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Molecular simulation using transfer-learned potentials for the disordered nanoscale structure of nitrogen-doped nanoporous carbons

Machine learning (ML)-based molecular dynamics (MD) simulations of the formation of a class of N-doped nanoporous carbons are performed to assess their disordered partially graphitized nanoscale structure. The study is motivated by the effectiveness of so-called nitrogen assembly carbons (NACs) for catalysis applications. Benchmark simulations for pure-C disordered graphitic systems reveal the importance of reliably capturing the vdW component of the potentials in order to accurately describe the tendency for layering of disordered graphene-like sheets. In our modeling, this is achieved by a transfer learning strategy incorporating features of the energetics from the optB88-vdW DFT functional into potentials initially trained with a less expensive functional, thereby providing a superior description of the pure-C systems. Generation from MD simulations of realistic partially graphitized structures is significantly more challenging for N-doped versus for pure C systems. However, such structures are achieved by a tailored MD simulation protocol mimicking the experimental synthesis process and in particular incorporating an annealing and subsequent quenching stages. Simulated PXRD patterns effectively reproduce the features of experimental observations for NACs, including the appearance of a prominent but broad (002) peak at around 25, and the development of another weaker feature associated with in-layer ordering of mixed C-N graphene-like sheets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecular simulation of the structural and thermodynamic properties of n-alkane/brine interfacial systems with nonionic surfactants

All-atom molecular dynamics (MD) simulations are used to study the structural and thermodynamic properties of water + n-heptane interfacial systems in the presence of salinity (NaCl, NaI, KCl, and KI) and two different nonionic surfactants. Excellent qualitative and quantitative agreement with interfacial tension experimental data is obtained, but this requires applying a charge scaling factor to the ionic species, suggesting the likely role of polarizability effects. Tensoactive behavior is observed for the NaI and KI systems, coinciding with layering of the iodide species near the interface. Further, there are significant interaction differences between the surfactants and the different ionic species, but the structural and thermodynamic behavior of the surfactant molecules is relatively unaffected by the specific salt species. Our analysis suggest that the surfactant-surfactant interactions play a critical role in determining the interfacial behavior, with a much smaller impact associated with the composition of the brine phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NNL.Fe.qSNAP-ZBL.2024.1: A Fe Spectral Neighbor Analysis Potential for Radiation Damage Simulations

The NNL.Fe.qSNAP-ZBL.2024.1 machine-learned potential (MLP) has been generated to support the development of an elemental body-centered cubic (BCC) Fe athermal recombination corrected neutron damage model and simulations of primary recoil atom (PRA) cascades in BCC Fe. This MLP is a quadratic spectral neighbor analysis potential (qSNAP) hybridized with the universal Ziegler-Beirsack-Littmark (ZBL) potential at short-range and is named according to Naval Nuclear Laboratory MLP naming conventions (NNL.material-system.MLP-type.year.version). Training set calculations for Fe are presented along with the subsequent MLP fitting procedure. A key criterion of the fitting procedure is that ZBL describes the short-range interaction with minimal impact on the MLP. The MLP is compared to density functional theory (DFT) predicted properties relevant to radiation damage simulation, including threshold displacement energies, for validation. The NNL.Fe.qSNAP-ZBL.2024.1 potential is considered suitable for molecular dynamics (MD) simulations of radiation defects up to 800 K and PRA cascades in BCC Fe up to around 10 keV. The potential can additionally be used on a limited basis for recoils of 10–20 keV, within which range the emergence of structures outside the training set in cascade simulations may cause system instabilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Coarse-grained explicit-solvent molecular dynamics simulations of semidilute unentangled polyelectrolyte solutions

