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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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Development of a 3-D upwind PNS code for chemically reacting hypersonic flowfields

Two new parabolized Navier-Stokes (PNS) codes were developed to compute the three-dimensional, viscous, chemically reacting flow of air around hypersonic vehicles such as the National Aero-Space Plane (NASP). The first code (TONIC) solves the gas dynamic and species conservation equations in a fully coupled manner using an implicit, approximately-factored, central-difference algorithm. This code was upgraded to include shock fitting and the capability of computing the flow around complex body shapes. The revised TONIC code was validated by computing the chemically-reacting (M(sub infinity) = 25.3) flow around a 10 deg half-angle cone at various angles of attack and the Ames All-Body model at 0 deg angle of attack. The results of these calculations were in good agreement with the results from the UPS code. One of the major drawbacks of the TONIC code is that the central-differencing of fluxes across interior flowfield discontinuities tends to introduce errors into the solution in the form of local flow property oscillations. The second code (UPS), originally developed for a perfect gas, has been extended to permit either perfect gas, equilibrium air, or nonequilibrium air computations. The code solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that was modified to account for real gas effects. The dissipation term associated with this algorithm is sufficiently adaptive to flow conditions that, even when attempting to capture very strong shock waves, no additional smoothing is required. For nonequilibrium calculations, the code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. This code was used to calculate the hypersonic, laminar flow of chemically reacting air over cones at various angles of attack. In addition, the flow around the McDonnel Douglas generic option blended-wing-body was computed and comparisons were made between the perfect gas, equilibrium air, and the nonequilibrium air results.

Tannehill, J. C.↗
DOE OSTI2023

Ecological divergence of syntopic marine bacterial species is shaped by gene content and expression

Identifying mechanisms by which bacterial species evolve and maintain genomic diversity is particularly challenging for the uncultured lineages that dominate the surface ocean. A longitudinal analysis of bacterial genes, genomes, and transcripts during a coastal phytoplankton bloom revealed two co-occurring, highly related Rhodobacteraceae species from the deeply branching and uncultured NAC11-7 lineage. These have identical 16S rRNA gene amplicon sequences, yet their genome contents assembled from metagenomes and single cells indicate species-level divergence. Moreover, shifts in relative dominance of the species during dynamic bloom conditions over 7 weeks confirmed the syntopic species’ divergent responses to the same microenvironment at the same time. Genes unique to each species and genes shared but divergent in per-cell inventories of mRNAs accounted for 5% of the species’ pangenome content. These analyses uncover physiological and ecological features that differentiate the species, including capacities for organic carbon utilization, attributes of the cell surface, metal requirements, and vitamin biosynthesis. Such insights into the coexistence of highly related and ecologically similar bacterial species in their shared natural habitat are rare.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

The core metabolome and root exudation dynamics of three phylogenetically distinct plant species

Abstract Root exudates are plant-derived, exported metabolites likely shaping root-associated microbiomes by acting as nutrients and signals. However, root exudation dynamics are unclear and thus also, if changes in exudation are reflected in changes in microbiome structure. Here, we assess commonalities and differences between exudates of different plant species, diurnal exudation dynamics, as well as the accompanying methodological aspects of exudate sampling. We find that exudates should be collected for hours rather than days as many metabolite abundances saturate over time. Plant growth in sterile, nonsterile, or sugar-supplemented environments significantly alters exudate profiles. A comparison of Arabidopsis thaliana , Brachypodium distachyon , and Medicago truncatula shoot, root, and root exudate metabolite profiles reveals clear differences between these species, but also a core metabolome for tissues and exudates. Exudate profiles also exhibit a diurnal signature. These findings add to the methodological and conceptual groundwork for future exudate studies to improve understanding of plant-microbe interactions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Modeling the Joint Effects of Vegetation Characteristics and Soil Properties on Ecosystem Dynamics in a Panama Tropical Forest

