Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “descriptors”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Chespa: Streamlining Expansive Chemical Space Evaluation of Molecular Sets

Thousands of chemical properties can be calculated for small molecules, which can be used to place the molecules within the context of a broader “chemical space.” These definitions vary based on compounds of interest and the goals for the given chemical space definition. Here, we introduce a customizable (i.e., modular) Python module, chespa, built to easily assess different chemical space definitions through cluster-ing of compounds in these spaces and visualize trends of these clusters. To demonstrate this, chespa currently streamlines prediction of vari-ous molecule descriptors (predicted chemical properties, molecular substructures, AI-based chemical space, and chemical class ontology) in order to test 6 different chemical space definitions. Furthermore, we investigated how these varying definitions trend with mass spectrometry (MS)-based observability, i.e., the ability of a molecule to be observed with MS (e.g., as a function of the molecule ionizability), using an example data set from the U.S. EPA's Non-Targeted Analysis Collaborative Trial (ENTACT), where blinded samples had been analyzed previously, providing 1,398 data points. Improved understanding of observability would offer many advantages in small molecule identifica-tion, such as (i) a priori selection of experimental conditions based on suspected sample composition, (ii) the ability to reduce the number of candidate structures during compound identification by removing those less likely to ionize, and, in turn, (iii) a reduced false discovery rate and increased confidence in identifications. Factors controlling observability are not fully understood, making prediction of this property non-trivial and a prime candidate for chemical space analysis. Chespa is available at github.com/pnnl/chespa.

Nunez, Jamie↗
DOE OSTI2024

Ice Phase Classification Made Easy with Score-Based Denoising

Accurate identification of ice phases is essential for understanding various physicochemical phenomena. However, such classification for structures simulated with molecular dynamics is complicated by the complex symmetries of ice polymorphs and thermal fluctuations. For this purpose, both traditional order parameters and data-driven machine learning approaches have been employed, but they often rely on expert intuition, specific geometric information, or large training data sets. In this work, we present an unsupervised phase classification framework that combines a score-based denoiser model with a subsequent model-free classification method to accurately identify ice phases. Further, the denoiser model is trained on perturbed synthetic data of ideal reference structures, eliminating the need for large data sets and labeling efforts. The classification step utilizes the smooth overlap of atomic position (SOAP) descriptors as the atomic fingerprint, ensuring Euclidean symmetries and transferability to various structural systems. Our approach achieves a remarkable 100% accuracy in distinguishing ice phases of test trajectories using only seven ideal reference structures of ice phases as model inputs. This demonstrates the generalizability of the score-based denoiser model in facilitating phase identification for complex molecular systems. The proposed classification strategy can be broadly applied to investigate structural evolution and phase identification for a wide range of materials, offering new insights into the fundamental understanding of water and other complex systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A Comprehensive Machine Learning Model for Metal–Ligand Binding Prediction: Applications in Chemistry and Biology

A machine-learning (ML) model that predicts metal–ligand binding constants was developed using the open-source Chemprop software. The model was trained on over 30,000 experimental log K 1 values, which include both protonation and metal–ligand stability constants, comprising over 3500 ligands and 10 2 metal ions from 73 total elements, thus generalizing beyond existing limited approaches, which focus only on specific metals or ligand families. The best-performing model included a combination of SMILES-based molecular representations along with descriptors for the metal ion and experimental conditions. It had an external test R 2 value of 0.942, and MAE value of 0.834. A “SMILES-only” simpler version also produced accurate predictions and preserved the binding trends, serving as a quick and easily accessible alternative for users without computational expertise. The SMILES-only model performed comparably to density functional theory (DFT) calculations but utilized a fraction of the computational resources. The model was successfully applied across diverse domains, including bioinorganic chemistry, heavy metal remediation, and sensor development and demonstrated its effectiveness as a rapid and reliable screening tool for both academic and industrial uses.

