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At least 1,153 records · Page 64

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

In the last 50 years there has been a tremendous progress in solving numerically the Navier-Stokes equations using finite differences, finite elements, spectral, and even meshless methods. Yet, in many real cases, we still cannot incorporate seamlessly (multi-fidelity) data into existing algorithms, and for industrial-complexity applications the mesh generation is time consuming and still an art. Moreover, solving ill-posed problems (e.g., lacking boundary conditions) or inverse problems is often prohibitively expensive and requires different formulations and new computer codes. Here, we employ physics-informed neural networks (PINNs), encoding the governing equations directly into the deep neural network via automatic differentiation, to overcome some of the aforementioned limitations for simulating incompressible laminar and turbulent flows. We develop the Navier-Stokes flow nets (NSFnets) by considering two different mathematical formulations of the Navier-Stokes equations: the velocity-pressure (VP) formulation and the vorticity-velocity (VV) formulation. Since this is a new approach, we first select some standard benchmark problems to assess the accuracy, convergence rate, computational cost and flexibility of NSFnets; analytical solutions and direct numerical simulation (DNS) databases provide proper initial and boundary conditions for the NSFnet simulations. The spatial and temporal coordinates are the inputs of the NSFnets, while the instantaneous velocity and pressure fields are the outputs for the VP-NSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VV-NSFnet. This is unsupervised learning and, hence, no labeled data are required beyond boundary and initial conditions and the fluid properties. The residuals of the VP or VV governing equations, together with the initial and boundary conditions, are embedded into the loss function of the NSFnets. No data is provided for the pressure to the VP-NSFnet, which is a hidden state and is obtained via the incompressibility constraint without extra computational cost. Unlike the traditional numerical methods, NSFnets inherit the properties of neural networks (NNs), hence the total error is composed of the approximation, the optimization, and the generalization errors. Here, we empirically attempt to quantify these errors by varying the sampling (“residual”) points, the iterative solvers, and the size of the NN architecture. For the laminar flow solutions, we show that both the VP and the VV formulations are comparable in accuracy but their best performance corresponds to different NN architectures. The initial convergence rate is fast but the error eventually saturates to a plateau due to the dominance of the optimization error. For the turbulent channel flow, we show that NSFnets can sustain turbulence at , but due to expensive training we only consider part of the channel domain and enforce velocity boundary conditions on the subdomain boundaries provided by the DNS data base. We also perform a systematic study on the weights used in the loss function for balancing the data and physics components, and investigate a new way of computing the weights dynamically to accelerate training and enhance accuracy. In the last part, we demonstrate how NSFnets should be used in practice, namely for ill-posed problems with incomplete or noisy boundary conditions as well as for inverse problems. We obtain reasonably accurate solutions for such cases as well without the need to change the NSFnets and at the same computational cost as in the forward well-posed problems. As a result, we also present a simple example of transfer learning that will aid in accelerating the training of NSFnets for different parameter settings.

97 MATHEMATICS AND COMPUTING↗

Nuclear explosion monitoring network design considerations

Design of an efficient monitoring network requires information on the type and size of releases to be detected, the accuracy and reliability of the measuring equipment, and the desired network performance. This work provides a scientific basis for optimizing or minimizing networks of 133 Xe samplers to achieve a desired performance level for different levels of release. The approach of this work varies the density of sampling locations to find optimal location subsets, and to explore the properties of variations of those subsets – how crucial is a specific subset; are substitutions problematic? The choice of possible station locations is arbitrary but constrained to some extent by the location of islands, land masses, difficult topography (mountains, etc.) and the places where infrastructure exists to run and support a sampler. Performance is evaluated using hypothetical releases and atmospheric transport models that cover an entire year.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Link statistics of dislocation network during strain hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

Crystal plasticity↗

Network structure in alteration layer of boroaluminosilicate glass formed by aqueous corrosion