Abstract In tropical forests, both vegetation characteristics and soil properties are important not only for controlling energy, water, and gas exchanges directly but also determining the competition among species, successional dynamics, forest structure and composition. However, the joint effects of the two factors have received limited attention in Earth system model development. Here we use a vegetation demographic model, the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) implemented in the Energy Exascale Earth System Model (E3SM) Land Model (ELM), ELM‐FATES, to explore how plant traits and soil properties affect tropical forest growth and composition concurrently. A large ensemble of simulations with perturbed vegetation and soil hydrological parameters is conducted at the Barro Colorado Island, Panama. The simulations are compared against observed carbon, energy, and water fluxes. We find that soil hydrological parameters, particularly the scaling exponent of the soil retention curve ( B sw ), play crucial roles in controlling forest diversity, with higher B sw values (>7) favoring late successional species in competition, and lower B sw values (1 ∼ 7) promoting the coexistence of early and late successional plants. Considering the additional impact of soil properties resolves a systematic bias of FATES in simulating sensible/latent heat partitioning with repercussion on water budget and plant coexistence. A greater fraction of deeper tree roots can help maintain the dry‐season soil moisture and plant gas exchange. As soil properties are as important as vegetation parameters in predicting tropical forest dynamics, more efforts are needed to improve parameterizations of soil functions and belowground processes and their interactions with aboveground vegetation dynamics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

From classical to quantum dynamics of atomic and ionic species interacting with graphene and its analogue

Graphene and its analogues offer a broad range of application opportunities for (opto)-electronics, sensing, catalysis, phase separation, energy conversion and storage, etc. Engineering graphene properties often relies on its controllable functionalization, defect formation and patterning, and reactive gas etching. In this chapter, we survey the dynamics of graphene using classical and quantum-classical dynamics methods. We discuss the reactivity, scattering, and transmission of atomic and ionic species including Ar cluster ion, H/D, and H+/D+ on graphene flakes of various sizes, focusing on the atomic-scale motion and energy dissipation pathways involved in forming and breaking covalent bonding. Discussions on the nuclear quantum effects of light species, the effects of isotopic substitution, and the methodologies for such modeling are also included.

Garashchuk, Sofiya V.↗
NASA NTRS1991

The chemical composition of the dust-free Martian atmosphere - Preliminary results of a two-dimensional model

This paper describes a two-dimensional model of the Martian atmosphere, in which chemical, radiative and dynamical processes are treated interactively. The model is developed for a carbon dioxide-hydrogen-oxygen-nitrogen atmosphere and provides estimates of concentrations for 19 chemical species. The dynamical equations are expressed in the transformed Eulerian coordinates. The wave driving and eddy mixing coefficients resulting from gravity and Rossby wave absorption are computed consistently with the evolving distribution of the mean zonal wind. The net diabatic heating/cooling rate is derived from a detailed radiative scheme including the contributions of CO2, O3, H2O and O2, and is computed consistently with the calculated distribution of temperature and trace species quantities. The computed temperature field as well as the meridional and seasonal variations of ozone column abundance are in good agreement with the distributions observed by Mariner 9 and Viking spacecrafts and the results obtained by previous studies. The present version of the model does not include the effects of dust, clouds and polar hood and only the chemistry in a dust-free atmosphere is considered.

Moreau, D.↗
DOE OSTI2024

In-Situ Species Concentration Measurements In Ammonia-Mix Flames Using Ftir Spectroscopy

Hydrogen and ammonia represent two carbon-free fuel sources that could be used in place of current fossil energy sources in combustion systems. To develop optimized ammonia combustion systems, validated modeling tools are needed. In the open literature, it has been shown that the complex chemistry associated with fuel-bound nitrogen contained in ammonia differs greatly from natural gas or hydrogen combustion. As a result, several new chemical kinetic mechanisms have been developed. Many of these mechanisms have been validated experimentally, however this has primarily focused on bulk parameters such as laminar flame speed and ignition delay time. Critically, high quality measurements of species concentrations are needed under controlled conditions which are easily represented by simple models. In this paper, direct, in-situ measurements of species concentrations and gas temperature are performed in a laminar flat-flame burner. This arrangement enables comparison with 1D model predictions, better isolating chemical kinetics from the fluid dynamics. Quantitative species concentrations are determined by absorption spectroscopy using an FTIR spectrometer. Fuel compositions representative of cracked ammonia (NH 3 /H 2 ) and ammonia-natural gas (NH 3 /CH 4 ) are considered for rich and lean equivalence ratios. A major focus of the paper is on the selection of spectral features for nitric oxide and ammonia and correcting for large amounts of baseline H 2 O absorption.

