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DOE OSTI2024

Chemical Bonding and the Role of Node-Induced Electron Confinement

The chemical bond is the cornerstone of chemistry, providing a conceptual framework to understand and predict the behavior of molecules in complex systems. However, the fundamental origin of chemical bonding remains controversial and has been responsible for fierce debate over the past century. Here, in this study, we present a unified theory of bonding, using a separation of electron delocalization effects from orbital relaxation to identify three mechanisms [node-induced confinement (typically associated with Pauli repulsion, though more general), orbital contraction, and polarization] that each modulate kinetic energy during bond formation. Through analysis of a series of archetypal bonds, we show that an exquisite balance of energy-lowering delocalizing and localizing effects are dictated simply by atomic electron configurations, nodal structure, and electronegativities. The utility of this unified bonding theory is demonstrated by its application to explain observed trends in bond strengths throughout the periodic table, including main group and transition metal elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Ab Initio Polariton Spectra of ZnTPP Molecules Collectively Coupled Inside an Optical Cavity

Exciton-polaritons are quasi-particles formed by the quantum mechanical hybridization of electronic and photonic excitations. Despite extensive investigations, a fundamental understanding of molecular polariton spectra and the polariton delocalization from an ab initio theoretical perspective remains elusive. We simulate experimentally measured linear transmission spectroscopy of many Zinc(II) tetraphenylporphyrin (ZnTPP) molecules collectively coupled to a cavity from first principles. Our theoretical approach incorporates many low-lying electronic excitations in ZnTPP molecules, as well as collective light-matter couplings between ZnTPP and the quantized radiation modes, both of which are shown to be the key to accurately recovering the experimental spectra. We further analyzed to what extent the polariton and dark states are delocalized over many molecules, for the first time, using fully ab initio descriptions of the molecules. We finally investigate the line width as a function of detuning, providing new theoretical insights into the experimentally observed motional narrowing behavior. Our work presents first-ofits- kind theoretical studies on molecular polariton spectra, offering a new perspective on molecular polariton formation in realistic ab initio molecular systems whose rich, many-state nature provides spectral features enabled by the high density of electronic states beyond simple quantum optics models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Chemolithoautotroph distributions across the subsurface of a convergent margin

Subducting oceanic crusts release fluids rich in biologically relevant compounds into the overriding plate, fueling subsurface chemolithoautotrophic ecosystems. To understand the impact of subsurface geochemistry on microbial communities, we collected fluid and sediments from 14 natural springs across a ~200 km transect across the Costa Rican convergent margin and performed shotgun metagenomics. The resulting 404 metagenome-assembled genomes (MAGs) cluster into geologically distinct regions based on MAG abundance patterns: outer forearc-only (25% of total relative abundance), forearc/arc-only (38% of total relative abundance), and delocalized (37% of total relative abundance) clusters. In the outer forearc, Thermodesulfovibrionia, Candidatus Bipolaricaulia, and Firmicutes have hydrogenotrophic sulfate reduction and Wood-Ljungdahl (WL) carbon fixation pathways. In the forearc/arc, Anaerolineae, Ca. Bipolaricaulia, and Thermodesulfovibrionia have sulfur oxidation, nitrogen cycling, microaerophilic respiration, and WL, while Aquificae have aerobic sulfur oxidation and reverse tricarboxylic acid carbon fixation pathway. Transformation-based canonical correspondence analysis shows that MAG distribution corresponds to concentrations of aluminum, iron, nickel, dissolved inorganic carbon, and phosphate. While delocalized MAGs appear surface-derived, the subsurface chemolithoautotrophic, metabolic, and taxonomic landscape varies by the availability of minerals/metals and volcanically derived inorganic carbon. Furthermore, the WL pathway persists across all samples, suggesting that this versatile, energy-efficient carbon fixation pathway helps shape convergent margin subsurface ecosystems.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Tuning the reactivity of carbon surfaces with oxygen-containing functional groups

