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Hybrid n = 1 Ruddlesden-Popper perovskites with aromatic ammonium cations like benzylammonium (BzA) and phenethylammonium (PEA) have been shown to adopt polar structures and exhibit ferroelectricity, but many of the examples discovered thus far contain either Pb or Cd. Here, we describe the synthesis and structural characteriza-tion of four layered halide double perovskites: (BzA)4AgBiBr8, (PEA)4AgBiBr8, (BzA)4AgInCl8, and (PEA)4AgInCl8. In all four compounds the inorganic layers exhibit a chessboard ordering of Ag+ and Bi3+/In3+ and the layers stack in a coherent pattern that maintains the ordering over three-dimensional space. The octahedra sur-rounding Ag+ show a large axial compression, which results in much shorter bonds to the terminal halide ions than to the bridging halide ions, whereas the bismuth- and indium-centered octahedra show only small distortions. There appears to be a competition between polar distortions of the octahedra and octahedral tilting, both of which can optimize hydrogen bonding interactions between the ammonium cations and the inorganic layers. Unlike the Pb- or Cd-containing analogs, the double perovskites seem to favor patterns of octahedral tilting that suppress po-lar ordering of the organic cations. The packing of the organic cations depends on both their conformational flexi-bility and the lateral dimensions of the inorganic layer. These forces favor intra-layer edge-to-face interaction be-tween aromatic rings in the three of the four compounds. The lone exception is (PEA)4AgBiBr8, which forms weak inter-layer edge-to-face interactions between aromatic rings and slip-stacked packing within each organic layer. 

A symmetry mode analysis yields 47 symmetrically distinct patterns of octahedral tilting in hybrid organic–inorganic layered perovskites that adopt then= 1 Ruddlesden–Popper (RP) structure. The crystal structures of compounds belonging to this family are compared with the predictions of the symmetry analysis. Approximately 88% of the 140 unique structures have symmetries that agree with those expected based on octahedral tilting alone, while the remaining compounds have additional structural features that further lower the symmetry, such as asymmetric packing of bulky organic cations, distortions of metal-centered octahedra or a shift of the inorganic layers that deviates from thea/2 +b/2 shift associated with the RP structure. The structures of real compounds are heterogeneously distributed amongst the various tilt systems, with only 9 of the 47 tilt systems represented. No examples of in-phase ψ-tilts about theaand/orbaxes of the undistorted parent structure were found, while at the other extreme ∼66% of the known structures possess a combination of out-of-phase ϕ-tilts about theaand/orbaxes and θ-tilts (rotations) about thecaxis. The latter combination leads to favorable hydrogen bonding interactions that accommodate the chemically inequivalent halide ions within the inorganic layers. In some compounds, primarily those that contain either Pb²⁺or Sn²⁺, favorable hydrogen bonding interactions can also be achieved by distortions of the octahedra in combination with θ-tilts. 

We develop a framework for sampling from discrete distributions $$\mu$$ on the hypercube $$\{\pm 1\}^n$$ by sampling from continuous distributions supported on $$\mathbb{R}^n$$ obtained by convolution with spherical Gaussians. We show that for well-studied families of discrete distributions $$\mu$$, convolving $$\mu$$ with Gaussians yields well-conditioned log-concave distributions, as long as the variance of the Gaussian is above an $O(1)$ threshold. We then reduce the task of sampling from $$\mu$$ to sampling from Gaussian-convolved distributions. Our reduction is based on a stochastic process widely studied under different names: backward diffusion in diffusion models, and stochastic localization. We discretize this process in a novel way that allows for high accuracy and parallelism. As our main application, we resolve open questions Anari, Hu, Saberi, and Schild raised on the parallel sampling of distributions that admit parallel counting. We show that determinantal point processes can be sampled via RNC algorithms, that is in time $$\log(n)^{O(1)}$$ using $$n^{O(1)}$$ processors. For a wider class of distributions, we show our framework yields Quasi-RNC sampling, i.e., $$\log(n)^{O(1)}$$ time using $$n^{O(\log n)}$$ processors. This wider class includes non-symmetric determinantal point processes and random Eulerian tours in digraphs, the latter nearly resolving another open question raised by prior work. Of potentially independent interest, we introduce and study a notion of smoothness for discrete distributions that we call transport stability, which we use to control the propagation of error in our framework. Additionally, we connect transport stability to constructions of optimally mixing local random walks and concentration inequalities. 

Mesoporous polyetherimides are important high-performance polymers. Conventional strategies to prepare porous polyetherimides, and polyimide in general, are based on covalent organic framework or thermolysis of sacrificial polymers. The former produces micropores due to intrinsically crosslinked microstructures, and the latter results in macropores because of a blowing effect by the sacrificial polymers. The preparation of mesopores remains a challenge. Here we have prepared mesoporous polyetherimide films by hydrolyzing polylactide- b -polyetherimide- b -polylactide (AIA). Controlled by molecular weight and volume fraction of polylactide in AIA, the porous films exhibit an average pore width of 24 nm. The mesoporous polyetherimide films exhibit a storage modulus of ∼1 GPa at ambient temperatures. This work advances the chemistry of high-performance polymers and provides an alternative strategy to prepare mesoporous polymers, enabling potential use as high-performance membranes for separation, purification, and electrochemistry. 

Two novel ternary compounds from the pseudobinary CH3NH3X–AgX (X = Br, I) phase diagrams are reported. CH3NH3AgBr2 and CH3NH3Ag2I3 were synthesized via solid state sealed tube reactions and the crystal structures were determined through a combination of single crystal and synchrotron X-ray powder diffraction. Structurally, both compounds consist of one-dimensional ribbons built from silvercentered tetrahedra. The structure of CH3NH3AgBr2 possesses orthorhombic Pnma symmetry and is made up of zig-zag chains where each silver bromide tetrahedron shares two edges with neighboring tetrahedra. The tetrahedral coordination of silver is retained in CH3NH3Ag2I3, which has monoclinic P21/m symmetry, but the change in stoichiometry leads to a greater degree of edge-sharing connectivity within the silver iodide chains. With band gaps of 3.3 eV (CH3NH3Ag2I3) and 4.0 eV (CH3NH3AgBr2) the absorption onsets of the ternary phases are significantly blue shifted from the binary silver halides, AgBr and AgI, due in part to the decrease in electronic dimensionality. The compounds are stable for at least one month under ambient conditions and are thermally stable up to approximately 200 1C. Density functional theory calculations reveal very narrow valence bands and moderately disperse conduction bands with Ag 5s character. Bond valence calculations are used to analyze the hydrogen bonding between methylammonium cations and coordinatively unsaturated halide ions. The crystal chemistry of these compounds helps to explain the dearth of iodide double perovskites in the literature.