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At least 1,459 records · Page 81

Experimental calibration of silicon and oxygen isotope fractionations between quartz and water at 250°C by in situ microanalysis of experimental products and application to zoned low δ 30 Si quartz overgrowths

The interpretation of silicon isotope data for quartz is hampered by the lack of experimentally determined fractionation factors between quartz and fluid. Further, there is a large spread in published oxygen isotope fractionation factors at low temperatures, primarily due to extrapolation from experimental calibrations at high temperature. We report the first measurements of silicon isotope ratios from experimentally precipitated quartz and estimate the equilibrium fractionation vs. dissolved silica using a novel in situ analysis technique applying secondary ion mass spectrometry to directly analyze experimental products. These experiments also yield a new value for oxygen isotope fractionation. Quartz overgrowths up to 235 μm thick were precipitated in silica–H 2 O–NaOH–NaCl fluids, at pH 12–13 and 250 °C. At this temperature, 1000lnα 30 Si(Qtz–fluid) = 0.55 ± 0.10‰ and 1000lnα 18 O(Qtz–fluid) = 10.62 ± 0.13‰, yielding the relations 1000lnα 30 Si(Qtz–fluid) = (0.15 ± 0.03) * 10 6 /T 2 and 1000lnα 18 O(Qtz–fluid) = (2.91 ± 0.04) * 10 6 /T 2 when extended to zero fractionation at infinite temperature. Values of δ 30 Si(Qtz) from diagenetic cement in sandstones from the basal Cambrian Mt. Simon Formation in central North America range from 0 to ₋5.4‰. Paired δ 18 O and δ 30 Si values from individual overgrowths preserve a record of Precambrian weathering and fluid transport. In conclusion, the application of the experimental quartz growth results to observations from natural sandstone samples suggests that precipitation of quartz at low temperatures in nature is dominated by kinetic, rather than equilibrium, processes.

58 GEOSCIENCES↗

Hydrothermal transport, deposition, and fractionation of the REE: Experimental data and thermodynamic calculations

For many years, our understanding of the behavior of the REE in hydrothermal systems was based on semi-empirical estimates involving extrapolation of thermodynamic data obtained at 25 °C. Since then, a substantial body of experimental data has accumulated on the stability of aqueous complexes of the REE. These data have shown that some of the predictions of Haas et al. (1995) are accurate, but others may be in error by several orders of magnitude. However, application of the data in modeling hydrothermal transport and deposition of the REE has been severely hampered by the lack of data on the thermodynamic properties of even the most common REE minerals. The discrepancies between the predictions and experimental determinations of the thermodynamic properties of aqueous REE species, together with the paucity of data on the stability of REE minerals, raise serious questions about the reliability of some models that have been proposed for the hydrothermal mobility of these critical metals. In this contribution, we review a body of high-temperature experimental data collected over the past 15 years on the stability of REE aqueous species and minerals. Using this new thermodynamic dataset, we re-evaluate the mechanisms responsible for hydrothermal transport and deposition of the REE. We also discuss the mechanisms that can result in REE fractionation during their hydrothermal transport and deposition. Here, our calculations suggest that in hydrothermal solutions, the main REE transporting ligands are chloride and sulfate, whereas fluoride, carbonate, and phosphate likely play an important role as depositional ligands. In addition to crystallographic fractionation, which is based on the differing affinity of mineral structures for the REE, our models suggest that the REE can be fractionated hydrothermally due to the differences in the stability of the LREE and HREE as aqueous chloride complexes.