Oxygen-containing carbons are promising supports and metal-free catalysts for many reactions. However, distinguishing the role of various oxygen functional groups and quantifying and tuning each functionality is still difficult. Here we investigate the role of Brønsted acidic oxygen-containing functional groups by synthesizing a diverse library of materials. By combining acid-catalyzed elimination probe chemistry, comprehensive surface characterizations, 15N isotopically labeled acetonitrile adsorption coupled with magic-angle spinning nuclear magnetic resonance, machine learning, and density-functional theory calculations, we demonstrate that phenolic is the main acid site in gas-phase chemistries and unexpectedly carboxylic groups are much less acidic than phenolic groups in the graphitized mesoporous carbon due to electron density delocalization induced by the aromatic rings of graphitic carbon. The methodology can identify acidic sites in oxygenated carbon materials in solid acid catalyst-driven chemistry.

Zhou, Jiahua↗

DOE OSTI2025

Effective bands and band-like electron transport in amorphous solids

The localization of electrons caused by atomic disorder is a well-known phenomenon. However, under which circumstances electrons remain delocalized and retain band-like characteristics even when the crystal structure is completely absent, as found in certain amorphous solids, is less well understood. Here, in this study, to probe this phenomenon, we develop a fully first-principles description of the electronic structure and charge transport in amorphous materials, which combines a representation of the amorphous state as a composite (ensemble) of local environments and the state-of-the-art many-body electronic structure methods. Using amorphous In 2 O 3 as an example, we demonstrate the accuracy of our approach in reproducing the band-like nature of the conduction electrons as well as their disorder-limited mobility. Our approach reveals the physical origins responsible for the electron delocalization and survival of the band dispersions despite the absence of long-range order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Attosecond spectroscopy of size-resolved water clusters

Electron dynamics in water are of fundamental importance for a broad range of phenomena, but their real-time study faces numerous conceptual and methodological challenges. Here, in this paper, we introduce attosecond size-resolved cluster spectroscopy and build up a molecular-level understanding of the attosecond electron dynamics in water. We measure the effect that the addition of single water molecules has on the photoionization time delays of water clusters. We find a continuous increase of the delay for clusters containing up to four to five molecules and little change towards larger clusters. We show that these delays are proportional to the spatial extension of the created electron hole, which first increases with cluster size and then partially localizes through the onset of structural disorder that is characteristic of large clusters and bulk liquid water. These results indicate a previously unknown sensitivity of photoionization delays to electron-hole delocalization and indicate a direct link between electronic structure and attosecond photoionization dynamics. Our results offer new perspectives for studying electron-hole delocalization and its attosecond dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Quantitative relationships between film morphology, charge carrier dynamics, and photovoltaic performance in bulk-heterojunction binary vs. ternary acceptor blends

Addressing pertinent and perplexing questions regarding why nonfullerene acceptors (NFAs) promote higher power conversion efficiencies (PCEs) than traditional fullerenes and how photoactive bulk heterojunction (BHJ) film morphology, charge photogeneration, and recombination dynamics dictate solar cell performance have stimulated many studies of polymer solar cells (PSCs), yet quantitative relationships remain limited. Better understanding in these areas offers the potential to advance materials design and device engineering, afford higher PCEs, and ultimate commercialization. Here we probe quantitative relationships between BHJ film morphology, charge carrier dynamics, and photovoltaic performance in model binary and ternary blend systems having a wide bandgap donor polymer, a fullerene, and a promising NFA. We show that optimal PC 71 BM incorporation in a PBDB-TF:ITIC-Th binary system matrix retains the original π-face-on orientation, ITIC-Th crystallinity and BHJ film crystallite dimensions, and reduces film upper surface ITIC-Th segregation. Such morphology changes together simultaneously increase hole (μ h ) and electron (μ e ) mobilities, facilitate light-activated ITIC-Th to PC 71 BM domain electron delocalization, reduce free charge carrier (FC) bimolecular recombination (BR) within PBDB-TF:ITIC-Th mixed regions, and increase FC extraction pathways viaPBDB-TF:PC 71 BM pairs. The interplay of these effects yields significantly enhanced inverted cell short-circuit current density (J SC ), fill factor (FF), and PCE. Unexpectedly, we also find that excessive PC 71 BM in the PBDB-TF:ITIC-Th binary system alters the PBDB-TF orientation to π-edge-on, increases large scale PC 71 BM-rich aggregations and BHJ upper surface PC 71 BM composition. Further, these morphology changes increase parasitic decay processes such as intersystem crossing from photoexcited PC 71 BM, compromising the J SC , FF, and PCE metrics. ITIC-Th X-ray diffraction reveals a unique sidechain-dominated molecular network with previously unknown sidechain-end group stacking, rationalizing the STEM and GIWAXS results, photophysics, and the high μ e . DFT computation reveals charge transfer networks within ITIC-Th crystallites, supporting excited-state electron delocalization from ITIC-Th to PC 71 BM. This structure–property understanding leads to a newly reported NFA blend with PCE near 17%.