Exogenously-added LiCl has been shown to slightly accelerate the corrosion rate of a boroaluminosilicate glass called International Simple Glass (ISG) in aqueous solutions over forward- and residual-rate regimes, while KCl and CsCl impede. To understand the effect of exogenously added electrolytes on resulting hydrous species and the network structure of alteration layers, infrared spectroscopy was implemented. It was found that the fraction of molecular water relative to the surface-bound hydroxyl species is lower in the KCl and CsCl conditions compared to the LiCl and pure water conditions. An approximation for the spectral features of the thin surface films from an experimentally-obtained specular-reflectance infrared (SR-IR) spectrum was proposed; results indicate no significant difference in the Si-O bonding network of the alteration layers formed in the presence of exogenously added LiCl, KCl and CsCl. Furthermore, the observed change in corrosion rates might be linked to the relative abundance of molecular water species in the porous network, rather than the silicate bonding structure.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

A Convolutional Neural Network Model for Battery Capacity Fade Curve Prediction using Early Life Data

Herein, early prediction of battery performance degradation trends can facilitate research of new materials and cell designs, rapid deployment of batteries in real-world applications, timely replacement of batteries in critical applications, and even the secondary use market. In this study, we design a convolutional neural network model to predict the entire battery capacity fade curve - a critical indicator of battery performance degradation - using first 100 cycles of data (~ three weeks of testing). We use the discharge voltage-capacity curves as input to the model and automate the feature extraction process through the convolutional layers of the network. Our approach can predict the per cycle capacity fade rate and rollover cycle (knee point) in the capacity fade curve, which indicate the onset of rapid capacity decay. On the publicly available graphite/LiFePO 4 battery dataset, optimized networks predict the capacity fade curves, rollover cycle, and end of life with 3.7% (worst-case), 19%, and 17% mean absolute percentage errors, respectively.

25 ENERGY STORAGE↗

The influence of preexisting host rock damage on fault network localization

The transition from stable to unstable fracture propagation occurs when fractures begin to interact and link. Thus, fracture network coalescence controls how rocks and engineered structures fail. Here, to constrain the factors that influence localization in shear zones under brittle conditions, we build discrete element method models with a rough fault embedded in a shear zone. We add varying numbers of diffuse, randomly-placed weaknesses to examine the influence of diffuse damage on fracture network localization. The number of weaknesses controls the localization behavior of the fault network and the final fault geometry. We quantify localization using the Gini coefficient of the fracture volume, which measures the nonuniformity in a population. Each model generally increases in localization toward failure. However, models with more diffuse damage experience delocalization phases that are superimposed on the overall trend of increasing localization. The observed link between delocalization and host rock damage may help explain the varying localization of low magnitude seismicity in southern California. Models with more diffuse damage produce more complex fault geometries comprised of several parallel strands of wing cracks. The propagation of these wing cracks reduces the shear stress acting on the model boundaries, indicating that this fracture development increases the mechanical efficiency of the system.

58 GEOSCIENCES↗

Enriching OpenStreetMap network data for transportation applications: Insights into the impact of urban congestion on accessibility

OpenStreetMap (OSM) data is a valuable open-source resource for various transportation, traffic, and planning applications. However, OSM network data lack operating traffic speed information, which is critical for transport planning and operations. Addressing this shortcoming, this study leverages commercial vendor data (to serve as ground truth) with exogenous, open-source variables characterizing local transport infrastructure, land use, and demographic information to predict average congested traffic speeds on OSM networks. Three machine-learning models were tested and estimated for OSM links with and without speed limit information in the Denver metropolitan region. Among these, XGBoost performed best, with mean absolute errors of 3.27 and 3.62 mph for links with and without speed limits, respectively. The developed models accurately predicted traffic speeds for different hours and days of the week compared to ground truth data. Using these predicted speeds, drive accessibility scores were computed for the Denver region for different time periods using the Mobility Energy Productivity (MEP) metric to understand the impact of congestion on energy-efficient accessibility. Results show that congestion-adjusted drive accessibility can be significantly lower compared to accessibility calculated using free flow speeds. Specifically, weekday evening hours saw a 42 % drop in accessibility due to reduced speeds, particularly around downtown Denver. Across the Denver metro region, approximately half as many opportunities and jobs are accessible in under 20 min by car during the evening peak period relative to free flow conditions. These findings underscore the importance of using congestion-adjusted operating speeds rather than speed limits in accessibility calculations, as reliance on speed limits can substantially overestimate energy-efficient drive accessibility in large, car-centric cities susceptible to significant congestion. In conclusion, the methodology presented here could further enrich OSM network data, making them useful for an even broader range of transportation applications.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Lie–Poisson Neural Networks (LPNets): Data-based computing of Hamiltonian systems with symmetries

