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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 217 records · Page 12

Deep-ultraviolet ptychographic pocket-scope (DART): mesoscale lensless molecular imaging with label-free spectroscopic contrast

The mesoscale characterization of biological specimens has traditionally required compromises between resolution, field-of-view, depth-of-field, and molecular specificity, with most approaches relying on external labels. Here we present the Deep-ultrAviolet ptychogRaphic pockeT-scope (DART), a handheld platform that transforms label-free molecular imaging through intrinsic deep-ultraviolet spectroscopic contrast. By leveraging biomolecules’ natural absorption fingerprints and combining them with lensless ptychographic microscopy, DART resolves down to 308-nm linewidths across centimeter-scale areas while maintaining millimeter-scale depth-of-field. The system’s virtual error-bin methodology effectively eliminates artifacts from limited temporal coherence and other optical imperfections, enabling high-fidelity molecular imaging without lenses. Through differential spectroscopic imaging at deep-ultraviolet wavelengths, DART quantitatively maps nucleic acid and protein distributions with femtogram sensitivity, providing an intrinsic basis for explainable virtual staining. We demonstrate DART’s capabilities through imaging of tissue sections, cytopathology specimens, blood cells, and neural populations, revealing detailed molecular contrast without external labels. The combination of high-resolution molecular mapping and broad mesoscale imaging in a portable platform opens new possibilities from rapid clinical diagnostics, tissue analysis, to biological characterization in space exploration.

60 APPLIED LIFE SCIENCES↗

Effects of pH on an IDP conformational ensemble explored by molecular dynamics simulation

The conformational ensemble of intrinsically disordered proteins, such as α-synuclein, are responsible for their function and malfunction. Misfolding of α-synuclein can lead to neurodegenerative diseases, and the ability to study their conformations and those of other intrinsically disordered proteins under varying physiological conditions can be crucial to understanding and preventing pathologies. In contrast to well-folded peptides, a consensus feature of IDPs is their low hydropathy and high charge, which makes their conformations sensitive to pH perturbation. We examine a prominent member of this subset of IDPs, α-synuclein, using a divide-and-conquer scheme that provides enhanced sampling of IDP structural ensembles. We constructed conformational ensembles of α-synuclein under neutral (pH ~ 7) and low (pH ~ 3) pH conditions and compared our results with available information obtained from smFRET, SAXS, and NMR studies. Specifically, α-synuclein has been found to in a more compact state at low pH conditions and the structural changes observed are consistent with those from experiments. We also characterize the conformational and dynamic differences between these ensembles and discussed the implication on promoting pathogenic fibril formation. We find that under low pH conditions, neutralization of negatively charged residues leads to compaction of the C-terminal portion of α-synuclein while internal reorganization allows α-synuclein to maintain its overall end-to-end distance. Here, we also observe different levels of intra-protein interaction between three regions of α-synuclein at varying pH and a shift towards more hydrophilic interactions with decreasing pH.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Shock-induced transformation of nitinol shape memory alloy: Effect of stress state on transformation

Due to its numerous practical applications and intriguing phase transformation behavior, shape memory alloys (SMAs) have garnered significant research and development interests. In the past, most studies on the mechanical behavior of SMAs have been conducted under uniaxial stress loadings. Limited research on SMAs under shock loading has not provided conclusive results regarding their transformation behavior and transformation stress under such loading. Additionally, there is a lack of comprehensive understanding regarding the effects of different stress states on transformation behavior. The main objectives of this study are to address these issues. To achieve these objectives, a series of shock wave experiments were designed and conducted. Additionally, quasi-static and dynamic uniaxial stress experiments were carried out to establish a baseline for comparison. The results revealed that the transformation stress under dynamic uniaxial strain shock loading was approximately 1.92 GPa in contrast to 0.5 GPa (quasi-static) to 0.8 GPa (dynamic) observed in uniaxial stress loading. The transformation behavior exhibited noticeable rate sensitivity for both types of loading. There appeared to be a critical strain rate above which the austenite phase was driven to a metastable state. This estimated critical axial strain rate along the loading direction was approximately 2 × 10 3 /s–4 × 10 3 /s for uniaxial stress loading and approximately 2 × 10 6 /s for uniaxial strain loading. The apparent high transformation stress for uniaxial strain loading can likely be attributed to a combination of high-pressure confinement and high strain rate. Furthermore, determining their relative contributions remains an open issue.