In this study, we present results from explicit-solvent coarse-grained molecular dynamics (MD) simulations of fully charged, salt-free, and unentangled polyelectrolytes in semidilute solutions. The inclusion of a polar solvent in the model allows for a more physical representation of these solutions at concentrations, where the assumptions of a continuum dielectric medium and screened hydrodynamics break down. The collective dynamic structure factor of polyelectrolytes, S(q, t), showed that at q > q*, where q* = 2π/ξ is the polyelectrolyte peak in the structure factor S(q) and ξ is the correlation length, the relaxation time obtained from fits to stretched exponential was $\tau$ KWW ~ q -3 , which describes unscreened Zimm-like dynamics. This is in contrast to implicit-solvent simulations using a Langevin thermostat where $\tau$ KWW ~ q -2 . At q < q*, a crossover region was observed that eventually transitions to another inflection point $\tau$ KWW ~ q -2 at length scales larger than ξ for both implicit- and explicit-solvent simulations. The simulation results were also compared to scaling predictions for correlation length, ξ ~ c$-½\atop{p}$, specific viscosity, η sp ~ c$½\atop{p}$, and diffusion coefficient, D ~ c$0\atop{p}$, where c p is the polyelectrolyte concentration. The scaling prediction for ξ holds; however, deviations from the predictions for η sp and D were observed for systems at higher c p , which are in qualitative agreements with recent experimental results. This study highlights the importance of explicit-solvent effects in molecular dynamics simulations, particularly in semidilute solutions, for a better understanding of polyelectrolyte solution behavior.

36 MATERIALS SCIENCE↗

Molecular Dynamics Simulation of the Structures, Dynamics, and Aggregation of Dissolved Organic Matter

Dissolved organic matter (DOM) plays a significant role in the transport and transformation of pollutants in the aquatic environment. However, the experimental characterization of DOM has been limited mainly to bulk properties, and the molecular-level interactions among various components of DOM remain to be fully characterized. In this study, we use molecular dynamics (MD) simulations to probe the structural properties of model DOM systems at atomic detail. The 200 ns simulations, validated by available experimental data, reveal processes and mechanisms by which chemical species (cations, peptides, lipids, lignin, carbohydrates, and some low-molecular-weight aliphatic and aromatic compounds) aggregate to form complex DOM. The DOM aggregates are dynamic, consisting of a hydrophobic core and amphiphilic exterior. The lipid tails and other hydrophobic fragments form the core, with hydrophilic and amphiphilic groups exposed to water, making DOM accessible to both polar and nonpolar species. Thus, the lipid component acts as a nucleator, whereas cations (especially Ca 2+ ) connect the molecular fragments on the surface by coordinating with the O-containing functional groups of DOM. The structural details revealed here provide new insights including surface accessible atoms, overall assemblage, and interactions among the molecules of DOM for understanding the kinetics and mechanisms through which DOM interacts with metal and other contaminants.

54 ENVIRONMENTAL SCIENCES↗

The Single Residue K12 Governs the Exceptional Voltage Sensitivity of Mitochondrial Voltage-Dependent Anion Channel Gating

The voltage-dependent anion channel (VDAC) is a β-barrel channel of the mitochondrial outer membrane (MOM) that passively transports ions, metabolites, polypeptides, and single-stranded DNA. VDAC responds to a transmembrane potential by “gating,” i.e. transitioning to one of a variety of low-conducting states of unknown structure. The gated state results in nearly complete suppression of multivalent mitochondrial metabolite (such as ATP and ADP) transport, while enhancing calcium transport. Voltage gating is a universal property of β-barrel channels, but VDAC gating is anomalously sensitive to transmembrane potential. Here, we show that a single residue in the pore interior, K12, is responsible for most of VDAC’s voltage sensitivity. Using the analysis of over 40 μs of atomistic molecular dynamics (MD) simulations, we explore correlations between motions of charged residues inside the VDAC pore and geometric deformations of the β-barrel. Residue K12 is bistable; its motions between two widely separated positions along the pore axis enhance the fluctuations of the β-barrel and augment the likelihood of gating. Single channel electrophysiology of various K12 mutants reveals a dramatic reduction of the voltage-induced gating transitions. The crystal structure of the K12E mutant at a resolution of 2.6 Å indicates a similar architecture of the K12E mutant to the wild type; however, 60 μs of atomistic MD simulations using the K12E mutant show restricted motion of residue 12, due to enhanced connectivity with neighboring residues, and diminished amplitude of barrel motions. We conclude that β-barrel fluctuations, governed particularly by residue K12, drive VDAC gating transitions.