58 GEOSCIENCES↗

Hydrothermal solubility of Dy hydroxide as a function of pH and stability of Dy hydroxyl aqueous complexes from 25 to 250 °C

The rare earth elements (REE) have important applications in green energy technologies. The formation of mineral deposits in geologic systems commonly involves hydrothermal fluids which can mobilize the REE. However, the REE speciation is not well known as a function of pH. The thermodynamic properties of REE hydroxyl complexes used in geochemical models are based on the Helgeson-Kirkham-Flowers (HKF) equation of state parameters which were derived by extrapolation of low temperature experimental and estimated data. In this study, Dy hydroxide solubility experiments are combined with available literature data to improve these models from 25 to 250 °C and optimize the thermodynamic properties of Dy 3+ and Dy hydroxyl complexes using GEMSFITS. Batch-type solubility experiments were conducted from 150 to 250 °C and at saturated water vapor pressure in perchloric acid solutions with initial pH values of 2 to 5 in 0.5 pH unit increments. The measured solubility of Dy hydroxide is retrograde with temperature and decreases with pH. The logarithm of total dissolved Dy molality ranges from –2.3 to –5.3 at 150 °C (pH 4.7–5.5), from –2.4 to –5.6 at 200 °C (pH 3.9–5.1), and from –3.7 to –6.9 at 250 °C (pH of 3.4 and 5.0). The optimized standard partial molal Gibbs energies of formation (Δ f G° T ) derived for Dy 3+ and DyOH 2+ display a close to linear relationship with temperature, fitting with previous optimizations based on DyPO 4 solubility data in the literature. A comparison of the optimized ΔfG°T values for aqueous Dy species with predictions from available HKF parameters indicates significant differences ranging from +11 to –26 kJ/mol between 25 and 250 °C. The experimental fits are used to derive the Dy hydroxide solubility products (K s0 ) and formation constants for the hydrolysis of Dy (β n with n = 1 to 3; Dy 3+ + nOH – = DyOH n 3-n ) as a function of temperature. The optimization method presented yields accurate thermodynamic properties for the Dy 3+ aqua ions and the DyOH 2+ species at the acidic to mildly acidic pH studied whereas more experimental work is needed at near-neutral and alkaline conditions to better constrain the other hydroxyl complexes. Furthermore, the optimized thermodynamic data have a significant impact on geochemical modeling of the mobility and solubility of REE minerals in acidic hydrothermal fluids.

58 GEOSCIENCES↗

Silicate coating to prevent leaching from radiolabeled surrogate far-field fallout in aqueous environments

Recent characterization of radioactive particles indicate that a large percentage of the radioactivity observed during the Fukushima Daiichi nuclear meltdown was insoluble 137 Cs bound within silica microparticles. Therefore, much of the decontamination research performed prior to the Fukushima incident that used either soluble radionuclides deposited onto wet surfaces or large (~100 μm) particles characteristic of nuclear weapons fallout do not accurately represent the characteristics of potential contamination. Thus, the common practice of extrapolating radioactive decontamination methods generically to all radioactive release events is, at best, suspect. In response, a method to produce chemically-inert, radiolabeled silica particles was developed. Binding 152 Eu within a sodium silicate coating required proper temperature control and ethanol was beneficial as a volatile dispersant to limit residues. In the end, a step-wise method, which first deposited 152 Eu or 241 Am as a nitrate salt, decomposed the salt to a sesquioxide, and finally coated the surface with sodium silicate led to dispersed particles of the desired 2 or 0.5 μm diameters. Dynamic light scattering and scanning election microscopy confirmed the particle size was unchanged. Leaching studies into several common decontaminants were performed to ensure particle inertness. In this paper, our approach allows for substitution of other radionuclides making it a robust, simple, and novel method to produce inert particle surrogates for a release event that allows direct comparison of decontamination techniques and contaminant fate studies, greatly aiding the development of response and recovery plans.

61 RADIATION PROTECTION AND DOSIMETRY↗

Evaluation of dual-weighted residual and machine learning error estimation for projection-based reduced-order models of steady partial differential equations

Projection-based reduced-order models (pROMs) show great promise as a means to accelerate many-query applications such as forward error propagation, solving inverse problems, and design optimization. In order to deploy pROMs in the context of high-consequence decision making, accurate error estimates are required to determine the region(s) of applicability in the parameter space. The following paper considers the dual-weighted residual (DWR) error estimate for pROMs and compares it to another promising pROM error estimate, machine learned error models (MLEM). Here, we show how DWR can be applied to ROMs and then evaluate DWR on two partial differential equations (PDEs): a two-dimensional linear convection–reaction–diffusion equation, and a three-dimensional static hyper-elastic beam. It is shown that DWR is able to estimate errors for pROMs extrapolating outside of their training set while MLEM is best suited for pROMs used to interpolate within the pROM training set.

