Search NASA⌕ Search

SEARCH · Search NASA

Results for “Describing function”

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 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Heat transport and temperature boundary-layer profiles in closed turbulent Rayleigh–Bénard convection with slippery conducting surfaces

Here, we report direct numerical simulations (DNS) of the Nusselt number Nu , the vertical profiles of mean temperature Θ(z) and temperature variance Ω(z) across the thermal boundary layer (BL) in closed turbulent Rayleigh–Bénard convection (RBC) with slippery conducting surfaces ( z is the vertical distance from the bottom surface). The DNS study was conducted in three RBC samples: a three-dimensional cuboid with length L=H and width W=H/4 ( H is the sample height), and two-dimensional rectangles with aspect ratios Γ≡L/H=1 and 10. The slip length b for top and bottom plates varied from 0 to ∞ . The Rayleigh numbers Ra were in the range 10 6 $⩽$Ra$⩽$10 10 and the Prandtl number Pr was fixed at 4.3 . As b increases, the normalised Nu/Nu 0 ( Nu 0 is the global heat transport for b =0 ) from the three samples for different Ra and Γ can be well described by the same function Nu/Nu 0 = N 0 tanh( b /λ 0 )+1 , with N 0 =0.8±0.03 . Here λ 0 ≡ L /(2 Nu 0 ) is the thermal boundary layer thickness for b =0 . Considering the BL fluctuations for Pr >1, one can derive solutions of temperature profiles Θ(z) and Ω(z) near the thermal BL for b $⩾$ 0 . When b =0 , the solutions are equivalent to those reported by Shishkina et al. ( Phys. Rev. Lett. , vol. 114, 2015, 114302) and Wang et al. ( Phys. Rev. Fluids , vol. 1, 2016, 082301(R)), respectively, for no-slip plates. For b >0, the derived solutions are in excellent agreement with our DNS data for slippery plates.

42 ENGINEERING↗
DOE OSTI2017

Anaerobic Heme Degradation: ChuY Is an Anaerobilin Reductase That Exhibits Kinetic Cooperativity

Heme catabolism is an important biochemical process that many bacterial pathogens utilize to acquire iron. However, tetrapyrrole catabolites can be reactive and often require further processing for transport out of the cell or conversion to another useful cofactor. In previous work, we presented in vitro evidence of an anaerobic heme degradation pathway in Escherichia coli O157:H7. Consistent with reactions that have been reported for other radical S-adenosyl-l-methionine methyltransferases, ChuW transfers a methyl group to heme by a radical-mediated mechanism and catalyzes the β-scission of the porphyrin macrocycle. Here, this facilitates iron release and the production of a new linear tetrapyrrole termed “anaerobilin”. In this work, we describe the structure and function of ChuY, an enzyme expressed downstream from chuW within the same heme utilization operon. ChuY is structurally similar to biliverdin reductase and forms a dimeric complex in solution that reduces anaerobilin to the product we have termed anaerorubin. Steady state analysis of ChuY exhibits kinetic cooperativity that is best explained by a random addition mechanism with a kinetically preferred path for initial reduced nicotinamide adenine dinucleotide phosphate binding.

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

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance

Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.

algorithmic development↗
DOE OSTI2018

Improvements to the AMOEBA Force Field by Introducing Anisotropic Atomic Polarizability of the Water Molecule

Here in this work, we have developed an anisotropic polarizable model for the AMOEBA force field that is derived from electrostatic fitting on a gas phase water molecule as the primary approach to improve the many-body polarization model. We validate our approach using small to large water cluster benchmark data sets and ambient liquid water properties and through comparisons to a variational energy decomposition analysis breakdown of molecular interactions for water and water–ion trimer systems. We find that the accounting of anisotropy polarization for a single water molecule demonstrably improves the description of the many-body polarization energy in all cases. This study provides a proof of principle for extending our protocol for developing a general purpose anisotropic polarizable force field for other biological and material functional groups to better describe complex and asymmetric environments for which accurate polarization models are most needed.