36 MATERIALS SCIENCE↗
DOE OSTI2024

In-Situ Species Concentration Measurements in Ammonia-Mix Flames Using FTIR Spectroscopy

Hydrogen and ammonia represent two carbon-free fuel sources that could be used in place of current fossil energy sources in combustion systems. To develop optimized ammonia combustion systems, validated modeling tools are needed. In the open literature, it has been shown that the complex chemistry associated with fuel-bound nitrogen contained in ammonia differs greatly from natural gas or hydrogen combustion. As a result, several new chemical kinetic mechanisms have been developed. Many of these mechanisms have been validated experimentally, however this has primarily focused on bulk parameters such as laminar flame speed and ignition delay time. Critically, high quality measurements of species concentrations are needed under controlled conditions which are easily represented by simple models. In this paper, direct, in-situ measurements of species concentrations and gas temperature are performed in a laminar flat-flame burner. This arrangement enables comparison with 1D model predictions, better isolating chemical kinetics from the fluid dynamics. Quantitative species concentrations are determined by absorption spectroscopy using an FTIR spectrometer. Fuel compositions representative of cracked ammonia (NH3/H2) and ammonia-natural gas (NH3/CH4) are considered for rich and lean equivalence ratios. A major focus of the paper is on the selection of spectral features for nitric oxide and ammonia and correcting for large amounts of baseline H2O absorption.

Bedick, Clinton↗
DOE OSTI2026

Complex Dynamics in Argyrodite Solid-State Ion Conductors

Argyrodites are a compositionally diverse family of materials that exhibit remarkable ion transport properties. While the average crystal structures of argyrodites have been extensively studied, ion transport in these materials is governed by a confluence of dynamic processes spanning the cation, anion, and polyanionic sublattices. This Perspective synthesizes recent advances in understanding the role of dynamics in structural behavior and ion transport properties. We examine the compositional and structural motifs that govern order−disorder transitions within the argyrodite family and further explore how ion hopping is facilitated by lattice dynamics, from long-range phonons to local rotational dynamics of polyanionic species. Through the lens of dynamics spanning multiple time and length scales, we establish guiding principles that govern transport phenomena and highlight avenues of future study for the argyrodite family of ion conductors.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Enhanced Activity from Coordinatively Unsaturated and Dynamic Zeolite-Bound Organoscandium Species

Scandium borohydride grafted into the micropores of the faujasite zeolite HY30 catalyzes the C–H borylation of benzene, whereas silica-grafted species are inactive. This catalytic activity may originate from grafting at a Brønsted acid site leading to a more electron-deficient rare earth center. Herein, we apply multinuclear double-resonance nuclear magnetic resonance (NMR) experiments to probe the structure and dynamics of zeolite- and silica-bound scandium borohydride complexes. The experiments reveal that scandium centers located within the zeolite micropores, in proximity to Al-created Brønsted sites, are more dynamic than rigid scandium sites grafted on silanols. Through a combination of NMR and molecular dynamics simulations, we show that the coordination of the scandium in the zeolite is labile, with the metal exchanging between two binding sites. As a result, the weak electron donation from the support that enables the movement of the Sc center leads to the formation of an undercoordinated metal center that cannot exist on silica, ultimately leading to the new catalytic activity of the species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2015

Investigation of North American Vegetation Variability under Recent Climate: A Study Using the SSiB4/TRIFFID Biophysical/Dynamic Vegetation Model