42 ENGINEERING↗

A multifidelity deep operator network approach to closure for multiscale systems

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies, even instabilities, due to the improper accounting of the interaction between the resolved and unresolved scales of the multiscale system (known as the closure problem). In the current work, we interpret closure as a multifidelity problem and use a multifidelity deep operator network (DeepONet) framework to address it. In addition, to enhance the stability and/or accuracy of the multifidelity-based closure, we employ the recently developed ``in-the-loop" training approach from the literature on coupling physics and machine learning models. The resulting approach is tested on shock advection for the one-dimensional viscous Burgers equation and vortex merging for the two-dimensional Navier-Stokes equations. Furthermore, the numerical experiments show significant improvement of the predictive ability of the closure-corrected PROM over the un-corrected one both in the interpolative and the extrapolative regimes.

42 ENGINEERING↗

tLaSDI: Thermodynamics-informed latent space dynamics identification

Here we propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

97 MATHEMATICS AND COMPUTING↗

Mesh-based super-resolution of fluid flows with multiscale graph neural networks

A graph neural network (GNN) approach is introduced in this work which enables mesh-based three-dimensional super-resolution of fluid flows. In this framework, the GNN is designed to operate not on the full mesh-based field at once, but on localized meshes of elements (or cells) directly. To facilitate mesh-based GNN representations in a manner similar to spectral (or finite) element discretizations, a baseline GNN layer (termed a message passing layer, which updates local node properties) is modified to account for synchronization of coincident graph nodes, rendering compatibility with commonly used element-based mesh connectivities. Furthermore, the architecture is multiscale in nature, and is comprised of a combination of coarse-scale and fine-scale message passing layer sequences (termed processors) separated by a graph unpooling layer. The coarse-scale processor embeds a query element (alongside a set number of neighboring coarse elements) into a single latent graph representation using coarse-scale synchronized message passing over the element neighborhood, and the fine-scale processor leverages additional message passing operations on this latent graph to correct for interpolation errors. Demonstration studies are performed using hexahedral mesh-based data from Taylor–Green Vortex and backward-facing step flow simulations at Reynolds numbers of 1600 and 3200. Through analysis of both global and local errors, the results ultimately show how the GNN is able to produce accurate super-resolved fields compared to targets in both coarse-scale and multiscale model configurations. Reconstruction errors for fixed architectures were found to increase in proportion to the Reynolds number. Geometry extrapolation studies on a separate cavity flow configuration show promising cross-mesh capabilities of the super-resolution strategy.

Backward-facing step↗

Studies of premixed and non-premixed hydrogen flames

The hydrogen oxidation chemistry constitutes the foundation of the kinetics of all carbon- and hydrogen-containing fuels. The validation of rate constants of hydrogen-related reactions can be complicated by uncertainties associated with experimental data caused by the high reactivity and diffusivity of hydrogen.Here, accurate experimental data on flame propagation and extinction were determined for premixed and non-premixed hydrogen flames at pressures between p = 1 and 7 atm. The experiments were designed to sensitize the three-body H + O 2 + M → HO 2 + M reaction, whose rate is subject to notable uncertainty. This was achieved by increasing the pressure and by adding to the reactants H 2 O and CO 2 whose collision efficiencies are high compared to other species. In the present study, directly measured flame properties were compared against computed ones, in order to eliminate uncertainties associated with extrapolations, as is the case for laminar flame speeds. The measured extinction strain rates exhibit both a positive and negative dependence on pressure with and without weighting with the density, and this non-monotonic behavior is caused by the competition between the H + O 2 → O + OH and H + O 2 + M → HO 2 + M reactions as well as HO 2 kinetic pathways as pressure increases. The various kinetic models considered in this investigation did not reproduce equally well the non-premixed flame extinction data with added H 2 O. Yet, the predicted extinction strain rates were consistent between the various models in the case of added CO 2 . Finally, it was shown that the formulation of binary diffusion coefficient pairs including H–N 2 and H 2 –N 2 has a first order effect on the prediction of extinction strain rates of non-premixed H 2 flames.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantitative acetylene measurements in laminar and turbulent flames using 1D Raman/Rayleigh scattering