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

In Situ Studies of Methanol Decomposition Over Cu(111) and Cu2O/Cu(111): Effects of Reactant Pressure, Surface Morphology, and Hot Spots of Active Sites

The dissociative adsorption of methanol was investigated on Cu(111) and ultrathin Cu 2 O films. We employed synchrotron-based Ambient Pressure X-ray Photoelectron Spectroscopy (AP-XPS) and Scanning Tunneling Microscopy (STM) to study the dynamics of gas–solid interactions, and calculations based on Density Functional Theory (DFT) were used to examine the reaction path. C 1s XPS spectra revealed that methanol underwent dissociative adsorption on plain Cu(111) to form methoxy (CH 3 O), formaldehyde (H 2 CO), and formate (HCOO) at a pressure range of 0.5–10 mTorr, with these species remaining on the surface after evacuation. This was accompanied by the appearance of a low coverage (~0.05 ML) of O ads in the O 1s which can be considered a highly active site for methanol activation. The high activity is apparent by a coverage of 0.8 ML of methoxy at room temperature. STM was unable to image these species at room temperature as they were highly mobile on metallic copper. In contrast, for CH 3 OH on Cu 2 O/Cu(111), STM showed clear hot spots for reaction and a complex array of adsorption structures. On the oxide substrate, there was decomposition of methanol to H 2 CO, CH 3 O, HCOO, and hydrocarbon species (CH x ) due to the subsequent interactions of methanol with lattice oxygen. Cu(111) remained entirely saturated with decomposition products under 10 mTorr of methanol (θ ≈ 0.97 ML), whereas the Cu 2 O overlayer was saturated at a much lower coverage (θ ≈ 0.30 ML). STM revealed rows and step edges of Cu 2 O decorated with decomposition products and metallic Cu islands ~5 nm in size. The difference in activity between Cu(111) and Cu 2 O/Cu(111) is attributed to the significant amount of O present on the oxide surface. Additionally, Density Functional theory (DFT) calculations described the XPS measurements well, showing a likely methanol dissociation to *CH 3 O and therefore a surface reduction. More importantly, the DFT results revealed that it was the chemisorbed oxygen on Cu 2 O/Cu(111) which oxidized the dissociated *CH 3 O to *HCOO and eventually CO 2 , while the reaction only involving upper oxygen on the Cu 2 O hexagonal ring led to the formation of H 2 CO.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Nanocomposites Based on Coil-Comb Diblock Copolymers

The polymer chain architecture is an important factor determining the phase behavior of nanoparticle (NP) assembly in polymer matrices. Block copolymers (BCPs) containing a random copolymer (RCP) block present a convenient variation on traditional BCPs to tune the interaction parameters between the polymer blocks and the nanofillers as well as to evaluate the effect of the chain architecture on the NP arrangements within BCP microdomains. Here, we synthesized BCPs with a coil polystyrene (PS) block and a comb RCP block through reversible addition-fragmentation chain transfer polymerization. The RCP block consists of methyl- and lauryl acrylates, the latter of which confers a long-chain alkyl moiety to favorably interact with alkyl-passivated NPs. BCPs showing lamellar, cylindrical, and mixed morphologies were obtained by varying the volume fractions of the RCP block (f RCP ). In comparison to coil-coil BCP, the coil-comb BCPs show highly asymmetric phase behavior with respect to fRCP, where lamellar morphologies were observed at fRCP from 0.31 to 0.51. NPs in the size of 4-5 nm were successfully incorporated in the RCP block of the BCPs with periodicities of 30-60 nm. An order-to-order phase transition from lamellae to PS cylinders was observed after the addition of only 1-2 vol % 5 nm NPs into the BCP with a periodicity of 25 nm and f RCP of 0.51. Self-consistent field theory-density functional theory simulations qualitatively described the observed morphologies and phase transitions in the nanocomposites. Here, the current study presents a platform to fabricate nanocomposites with NP assemblies in coil-comb BCPs that contain a random copolymer block and provides insight into how polymer chain architectures can affect the phase behavior of BCPs and nanocomposites.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Time-Dependent Consolidation in Porous Geomaterials at In Situ Conditions of Temperature and Pressure

