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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Impact of functional groups on the electrocatalytic hydrogenation of aromatic carbonyls to alcohols

We report that electrocatalytic hydrogenation (ECH) of biomass-derived feedstocks has a critical dependence on the molecular structure of the organic and its adsorption on the electrode surface. In this study, we investigated the role of functional groups in the adsorption of the organic molecule on the charged Pd (111) surface and its subsequent effect on organic reduction in electrochemical hydrogenation of organic molecules. With three aromatic carbonyls of benzaldehyde (BZD), acetophenone (ACE), and vanillin (VAN), we rationalize molecular-scale adsorption and interfacial charge transfer processes by employing density-functional-theory based ab initio molecular dynamics simulations. We observe that the functional group and electrode charge strongly affect the proximity of organic molecule to the Pd (111) surface, where distances of aromatic ring and carbonyl group of the organic on the electrode change distinctively with functional groups and charge state of electrode, which strongly impact reduction of organics on the surface. Calculations of differential electron density show the strongest reduction with benzaldehyde via interfacial electron transfer from the charged Pd surface. We also observe that the interaction between the functional groups and solvent (VAN > BZD > ACE) significantly influence the organic interaction with the charged electrode (BZD > VAN > ACE), resulting in the net interaction energy between the organic and the electrode in the order of BZD > ACE > VAN. Experimental measurement of ECH rate also show the same trend of the net interaction energy. These results demonstrate the significance of solvent effect on the reducibility of organic molecules on electrodes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Connectivity-Dependent Exciton–Phonon Coupling in Cesium Bismuth Halide Quantum Dots

Metal halide octahedra form the fundamental functional building blocks of metal halide perovskites, dictating their structures, optical properties, electronic structures, and dynamics. Here, in this study, we show that the connectivity of bismuth halide octahedra in Cs 3 Bi 2 Br 9 and Cs 3 Bi 2 I 9 quantum dots (QDs) changes with different halide elements. We use first-principles calculations to reveal the key role of the connectivity of bismuth halide octahedra on the wave function symmetry, Huang-Rhys factor, and exciton-phonon interaction strength. Following QD synthesis via a ligand-mediated transport method, the effect of connectivity is verified with transient absorption spectroscopy, where we contrast Cs 3 Bi 2 Br 9 and Cs 3 Bi 2 I 9 QD exciton dynamics. In photoexcited Cs 3 Bi 2 I 9 QDs, phonons related to the vibrational motions of face-sharing [BiI 6 ] 3- bioctahedra couple strongly to the electronic state and drive rapid carrier relaxation. Equivalent signals are not observed for photoexcited Cs 3 Bi 2 Br 9 QDs, implying a lack of phonon involvement in band-edge absorption and subsequent exciton relaxation. Our findings suggest that structural engineering can effectively tune the exciton-phonon coupling and therefore influence exciton relaxation and recombination in perovskite nanomaterials.

TDDFT↗
DOE OSTI2022

Presentation of gas-phase-reactant-accessible single-rhodium-atom catalysts for CO oxidation, via MOF confinement of an Anderson polyoxometalate

Geometric or electronic confinement of guests within nanoporous hosts holds promise for imparting catalytic functionality, including single-metal-atom catalytic functionality, to existing materials. When the nanoporous host is a metal–organic framework (MOF), single-metal-ion catalysts have typically been installed by grafting to an open site on an inorganic node, with the node effectively becoming the support for the catalyst. This approach, however, imposes compositional constraints, as the node not only needs to be receptive to grafting, but also must be capable of stabilizing the framework against solvent evacuation, chemical exposure, and heating. Here, we show that disk-like, Anderson polyoxometalate clusters (RhMo 6 O 24 n- and Mo 7 O 24 m- ; POMs) can be confined in pore-specific and orientation-specific fashion within the hierarchically porous, Zr(IV)-based MOF, NU1K. Self-limiting loading of one cluster per pore, and associated nano-confinement, serve to isolate each POM and prevent consolidation caused by sintering. Additionally, the oriented confinement serves to expose individual rhodium atoms to candidate gas-phase reactants, while enabling the rhodium atom to employ a well-defined oxy-molybdenum cluster, rather than a MOF node, as a support. Synchrotron-based difference-electron-density maps and differential pair-distribution-function analyses of scattered X-rays establish cluster siting and orientation and confirm isolation. Nanoconfined (i.e., MOF- and POM-confined) single-rhodium(III)-atoms are catalytically competent for an illustrative gas-phase reaction, CO oxidation by O 2 , with the MOF-isolated POM enormously outperforming nonporous, MOF-free, solid (NH 4 ) 3 [H 6 RhMo 6 O 24 ]·6H 2 O. This paper highlights the value of MOF-based nano-confinement and oriented isolation of planar POMs as a means of uniformly presenting and stabilizing potent single-metal-atom catalysts, in reactant-accessible form, on well-defined supports.