59 BASIC BIOLOGICAL SCIENCES↗

How Rigid Are Anthranilamide Molecular Electrets?

As important as molecular electrets are for electronic materials and devices, conformational fluctuations strongly impact their macrodipoles and intrinsic properties. Herein, we employ molecular dynamics (MD) simulations with the polarizable charge equilibrium (PQEq) method to investigate the persistence length (L P ) of molecular electrets composed of anthranilamide (Aa) residues. The PQEq-MD dissipates the accepted static notions about Aa macromolecules, and L P represents the shortest Aa rigid segments. The classical model with a single L P value does not describe these oligomers. Introducing multiple L P values for the same macromolecule follows the observed trends and discerns the enhanced rigidity in their middle sections from the reduced stiffness at their terminal regions. Furthermore, L P distinctly depends on solvent polarity. The Aa oligomers maintain extended conformations in nonpolar solvents with L P exceeding 4 nm, while in polar media, increased conformational fluctuations reduce L P to about 2 nm. These characteristics set key guidelines about the utility of Aa conjugates for charge-transfer systems within organic electronics and energy engineering.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deformation behavior of annealed Cu64Zr36 metallic glass via molecular dynamics simulations

In the present work, we investigate the isothermal annealing process of Cu 64 Zr 36 metallic glass (MG) by means of molecular dynamics (MD) simulations, and characterize the compression properties under different temperatures and compressive rates. The pair distribution functions, the bond-orientational order, and the cluster-type index method are modeled and analyzed to characterize changes in the structure. Results of the modeling and analysis reveal that the MgZn 2 -type Laves, MgCu 2 -type Laves and five-fold local symmetry structures can be formed during the isothermal holding at 950 K. Study on the compression properties shows that at a fixed strain rate, the yield strength and yield drop all increase with decreasing temperature. At a fixed temperature, however, the increase of the strain rate leads to a noticeable increase in the yield strength at 600 K, but has little effect on yield strength at 10 K. Moreover, the modeling and analysis of the structure at a temperature of 10 K and strain-rate of 5 × 10 7 s -1 demonstrate that the order-disorder transformation initiates the shear band.

36 MATERIALS SCIENCE↗

On the Rapid Calculation of Binding Affinities for Antigen and Antibody Design and Affinity Maturation Simulations

The accurate and efficient calculation of protein-protein binding affinities is an essential component in antibody and antigen design and optimization, and in computer modeling of antibody affinity maturation. Such calculations remain challenging despite advances in computer hardware and algorithms, primarily because proteins are flexible molecules, and thus, require explicit or implicit incorporation of multiple conformational states into the computational procedure. The astronomical size of the amino acid sequence space further compounds the challenge by requiring predictions to be computed within a short time so that many sequence variants can be tested. In this study, we compare three classes of methods for antibody/antigen (Ab/Ag) binding affinity calculations: (i) a method that relies on the physical separation of the Ab/Ag complex in equilibrium molecular dynamics (MD) simulations, (ii) a collection of 18 scoring functions that act on an ensemble of structures created using homology modeling software, and (iii) methods based on the molecular mechanics-generalized Born surface area (MM-GBSA) energy decomposition, in which the individual contributions of the energy terms are scaled to optimize agreement with the experiment. When applied to a set of 49 antibody mutations in two Ab/HIV gp120 complexes, all of the methods are found to have modest accuracy, with the highest Pearson correlations reaching about 0.6. In particular, the most computationally intensive method, i.e., MD simulation, did not outperform several scoring functions. The optimized energy decomposition methods provided marginally higher accuracy, but at the expense of requiring experimental data for parametrization. Within each method class, we examined the effect of the number of independent computational replicates, i.e., modeled structures or reinitialized MD simulations, on the prediction accuracy. We suggest using about ten modeled structures for scoring methods, and about five simulation replicates for MD simulations as a rule of thumb for obtaining reasonable convergence. We anticipate that our study will be a useful resource for practitioners working to incorporate binding affinity calculations within their protein design and optimization process.