14 SOLAR ENERGY↗

DOE OSTI2024

High-resolution infrared spectroscopy of jet cooled cyclobutyl in the α-CH stretch region: large-amplitude puckering dynamics in a 4-membered ring radical

We report gas-phase cyclobutyl radical (c-C 4 H 7 ) is generated at a rotational temperature of T rot = 26(1) K in a slit-jet discharge mixture of 70% Ne/30% He and 0.5–0.6% cyclobromobutane (c-C 4 H 7 Br). A fully rovibrationally resolved absorption spectrum of the α-CH stretch fundamental band between 3062.9 cm −1 to 3075.7 cm −1 is obtained and analyzed, yielding first precision structural and dynamical information for this novel radical species. The α-CH stretch band origin is determined to be 3068.7887(4) cm −1 , which implies only a modest (≈0.8 cm −1 ) blue shift from rotationally unresolved infrared spectroscopic studies of cyclobutyl radicals in liquid He droplets [ A. R. Brown, P. R. Franke and G. E. Douberly, J. Phys. Chem. A , 2017, 121 , 7576–7587]. Of particular dynamical interest, a one-dimensional potential energy surface with respect to the ring puckering coordinate is computed at CCSD(T)/ANO2 level of theory and reveals a double minimum C s puckered geometry, separated by an exceedingly shallow planar C 2v transition state barrier (E barr ≈ 1 cm −1 ). Numerical solutions on this double minimum potential yield a zero-point energy for the ground state (E zero-point ≈ 27 cm −1 ) greatly in excess of the interconversion barrier. This is indicative of highly delocalized, large amplitude motion of the four-membered ring structure, for which proper vibrationally averaging of the moment of inertia tensor reproduces the experimentally determined inertial defect remarkably well. Finally, intensity alternation in the experimental spectrum due to nuclear spin statistics upon exchange of three indistinguishable H atom pairs (IH = ½) matches K a + K c = even : odd = 36 : 28 predictions, implying that the unpaired electron in the radical center lies in an out-of-plane p π orbital. Thus, high-resolution infrared spectroscopy provides first experimental confirmation of a shallow double minimum ring puckering potential with a highly delocalized ground state wave function peaked at a planar C 2v transition state geometry consistent with a cyclobutyl π radical.

Chemistry↗

DOE OSTI2021

Oscillatory Spreading and Inertia in Power Grids

The increase in variable renewable generators (VRGs) in power systems has altered the dynamics from a historical experience. VRGs introduce new sources of power oscillations, and the stabilizing response provided by synchronous generators (SGs, e.g., natural gas, coal, etc.), which help avoid some power fluctuations, will lessen as VRGs replace SGs. These changes have led to the need for new methods and metrics to quickly assess the likely oscillatory behavior for a particular network without performing computationally expensive simulations. This work studies the impact of a critical dynamical parameter - the inertia value - on the rest of a power system's oscillatory response to representative VRG perturbations. We use a known localization metric in a novel way to quantify the number of nodes responding to a perturbation and the magnitude of those responses. This metric allows us to relate the spread and severity of a system's power oscillations with inertia. We find that as inertia increases, the system response to node perturbations transitions from localized (only a few close nodes respond) to delocalized (many nodes across the network respond). We introduce a heuristic computed from the network Laplacian to relate this oscillatory transition to the network structure. We show that our heuristic accurately describes the spread of oscillations for a realistic power-system test case. Using a heuristic to determine the likely oscillatory behavior of a system given a set of parameters has wide applicability in power systems, and it could decrease the computational workload of planning and operation.