36 MATERIALS SCIENCE↗

Homologous mutations in human β, embryonic, and perinatal muscle myosins have divergent effects on molecular power generation

Mutations at a highly conserved homologous residue in three closely related muscle myosins cause three distinct diseases involving muscle defects: R671C in β-cardiac myosin causes hypertrophic cardiomyopathy, R672C and R672H in embryonic skeletal myosin cause Freeman–Sheldon syndrome, and R674Q in perinatal skeletal myosin causes trismus-pseudocamptodactyly syndrome. It is not known whether their effects at the molecular level are similar to one another or correlate with disease phenotype and severity. To this end, we investigated the effects of the homologous mutations on key factors of molecular power production using recombinantly expressed human β, embryonic, and perinatal myosin subfragment-1. We found large effects in the developmental myosins but minimal effects in β myosin, and magnitude of changes correlated partially with clinical severity. The mutations in the developmental myosins dramatically decreased the step size and load-sensitive actin-detachment rate of single molecules measured by optical tweezers, in addition to decreasing overall enzymatic (ATPase) cycle rate. In contrast, the only measured effect of R671C in β myosin was a larger step size. Our measurements of step size and bound times predicted velocities consistent with those measured in an in vitro motility assay. Finally, molecular dynamics simulations predicted that the arginine to cysteine mutation in embryonic, but not β, myosin may reduce pre-powerstroke lever arm priming and ADP pocket opening, providing a possible structural mechanism consistent with the experimental observations. This paper presents direct comparisons of homologous mutations in several different myosin isoforms, whose divergent functional effects are a testament to myosin’s highly allosteric nature.

59 BASIC BIOLOGICAL SCIENCES↗

Angle-resolved polarized Raman spectroscopy study of phosphorene nanoribbons

We present a systematic angle-resolved polarized Raman spectroscopy (ARPRS) study of black phosphorus (BP) nanostructures formed via electrochemical sodium- and lithium-ion intercalation. Sodium intercalation leads to bundles of densely packed, highly uniform phosphorene nanoribbons (PNRs) separated by parallel amorphous channels, whereas lithium intercalation results in shorter, irregular nanoribbon-like segments with lower aspect ratios. In both cases, six additional Raman peaks (P1–P6) appear alongside the three primary Raman-active modes of BP (A$^{1}_{g}$, B 2g , and A$^{2}_{g}$). These peaks are attributed to the amorphous regions, as confirmed by their isotropic angular dependence in ARPRS measurements. The three BP modes show pronounced angular variations that differ significantly between the two intercalated samples. In sodium-intercalated BP, A$^{1}_{g}$ and A$^{2}_{g}$ modes retain a dumbbell-like angular dependence under parallel polarization with enhanced anisotropy and reduced symmetry under crossed polarization. At the same time, the B 2g mode transitions from four-lobed (cloverleaf) polar plot to a butterfly-like one. In contrast, lithium-intercalated BP exhibits weaker anisotropy and less distinct angular polar plots for all three modes. These differences reflect the sensitivity of phonon behavior to underlying nanostructure morphology. The vibrational frequencies density of states (FDOS) calculations attribute the B 2g mode transformation to phonon band folding and mode mixing in PNRs. This study demonstrates the power of ARPRS in probing phonon-structure relationships and highlights the influence of edge geometry and quantum confinement on phonon dispersion in PNRs.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Three New Late-type Stellar Companions to Very Dusty WISE Debris Disks Identified with SPHERE Imaging

