 4 (with γ_HS ≈ 2/3) and 4 (with γ_HS ≈ 1/3), respectively. Below c.a. 20 K, structural and magnetic analyses show the photogeneration of a metastable HS*, state 6. The room-temperature single-step hysteretic regime appears with release of the guest (x = 0, 1) and the elastic frustration, and reversibly switches back to the original four-step behaviour upon guest re-adsorption. Both uncommon relevant SCO events meeting in the same material represent a rare opportunity to compare them in the frame of antiferro- and ferro-elastic transitions.

Reversible switch between a robust bistable two-state room temperature spin crossover (SCO) and its transformation in a four-stepped elastically frustrated SCO due to guest inclusion in a metal–organic Hofmann framework.     

Controlling multiple orderings in metal thiocyanate molecular perovskites Ax{Ni[Bi(SCN)6]}

We report four new A-site vacancy ordered thiocyanate double double perovskites, , A = K⁺, NH₄⁺, CH₃(NH₃)⁺ (MeNH₃⁺) and C(NH₂)₃⁺ (Gua⁺), including the first examples of thiocyanate perovskites containing organic A-site cations. We show, using a combination of X-ray and neutron diffraction, that the structure of these frameworks depends on the A-site cation, and that these frameworks possess complex vacancy-ordering patterns and cooperative octahedral tilts distinctly different from atomic perovskites. Density functional theory calculations uncover the energetic origin of these complex orders and allow us to propose a simple rule to predict favoured A-site cation orderings for a given tilt sequence. We use these insights, in combination with symmetry mode analyses, to show that these complex orders suggest a new route to non-centrosymmetric perovskites, and mean this family of materials could contain excellent candidates for piezo- and ferroelectric applications.

Metal thiocyanate hybrid perovskites can have multiple simultaneous complex orderings and combining these orderings appropriately can produce non-centrosymmetric structures.