Analysis of quartz sandstones shows that grain-scale crushing (fracture and rearrangement) and associated sealing of fractures contribute significantly to consolidation. The crushing strength (P*) for granular material is defined by laboratory experiments conducted at strain rates of 10 -4 to 10 -5 s -1 and room temperature. Based on experiments, many sandstones would require burial depths in excess of the actual maximum burial depth to create observed microstructure and density. In this paper, we use experiments and soil mechanics principles to determine rate laws for brittle consolidation of fine-grained quartz sand to better estimate in situ failure conditions of porous geomaterials. Experiments were conducted on St. Peter sand utilizing different isostatic consolidation and creep load paths at temperatures to 200 °C and at strain rates of 10 -4 to 10 -10 s -1 . Experiment results are consistent with observed rate dependence of consolidation in soils, and P* for sand can be identified by the change in the dependence of consolidation rate with stress, allowing the extrapolation of P* determined in the laboratory to geologic rates and temperatures. Additionally, normalized P* values can be described by a polynomial function to quantify temperature, stress, and strain-rate relationships for the consolidation of porous geomaterials by subcritical cracking. At geologic loading rates, P* for fine-grained quartz sand is achieved within ~3-km burial depth, and thus, shear-enhanced compaction under nonisostatic stress can occur at even shallower depths. Finally, these results demonstrate that time and temperature effects must be considered for predicting the brittle consolidation of sediments in depositional basins, petroleum reservoirs, and engineering applications.

58 GEOSCIENCES↗
DOE OSTI2023

Photonically active bowtie nanoassemblies with chirality continuum

Chirality is a geometrical property described by continuous mathematical functions. However, in chemical disciplines, chirality is often treated as a binary left or right characteristic of molecules rather than a continuity of chiral shapes. Although they are theoretically possible, a family of stable chemical structures with similar shapes and progressively tuneable chirality is yet unknown. Here we show that nanostructured microparticles with an anisotropic bowtie shape display chirality continuum and can be made with widely tuneable twist angle, pitch, width, thickness and length. The self-limited assembly of the bowties enables high synthetic reproducibility, size monodispersity and computational predictability of their geometries for different assembly conditions. The bowtie nanoassemblies show several strong circular dichroism peaks originating from absorptive and scattering phenomena. Unlike classical chiral molecules, these particles show a continuum of chirality measures that correlate exponentially with the spectral positions of the circular dichroism peaks. Finally, Bowtie particles with variable polarization rotation were used to print photonically active metasurfaces with spectrally tuneable positive or negative polarization signatures for light detection and ranging (LIDAR) devices.

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

Semi-empirical model for Henry’s law constant of noble gases in molten salts

Henry’s law constant, which describes the proportionality of dissolved gas to partial pressure of free gas in liquid–gas equilibrium systems, can also be applied to mass transport applications. In this work, we investigated an approach for determining the solubility of noble gases in a molten salt liquid utilizing the equilibrium concept of Henry’s gas constant. Henry’s gas constant is described as a mathematical function dependent on the van der Waals radius of the noble gas and the temperature of the molten salt. The alteration in Gibbs free energy encompasses contributions from both surface and volume energies. Enthalpy and entropy are deduced from these surface and volume energies in the Gibbs free energy formulation. A comparative analysis was conducted between the conventional method and our proposed model. Moreover, useful chemical properties can be determined from examination of surface and volume energies. Our findings provide an accurate and general theory of Gibbs free energy that can be validated experimentally based on the model proposed herein. This work unifies the prediction of Henry gas constant and subsequently the entropy and enthalpy calculation for noble gases in a molten salt solution to a single functional form using van der Waals radius of the gas and temperature of the system. This functional form is then used to perform a multiple regression method to find two parameters corresponding to the surface energy and volume energy. These two parameters are consistent between all combinations of noble gas and molten salt.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Eu 2+ –Eu 3+ valence transition in double, Eu-, and Na-doped PbSe from transport, magnetic, and electronic structure studies