Debris disk stars are good targets for high-contrast imaging searches for planetary systems, since debris disks have been shown to have a tentative correlation with giant planets. We selected 20 stars identified as debris disk hosts by the WISE mission, with particularly high levels of warm dust. We observed these with the VLT/SPHERE high-contrast imaging instrument with the goal of finding planets and imaging the disks in scattered light. Our survey reaches a median 5σ sensitivity of 10.4 M {sub J} at 25 au and 5.9 M {sub J} at 100 au. We identified three new stellar companions (HD 18378B, HD 19257B, and HD 133778B): two are mid-M-type stars and one is a late-K or early-M star. Three additional stars have very widely separated stellar companions (all at >2000 au) identified in the Gaia catalog. The stars hosting the three SPHERE-identified companions are all older (≳700 Myr), with one having recently left the main sequence and one a giant star. We infer that the high volumes of dust observed around these stars has been caused by a recent collision between the planets and planetesimal belts in the system, although for the most evolved star, mass loss could also be responsible for the infrared excess. Future mid-infrared spectroscopy or polarimetric imaging may allow the positions and spatial extent of these dust belts to be constrained, thereby providing evidence as to the true cause of the elevated levels of dust around these old systems. None of the disks in this survey is resolved in scattered light.

47 OTHER INSTRUMENTATION↗

Search for the Chiral Magnetic Effect with charge-dependent azimuthal correlations in Xe–Xe collisions at s NN = 5.44 TeV

Charge-dependent two- and three-particle correlations measured in Xe–Xe collisions at $\sqrt{s_{NN}}$ = TeV are presented. Results are obtained for charged particles in the pseudorapidity range |η| and transverse momentum interval 02. ≤ p T < GeV/c for different collision centralities. The three-particle correlator γ αβ ≡ $\langle$cos(φ α + φ β - 2Ψ a )$\rangle$, calculated for different combinations of charge sign α and β, is expected to be sensitive to the presence of the Chiral Magnetic Effect (CME). Its magnitude is similar to the one observed in Pb–Pb collisions in contrast to a smaller CME signal in Xe–Xe collisions than in Pb–Pb collisions predicted by Monte Carlo (MC) calculations including a magnetic field induced by the spectator protons. These observations point to a large non-CME contribution to the correlator. Furthermore, the charge dependence of γ αβ can be described by a blast wave model calculation that incorporates background effects and by the Anomalous Viscous Fluid Dynamics model with values of the CME signal consistent with zero. The Xe–Xe and Pb–Pb results are combined with the expected CME signal dependence on the system size from the MC calculations including a magnetic field to obtain the fraction of CME contribution in γ αβ , $f$ CME . The CME fraction is compatible with zero for the 30% most central events in both systems and then becomes positive. This yields an upper limit of 2% (3%) and 25% (32%) at 95% (99.7%) confidence level for the CME signal contribution to γ αβ in the 0–70% Xe–Xe and Pb–Pb collisions, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Speciation and Organic Phase Structure in Nitric Acid Extraction with Trioctylamine

Understanding chemical speciation and intermolecular interactions in multicomponent liquids is essential to understanding their phase and chemical equilibria, which underpin chemical separation processes, including solvent extraction. Here we report on the extraction of nitric acid from its aqueous solutions into organic solutions of trioctylamine (TOA) in toluene, investigated with spectroscopic, X-ray scattering, and computational tools to understand molecular speciation in the organic phase and its relationship with the nanoscale structure of the organic phase. Trends in acid and water extraction clearly show two and three regimes, respectively, indicating different stoichiometric relationships, but speciation of HNO 3 , water, and amine in these regimes is not apparent. 1 H NMR of the organic phase shows that there are at least two distinct acidic protons in the organic phase while ATR-FTIR results show that the organic phase with excess acid extraction is a mixture of trioctylammonium-nitrate ion pairs (TOAHNO 3 ), and undissociated HNO 3 molecules. Comparison with DFT-computed IR spectra show that the chain-like configurations of TOAHNO 3 HNO 3 H 2 O are favored over TOAHNO 3 H 2 OHNO 3 , i.e., direct interaction between the nitrate and HNO 3 molecules is more favored compared to a water-mediated interaction. SAXS of the organic phases were modeled as sums of Ornstein-Zernike (O-Z) scattering and a prepeak feature in the higher Q region that corresponds to extractant packing. The extraction of undissociated HNO 3 by the ion pairs leads to an increased X-ray scattering contrast in the organic phase without any significant change in the correlation length. These results show that the organic phase nanostructure is more sensitive to the concentration of TOAHNO 3 and is relatively unaffected by excess acid extraction. Finally, these findings will enable a molecular understanding of the mechanisms behind metal extraction from acidic media with basic extractants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Suppression of Composition g -modes in Chemically Equilibrating Warm Neutron Stars