Ligands↗
DOE OSTI2025

Cluster-Graph Fingerprinting: A Framework for Quantitative Analysis of Machine-Learned Interatomic Model Training and Simulation Data

Machine-learned interatomic models represent a significant advancement in simulation methods, extending the predictive ability of first-principles methods to previously inaccessible length and time scales. However, the data-driven nature of these models can lead to difficult-to-detect errors that can compromise prediction accuracy. To address this challenge, we introduce a novel fingerprinting approach based on the Chebyshev Interaction Model for Efficient Simulation (ChIMES) ML-IAM graph-based descriptor. Our strategy enables efficient and statistically rigorous analysis of system configurations used in ML-IAM training and those generated by their application, e.g., in molecular dynamics simulations. We demonstrate that these fingerprints can effectively assess novelty of a configuration relative to an existing data set and determine dissimilarity among individual configurations, which are two key tasks in workflows for active learning-based ML-IAM training, data set curation, and on-the-fly uncertainty quantification.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Stability Analysis of Substituted Cobaltocenium [Bis(cyclopentadienyl)cobalt(III)] Employing Chemistry-Informed Neural Networks

Cobaltocenium derivatives are promising components of the anion exchange membranes due to their excellent thermal and alkaline stability under the operating conditions of a fuel cell. Here we present an efficient modeling approach of assessing the chemical stability of substituted cobaltocenium CoCp 2 + based on the computed electronic structure enhanced by machine learning techniques. Within the aqueous environment, the positive charge of the metal cation is balanced by the hydroxide anion through formation of the CoCp 2 + OH¯ complexes, whose dissociation is studied within the implicit solvent employing density functional theory. The data set of about 118 species based on 42 substituent groups characterized by a range of electron- donating (ED) and electron-withdrawing (EW) properties is constructed and analyzed. Given 12 carefully chosen chemistry-informed descriptors of the complexes and relevant fragments, the stability of the complexes is found to strongly correlate with the energies of the highest occupied and lowest unoccupied molecular orbitals, modulated by a switching function of the Hirshfeld charge. The latter is used as a measure of the electron withdrawing-donating character of the substituents. Based on this observation from the conventional regression analysis, two fully connected, feed-forward neural network (FNN) models with different unit structures, called the chemistry-informed (CINN) and the quadratic (QNN) neural networks, are developed. Both models predict the bond dissociation energies of the cobaltocenium complexes with mean relative errors less than 5.40% and average absolute errors less than 0.94 kcal/mol. The results show the potential of QNN to efficiently capture more complex relationships. Here, the concept of incorporating the domain (chemical) knowledge/insight into the neural network structure paves the way to applications of machine learning techniques with small data sets, ultimately leading to better predictive models compared to the conventional regression analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Machine Learning Predictions of Simulated Self-Diffusion Coefficients for Bulk and Confined Pure Liquids

Diffusion properties of bulk fluids have been predicted using empirical expressions and machine learning (ML) models, suggesting that predictions of diffusion also should be possible for fluids in confined environments. The ability to quickly and accurately predict diffusion in porous materials would enable new discoveries and spur development in relevant technologies such as separations, catalysis, batteries, and subsurface applications. Here in this work, we apply artificial neural network (ANN) models to predict the simulated self-diffusion coefficients of real liquids in both bulk and pore environments. The training data sets were generated from molecular dynamics (MD) simulations of Lennard-Jones particles representing a diverse set of 14 molecules ranging from ammonia to dodecane over a range of liquid pressures and temperatures. Planar, cylindrical, and hexagonal pore models consisted of walls composed of carbon atoms. Our simple model for these liquids was primarily used to generate ANN training data, but the simulated self-diffusion coefficients of bulk liquids show excellent agreement with experimental diffusion coefficients. ANN models based on simple descriptors accurately reproduced the MD diffusion data for both bulk and confined liquids, including the trend of increased mobility in large pores relative to the corresponding bulk liquid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Density Functional Tight-Binding Models for Band Structures of Transition-Metal Alloys and Surfaces across the d -Block