The Eu atoms in Pb 1-x Eu x Se have long been assumed to be divalent. We show that p-type doping of this magnetic semiconductor alloy with Na can modify the effective Eu valence: a mixed, Eu 2+ –Eu 3+ state appears in Pb 1-x-y Eu x Na y Se at particular values of y. Magnetization, carrier concentration, resistivity, and thermopower of Pb 1-x-y Eu x Na y Se are reported for a number of samples with different x and y. A pronounced increase in thermopower at a given carrier concentration was identified and attributed to the presence of enhanced ionized impurity scattering. A strong decrease in the hole concentration is observed in Pb1-yNaySe when Eu is added to the system, which we attribute to a Eu 2+ –Eu 3+ self-ionization process. This is evidenced by magnetization measurements, which reveal a significant reduction of the magnetic moment of Pb 1-x Eu x Se upon alloying with Na. Further, a deviation of magnetization from a purely paramagnetic state, described by a Brillouin function, identifies antiferromagnetic interactions between the nearest-neighbor Eu atoms: a value of J ex /k B = -0.35 K was found for the exchange coupling parameter. The conclusion of a Eu 2+ –Eu 3+ self-ionization process being in effect is supported further by the electronic structure calculations, which show that an instability of the 4f 7 configuration of the Eu 2+ ion appears with Na doping. In conclusion, schematically, it was found that the Eu 4f levels form states near enough to the Fermi energy that hole doping can lower the Fermi energy and trigger a reconfiguration of a 4f electronic shell.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Combining Landau–Zener theory and kinetic Monte Carlo sampling for small polaron mobility of doped BiVO 4 from first-principles

Transition metal oxides such as BiVO 4 are promising photoelectrode materials for solar-to-fuel conversion applications. However, their performance is limited by the low carrier mobility (especially electron mobility) due to the formation of small polarons. Recent experimental studies have shown improved carrier mobility and conductivity by atomic doping; however the underlying mechanism is not understood. A fundamental atomistic-level understanding of the effects on small polaron transport is critical to future material design with high conductivity. We studied the small polaron hopping mobility in pristine and doped BiVO 4 by combining Landau–Zener theory and kinetic Monte Carlo (kMC) simulation fully from first-principles, and investigated the effect of dopant–polaron interactions on the mobility. We found that polarons are spontaneously formed at V in both pristine and Mo/W doped BiVO 4 , which can only be described correctly by density functional theory (DFT) with the Hubbard correction (DFT+U) or hybrid exchange-correlation functional but not local or semi-local functionals. We found that DFT+U and dielectric dependant hybrid (DDH) functionals give similar electron hopping barriers, which are also similar between the room temperature monoclinic phase and the tetragonal phase. The calculated electron mobility agrees well with experimental values, which is around 10 -4 cm 2 V -1 s -1 . We found that the electron polaron transport in BiVO4 is neither fully adiabatic nor nonadiabatic, and the first and second nearest neighbor hoppings have significantly different electronic couplings between two hopping centers that lead to different adiabaticity and prefactors in the charge transfer rate, although they have similar hopping barriers. Without considering the detailed adiabaticity through Landau–Zener theory, one may get qualitatively wrong carrier mobility. We further computed polaron mobility in the presence of different dopants and showed that Cr substitution of V is an electron trap while Mo and W are “repulsive” centers, mainly due to the minimization of local lattice expansion by dopants and electron polarons. The dopants with “repulsive” interactions to polarons are promising for mobility improvement due to larger wavefunction overlap and delocalization of locally concentrated polarons.