We investigate the impact of chemical equilibration and the resulting bulk viscosity on nonradial oscillation modes of warm neutron stars at temperatures up to T ≈ 5 MeV, relevant for protoneutron stars and neutron star postmerger remnants. In this regime, the relaxation rate of weak interactions becomes comparable to the characteristic frequencies of composition g-modes in the core, resulting in resonant damping. To capture this effect, we introduce the dynamical sound speed, a complex, frequency-dependent generalization of the adiabatic sound speed that encodes both the restoring force and the dissipative effects of bulk compression. Using realistic weak reaction rates and three representative equations of state, we compute the complex frequencies of composition g-modes with finite-temperature profiles. We find that bulk viscous damping becomes increasingly significant with temperature and can completely suppress composition g-modes. In contrast, the f-mode remains largely unaffected by bulk viscosity due to its nearly divergence-free character. Our results highlight the sensitivity of g-mode behavior to thermal structure, weak reaction rates, and the equation of state, and establish the dynamical sound speed as a valuable descriptor characterizing oscillation properties in dissipative neutron star matter.

Neutron stars↗

Quantum sensing using a qubit for the detection of ionizing radiation

Quantum sensing utilizes the inherent sensitivity of a quantum system to external stimuli. Our goal is to leverage this sensitivity to develop a quantum sensor designed for the detection of ionizing radiation. Here we report on the design, fabrication, and measurement of a new quantum device for hard x-ray and gamma-ray detection. Our quantum device is based on a superconducting quantum bit (qubit) with superconducting tunnel junctions as the core device elements. We describe our experimental investigation directed toward the detection metrics of energy resolution, dynamic range, and active area. In contrast to existing superconducting detectors, the active area per qubit may be much larger than the physical area of the tunnel junctions or the physical area of the qubit device, due to the sensitivity of quantum coherence to ionizing radiation deposition within a radius on the millimeter or centimeter scale. Furthermore, our experimental design enables an ionizing radiation source at room temperature to be detected by our quantum sensor at low temperature.

qubit↗

Towards operational atmospheric correction of airborne hyperspectral imaging spectroscopy: Algorithm evaluation, key parameter analysis, and machine learning emulators

Atmospheric correction of airborne hyperspectral imaging spectroscopy (AHIS) to obtain high-quality surface reflectance is the prerequisite for remote sensing applications. Over the last decades, different atmospheric correction methods have been developed based on radiative transfer models (RTMs), however, the relative performances of different algorithms are unclear. Automated operational atmospheric correction methods to process large-volume AHIS data in a high-accurate and high-throughput manner are still lacking. Therefore, this study proposed an operational atmospheric correction pipeline for deriving surface reflectance from AHIS data. To ensure the accuracy and efficiency of the pipeline, we focused on three specific aspects: (1) selecting a suitable RTM for the development of atmospheric lookup tables (LUTs) by comparing the commercial MODerate resolution atmospheric TRANsmission (MODTRAN) and open-sourced Library for Radiative TRANsfer (LibRadTRAN) models, where the widely-used software, Atmospheric/Topographic Correction for Airborne Imagery (ATCOR), was used as benchmarks; (2) identifying key atmospheric correction parameters and determining suitable sources for parameter retrievals including AHIS, Moderate Resolution Imaging Spectroradiometer (MODIS), and AErosol RObotic NETwork (AERONET); and (3) testing the performance of using machine learning emulators to speed up the RTM-based atmospheric correction. Results indicate that (1) atmospheric correction based on MODTRAN LUTs can produce surface reflectance accurately with mean absolute errors < 0.05 and cosine similarities > 0.98 compared to field measurements, which is comparable to the software ATCOR and slightly outperforms the LibRadTRAN LUTs; (2) sobol global sensitivity analysis demonstrates that in the atmospheric correction, visibility and water vapor are two key parameters that can be accurately derived from AHIS in contrast to MODIS or AERONET data; and (3) Random Forest emulators can produce accurate estimations of surface reflectance with mean absolute errors < 0.03 and cosine similarities > 0.98 for higher processing efficiency and determine a suitable set of wavelengths for retrieving atmospheric visibility and water vapor. In conclusion, the proposed atmospheric correction pipeline also improved the four-stream radiative transfer theory for airborne applications by considering adjacent effects from airborne surrounding pixels and can also be applied for atmospheric correction of hyperspectral data from spaceborne missions.