Recent studies have shown that current dynamic vegetation models have serious weaknesses in reproducing the observed vegetation dynamics and contribute to bias in climate simulations. This study intends to identify the major factors that underlie the connections between vegetation dynamics and climate variability and investigates vegetation spatial distribution and temporal variability at seasonal to decadal scales over North America (NA) to assess a 2-D biophysical model/dynamic vegetation model's (Simplified Simple Biosphere Model version 4, coupled with the Top-down Representation of Interactive Foliage and Flora Including Dynamics Model (SSiB4/TRIFFID)) ability to simulate these characteristics for the past 60 years (1948 through 2008). Satellite data are employed as constraints for the study and to compare the relationships between vegetation and climate from the observational and the simulation data sets. Trends in NA vegetation over this period are examined. The optimum temperature for photosynthesis, leaf drop threshold temperatures, and competition coefficients in the Lotka-Volterra equation, which describes the population dynamics of species competing for some common resource, have been identified as having major impacts on vegetation spatial distribution and obtaining proper initial vegetation conditions in SSiB4/TRIFFID. The finding that vegetation competition coefficients significantly affect vegetation distribution suggests the importance of including biotic effects in dynamical vegetation modeling. The improved SSiB4/TRIFFID can reproduce the main features of the NA distributions of dominant vegetation types, the vegetation fraction, and leaf area index (LAI), including its seasonal, interannual, and decadal variabilities. The simulated NA LAI also shows a general increasing trend after the 1970s in responding to warming. Both simulation and satellite observations reveal that LAI increased substantially in the southeastern U.S. starting from the 1980s. The effects of the severe drought during 1987-1992 and the last decade in the southwestern U.S. on vegetation are also evident from decreases in the simulated and satellite-derived LAIs. Both simulated and satellite-derived LAIs have the strongest correlations with air temperature at northern middle to high latitudes in spring reflecting the effect of these climatic variables on photosynthesis and phenological processes. Meanwhile, in southwestern dry lands, negative correlations appear due to the heat and moisture stress there during the summer. Furthermore, there are also positive correlations between soil wetness and LAI, which increases from spring to summer. The present study shows both the current improvements and remaining weaknesses in dynamical vegetation models. It also highlights large continental-scale variations that have occurred in NA vegetation over the past six decades and their potential relations to climate. With more observational data availability, more studies with differentmodels and focusing on different regions will be possible and are necessary to achieve comprehensive understanding of the vegetation dynamics and climate interactions.

climate variability↗
NASA NTRS1988

Photochemical modeling of the Antarctic stratosphere: Observational constraints from the airborne Antarctic ozone experiment and implications for ozone behavior

The rapid decrease in O3 column densities observed during Antarctic spring has been attributed to several chemical mechanisms involving nitrogen, bromine, or chlorine species, to dynamical mechanisms, or to a combination of the above. Chlorine-related theories, in particular, predict greatly elevated concentrations of ClO and OClO and suppressed abundances of NO2 below 22 km. The heterogeneous reactions and phase transitions proposed by these theories could also impact the concentrations of HCl, ClNO3 and HNO3 in this region. Observations of the above species have been carried out from the ground by the National Ozone Expedition (NOZE-I, 1986, and NOZE-II, 1987), and from aircrafts by the Airborne Antarctic Ozone Experiment (AAOE) during the austral spring of 1987. Observations of aerosol concentrations, size distribution and backscattering ratio from AAOE, and of aerosol extinction coefficients from the SAM-II satellite can also be used to deduce the altitude and temporal behavior of surfaces which catalyze heterogeneous mechanisms. All these observations provide important constraints on the photochemical processes suggested for the spring Antarctic stratosphere. Results are presented for the concentrations and time development of key trace gases in the Antarctic stratosphere, utilizing the AER photochemical model. This model includes complete gas-phase photochemistry, as well as heterogeneous reactions. Heterogeneous chemistry is parameterized in terms of surface concentrations of aerosols, collision frequencies between gas molecules and aerosol surfaces, concentrations of HCl/H2O in the frozen particles, and probability of reaction per collision (gamma). Values of gamma are taken from the latest laboratory measurements. The heterogeneous chemistry and phase transitions are assumed to occur between 12 and 22 km. The behavior of trace species at higher altitudes is calculated by the AER 2-D model without heterogeneous chemistry. Calculations are performed for solar illumination conditions typical of 60, 70, and 80 S, from July 15 to October 31.