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

Density functional theory studies of transition metal carbides and nitrides as electrocatalysts

Transition metal carbides and nitrides are interesting non-precious materials that have been shown to replace or reduce the loading of precious metals for catalyzing several important electrochemical reactions. The purpose of this review is to summarize density functional theory (DFT) studies, describe reaction pathways, identify activity and selectivity descriptors, and present a future outlook in designing carbide and nitride catalysts for the hydrogen evolution reaction (HER), oxygen evolution reaction (OER), oxygen reduction reaction (ORR), nitrogen reduction reaction (N 2 RR), CO 2 reduction reaction (CO 2 RR) and alcohol oxidation reactions. Furthermore, this topic is of high interest to scientific communities working in the field of electrocatalysis and this review should provide theoretical guidance for the rational design of improved carbide and nitride electrocatalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Enhancement of Raman scattering from molecules placed near metal nanoparticles

Large Raman scattering cross sections from molecules on surfaces of metallic nanoparticles are described within a renormalization-group theory. In this approach the valence electrons of the molecules are embedded in an effective medium described by a dielectric function, which integrates out the effect of the plasmonic excitations of the metallic nanoparticles. The source of the enhanced photon inelastic scattering is produced by the resonant excitation of surface plasmons at the metallic nanoparticles. Here, a similar theory has been successfully used to explain the resonant x-ray inelastic scattering and the behavior of nonlinear susceptibilities at the x-ray edges

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Polarizable charge equilibration model for predicting accurate electrostatic interactions in molecules and solids

Electrostatic interactions play a critical role in determining the properties, structures, and dynamics of chemical, biochemical, and material systems. These interactions are described well at the level of quantum mechanics (QM) but not so well for the various models used in force field simulations of these systems. In this paper, we propose and validate a new general methodology, denoted PQEq, to predict rapidly and dynamically the atomic charges and polarization underlying the electrostatic interactions. Here the polarization is described using an atomic sized Gaussian shaped electron density that can polarize away from the core in response to internal and external electric fields, while at the same time adjusting the charge on each core (described as a Gaussian function) so as to achieve a constant chemical potential across all atoms of the system. The parameters for PQEq are derived from experimental atomic properties of all elements up to Nobelium (atomic no. = 102). Additionally, we validate PQEq by comparing to QM interaction energy as probe dipoles are brought along various directions up to 30 molecules containing H, C, N, O, F, Si, P, S, and Cl atoms. We find that PQEq predicts interaction energies in excellent agreement with QM, much better than other common charge models such as obtained from QM using Mulliken or ESP charges and those from standard force fields (OPLS and AMBER). Since PQEq increases the accuracy of electrostatic interactions and the response to external electric fields, we expect that PQEq will be useful for a large range of applications including ligand docking to proteins, catalytic reactions, electrocatalysis, ferroelectrics, and growth of ceramics and films, where it could be incorporated into standard force fields as OPLS, AMBER, CHARMM, Dreiding, ReaxFF, and UFF.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Average neutron time-of-flight instrument response function inferred from single D-T neutron events within a plastic scintillator

The apparent ion temperature and neutron-reaction history are important characteristics of a fusion plasma. Extracting these quantities from a measured neutron-time-of-flight signal requires accurate knowledge of the instrument response function (IRF). This paper describes a novel method for obtaining the IRF directly for single DT neutron interactions by utilizing n-alpha coincidence. The t(d,α)n nuclear reaction was produced at Sandia National Laboratories’ Ion Beam Laboratory using a 300 keV Cockcroft-Walton generator to accelerate a 2.5 μA beam of 175 keV D + ions into a stationary ErT 2 target. The average neutron IRF was calculated by taking a time-corrected average of individual neutron events within an EJ-228 plastic scintillator. The scintillator was coupled to two independent photo-multiplier tubes operated in the current mode: a Hamamatsu 5946 mod-5 and a Photek PMT240. Finally, the experimental setup and results will be discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Experimental observation of cnoidal waveform of nonlinear dust acoustic waves