47 OTHER INSTRUMENTATION↗

Invited article: X-ray phase contrast imaging in inertial confinement fusion and high energy density research

X-ray phase contrast imaging (XPCI) provides enhanced image contrast beyond absorption-based x-ray imaging alone due to refraction and diffraction from gradients in the object material density. It is sensitive to small variations in density, such as internal voids, cracks, grains, defects, and material flow, as well as to stronger density variations such as from a shock wave. Beyond its initial use in biology and materials science, XPCI is now routinely used in inertial confinement fusion (ICF) and high energy density (HED) research, first to characterize ICF capsules and targets, and later applied in dynamic experiments, where coherent x-ray sources, ultrafast x-ray pulses, and high temporal and spatial resolution are required. In this Review article, XPCI image formation theory is presented, its diverse use in ICF and HED research is discussed, the unique requirements for ultrafast XPCI imaging are given, as well as current challenges and issues in its use.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Evaporation barrier for dark matter in celestial bodies

The minimum testable dark matter (DM) mass for almost all DM signatures in celestial bodies is determined by the rate at which DM evaporates. DM evaporation has previously been calculated assuming a competition between the gravitational potential of the object, and thermal kicks from the celestial-body matter. We point out a new effect, where mediators with a range larger than the interparticle spacing induce a force proportional to the density gradient of celestial objects, forming an evaporation barrier for the DM. This effect can be so significant that evaporation does not occur even for sub-MeV DM, in stark contrast to previous calculations. This opens up a wide range of new light DM searches, many orders of magnitude in DM mass below the sensitivity of direct detection.

79 ASTRONOMY AND ASTROPHYSICS↗

Fabrication-robust silicon photonic devices in standard sub-micron silicon-on-insulator processes

Perturbations to the effective refractive index from nanometer-scale fabrication variations in waveguide geometry plague high index-contrast photonic platforms; this includes the ubiquitous sub-micron silicon-on-insulator (SOI) process. Such variations are particularly troublesome for phase-sensitive devices, such as interferometers and resonators, which exhibit drastic changes in performance as a result of these fabrication-induced phase errors. In this Letter, we propose and experimentally demonstrate a design methodology for dramatically reducing device sensitivity to silicon width variations. We apply this methodology to a highly phase-sensitive device, the ring-assisted Mach–Zehnder interferometer (RAMZI), and show comparable performance and footprint to state-of-the-art devices, while substantially reducing stochastic phase errors from etch variations. This decrease in sensitivity is directly realized as energy savings by significantly reducing the required corrective thermal tuning power, providing a promising path toward ultra-energy-efficient large-scale silicon photonic circuits.

Rizzo, Anthony (ORCID:000000034752797X)↗

Climatological sensitivities of shallow-cumulus bulk entrainment in continental and oceanic locations

Cumulus entrainment is a complex process that has long challenged conceptual understanding and atmospheric prediction. To investigate this process observationally, two retrievals are used to generate multi-year climatologies of shallow-cumulus bulk entrainment ( ϵ ) at two Atmospheric Radiation Measurement cloud observatories, one in the US southern Great Plains (SGP) and the other in the Azores archipelago in the eastern North Atlantic (ENA). The statistical distributions of ϵ thus obtained, as well as certain environmental and cloud-related sensitivities of ϵ , are consistent with previous findings from large-eddy simulations. The retrieved ϵ robustly increases with cloudlayer relative humidity and decreases in wider clouds and cloud ensembles with larger cloud-base mass fluxes. While ϵ also correlates negatively with measures of cloud-layer vigor (e.g., maximum in-cloud vertical velocity and cloud depth), the extent to which these metrics actually regulate ϵ (or vice-versa) is unclear. Novel sensitivities of ϵ include a robust decrease of ϵ with increasing subcloud wind speed in oceanic flows, as well as a decrease of ϵ with increasing cloud-base mass flux in individual cumuli. A strong land–ocean contrast in ϵ is also found, with median values of 0.5-0.6 km -1 at the continental SGP site and and 1.0-1.1 km -1 at the oceanic ENA site. This trend is associated with drier and deeper cloud layers, along with larger cloud-base mass fluxes, at SGP, all of which favor reduced ϵ . The flow-dependence of retrieved ϵ implies that its various sensitivities should be accounted for in cumulus parameterization schemes.