An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson bracket and the Hamiltonian. Hamiltonian systems with symmetries, whose paradigm examples are the Lie–Poisson systems, have been shown to describe a broad category of physical phenomena, from satellite motion to underwater vehicles, fluids, geophysical applications, complex fluids, and plasma physics. The Poisson bracket in these systems comes from the symmetries, while the Hamiltonian comes from the underlying physics. We view the symmetry of the system as primary, hence the Lie–Poisson bracket is known exactly, whereas the Hamiltonian is regarded as coming from physics and is considered not known, or known approximately. Using this approach, we develop a network based on transformations that exactly preserve the Poisson bracket and the special functions of the Lie–Poisson systems (Casimirs) to machine precision. We present two flavors of such systems: one, where the parameters of transformations are computed from data using a dense neural network (LPNets), and another, where the composition of transformations is used as building blocks (G-LPNets). We also show how to adapt these methods to a larger class of Poisson brackets. We apply the resulting methods to several examples, such as rigid body (satellite) motion, underwater vehicles, a particle in a magnetic field, and others. The methods developed in this paper are important for the construction of accurate data-based methods for simulating the long-term dynamics of physical systems.

Data-based modeling↗

Isomerization kinetics of azobenzene crosslinked to a liquid crystal polymer network

Azobenzene is an important chromophore having numerous applications that are a direct implication of its ability to change shape upon irradiation with a suitable wavelength. Here, in this study, photoisomerization kinetics of a diacrylate azobenzene molecule (A3MA) cross-linked to a liquid crystal polymer network (LCN) is investigated. Isomerization experiments were conducted on planar LCN thin films with varying cross-linking densities for a fixed azobenzene concentration. The experiments were conducted at approximately 26 °C, which is significantly below each film’s glass transition temperature. The forward trans-cis and reverse cis-trans isomerization slows down in crosslinked azobenzene liquid crystal polymer networks (ALCNs) as compared to a solution and an uncrosslinked polymer mixture. The observed slowdown is due to the reduction in the free volume and increased steric hindrances with an increase in crosslinking. A single-term first-order kinetics rate equation is known to describe the isomerization kinetics in solutions or uncrosslinked mixtures while the same form fails to represent the reaction kinetics in moderate to highly cross-linked ALCNs. Our results for the first time indicate that a two-term first-order reaction rate is an accurate way to describe the forward trans-cis and reverse thermal cis-trans isomerization in crosslinked azobenzene liquid crystal polymer networks. In addition, the effect of film thickness and incident intensities on the reaction kinetics is investigated. Finally, the two-term isomerization kinetics is incorporated into a finite element photo-chemo-mechanical model to reveal the consequent slowdown in the actuation response of ALCN films. The current findings will be of particular interest to theoreticians and experimentalists alike, for it will help predict and understand accurately the responses of azobenzene-based coatings, and actuators and may have potential applications in underwater soft robotics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The impact of the third O 2 addition reaction network on ignition delay times of neo-pentane