The experimentally measured waveform of nonlinear dust acoustic waves in a plasma is shown to be accurately described by a cnoidal function. This function, which is predicted by nonlinear theory, has broad minima and narrow peaks. Fitting the experimental waveforms to the cnoidal function also provides a measure of the wave’s nonlinearity, namely, the elliptical parameter k. By characterizing experimental results at various wave amplitudes, we confirm that the parameter k increases and approaches a maximum value of unity, as the wave amplitude is increased. Here, the underlying theory that predicts the cnoidal waveform as an exact solution of a Korteweg-de Vries model equation takes account of the streaming ions that are responsible for the spontaneous excitation of the dust acoustic waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

The Random Ray Method Versus Multigroup Monte Carlo: The Method of Characteristics in OpenMC and SCONE

The Random Ray Method (TRRM) is a recently developed approach to solving neutral particle transport problems based on the Method of Characteristics. While the method previously has been implemented only in closed-source or limited-functionality codes, this work describes its implementation in two open-source Monte Carlo codes: OpenMC and SCONE. The random ray implementations required small modifications to the existing Multigroup Monte Carlo (MGMC) solvers, offering a rare venue for redundant, fine-grained, "apples-to-apples" speed and accuracy comparisons between transport methods. To this end, TRRM and MGMC solvers are evaluated against each other using each code's native capabilities on reactor eigenvalue problems with different degrees of energy discretization. On the C5G7 benchmark (featuring only seven energy groups), TRRM achieves a maximum pin power error comparable to or lower than that of MGMC for a given run time. On a problem with 69 energy groups, MGMC is found to scale more efficiently, obtaining a lower pin power error for a given run time. However, the defining difference between the two transport methods is found to be their vastly different uncertainty distributions. Specifically, TRRM is found to maintain similar levels of accuracy and uncertainty throughout the simulation domain whereas MGMC can exhibit orders-of-magnitude greater errors in areas of the problem that feature low neutron flux. For instance, TRRM provided an up to 373 times speed advantage compared with MGMC for computing the flux in low-flux regions in the moderator surrounding the C5G7 core.

42 ENGINEERING↗
DOE OSTI2020

Crystallography of Reactive Intermediates

Metal–ligand (M–L) multiply bonded complexes hold a central place in inorganic chemistry and catalysis: From fundamental and historical perspectives, these species have played a critical role in the articulation of important bonding principles (i.e. the vanadyl ion in the development of molecular orbital theory); from a practical perspective, these species are critical intermediates in a variety of chemical reactions (i.e. N 2 and O 2 reduction, H 2 O oxidation, and C–H functionalization). For many high-valent, early metal complexes, overlap of ligand-based electrons with vacant π-symmetry orbitals leads to strong M–L multiple bonds. The stability of these species enables straightforward characterization with a suite of standard spectroscopic and diffraction-based experiments. Mid- and late-transition metal complexes, with attendant higher d-electron counts, often support more reactive M–L multiply bonded fragments. The reactivity of these species simultaneously renders them attractive intermediates for catalysis but challenging synthetic targets to observe and characterize. A number of important strategies have been advanced to enable experimental characterization of mid- to late-metal–ligand multiply bonded species. Synthetic manipulation of the coordination geometry and ligand donicity, as well as introduction of sterically encumbering ligands, have each emerged as powerful methods to tame the inherent reactivity of kinetically labile M–L multiple bonds. While these efforts have resulted in families of well-characterized complexes and provided critical insights regarding structure and bonding, the synthetic derivatization required to stabilize M–L fragments of interest often obviates the substrate functionalization activity relevant to catalysis. Photochemical synthesis of reactive species provides a conceptually attractive strategy to generate reactive M–L fragments under conditions compatible with time-resolved or cryogenic steady-state characterization, and photogeneration has enabled observation of a number of reactive M–L fragments. The suite of tools available to characterize photogenerated reactive species is often more limited than typical for kinetically stabilized complexes and structural characterization is typically not possible. Recently, photocrystallographic experiments, in which reactive M–L multiply bonded intermediates are generated within single-crystal matrices, have been advanced as a strategy to interrogate the structures of reactive intermediates in C–H functionalization. Lastly, this Comment describes the historical antecedents to these experiments, highlights examples of photocrystallographic characterization of reactive intermediates, and discusses future opportunities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