59 BASIC BIOLOGICAL SCIENCES↗

Diffusion characteristics of water molecules in a lamellar structure formed by triblock copolymers

The distribution and diffusion of water molecules are playing important roles in determining self-assembly and transport properties of polymeric systems. Small-angle neutron scattering (SANS) experiments and molecular dynamics (MD) simulation have been applied to understand the distribution of water molecules and their dynamics in the lamellar membrane formed by Pluronic L62 block copolymers. Penetration of water molecules into the polyethylene oxide (PEO) layers of the membranes has been estimated using scattering length density (SLD) profiles obtained from SANS measurements, which agree well with the molecular distribution observed from MD simulations. The water diffusion coefficient at different regions of the lamellar membrane was further investigated using MD simulation. The diffusion characteristic shows a transition from normal to anomalous diffusion as the position of the water molecule changes from the bulk to PEO and to the polypropylene oxide (PPO) layer. Here we find that water molecules within the PEO or PPO layers follow subdiffusive dynamics, which can be interpreted by the model of fractional Brownian motion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Strongly Anisotropic Thermomechanical Response to Shock Wave Loading in Oriented Samples of the Triclinic Molecular Crystal 1,3,5-Triamino-2,4,6-trinitrobenzene

All-atom molecular dynamics (MD) simulations were used to study shock wave loading in oriented single crystals of the highly anisotropic triclinic molecular crystal 1,3,5-triamino-2,4,6-trinitrobenzene (TATB). The crystal structure consists of planar hydrogen-bonded sheets of individually planar TATB molecules that stack into graphitic-like layers. Shocks were studied for seven systematically prepared crystal orientations with limiting cases that correspond to shock propagation exactly perpendicular and exactly parallel to the graphitic-like layers. The simulations were performed for initially defect-free crystals using a reverse-ballistic configuration that generates explicit, supported shocks. Final longitudinal stress components are between ≈8.5 and ≈10.5 GPa for the 1.0 km s –1 impact speed studied. Orientation-dependent properties are reported including shock speeds, stresses, temperatures, compression ratios, and local material strain rates. Spatiotemporal maps of the temperature, stress tensor, material flow, and molecular orientations reveal complicated processes that arise for specific shock directions. Furthermore, the results indicate that TATB shock response is highly sensitive to crystal orientation, with significant qualitative differences for the time evolution of the stress tensor and temperature, elastic/inelastic compression response, defect formation and growth, critical von Mises stress, and strain rates during shock rise that span nearly an order of magnitude. A variety of inelastic deformation mechanisms are identified, ranging from crumpling of graphitic-like layers to dislocation-mediated plasticity to intense shear strain localization. To our knowledge, these are the first systematic MD simulations and analysis of explicit shock wave propagation along nontrivial crystal directions in a triclinic molecular crystal.

36 MATERIALS SCIENCE↗

Primary defect production from molecular dynamics simulations of high-energy displacement cascades in NbMoTaW alloys

In this work, we report on large-scale molecular-dynamics (MD) simulations of displacement cascades in equiatomic NbMoTaW alloys at PKA energies ranging from 0.15 to 150 keV. We find defect production to be strongly dependent on recoil energy, scaling sublinearly up to 10 keV, and linearly thereafter. We find the sublinear regime to be defined by low values of surviving Frenkel pairs, typically found as isolated point defects or small defect clusters, while at higher recoil energies dense cascades become more frequent, leading to splitting into subcascades and the production of relatively large prismatic-dislocation loops with ⟨111⟩ and ⟨001⟩ Burgers vectors. These loops immobilize large fractions of defects, leading to a rapid growth of the number of surviving defects in the linear regime. We also anneal post-cascade defect configurations using object-kinetic Monte Carlo (OKMC) simulations to account for intracascade recombination on time scales not accessible to MD simulations. Cascade annealing is strongly temperature dependent, with the OKMC simulations only showing significant recovery at 1000 K but not below. Our results are in general agreement with existing published data for refractory concentrated alloys.