Our research presents the extension of the established detection of seven major species in 1D Raman/Rayleigh measurements to incorporate acetylene (C 2 H 2 ) as an eighth species. Acetylene is an important soot precursor which is generated in hydrocarbon flames as an intermediate species following decomposition. It occurs over a broad temperature range in flames and has been identified as a potentially detectable species in 1D Raman/Rayleigh measurements. In this paper, we discuss the Raman spectral signature of acetylene, its temperature dependence, calibration procedures, and the interference with other Raman-active species, C 2 and broadband interferences, all of which are essential to quantify for accurate data processing. In this regard, Raman measurements in laminar and turbulent dimethyl ether flames were acquired. The data are spectrally analyzed and low-temperature calibrations of the Raman response are combined with an extrapolation model for high temperatures in order to place the acetylene signals on an absolute scale. Single-shot and conditional-mean values are presented as a function of mixture fraction for a laminar partially-premixed DME/air flame. Measurements from the laminar flame are compared to a 1D laminar flame calculation to assess the accuracy of the calibration and analysis procedures. Furthermore, detection limits, signal-to-noise, and signal-to-interference ratio of the C 2 H 2 measurement are discussed, and single-shot measurements of acetylene in a turbulent DME/air jet flame are demonstrated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Measuring the soot onset temperature in high-pressure n-dodecane spray pyrolysis

In this paper, soot formation in pyrolyzing sprays of n-dodecane is visualized and quantified in a high-pressure, high-temperature, constant-volume spray chamber at 38 bar, 76 bar, and 114 bar. Sprays of n-dodecane are injected at 500 bar from a single-hole, 186-µm orifice diameter fuel injector. We quantify the temporal evolution of the soot optical thickness and the total soot mass formed in the pyrolyzing sprays using a high-speed extinction imaging diagnostic. The vessel ambient temperature and pressure are varied independently to identify the soot onset temperature for n-dodecane pyrolysis. Linear extrapolation of the maximum soot formation rates as a function of ambient temperature reveals a soot onset temperature near 1450 K. Finally, the onset temperature determined here for n-dodecane is within 50 K of those previously measured along the centerline of atmospheric pressure coflow diffusion flames for smaller alkane fuels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Accounting for uncertainty in RCCE species selection

A framework is presented to quantify, based on Bayesian evidence, the relative plausibility of species se- lection options in rate-controlled constrained equilibrium (RCCE) reduced chemical models, accounting for uncertainty in the kinetic parameters and experimental data used to refine them. This approach bal- ances the joint goals of matching available data and avoiding overfitting, which is well-understood to limit extrapolative capacity for true prediction. The methodology is applied to homogeneous autoigni- tion, where predictions are known to be particularly sensitive to chemical model details, specially at low temperatures. It is first introduced for hydrogen–air autoignition using an established mechanism, then demonstrated in two applications of methane–air autoignition using the larger GRI-1.2 mechanism. This larger mechanism significantly increases the computational cost of model selection (though not of the subsequent application in predictions), which is alleviated with a time-scale-guided pre-sorting strategy. Uses and extensions of this new formulation are discussed.

08 HYDROGEN↗

Burning velocities of R-32/O 2 /N 2 mixtures: Experimental measurements and development of a validated detailed chemical kinetic model