54 ENVIRONMENTAL SCIENCES↗

Sensitivity of the Shallow‐To‐Deep Convective Transition to Moisture and Wind Shear in the Amazon

Deep convection is the primary influence on weather and climate in tropical regions. However, understanding and simulating the shallow‐to‐deep (STD) convective transition has long been challenging. Here, we conduct high‐resolution numerical simulations to assess the environmental controls on the evolution of isolated convection in the Amazon during the wet season. The large‐scale forcing derived through a constrained variational analysis approach for the GoAmazon2014/5 Experiment is used in the simulations. Through sensitivity experiments, we examine the relative importance of moisture and wind shear in controlling the shallow‐to‐deep convective transition for isolated convective events. Convection exhibits the greatest sensitivity to humidity within the lowest 1.5 km, where a 4 mm reduction in column water vapor nearly suppresses ice water formation on deep convective days. In contrast, a reduction in column water vapor in the free troposphere by a factor of two or more is necessary to produce a comparable impact on convection. Increasing low‐level wind speed from 6 to 9 m s -1 enhances afternoon deep convection, raising the cloud ice mixing ratio by approximately 25%. Conversely, upper‐level wind shear reveals the weakest correlation with daytime convection in our simulations. Our results help characterize the role of moisture and wind shear on the STD transition and our understanding of the underlying mechanisms.

environmental controls↗

Gold leaf phantom development for the assessment of proton radiographic sensitivity limits simulating gold nanoparticle tagged tumors

Proton radiography may guide proton therapy cancer treatments with beam’s-eye-view anatomical images and a proton-based estimation of proton stopping power. However, without contrast enhancement, proton radiography will not be able to distinguish tumor from tissue. To provide this contrast, functionalized, high-Z nanoparticles that specifically target a tumor could be injected into a patient before imaging. We conducted this study to understand the ability of gold, as a high-Z, biologically compatible tracer, to differentiate tumors from surrounding tissue. We indicate that AuNP-enhanced proton radiography might be a feasible technology to provide image-guidance to proton therapy, potentially reducing off-target effects and sparing nearby tissue. These data can be used to develop treatment plans and clinical applications can be derived from the simulations.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Site-specific electronic structure of covalently linked bimetallic dyads from nitrogen K-edge x-ray absorption spectroscopy

A nitrogen K-edge x-ray absorption near-edge structure (XANES) survey is presented for tetrapyrido[3,2-a:',3'-c:3'',2''-h:2''',3'''-j]phenazine (tpphz)-bridged bimetallic assemblies that couple chromophore and catalyst transition metal complexes for light driven catalysis, as well as their individual molecular constituents. We demonstrate the high N site sensitivity of the N pre-edge XANES features, which are energetically well-separated for the phenazine bridge N atoms and for the individual metal-bound N atoms of the inner coordination sphere ligands. By comparison with the time-dependent density functional theory calculated spectra, we determine the origins of these distinguishable spectral features. We find that metal coordination generates large shifts toward higher energy for the metal-bound N atoms, with increasing shift for 3d < 4d < 5d metal bonding. This is attributed to increasing ligand-to-metal σ donation that increases the effective charge of the bound N atoms and stabilizes the N 1s core electrons. In contrast, the phenazine bridge N pre-edge peak is found at a lower energy due to stabilization of the low energy electron accepting orbital localized on the phenazine motif. While no sensitivity to ground state electronic coupling between the individual molecular subunits was observed, the spectra are sensitive to structural distortions of the tpphz bridge. Here these results demonstrate N K-edge XANES as a local probe of electronic structure in large bridging ligand motifs, able to distinctly investigate the ligand-centered orbitals involved in metal-to-ligand and ligand-to-ligand electron transfer following light absorption.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