In this work, we studied the oxidation of neo-pentane by combining experiments, theoretical calculations, and mechanistic developments to elucidate the impact of the 3rd O 2 addition reaction network on ignition delay time predictions. The experiments are based on photoionization mass spectrometry in jet-stirred and time-resolved flow reactors allowing for sensitive detection of the keto-hydroperoxide (KHP) and keto-dihydroperoxide (KDHP) intermediates. With neo-pentane exhibiting a unique symmetric molecular structure, which consequently results only in single KHP and KDHP isomers, theoretical calculations of ionization and fragment appearance energies and of absolute photoionization cross sections enabled the unambiguous identification and quantification of the KHP intermediate. Its temperature and time-resolved profiles together with calculated and experimentally observed KHP-to-KDHP signal ratios were compared to simulation results based on a newly developed mechanism that describes the 3rd O 2 addition reaction network. A satisfactory agreement has been observed between the experimental data points and the simulation results, thus adding confidence to the model's overall performance. Finally, this mechanism was used to predict ignition delay times reported previously in shock tube and rapid compression machine experiments (J. Bugler et al., Combust. Flame 163 (2016) 138–156). While the model accurately reproduces the experimental data, simulations with and without the 3rd O 2 addition reaction network included reveal only a negligible effect on the predicted ignition delay times at 10 and 20 atm. According to model calculations, low temperatures and high pressures promote the importance of the 3rd O2 addition reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Networks and interfaces as catalysts for polymer materials innovation

Autonomous experimental systems offer a compelling glimpse into a future where closed-loop, iterative cycles—performed by machines and guided by artificial intelligence (AI) and machine learning (ML)—play a foundational role in materials research and development. This perspective draws attention to the roles of networks and interfaces—of and between humans and machines—for the purpose of generating knowledge and accelerating innovation. Polymers, a class of materials with massive global impact, present a unique opportunity for the application of informatics and automation to pressing societal challenges. To develop these networks and interfaces in polymer science, the Community Resource for Innovation in Polymer Technology (CRIPT)—a polymer data ecosystem based on novel polymer data model, representation, search, and visualization technologies—is introduced. The ongoing co-design efforts engage stakeholders in industry, academia, and government to uncover rapidly actionable, high-impact opportunities to build networks, bridge interfaces, and catalyze innovation in polymer technology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electrochemical Control of Magnetism on the Breathing Kagome Network of Li x ScMo 3 O 8

Controlling properties within a given functional inorganic material structure type is often accomplished through tuning the electronic occupation, which is in turn dictated by the elemental composition determined at the time of material preparation. We employ electrochemical control of the lithium content, with associated electronic occupancy control, to vary the magnetic properties of a material where a kagome-derived network of Mo 3 triangles carry the spin. In this case, Li is electrochemically inserted into LiScMo 3 O 8 , a layered compound containing a breathing Mo kagome network. Up to two additional Li can be inserted into LiScMo 3 O 8 , transforming it into Li 3 ScMo 3 O 8 . Li 2 ScMo 3 O 8 prepared by electrochemical lithiation is compared to the quantum spin liquid candidate compound Li 2 ScMo 3 O 8 prepared through high-temperature solid-state methods, which has a slightly different structural stacking sequence but a similar kagome-derived network. Magnetic measurements are supported by first-principles calculations, showing that electrons remain localized on the Mo clusters throughout the doping series. As x is varied in Li x ScMo 3 O 8 , the measurements and calculations reveal the evolution from a diamagnetic band insulator at x = 1 to a geometrically frustrated magnet at x = 2, back to a diamagnetic insulator at x = 3. These results indicate a likelihood of strong coupling between the degree of Li disorder and charge/magnetic ordering over the Mo 3 clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Covalent Adaptable Networks: Reprocessable Cross-Linked Polymers

Thermoset polymers have desirable properties, such as excellent thermal and mechanical stability, but their covalent cross-links typically prevent repair or recycling. By enabling and controlling dynamic exchange reactions within polymer networks, their covalent bonds rearrange and allow the polymer to be reshaped. These viscoelastic polymer networks, now known as covalent adaptable networks (CANs), are an important frontier for improving plastic circularity, as well as for designing valuable stimuli-responsive materials. This Review describes the history of CANs, dating back to the early days of polymer science, and the evolution of their classification and nomenclature. A comprehensive survey of dynamic reactions and linkage chemistries is provided, as well as methods to characterize and reprocess CANs. Beyond straightforward reprocessing, many advanced applications of CANs and their composites are now emerging. Lastly, we provide perspective on how the development of new chemistries, strategies to control stimuli-responsive bond exchange and mechanical properties, and a deep understanding of exchange reactions will advance this field toward scalable, sustainable, and high-value materials.