This work entails characterizing the flammability of the refrigerant R-32 (CH 2 F 2 ) by both experimental measurements and modeling. Burning velocities S u were measured using a constant-volume spherical-flame method for R-32/O2/N 2 mixtures with O 2 /N 2 ratios ranging from 21% (synthetic air) to 40%, pressures of (1 to 3) bar, and equivalence ratios $\phi$ of (0.8 to 1.3). Based on a critical assessment of available data, and extended by our own calculations, a detailed chemical kinetic model was developed and key reactions determined using reaction path and sensitivity analyses. Initiation and combustion were identified as distinct kinetic regimes and burning velocities were found to be controlled by two primary reactions: unimolecular decomposition of CH 2 F 2 → CHF + HF and the subsequent reaction, CHF + O 2 → CHFO + O, the latter reaction initiating the radical chain propagating and branching by producing O atoms. Sensitive rate constants in the kinetic model were critically adjusted within their uncertainties and current knowledge bounds to best fit the experimental burning velocities. We found that rate constants in the model could be adjusted to match a given experimental S u for specific conditions (O 2 loading, P, T, $\phi$). This, however, then fixes predicted burning velocities for other all conditions within (3 to 4)% if physically realistic rate parameters are maintained. Thus, the entire set of experimental data is fit, not just to particular conditions. Relative random uncertainties in the experimental Su measurements were (4 to 6)%, but assumptions made for thermal radiation lost by the burned gas in the spherical-flame experiments add an additional systematic uncertainty. Systematic differences between the limiting cases of adiabatic (no thermal radiation lost) and optically-thin (all thermal radiation lost) varied significantly with conditions and ranged from (4 to 30)% at high to low velocities, respectively, translating into uncertainties of (2 to 15)% considering the average of two limiting cases. Comparison of experimental and kinetically modeled Su values suggests that the burned gas tends towards the optically-thin limit at the lowest pressures and fuel loadings and toward the adiabatic limit at the highest pressures and loadings. We tested and found support for this conclusion with a detailed analysis as a function of all the conditions (T, P, % O 2 , $\phi$). This behavior appears to transition from optically-thin to adiabatic as the density of the initial fuel increases, which results in increased CO 2 in the burned gas and thus increased absorption of the thermal radiation (consistent with the Beer-Lambert Law). The validated detailed model based on evaluated kinetics is shown to accurately predict burning velocities for R-32 O 2 /N 2 mixtures over a wide range of conditions and provides a reliable basis for extrapolation to other conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Re-evaluation of rate constants for the reaction N 2 H 4 (+ M) $^→_←$ NH 2 + NH 2 (+ M)

Rate constants for the dissociation/recombination reaction N 2 H 4 (+ M) $^→_←$ NH 2 + NH 2 (+ M) are determined by a combination of quantum-chemical calculations and statistical unimolecular rate theory. Between 1100 and 2500 K, limiting low-pressure rate constants for hydrazine dissociation in the bath gas Ar of k 0 = [Ar] 6.1 × 10 20 (T/1000 K) –7.3 exp (-34490 K/T) cm 3 mol –1 s –1 , limiting high-pressure rate constants of k ∞ = 7.6 × 10 16 (T/1000 K) –1.0 exp(-33600 K/T) s –1 , and center broadening factors of the falloff curves (between 1100 and 1600 K in Ar) of F cent = 0.71 exp(- T/1460 K) + 0.29 exp(- T/21 K) + exp(-13400 K/T) were calculated. Using equilibrium constants K C = 1.7 × 10 3 (T/1000 K) –1.5 exp(-33,460 K/T) mol cm –3 , between 300 and 600 K limiting low-pressure rate constants for the reverse recombination of NH 2 radicals in the bath gas N 2 of k rec,0 = [N 2 ] 4.4 × 10 20 (T/400 K) –6.9 exp (-1630 K/T) cm 6 mol –2 s –1 , limiting high-pressure rate constants of k rec,∞ = 4.4 × 10 13 (T/1000 K) 0.44 exp(-140 K/T) cm 3 mol -1 s –1 , and center broadening factors (between 300 and 600 K in N 2 ) of F cent = exp(- T/1130 K) + exp (-10340 K/T) were obtained. A comparison with experimental results for hydrazine dissociation from the literature suggests incomplete falloff extrapolations toward k ∞ and experimental problems in the determination of k 0 at temperatures above about 1600 K. Finally, implications of the present re-evaluated rate constants for the modeling of high temperature ammonia oxidation kinetics are discussed, showing an only small influence of their precise values on the overall properties of the process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deep-freeze graph training for latent learning