Zhou, Xinran [Lawrence Berkeley National Laborator↗

The Potential Energy Hotspot: Effects of Impact Velocity, Defect Geometry, and Crystallographic Orientation

In energetic materials, the localization of energy into “hotspots” is known to dictate the initiation of chemical reactions and detonation. Recent all-atom simulations have shown that more energy is localized as internal potential energy (PE) than can be inferred from the kinetic energy (KE) alone. The mechanisms associated with pore collapse and hotspot formation are known to depend on pore geometry and dynamic material response such as plasticity. Therefore, we use molecular dynamics (MD) simulations to characterize shock-induced pore collapse and the subsequent formation of hotspots in 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a highly anisotropic molecular crystal, for various defect shapes, shock strengths, and crystallographic orientations. We find that the localization of energy as PE is consistently larger than the KE in cases with significant plastic deformation. Additionally, an analysis of MD trajectories reveals the underlying molecular- and crystal-level processes that govern the effect of orientation and pore shape on PE localization. We find that the regions of highest PE relate to the areas of maximum plastic deformation, while KE is maximized at the point of impact. Comparisons against octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) reveal less energy localization in TATB, which could be a contributing factor to the latter’s insensitivity.

36 MATERIALS SCIENCE↗

A coarse-grain force field based on quantum mechanics (CGq FF) for molecular dynamics simulation of poly(ethylene glycol)- block -poly(ε-caprolactone) (PEG- b -PCL) micelles

In order to provide the means to predict from molecular dynamics (MD) simulations the structures of copolymer-based micelles in solution, we developed coarse grain force field (CGq FF) parameters for poly(ethylene glycol) (PEG) and for poly(ε-caprolactone) (PCL). A key advance here is the use of quantum mechanics to train the parameters describing the non-bonded (NB) interactions between the CG beads. The functional forms are the same as the MARTINI CG FF so standard MD codes can be used. Our CGq FF describes well the experimentally observed properties for the polymer–air and polymer–water interfaces, indicating the accuracy of the NB interactions. Additionally, the structural properties (density, radius of gyration ( R g ), and end-to-end distance ( h )) match both experiment and all atom (AA) simulations. We illustrate the application of this CGq FF by following the formation of a spherical micelle from 250 chains of PEG 23 - b -PCL 9 diblock copolymer, each block with molecular weight of 1000 Daltons (10 500 beads, corresponding to 123 250 atoms), in a water box with 119 139 water beads (426 553 water molecules).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigating Lignin Aggregation and Interactions with Solvents during γ-Valerolactone (GVL) Pretreatment: A Combined Small Angle Neutron Scattering and Molecular Simulations Study

The strong tendency of lignin to aggregate in solution, coupled with limited understanding of how its molecular structure governs this behavior, hinders its effective utilization in biorefineries. Here, in this study, we investigated the solution behavior of lignin extracted from poplar using γ-valerolactone/water (GVL/H2O, 9:1 wt/wt) through combined small-angle neutron scattering (SANS) and molecular dynamics (MD) simulations. Lignin samples obtained at 100 °C (L100) and 120 °C (L120) differed in β–O–4 content, hydroxyl distribution, and S/G ratio, enabling direct assessment of how molecular composition governs solvation and aggregation. SANS showed that L120 formed rigid and elongated cylindrical aggregates at 25 °C that transitioned to more flexible spheroidal structures by 50 °C and remained stable up to 80 °C, whereas L100 adopted globular aggregates that progressively collapsed with increasing temperature. MD simulations reinforced these observations by showing that S-rich (L120-like) oligomers had larger radii of gyration, stronger solvent coordination driven by methoxy groups, and fewer lignin–lignin contacts. In contrast, G-rich (L100-like) oligomers displayed persistent aggregation and lower solubility. Collectively, these results reveal that increased aromatic methoxylation enhances lignin–solvent interactions and suppresses self-association, whereas reduced methoxylation and higher β–O–4 content promote persistent aggregation into colloid-like structures with restricted solvent penetration into the aggregate interior.

biorefinery pretreatment↗

Characterization of Heparin’s Conformational Ensemble by Molecular Dynamics Simulations and Nuclear Magnetic Resonance Spectroscopy