First-principles electronic structure simulations are an invaluable tool for understanding chemical bonding and reactions. While machine-learning models such as interatomic potentials significantly accelerate the exploration of potential energy surfaces, electronic structure information is generally lost. Particularly in the field of heterogeneous catalysis, simulated electron band structures provide fundamental insights into catalytic reactivity. This ab initio knowledge is preserved in semiempirical methods such as density functional tight binding (DFTB), which extend the accessible computational length and time scales beyond first-principles approaches. In this paper here we present Shell-Optimized Atomic Confinement (SOAC) DFTB electronic-part-only parametrizations for bulk and surface band structures of all d-block transition metals that enable efficient predictions of electronic descriptors for large structures or high-throughput studies on complex systems outside the computational reach of density functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Many-Body Benchmark of Electronic Charge and Spin Densities for Li 1–x NiO 2

Accurate benchmarks are particularly important for highly correlated oxides as mean-field approximations often fail to describe the subtle balance of charge transfer and magnetism in these materials with an accuracy comparable to experimental needs. Here we present accurate diffusion Monte Carlo (DMC) results of the electronic charge and spin densities for the tunable highly correlated oxide Li 1–x NiO 2 for x = 0, 1/2, and 1. To enable quantitative comparisons, we introduce a robust density-partitioning scheme, extending Voronoi analysis to assign atomic charges from spatially noisy DMC densities. We then benchmark common approximations used in density functional theory (DFT). Comparison against DMC shows that r 2 SCAN delivers the most balanced performance across charge, spin, and radial density descriptors, nearly reproducing DMC results for LiNiO 2 and apical Ni sites in Li 0.5 NiO 2 . Hybrid functionals (PBE0, SCAN0) perform unexpectedly poorly, and PBE + U + V yields inconsistent trends between charge and spin densities. Therefore, the r 2 SCAN functional minimizes errors relative to DMC while capturing the variable valence of the Ni ion and also retaining the computational efficiency of DFT for large-scale simulations of the tunable structural and electronic phases of Li1−xNiO2. Our study highlights the importance of accurate benchmarking of the fundamental quantities involved in DFT to select appropriate DFT approximations in order to advance the predictive modeling of charge-transfer-driven phenomena in correlated electron systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Development of Density Functional Tight-Binding Parameters Using Relative Energy Fitting and Particle Swarm Optimization

We provide a strategy to optimize density functional tight-binding (DFTB) parameterization for the calculation of the structures and properties of organic molecules consisting of hydrogen, carbon, nitrogen, and oxygen. We utilize an objective function based on similarity measurements and the Particle Swarm Optimization (PSO) method to find an optimal set of parameters. This objective function considers not only the common DFTB descriptors of binding energies and atomic forces but also incorporates relative energies of isomers into the fitting procedure for more chemistry-driven results. The quality in the description of the binding energies and atomic forces is measured based on the Ballester similarity index and relative energies through a similarity index induced by the Levenshtein edit distance to quantify the correct energetic order of isomers. Training and testing datasets were created to include all relevant chemical functional groups. Finally, the accuracy of this strategy is assessed, and its range of applicability is discussed by comparison against our previous parameterization. The improved performance of the new DFTB parameterization is validated with respect to the density functional theory large datasets QM-9 and ANI-1, where excellent agreement is found between the structures and properties available in these datasets, and the ones obtained with DFTB.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A Multiple Filter Based Neural Network Approach to the Extrapolation of Adsorption Energies on Metal Surfaces for Catalysis Applications

Computational catalyst discovery involves the development of microkinetic reactor models based on estimated parameters determined from density functional theory (DFT). For complex surface chemistries, the number of reaction intermediates can be very large, and the cost of calculating the adsorption energies by DFT for all surface intermediates even for one active site model can become prohibitive. In this paper, we have identified appropriate descriptors and machine learning models that can be used to predict a significant part of these adsorption energies given data on the rest of them. Furthermore, our investigations also included the case when the species data used to train the predictive model are of different size relative to the species the model tries to predict—this is an extrapolation in the data space which is typically difficult with regular machine learning models. Due to the relative size of the available data sets, we have attempted to extrapolate from the larger species to the smaller ones in the current work. Here, we have developed a neural network based predictive model that combines an established additive atomic contribution based model with the concepts of a convolutional neural network that, when extrapolating, achieves a statistically significant improvement over the previous models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Density Matrix Implementation of the Fermi–Löwdin Orbital Self-Interaction Correction Method