Sun, Molly [Northwestern University, Evanston, IL ↗

Pose Classification Using Three-Dimensional Atomic Structure-Based Neural Networks Applied to Ion Channel–Ligand Docking

The identification of promising lead compounds showing pharmacological activities toward a biological target is essential in early stage drug discovery. With the recent increase in available small-molecule databases, virtual high-throughput screening using physics-based molecular docking has emerged as an essential tool in assisting fast and cost-efficient lead discovery and optimization. However, the best scored docking poses are often suboptimal, resulting in incorrect screening and chemical property calculation. We address the pose classification problem by leveraging data-driven machine learning approaches to identify correct docking poses from AutoDock Vina and Glide screens. To enable effective classification of docking poses, we present two convolutional neural network approaches: a three-dimensional convolutional neural network (3D-CNN) and an attention-based point cloud network (PCN) trained on the PDBbind refined set. We demonstrate the effectiveness of our proposed classifiers on multiple evaluation data sets including the standard PDBbind CASF-2016 benchmark data set and various compound libraries with structurally different protein targets including an ion channel data set extracted from Protein Data Bank (PDB) and an in-house KCa3.1 inhibitor data set. Our experiments show that excluding false positive docking poses using the proposed classifiers improves virtual high-throughput screening to identify novel molecules against each target protein compared to the initial screen based on the docking scores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Robust Neural Network for Extracting Dynamics from Electrostatic Force Microscopy Data

Advances in scanning probe microscopy (SPM) methods such as time-resolved electrostatic force microscopy (trEFM) now permit the mapping of fast local dynamic processes with high resolution in both space and time, but such methods can be time-consuming to analyze and calibrate. Here, we design and train a regression neural network (NN) that accelerates and simplifies the extraction of local dynamics from SPM data directly in a cantilever-independent manner, allowing the network to process data taken with different cantilevers. We validate the NN’s ability to recover local dynamics with a fidelity equal to or surpassing conventional, more time-consuming, calibrations using both simulated and real microscopy data. We apply this method to extract accurate photoinduced carrier dynamics on n = 1 butylammonium lead iodide, a halide perovskite semiconductor film that is of interest for applications in both solar photovoltaics and quantum light sources. Lastly, we use SHapley Additive exPlanations to evaluate the robustness of the trained model, confirm its cantilever-independence, and explore which parts of the trEFM signal are important to the network.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces

Here, this paper focuses on the development of multifidelity modeling approaches using neural network surrogates, where training data arising from multiple model forms and resolutions are integrated to predict high-fidelity response quantities of interest at lower cost. We focus on the context of quantum chemistry and the integration of information from multiple levels of theory. Important foundations include the use of symmetry function-based atomic energy vector constructions as feature vectors for representing structures across families of molecules and single-fidelity neural network training capabilities that learn the relationships needed to map feature vectors to potential energy predictions. These foundations are embedded within several multifidelity topologies that decompose the high-fidelity mapping into model-based components, including sequential formulations that admit a general nonlinear mapping across fidelities and discrepancy-based formulations that presume an additive decomposition. Methodologies are first explored and demonstrated on a pair of simple analytical test problems and then deployed for potential energy prediction for C 5 H 5 using B2PLYP-D3/6-311++G(d,p) for high-fidelity simulation data and Hartree–Fock 6-31G for low-fidelity data. For the common case of limited access to high-fidelity data, our computational results demonstrate that multifidelity neural network potential energy surface constructions achieve roughly an order of magnitude improvement, either in terms of test error reduction for equivalent total simulation cost or reduction in total cost for equivalent error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling Liquid Water by Climbing up Jacob’s Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn–Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric–isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