Heparin is a highly charged, polysulfated polysaccharide and serves as an anticoagulant. Heparin binds to multiple proteins throughout the body, suggesting a large range of potential therapeutic applications. Although its function has been characterized in multiple physiological contexts, heparin’s solution conformational dynamics and structure–function relationships are not fully understood. Molecular dynamics (MD) simulations facilitate the analysis of a molecule’s underlying conformational ensemble, which then provides important information necessary for understanding structure–function relationships. However, for MD simulations to afford meaningful results, they must both provide adequate sampling and accurately represent the energy properties of a molecule. The aim of this study is to compare heparin’s conformational ensemble using two well-developed force fields for carbohydrates, known as GLYCAM06 and CHARMM36, using replica exchange molecular dynamics (REMD) simulations, and to validate these results with NMR experiments. In this work, the anticoagulant sequence, an ultra-low-molecular-weight heparin, known as Arixtra (fondaparinux, sodium), was simulated with both parameter sets. The results suggest that GLYCAM06 matches experimental nuclear magnetic resonance three-bond J-coupling values measured for Arixtra better than CHARMM36. In addition, NOESY and ROESY experiments suggest that Arixtra is very flexible in the sub-millisecond time scale and does not adopt a unique structure at 25 C. Moreover, GLYCAM06 affords a much more dynamic conformational ensemble for Arixtra than CHARMM36.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Using Computationally-Determined Properties for Machine Learning Prediction of Self-Diffusion Coefficients in Pure Liquids

The ability to predict transport properties of liquids quickly and accurately will greatly improve our understanding of fluid properties both in bulk and complex mixtures, as well as in confined environments. Such information could then be used in the design of materials and processes for applications ranging from energy production and storage to manufacturing processes. As a first step, we consider the use of machine learning (ML) methods to predict the diffusion properties of pure liquids. Recent results have shown that Artificial Neural Networks (ANNs) can effectively predict the diffusion of pure compounds based on the use of experimental properties as the model inputs. In the current study, a similar ANN approach is applied to modeling diffusion of pure liquids using fluid properties obtained exclusively from molecular simulations. A diverse set of 102 pure liquids is considered, ranging from small polar molecules (e.g., water) to large nonpolar molecules (e.g., octane). Self-diffusion coefficients were obtained from classical molecular dynamics (MD) simulations. Since nearly all the molecules are organic compounds, a general set of force field parameters for organic molecules was used. The MD methods are validated by comparing physical and thermodynamic properties with experiment. Computational input features for the ANN include physical properties obtained from the MD simulations as well as molecular properties from quantum calculations of individual molecules. Furthermore, fluid properties describing the local liquid structure were obtained from center of mass radial distribution functions (COM-RDFs). Feature sensitivity analysis revealed that isothermal compressibility, heat of vaporization, and the thermal expansion coefficient were the most impactful properties used as input for the ANN model to predict the MD simulated self-diffusion coefficients. The MD-based ANN successfully predicts the MD self-diffusion coefficients with only a subset (2 to 3) of the available computationally determined input features required. A separate ANN model was developed using literature experimental self-diffusion coefficients as model targets. Although this second ML model was not as successful due to a limited number of data points, a good correlation is still observed between experimental and ML predicted self-diffusion coefficients.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A molecular dynamics simulation study of thermal conductivity anisotropy in β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX)

Molecular dynamics (MD) simulations were used to predict the thermal conductivity of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) along directions normal to the (011), (110), and (010) crystal planes. These directions were selected based on the measured morphological importance of the corresponding crystal surfaces. A reverse non-equilibrium MD approach was used wherein a constant heat flux is imposed along a prescribed direction and the resulting steady-state temperature gradient determined. The coefficient of thermal conductivity λ is the quotient of heat flux and temperature gradient (i.e. Fourier's law). Finite-size effects and sensitivity to imposed heat flux were investigated. The results reveal a modest dependence of the conductivity on crystal orientation, significant finite-size effects, and low sensitivity to imposed flux so long as the Fourier's law analysis is limited to the spatial interval in the simulation cell for which the temperature gradient is constant. Infinite-length thermal conductivities were estimated by linear regression of λ -1 (L) versus reciprocal cell length L -1 for each direction. The predicted values are systematically larger, but within a factor of two, than most published experimental determinations, the latter of which were obtained for pressed-powder or composite samples rather than oriented single crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