We explore three seemingly disparate but related avenues of inquiry: expanding what is known about the properties of the poles of the Ihara zeta function, determining what information about a graph is recoverable from its Ihara zeta function, and strengthening the ties between the Ihara zeta functions of graphs which are related to each other through common operations on graphs. Using the singular value decomposition of directed edge matrices, we give an alternate proof of the bounds on the poles of Ihara zeta functions. We then give an explicit formula for the inverse of directed edge matrices and use the inverse to demonstrate that the sum of the poles of an Ihara zeta function is zero. Next we discuss the information about a graph recoverable from its Ihara zeta function and prove that the girth of a graph as well as the number of cycles whose length is the girth can be read directly off of the reciprocal of the Ihara zeta function. We demonstrate that a graph's chromatic polynomial cannot in general be recovered from its Ihara zeta function and describe a method for constructing families of graphs which have the same chromatic polynomial but different Ihara zeta functions. We also show that a graph's Ihara zeta function cannot in general be recovered from its chromatic polynomial. Then we make the deletion of an edge from a graph less jarring (from the perspective of Ihara zeta functions) by viewing it as the limit as k goes to infinity of the operation of replacing the edge in the original graph we wish to delete with a walk of length k. We are able to prove that the limit of the Ihara zeta functions of the resulting graphs is in fact the Ihara zeta function of the original with the edge deleted. We also improve upon the bounds on the poles of the Ihara zeta function by considering digraphs whose adjacency matrices are directed edge matrices

With the HTEM, an open online database containing experimental synthesis and characterization data of thin film inorganic materials, Talley et al. (2021) lay a foundation for a new era of high-throughput materials design.

Future lithium (Li) energy storage technologies, in particular solid-state configurations with a Li metal anode, opens up the possibility of using cathode materials that do not necessarily contain Li in its as-made state. To accelerate the discovery and design of such materials, we develop a general, chemically, and structurally agnostic methodology for identifying the optimal Li sites in any crystalline material. For a given crystal structure, we attempt multiple Li insertions at symmetrically in-equivalent positions by analyzing the electronic charge density obtained from first-principles density functional theory. In this report, we demonstrate the effectiveness of this procedure in successfully identifying the positions of the Li ion in well-known cathode materials using only the empty host (charged) material as guidance. Furthermore, applying the algorithm to over 2000 candidate cathode empty host materials we obtain statistics of Li site preferences to guide future developments of novel Li-ion cathode materials, particularly for solid-state applications.

Structure–property relationships form the basis of many design rules in materials science, including synthesizability and long-term stability of catalysts, control of electrical and optoelectronic behavior in semiconductors, as well as the capacity of and transport properties in cathode materials for rechargeable batteries. The immediate atomic environments (i.e., the first coordination shells) of a few atomic sites are often a key factor in achieving a desired property. Some of the most frequently encountered coordination patterns are tetrahedra, octahedra, body and face-centered cubic as well as hexagonal close packed-like environments. Here, we showcase the usefulness of local order parameters to identify these basic structural motifs in inorganic solid materials by developing classification criteria. We introduce a systematic testing framework, the Einstein crystal test rig, that probes the response of order parameters to distortions in perfect motifs to validate our approach. Subsequently, we highlight three important application cases. First, we map basic crystal structure information of a large materials database in an intuitive manner by screening the Materials Project (MP) database (61,422 compounds) for element-specific motif distributions. Second, we use the structure-motif recognition capabilities to automatically find interstitials in metals, semiconductor, and insulator materials. Our Interstitialcy Finding Tool (InFiT) facilitates high-throughput screenings of defect properties. Third, the order parameters are reliable and compact quantitative structure descriptors for characterizing diffusion hops of intercalants as our example of magnesium in MnO2-spinel indicates. Finally, the tools developed in our work are readily and freely available as software implementations in the pymatgen library, and we expect them to be further applied to machine-learning approaches for emerging applications in materials science.

Surface adsorption is a crucial step in numerous processes, including heterogeneous catalysis, where the adsorption of key species is often used as a descriptor of efficiency. We present here an automated adsorption workflow for semiconductors which employs density functional theory calculations to generate adsorption data in a high-throughput manner. Starting from a bulk structure, the workflow performs an exhaustive surface search, followed by an adsorption structure construction step, which generates a minimal energy landscape to determine the optimal adsorbate-surface distance. An extensive set of energy-based, charge-based, geometric, and electronic descriptors tailored toward catalysis research are computed and saved to a personal user database. The application of the workflow to zinc telluride, a promising CO₂ reduction photocatalyst, is presented as a case study to illustrate the capabilities of this method and its potential as a material discovery tool.

To accelerate the development of ion conducting materials, we present a general graph-theoretic analysis framework for ion migration in any crystalline structure. The nodes of the graph represent metastable sites of the migrating ion and the edges represent discrete migration events between adjacent sites. Starting from a collection of possible metastable migration sites, the framework assigns a weight to the edges by calculating the individual migration energy barriers between those sites. Connected pathways in the periodic simulation cell corresponding to macroscopic ion migration are identified by searching for the lowest-cost cycle in the periodic migration graph. To exemplify the utility of the framework, we present the automatic analyses of Li migration in different polymorphs of VO(PO4), with the resulting identification of two distinct crystal structures with simple migration pathways demonstrating overall <300 meV migration barriers.

In addition to being the core quantity in density-functional theory, the charge density can be used in many tertiary analyses in materials sciences from bonding to assigning charge to specific atoms. The charge density is data-rich since it contains information about all the electrons in the system. With the increasing prevalence of machine-learning tools in materials sciences, a data-rich object like the charge density can be utilized in a wide range of applications. The database presented here provides a modern and user-friendly interface for a large and continuously updated collection of charge densities as part of the Materials Project. In addition to the charge density data, we provide the theory and code for changing the representation of the charge density which should enable more advanced machine-learning studies for the broader community.

The local structure of a transition metal (TM) ion is a function of cation elements and valence states. More than that, in this work, by employing a trove of first-principles data of TM oxides, the local structures of TM cations are statistically analyzed to extract detailed information about cation site preference, bond length, site structural distortion, and cation magnetization. It is found that cation radius alone poorly describes the local structure of a transition metal oxide, while the statistics of coordination number as well as the TMO bond length distribution, especially that of the 3d TMs, can provide comprehensive knowledge for understanding the behavior of TM elements. Based on these statistics, the interplay of site distortion due to the Jahn-Teller effect, cation site similarity, and a new set of ionic radii are all obtained to chart the "persona" of transition metal ions in solids.

Band structures for electrons, phonons, and other quasiparticles are often an important aspect of describing the physical properties of periodic solids. Most commonly, energy bands are computed along a one-dimensional path of high-symmetry points and line segments in reciprocal space (the “k-path”), which are assumed to pass through important features of the dispersion landscape. However, existing methods for choosing this path rely on tabulated lists of high-symmetry points and line segments in the first Brillouin zone, determined using different symmetry criteria and unit cell conventions. Here we present a new “on-the-fly” symmetry-based approach to obtaining paths in reciprocal space that attempts to address the previous limitations of these conventions. Given a unit cell of a magnetic or nonmagnetic periodic solid, the site symmetry groups of points and line segments in the irreducible Brillouin zone are obtained from the total space group. The elements in these groups are used alongside general and maximally inclusive high-symmetry criteria to choose segments for the final k-path. A smooth path connecting each segment is obtained using graph theory. This new framework not only allows for increased flexibility and user convenience but also identifies notable overlooked features in certain electronic band structures. In addition, a more intelligent and efficient method for analyzing magnetic materials is also enabled through proper accommodation of magnetic symmetry.