The Fermi–Löwdin orbital self-interaction correction (FLOSIC) method effectively provides a transformation from canonical orbitals to localized Fermi–Löwdin orbitals which are used to remove the self-interaction error in the Perdew–Zunger (PZ) framework. This transformation is solely determined by a set of points in space, called Fermi–Löwdin descriptors (FODs), and the occupied canonical orbitals or the density matrix. In this work, we provide a detailed workflow for the implementation of the FLOSIC method for removal of self-interaction error in DFT calculations in an orbital-by-orbital basis that takes advantage of the unitary invariant nature of the FLOSIC method. In this way, it is possible to cast the self-consistent energy minimization at fixed FODs in the same manner than standard Kohn–Sham with one additional term in the Kohn–Sham Hamiltonian that introduces the PZ self-interaction correction. Each energy minimization iteration is divided in two substeps, one for the density matrix and one for the FODs. Expressions for the effective Kohn–Sham matrix and FOD gradients are provided such that its implementation is suitable for most electronic structure codes. Here, we analyze the convergence characteristics of the algorithm and present applications for the evaluation of NMR shielding constants and real-time time-dependent DFT simulations based on the Liouville–von Neumann equation to calculate excitation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Inferring the Energetics of CO 2 –Aniline Adduct Formation from Vibrational Spectroscopy

Control of atmospheric CO 2 is an important contemporary scientific and engineering challenge. Towards this goal, the reaction of CO 2 with amines to form carbamate bonds is an established method for CO 2 capture. However, controllable reversal of this reaction remains difficult and requires tuning the energetics of the carbamate bond. Through IR spectroscopy, we show that a characteristic frequency observed upon carbamate formation varies as a function of the substituent’s Hammett parameter for a family of para- substituted anilines. We present computational evidence that the vibrational frequency of the adducted CO 2 serves as a predictor of the energy of formation of the carbamate. Electron donating groups typically enhance the driving force of carbamate formation by transferring more charge to the adducted CO 2 and thus increasing the occupancy of the anti-bonding orbital in the carbon-oxygen bonds. Increased occupancy of the anti-bonding orbital within adducted CO 2 indicates a weaker bond, leading to a red shift in the characteristic carbamate frequency. As a result, our work serves the large field of CO 2 capture research where spectroscopic observables, such as IR frequencies, are more easily obtainable and can stand in as a descriptor of driving forces.

Amines↗
DOE OSTI2024

Comparison of Machine Learning Approaches for Prediction of the Equivalent Alkane Carbon Number for Microemulsions Based on Molecular Properties

The chemical properties of oils are vital in the design of microemulsion systems. The hydrophilic–lipophilic difference equation used to predict microemulsions’ phase behavior expresses the oils’ physiochemical properties as the equivalent alkane carbon number (EACN). The experimental determination of EACN requires knowledge of the temperature dependence of the microemulsion system and the effects of different surfactant concentrations. Thus, the experimental determination is time-intensive and tedious, requiring days to months for proper separations. Furthermore, the experiments require high purity of chemicals because microemulsions are sensitive to impurities. Our work focuses on the quick and reliable predictions of the EACN with machine learning (ML) models. Due to the immaturity of ML chemical predictions, we compare three graph neural networks (GNNs) and a gradient-boosted tree algorithm, known as XGBoost. The GNNs use the molecular structures represented as simplified molecular-input line-entry system (SMILES) codes for the initial input, which allows us to assess whether geometry optimization is necessary for reliable results. The XGBoost model also begins with the SMILES representations of the molecules but uses molecular descriptors instead of geometry optimizations. As a result, the best model tested (crystal graph convolutional neural network with Merck molecular force field-94) has an error of 1.15 EACN units of the true EACN for unknown data with the errors skewed toward zero and an R² score of 0.9

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Is the Local Ion Density Sufficient to Drive NaCl Nucleation from the Melt and Aqueous Solution?