dynamical systems↗

DOE OSTI2022

Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d 1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d 1 MOPs to be suitable for nearly eliminating all energetic delocalization and static correlation errors. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization and static correlation errors within a non-empirical framework.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Magnon-mediated qubit coupling determined via dissipation measurements

Controlled interaction between localized and delocalized solid-state spin systems offers a compelling platform for on-chip quantum information processing with quantum spintronics. Hybrid quantum systems (HQSs) of localized nitrogen-vacancy (NV) centers in diamond and delocalized magnon modes in ferrimagnets—systems with naturally commensurate energies—have recently attracted significant attention, especially for interconnecting isolated spin qubits at length-scales far beyond those set by the dipolar coupling. However, despite extensive theoretical efforts, there is a lack of experimental characterization of the magnon-mediated interaction between NV centers, which is necessary to develop such hybrid quantum architectures. Here, we experimentally determine the magnon-mediated NV–NV coupling from the magnon-induced self-energy of NV centers. Our results are quantitatively consistent with a model in which the NV center is coupled to magnons by dipolar interactions. This work provides a versatile tool to characterize HQSs in the absence of strong coupling, informing future efforts to engineer entangled solid-state systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Simulating dirty bosons on a quantum computer

Abstract Quantum computers hold the potential to unlock new discoveries in complex quantum systems by enabling the simulation of physical systems that have heretofore been impossible to implement on classical computers due to intractability. A system of particular interest is that of dirty bosons, whose physics highlights the intriguing interplay of disorder and interactions in quantum systems, playing a central role in describing, for instance, ultracold gases in a random potential, doped quantum magnets, and amorphous superconductors. Here, we demonstrate how quantum computers can be used to elucidate the physics of dirty bosons in one and two dimensions. Specifically, we explore the disorder-induced delocalized-to-localized transition using adiabatic state preparation. In one dimension, the quantum circuits can be compressed to small enough depths for execution on currently available quantum computers. In two dimensions, the compression scheme is no longer applicable, thereby requiring the use of large-scale classical state vector simulations to emulate quantum computer performance. In addition, simulating interacting bosons via emulation of a noisy quantum computer allowed us to study the effect of quantum hardware noise on the physical properties of the simulated system. Our results suggest that scaling laws control how noise modifies observables versus its strength, the circuit depth, and the number of qubits. Moreover, we observe that noise impacts the delocalized and localized phases differently. A better understanding of how noise alters the observed properties of the simulated system is essential for leveraging near-term quantum devices for simulation of dirty bosons, and indeed for condensed matter systems in general.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Glassy quantum nuclear pasta in neutron star crusts

We conduct a comprehensive survey of the shape parameter space of the nuclear pasta phases in neutron star crusts by conducting three-dimensional Hartree-Fock + BCS calculations. Spaghetti, waffles, lasagna, bicontinuous phases and cylindrical holes occupy local minima in the resulting constant-pressure Gibbs energy surfaces, implying multiple geometries coexist at a given depth. Notably, the bicontinuous phase, in which both the neutron gas and nuclear matter extend continuously in all dimensions appears over a large depth range. Our results support the idea that nuclear pasta is a glassy system. At a characteristic temperature, of order 10 8 – 10 9 K, different phases may become frozen into domains whose sizes we estimate to be 1–50 times the lattice spacing and over which the local density and electron fraction can vary. Above this temperature, very little long-range order exists and matter is an amorphous solid. Electron scattering off domain boundaries may contribute to the disorder resistivity of the pasta phases. Annealing of the domains may occur during cooling; repopulating of local minima during crustal heating might lead to temperature-dependent transport properties in the deep crust layers. We identify four regions distinguished by whether pasta is the true ground state, and whether the pasta structure allows delocalization of protons. The whole pasta region can occupy up to 70% of the crust by mass and 25% by thickness, and the layer in which protons are delocalized could occupy 45% of the crust mass and 15% of its thickness.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Magic-Angle Twisted Bilayer Graphene as a Topological Heavy Fermion Problem