Rodriguez, Jose M.↗
DOE OSTI2024

Water foraging with dynamic roots in E3SM; The role of roots in terrestrial ecosystem memory on intermediate timescales (Final Technical Report)

Terrestrial ecosystems can show sustained responses to stress events that may last for years after the initial perturbation. This phenomenon is referred to as legacy or memory and it emerges from a set of ecosystem processes that are poorly captured by Earth System and Land Surface Models. Consequently, these models struggle to predict the impact that extreme climate events have on surface energy, carbon and hydrological exchange once a stressor such as drought has relaxed or in response to repeated exposure to stress. In this project, we set out to test how the addition of dynamic root profiles in land surface models impact the capacity for Earth System Models, such as the Department of Energy’s E3SM, to capture realistic legacy effects. Observations have shown that vegetation shifts their root profiles during stress events to forage for water and these altered root profiles may take years to relax back to the initial state. We hypothesized that the alteration of the belowground root structures may be a source of terrestrial ecosystem legacy that is missing from models. To test this idea we undertook three core activities. (1) We developed a global-scale analysis of the impact of dynamic roots on ecosystem legacy building from a recently developed dynamic root module. (2) We developed new root dynamics in the DOE’s Energy Land Model (ELM) that allowed not only root profiles to shift their profile but also simultaneously alter carbon allocation to fine root pools. We then tested the impact of these new dynamics with intensive sensitivity analysis at four long-term AmeriFlux sites. (3) We undertook detailed isotopic analysis of tree rings from these AmeriFlux sites to assess ecophysiological and ecohydrological legacy to stress events that can be used to benchmark the sensitivity experiments with ELM. From these core activities, we report the following key findings. Firstly, on a global scale, the addition of dynamic roots led to chronically water-stressed ecosystems recovering faster to climate stress while wetter ecosystem showed enhanced legacy. This is because across ecosystems, stress events were almost universally associated with water shortages that led to the development of deeper root profiles. These deeper root profiles proved beneficial for recovery from drought stress. While the root dynamics did not universally improve the modeled representation of legacy it showed complex transient dynamics that emerge from the addition of dynamic roots. Secondly, the sensitivity analysis illustrated long term shifts in rooting depths away from the prescribed default profile suggesting that initializing of root profiles could benefit from spin-up simulations that converge on locally optimized root profiles. In addition, by enabling dynamic allocation some of the sites predicted unrealistically low allocation to roots (and high allocation to leaves). While these changes did not dramatically alter modeled gross primary productivity, they illustrated that without more sophisticated root processes in models, there is little penalty to dramatically disinvest in roots. Thirdly, the isotopic analysis of tree rings showed highly distinct legacy responses across species and sites. For example, T. canadensis showed reduced transpiration the year after stress events illustrated by sustained elevated $\delta^{18}$O. In contrast, A saccharum displayed elevated $\delta^{13}$C associated with reduced stomatal conductance in response to the previous years’ stress event. These geochemical signatures of legacy were present despite tree growth returning to normal the year after the stress. The results show the importance of species-level dynamics in legacy that are absent in modeling that assumes common traits within plant functional types. In summary, the work here established new avenues to explore root dynamics in models while illustrating how additional root processes are needed before dynamic carbon allocation can be implemented. Lastly, this project provided mentorship to a postdoctoral fellow, training for an early career scientist and multiple undergraduate students recruited from a minority serving institution.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Assessing mechanisms for microbial taxa and community dynamics using process models

Disentangling the assembly mechanisms controlling community composition, structure, distribution, functions, and dynamics is a central issue in ecology. Although various approaches have been proposed to examine community assembly mechanisms, quantitative characterization is challenging, particularly in microbial ecology. Here, we present a novel approach for quantitatively delineating community assembly mechanisms by combining the consumer–resource model with a neutral model in stochastic differential equations. Using time-series data from anaerobic bioreactors that target microbial 16S rRNA genes, we tested the applicability of three ecological models: the consumer–resource model, the neutral model, and the combined model. Our results revealed that model performances varied substantially as a function of population abundance and/or process conditions. The combined model performed best for abundant taxa in the treatment bioreactors where process conditions were manipulated. In contrast, the neutral model showed the best performance for rare taxa. Our analysis further indicated that immigration rates decreased with taxa abundance and competitions between taxa were strongly correlated with phylogeny, but within a certain phylogenetic distance only. The determinism underlying taxa and community dynamics were quantitatively assessed, showing greater determinism in the treatment bioreactors that aligned with the subsequent abnormal system functioning. Given its mechanistic basis, the framework developed here is expected to be potentially applicable beyond microbial ecology.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Tipping points emerge from weak mutualism in metacommunities

