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Register a new userUnderstanding the Geometric Diversity of Inorganic and Hybrid Frameworks through Structural Coarse-Graining
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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, by 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 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.
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Here we demonstrate that significant progress in this area may be achieved by introducing structural elements that form hydrogen bonds with environment. Considering several examples of hybrid framework materials with different structural ordering containing protonated sulfonium cation H3S+ that forms strong hydrogen bonds with electronegative halogen anions (Cl-, F-), we found that hydrogen bonding increases the structural stability of the material and may be used for tuning electronic states near the bandgap. We suggest that such a behavior has a universal character and should be observed in hybrid inorganic-organic framework materials containing protonated cations. This effect may serve as a viable route for optoelectronic and photovoltaic applications.
A fundamental challenge in materials science pertains to elucidating the relationship between stoichiometry, stability, structure, and property. Recent advances have shown that machine learning can be used to learn such relationships, allowing the stability and functional properties of materials to be accurately predicted. However, most of these approaches use atomic coordinates as input and are thus bottlenecked by crystal structure identification when investigating novel materials. Our approach solves this bottleneck by coarse-graining the infinite search space of atomic coordinates into a combinatorially enumerable search space. The key idea is to use Wyckoff representations -- coordinate-free sets of symmetry-related positions in a crystal -- as the input to a machine learning model. Our model demonstrates exceptionally high precision in discovering new stable materials, identifying 1,558 materials that lie below the known convex hull of previously calculated materials from just 5,675 ab-initio calculations. Our approach opens up fundamental advances in computational materials discovery.
We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic, Markovian jump process with a specific structure that lends itself naturally to coarse-graining. A perturbative analysis yields a reduced stochastic jump process that approximates the coarse-grained dynamics of the original system. This leads to a non-trivial fluctuation relation that is approximately satisfied by the coarse-grained dynamics. We illustrate our results by computing the large deviations of a particular stochastic jump process. Our results highlight the possibility that observed deviations from fluctuation relations might be due to the presence of unobserved degrees of freedom.
One-dimensional inorganic nanotubes hold promise for technological applications due to their distinct physical/chemical properties, but so far advancements have been hampered by difficulties in producing single-wall nanotubes with a well-defined radius. In this work we investigate, based on Density Functional Theory (DFT), the formation mechanism of 135 different inorganic nanotubes formed by the intrinsic self-rolling driving force found in asymmetric 2D Janus sheets. We show that for isovalent Janus sheets, the lattice mismatch between inner and outer atomic layers is the driving force behind the nanotube formation, while in the non-isovalent case it is governed by the difference in chemical bond strength of the inner and outer layer leading to steric effects. From our pool of candidate structures we have identified more than 100 tubes with a preferred radius below 35 {AA}, which we hypothesize can display unique properties compared to their parent 2D monolayers. Simple descriptors have been identified to accelerate the discovery of small-radius tubes and a Bayesian regression approach has been implemented to assess the uncertainty in our predictions on the radius.
Suppose we have a pair of information channels, $kappa_{1},kappa_{2}$, with a common input. The Blackwell order is a partial order over channels that compares $kappa_{1}$ and $kappa_{2}$ by the maximal expected utility an agent can obtain when decisions are based on the channel outputs. Equivalently, $kappa_{1}$ is said to be Blackwell-inferior to $kappa_{2}$ if and only if $kappa_{1}$ can be constructed by garbling the output of $kappa_{2}$. A related partial order stipulates that $kappa_{2}$ is more capable than $kappa_{1}$ if the mutual information between the input and output is larger for $kappa_{2}$ than for $kappa_{1}$ for any distribution over inputs. A Blackwell-inferior channel is necessarily less capable. However, examples are known where $kappa_{1}$ is less capable than $kappa_{2}$ but not Blackwell-inferior. We show that this may even happen when $kappa_{1}$ is constructed by coarse-graining the inputs of $kappa_{2}$. Such a coarse-graining is a special kind of pre-garbling of the channel inputs. This example directly establishes that the expected value of the shared utility function for the coarse-grained channel is larger than it is for the non-coarse-grained channel. This contradicts the intuition that coarse-graining can only destroy information and lead to inferior channels. We also discuss our results in the context of information decompositions.
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