Even though nucleation is ubiquitous in different science and engineering problems, investigating nucleation is extremely difficult due to the complicated ranges of time and length scales involved. In this work, we simulate NaCl nucleation in both molten and aqueous environments using enhanced sampling of all-atom molecular dynamics with deep-learning-based estimation of reaction coordinates. By incorporating various structural order parameters and learning the reaction coordinate as a function thereof, we achieve significantly improved sampling relative to traditional ad hoc descriptions of what drives nucleation, particularly in an aqueous medium. Our results reveal a one-step nucleation mechanism in both environments, with reaction coordinate analysis highlighting the importance of local ion density in distinguishing solid and liquid states. However, although fluctuations in the local ion density are necessary to drive nucleation, they are not sufficient. Our analysis shows that near the transition states, descriptors such as enthalpy and local structure become crucial. Furthermore, our protocol proposed here enables robust nucleation analysis and phase sampling and could offer insights into nucleation mechanisms for generic small molecules in different environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Affinity of Nicotinoids to a Model Nicotinic Acetylcholine Receptor (nAChR) Binding Pocket in the Human Brain

The binding affinity of nicotinoids to the binding residues of the a4ß2 variant of the nicotinic acetylcholine receptor (nAChR) was identified as a strong predictor of the nicotinoid’s addictive character. Using ab-iniito calculations for model binding pockets of increasing size comprising of 3, 6, and 14 amino acids (3AA, 6AA, and 14AA) that are derived from the crystal structure, the differences in binding affinity of 6 nicotinoids, namely nicotine (NIC), nornicotine (NOR), anabasine (ANB), anatabine (ANT), myosmine (MYO), and cotinine (COT) were correlated to their previously reported doses required for increases in intracranial self-stimulation (ICSS) thresholds, a metric for their addictive function. By employing the many body decomposition, the differences in the binding affinities of the various nicotinoids could be attributed mainly to the proton exchange energy between the Pyridine and non-Pyridine rings of the nicotinoids and the interactions between them and a handful of proximal amino acids, namely Trp156, Trpß57, Tyr100, and Tyr204. Interactions between the guest nicotinoid and the amino acids of the binding pocket were found to be mainly classical in nature, except for those between the nicotinoid and Trp156. The larger pockets were found to model binding structures more accurately and predicted the addictive character of all nicotinoids while smaller models, which are more computationally feasible, would only predict the addictive character of nicotinoids that are similar to nicotine. Here, the present study identifies the binding affinity of the guest nicotinoid to the host binding pocket as a strong descriptor of the nicotinoid’s addiction potential and as such it can be employed as a fast screening technique for the potential addiction of nicotine analogs.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Size and Stoichiometry Effects on the Reactivity of MoCy Nanoparticles Towards Ethylene