Magic-angle (θ=1.05°) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local flat-band orbitals (f) centered at the AA-stacking regions are responsible to the localization. A set of extended topological semimetallic conduction bands (c), which are at small energetic separation from the local orbitals, are responsible to the delocalization and transport. The topological flat bands of the BM model appear as a result of the hybridization of f and c electrons. This model then provides a new perspective for the strong correlation physics, which is now described as strongly correlated f electrons coupled to nearly free c electrons—we hence name our model as the topological heavy fermion model. Using this model, we obtain the U(4) and U(4)×U(4) symmetries of Refs. [1–5] as well as the correlated insulator phases and their energies. Simple rules for the ground states and their Chern numbers are derived. Moreover, features such as the large dispersion of the charge ±1 excitations [2,6,7], and the minima of the charge gap at the Γ M point can now, for the first time, be understood both qualitatively and quantitatively in a simple physical picture. Our mapping opens the prospect of using heavy-fermion physics machinery to the superconducting physics of MATBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Phonon-Induced Localization of Excitons in Molecular Crystals from First Principles

The spatial extent of excitons in molecular systems underpins their photophysics and utility for optoelectronic applications. Phonons are reported to lead to both exciton localization and delocalization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in particular, how localized states form, the role of specific vibrations, and the relative importance of quantum and thermal nuclear fluctuations. Here, we present a first-principles study of these phenomena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons, exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory, the ab initio GW-Bethe-Salpeter equation approach, finite-difference, and path integral techniques. In this study, we find that for pentacene zero-point nuclear motion causes uniformly strong localization, with thermal motion providing additional localization only for Wannier-Mott-like excitons. Anharmonic effects drive temperature-dependent localization, and, while such effects prevent the emergence of highly delocalized excitons, we explore the conditions under which these might be realized

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2022

Organic Macromolecular materials for Efficient Transport Properties in Light-Energy Conversion Applications. Final Report

We are grateful for the Department of Energy for support of this research related to the improvement of power conversion efficiency of organic photovoltaic architectures over the years. As we noted at the beginning and now, the fundamental photophysical pathways that connect the absorption of light to the production of charge carriers remain elusive in spite of continuing experimental and theoretical efforts. Our investigations were directed toward gaining information about the mechanism of this ultrafast, long-range charge separation in photovoltaic systems with non-fullerene acceptors. This problem is still of high importance for the organic photovoltaics because solving this problem will allow us to minimize the contribution of the geminate recombination and trapping the charges in bound charge transfer states. Extremely low charge separation driving energy specific to non-fullerene acceptor systems reduces the energy loss in organic photovoltaic cells making them competitive with inorganic and perovskite photovoltaic systems. A major accomplishment of this study was to detail the long-range ballistic charge separation in donor-non-fullerene acceptor photovoltaic systems. We have successfully probed the spatial structure of ultrafast long-range (~40nm) ballistic charge separation in donor-non-fullerene acceptor photovoltaic system. We performed a systematic investigation of the delocalized states in their connection to the efficient long-range charge separation using the pulse pair interferometric near-field microscopy method. This method possesses unique capability of detecting coherent effects with spatial resolution of few tens of nanometers. These measurements allowed us the determination of delocalized excitations locally in a thin film photovoltaic system and to be connected to the long-range charge separation and the power conversion efficiency. We also investigated long-lived coupled triplet pairs in a singlet fission process for the possibility of concerted extraction of two electrons from triplet entangled states. New experimental and theoretical approaches of the concerted double electron extraction were carried out. The impact of this work is the development of important structure-property relationships to the design criteria of more efficient organic photovoltaic cells in accordance with the BES mission.