The coexistence of obligate mutualists is often precariously close to tipping points where small environmental changes can drive catastrophic shifts in species composition. For example, microbial ecosystems can collapse by the decline of a strain that provides an essential resource on which other strains cross-feed. Here, we show that tipping points, ecosystem collapse, bistability and hysteresis arise even with very weak (non-obligate) mutualism provided the population is spatially structured. Based on numeric solutions of a metacommunity model and mean-field analyses, we demonstrate that weak mutualism lowers the minimal dispersal rate necessary to avoid stochastic extinction, while species need to overcome a mean threshold density to survive in this low dispersal rate regime. Our results allow us to make numerous predictions for mutualistic metacommunities regarding tipping points, hysteresis effects, and recovery from external perturbations, and let us draw general conclusions for ecosystems even with random, not necessarily mutualistic, interactions and systems with density-dependent dispersal rather than direct mutualistic interactions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

The Use of Microelectrodes in Molten Salt Electrochemistry

Molten salts have attracted considerable interest as essential media for advanced high-temperature technologies, including molten salt reactors, thermal energy storage, high-temperature electrolysis, and pyrochemical processing. Their ability to remain stable in liquid form at elevated temperatures, combined with favorable thermophysical properties and wide electrochemical windows, makes them highly suitable for applications involving heat transfer, energy storage, and hightemperature electrochemical processing. However, despite these advantages, molten salts present challenges due to their chemically reactive nature at high-temperatures, especially in the presence of oxidizing impurities. Salt chemistry can fluctuate through interactions with impurities over time, or fuel burnup in the case of molten salt reactors, often leading to the dissolution of metal species. This dynamic environment not only results in complex redox behavior but also promotes corrosion, which is rarely uniform and frequently manifests as localized degradation driven by structural materials’ compositional differences, electrochemical imbalances, and microstructural susceptibilities.

Kim, Changkyu [University of Wisconsin-Madison, WI↗
DOE OSTI2023

Make Selenium Reactive Again: Activating Elemental Selenium for Synthesis of Metal Selenides Ranging from Nanocrystals to Large Single Crystals

The inertness of elemental selenium is a significant obstacle in the synthesis of selenium-containing materials at low reaction temperatures. Over the years, several recipes have been developed to overcome this hurdle; however, most of the methods are associated with the use of highly toxic, expensive, and environmentally harmful reagents. As such, there is an increasing demand for the design of cheap, stable, and nontoxic reactive selenium precursors usable in the low-temperature synthesis of transition metal selenides with vast applications in nanotechnology, thermoelectrics, and superconductors. Herein, a novel synthetic route has been developed for activating elemental selenium by using a solvothermal approach. By comprehensive 77 Se NMR, Raman, and infrared spectroscopies and gas chromatography–mass spectrometry, we show that the activated Se solution contained HSe – , [Se–Se] 2– , and Se 2– ions, as well as dialkyl selenide (R 2 Se) and dialkyl diselenide (R–Se–Se–R) species in dynamic equilibrium. This also corresponded to the first observation of naked Se 2 2– in solution. The versatility of the developed Se precursor was demonstrated by the successful synthesis of (i) the polycrystalline room-temperature modification of the β-Ag 2 Se thermoelectric material; (ii) large single crystals of superconducting β-FeSe; (iii) CdSe nanocrystals with different particle sizes (3–10 nm); (iv) nanosheets of PtSe 2 ; and (v) mono- and dibenzyl selenides and diselenides at room temperature. In conclusion, The simplicity and diversity of the developed Se activation method holds promise for applied and fundamental research.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