Scientific and engineering advances are primarily driven by multi-tier conceptual constructs and conditional theoretical frameworks. The theories allow predictions of hypothetical system responses, given a set of approximate conditions (ranges of applicability) imposed on latent parameters that cannot be measured directly. Learning to estimate the latent variables (Latent Learning) helps to pinpoint the anticipated range-edge anomalies and improves the confidence in interpretation, interpolation and extrapolation of limited experimental data. Due to high dimensionality and extreme non-linearity of the materials science problems, very large datasets are typically required for conventional data-driven model development. The vital experimental data collection, particularly on microstructural phases, is very challenging, which makes it difficult to compile a high-quality database. Incorporation of the domain knowledge into the computational graph structure, initialization and optimization processes presents a viable mechanism for developing accurate models, with limited datasets. Furthermore, this study successfully utilized the approach to build the Deep Freeze Graph (DeepFreG) by mapping known causality relationships and by digitizing empirical domain knowledge for Latent Learning (LL), with specific applications in materials science.

36 MATERIALS SCIENCE↗

Developing a robust strength model using physically-informed genetic programming

The strength of materials is influenced by a range of external conditions, such as temperature and deformation rate. Consequently, materials that demonstrate substantial variations in their mechanical behavior due to fluctuations in temperature and strain rate require complex strength models to accurately predict material performance in real-world applications. To predict such complex behavior, a robust and flexible strength model is necessary. In this work, we utilize genetic programming-based symbolic regression (GPSR) to develop data-driven strength models that accurately represent the measured stress–strain responses of tin across a wide range of strain, strain rate and temperature regimes. The GPSR models are constrained by physically-informed conditions, which leads to significant improvement in extrapolation. The best model is integrated into a multi-physics code to perform Taylor impact simulations, validating the model’s accuracy and robustness. In conclusion, the model predictions showed excellent agreement with experimental results, particularly when compared to predictions using traditional strength models.

Genetic programming↗

Graph neural networks for CO 2 solubility predictions in Deep Eutectic Solvents

Deep Eutectic Solvents (DESs) are a promising class of solvents for CO 2 capture. DESs are complex mixtures that can be designed to optimize CO solubility and overall capture process efficiency. However, the vast design landscape of DES mixtures makes experimental investigation prohibitive; as such, there is a need for computational models that can quickly and efficiently navigate the design space and inform data collection efforts. In this work, we propose Graph Neural Network (GNN) models for predicting CO 2 solubility for DESs; the GNN leverages a mixture graph representation that captures the molecular structure of the DES components as well as their intermolecular interactions. Here, we compare the GNN framework against alternative architectures (neural networks, graph convolution networks, and random forests) and data representations (molecular fingerprints, sigma profiles, and graphs). We show that the proposed approach offers superior predictive performance; specifically, we show that solubility can be predicted reliably directly from molecular structure (without the need of using sigma profiles as proposed in previous studies). This result is important, as obtaining sigma profiles requires expensive density functional theory computations. We also explored the ability of GNNs to predict solubility for new DES mixtures and operating conditions. We found that the model extrapolates across temperature reliably. However, we also found deficiencies in the ability of the model to predict solubility for DES mixtures, pressures, and molar ratio not included in the training sets; we show that this is due to an inherent lack of chemical diversity in datasets available in the literature. The proposed computational capabilities can thus help navigate the design space of DES and inform data collection efforts. Our models, data, and benchmarks are shared as Python code implemented in Jupyter notebooks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A quantum Monte Carlo study of the molybdenum dimer (Mo 2 )

In this report we have studied the molybdenum dimer (Mo 2 ) system. The binding energy was calculated by means of the fixed-node DMC (FN-DMC) method. The Slater part of the trial wave function was constructed by the Selected-CI method by using the orbitals generated by the KS-DFT method with a hybrid meta-GGA exchange and correlation functional, TPSSh. We also carried out CCSD(T) calculations which were subsequently extrapolated to the complete basis set (CBS) limit. The results are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