Molybdenum carbides are promising catalysts alternative to Pt-group metals for the hydrogenation of unsaturated hydrocarbons. Nanostructuring has been shown to be an efficient way to boost the catalytic activity of these materials with MoCy nanoparticles (NPs) exhibiting a good performance when encapsulated inside zeolites or dispersed on inert supports such as carbon or gold. In this work, we focus on a systematic DFT study of the interaction of MoCy NPs with ethylene (C 2 H 4 ), as a general and simple approach for examining binding and activation of C≡C bonds. Models for 14 NPs, with a Mo/C ratio in the 0.67 to 2.00 range, have been built following a cascade procedure. Several chemical descriptors, including the adsorption energy, structural NPs distortion, C≡C deformation, and C 2 H 4 attachment energy have been analyzed along with a meticulous geometric and electronic characterization of bare NPs and C2H4 binding. The present results show that 1:1 stoichiometric Mo 6 C 6 , Mo 12 C 12 , and Mo 24 C 24 , and the non-stochiometric Mo 4 C 6 , Mo 8 C 12 (MetCar), and Mo 14 C 13 (Nanocube) are excellent systems for the binding and activation of ethylene, exhibiting a much bigger reactivity than a bulk δ-MoC(001) surface with a similar Mo:C ratio. In addition, C 2 H 4 binding on the NPs with a Mo/C < 1.08 is advantageous since, apart from a rather large adsorption energy, implies low energy values for NPs deformation (from 0.00 to 0.31 eV), C≡C distortion (from 0.30 to 0.52 eV), and C 2 H 4 attachment (from -2.12 to -2.58 eV). These theoretical results point to the ideal MoCy size and composition for C 2 H 4 binding, providing a background for further experimental studies aimed at the preparation of MoCy NPs as hydrogenation catalysts.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Identification of Active Metal Carbide and Nitride Catalytic Facets for Hydrodeoxygenation Reactions

The catalytic hydrodeoxygenation (HDO) reaction is of considerable interest for biomass conversion to valuable chemicals and fuels, where one of the critical bottlenecks is the lack of cost-effective and efficient catalysts. To discover cost-efficient catalysts for the HDO reaction, we employed a density functional theory-based hierarchical catalyst design strategy based on catalytic descriptors, reaction energy profiles, and microkinetic modeling (MKM). We focused on the carbide and nitride catalyst space, for which we calculated 121 catalyst surfaces of Mo 2 C, MoC, Mo 2 N, W 2 C, NbC, VC, VN, and NbN catalysts. Based on the computed surface energies, reaction energies of oxygen removal, carbon binding strength, and the surface area of nanoparticles, the likely active facets are the Mo 2 C(111), MoC(011), VN(100), Mo 2 N(001), Mo 2 N(011), and Mo 2 N(100) surfaces. Further, detailed energy profiles were obtained, and MKM was performed for a model reaction (glycolaldehyde + 2H 2 . ethylene + 2H 2 O) on the Mo 2 C(111), VN(100), and MoC(100) surfaces. Based on the computed volcano map obtained from MKM, the predicted active facets for this HDO reaction are the Mo 2 C(111), MoC(011), VN(011), Mo 2 N(001), Mo 2 N(011), and Mo 2 N(100) surfaces. Additionally, none of the carbide and nitride catalyst surfaces are located in the optimal catalytic activity part. Therefore, it is essential to modify the catalyst via adding dopants or alloying to improve the catalytic activity. Catalytic modifications that can destabilize the surface adsorption of O*/H 2 O* and decrease the energy barriers of O-H bond formation are recommended to facilitate the HDO on the carbide and nitride catalysts. These a priori investigations provide guidelines for future low-cost HDO catalyst development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Machine Learning Self-Diffusion Prediction for Lennard-Jones Fluids in Pores

Predicting the diffusion coefficient of fluids under nanoconfinement is important for many applications including the extraction of shale gas from kerogen and product turnover in porous catalysts. Due to the large number of important variables, including pore shape and size, fluid temperature and density, and the fluid–wall interaction strength, simulating diffusion coefficients using molecular dynamics (MD) in a systematic study could prove to be prohibitively expensive. Here, we use machine learning models trained on a subset of MD data to predict the self-diffusion coefficients of Lennard-Jones fluids in pores. Our MD data set contains 2280 simulations of ideal slit pore, cylindrical pore, and hexagonal pore geometries. We use the forward feature selection method to determine the most useful features (i.e., descriptors) for developing an artificial neutral network (ANN) model with an emphasis on easily acquired features. Our model shows good predictive ability with a coefficient of determination (i.e., R 2 ) of ~0.99 and a mean squared error of ~2.9 × 10 –5 . Finally, we propose an alteration to our feature set that will allow the ANN model to be applied to nonideal pore geometries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