14 SOLAR ENERGY↗

DOE OSTI2023

Biomimetic Light Harvesting Complexes Based on Self-Assembled Dye-DNA Nanostructures (Final Technical Report)

A fundamental limitation in the development of artificial molecular light harvesting structures is that generally if one places pigment molecules close enough to achieve very high energy transfer efficiency and absorbance cross section, the dyes interact in such a way that self-quenching occurs. This limits both the optical cross section and the overall efficiency of light capture in such systems. Nature overcomes this problem and achieves efficient energy transfer without self-quenching by controlling the environment, vibration characteristics, orientation and dynamics of the pigments involved in light harvesting. Natural light harvesting systems have evolved highly intricate chromophore architectures of protein-bound organic molecules that absorb and funnel solar energy with high efficiency and fast transfer rates using elegant excitonic circuitries. Nature achieves this precise control over the properties of pigment complexes by using specific proteins as templates to guide the formation of very well-defined pigment aggregates, groups of pigment molecules that are in close enough contact to undergo excitonic interactions resulting in new electronic properties that were not present in the monomer. In synthetic systems, pigment aggregates are well known, and J-aggregates and H-aggregates have been long studied for their unique properties. In Nature, the chlorosomes of green bacteria form what appear to be classical J-aggregates and the light harvesting complexes of purple nonsulfur bacteria form ring structures that have many of the properties of J-aggregates such as a red-shifted absorbance spectrum and excited states that are delocalized over multiple pigment molecules. These photosynthetic systems leverage the spectral and enhanced transport properties of J-like aggregates to achieve fast exciton transport within the antenna and thus high light-harvesting efficiency. The close interaction of the pigments results in substantial electronic coupling that lifts the degeneracy of excitonic states and therefore modifies the absorption and emission spectra of the monomer. In the case of J-aggregation, lower energy excitonic states acquire significant oscillator strength, resulting in a characteristic bathochromic shift of the absorption and fluorescence and often superradiant delocalized exciton states.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2021

Fracture Network Localization Preceding Catastrophic Failure in Triaxial Compression Experiments on Rocks

We quantify the spatial distribution of fracture networks throughout six in situ X-ray tomography triaxial compression experiments on crystalline rocks at confining stresses of 5–35 MPa in order to quantify how fracture development controls the final macroscopic failure of the rock, a process analogous to those that control geohazards such as earthquakes and landslides. Tracking the proportion of the cumulative volume of fractures with volumes >90th percentile to the total fracture volume, ∑ v 90 / v t o t indicates that the fracture networks tend to increase in localization toward these largest fractures for up to 80% of the applied differential stress. The evolution of this metric also matches the evolution of the Gini coefficient, which measures the deviation of a population from uniformity. These results are consistent with observations of localizing low magnitude seismicity before large earthquakes in southern California. In both this analysis and the present work, phases of delocalization interrupt the general increase in localization preceding catastrophic failure, indicating that delocalization does not necessarily indicate a reduction of seismic hazard. However, the proportion of the maximum fracture volume to the total fracture volume does not increase monotonically. Experiments with higher confining stress tend to experience greater localization. To further quantify localization, we compare the geometry of the largest fractures, with volumes >90th percentile, to the best fit plane through these fractures immediately preceding failure. The r 2 scores and the mean distance of the fractures to the plane indicate greater localization in monzonite than in granite. The smaller mean mineral diameter and lower confining stress in the granite experiments may contribute to this result. Tracking these various metrics of localization reveals a close association between macroscopic yielding and the acceleration of fracture network localization. Near yielding, ∑ v 90 / v t o t and the Gini coefficient increase while the mean distance to the final failure plane decreases. Macroscopic yielding thus occurs when the rate of fracture network localization increases.

58 GEOSCIENCES↗