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

Strong interlayer charge transfer due to exciton condensation in an electrically isolated GaAs quantum well bilayer

We introduce a design of electrically isolated “floating” bilayer GaAs quantum wells (QW), in which application of a large gating voltage controllably and highly reproducibly induces charges that remain trapped in the bilayer after removal of the gating voltage. At smaller gate voltages, the bilayer is fully electrically isolated from external electrodes by thick insulating barriers. This design permits full control of the total and differential densities of two coupled 2D electron systems. The floating bilayer design provides a unique approach for studying systems inaccessible by simple transport measurements. It also provides the ability to measure the charge transfer between the layers, even when the in-plane resistivities of the 2D systems diverge. We measure the capacitance and inter-layer tunneling spectra of the QW bilayer with independent control of the top and bottom layer electron densities. Our measurements display strongly enhanced inter-layer tunneling current at v T =1, a signature of exciton condensation of a strongly interlayer-correlated bilayer system. With fully tunable densities of individual layers, the floating bilayer QW system provides a versatile platform to access previously unavailable information on the quantum phases in electron bilayer systems.

42 ENGINEERING↗
DOE OSTI2025

Electrically‐Driven Metal‐Insulator Transitions Emerging from Localizing Current Density and Temperature

Negative differential resistance (NDR) is a key electronic response enabling two‐terminal artificial neurons that can be achieved through different physical phenomena, including phase‐homogeneous current density and temperature (electro‐thermal) localizations and spatially‐localized metal‐insulator phase transitions (MITs). These two effects have been observed to occur sequentially in select electrically‐biased transition metal oxides. However, it is unknown why and under what conditions localizing behaviors precede MITs, particularly as a function of device length scale. To this end, the interplay between phase‐homogeneous electro‐thermal localizations and MITs is investigated in a 3D multiphysics simulation of a lateral thin film device, using the material properties of the prototype MIT material VO 2 . These findings demonstrate that the MIT is nucleated through dynamically localizing current density and temperature. A critical device width (≈0.7 µm in this study) is identified, below which both the electrically‐induced electro‐thermal and phase inhomogeneities cease to appear. It is demonstrated that the formation of spatial inhomogeneities directly relates to device dimensions, and demonstrate the decoupling of NDR from the MIT through device scaling relationships. These results provide insight into the material phenomena underlying the material's electrical responses, clarifying conditions under which spatial inhomogeneities form in electrically‐biased MIT materials.

artificial neuron↗
DOE OSTI2020

Synthesis and characterization of Pt(Cu 0.67 Sn 0.33 )

Pt(Cu 0.67 Sn 0.33 ) has recently been found in a natural sample. In order to be able to characterize this new ternary compound, we synthesized it from the elements. Samples were characterized by X-ray powder diffraction, differential scanning calorimetry, thermal relaxation calorimetry, and scanning electron microscopy studies. Density functional theory-based model calculations complemented the experimental studies. Pt(Cu 0.67 Sn 0.33 )was already formed at a relatively low temperature of 773 K. Rietveld refinement of Pt(Cu 0.67 Sn 0.33 ) has been carried out in CuAu-type or L1 0 -type structure, space group P4/mmm, with Pt on 0,0,0 and disordered Cu and Sn on 1/2, 1/2, 1/2 and Z = 1. The lattice parameters are a = 2.823(1) Å, c = 3.64(1) Å, and V = 29.00(4) Å which are in good agreement with values obtained earlier on the natural sample and with the results of DFT calculations. The vibrational entropy for Pt(Cu 0.67 Sn 0.33 ) is $S_{298.15}^{vib}$ = 79.9(7) J mol -1 K -1 . The pressure dependence up to 36(2) GPa of the unit-cell volume and the lattice parameters and unit-cell volume have been obtained by synchrotron based powder diffraction using a diamond anvil cell. A fit of a 3rd-order Birch–Murnaghan equation of state to the Pt(Cu 0.67 Sn 0.33 )) (p,V)-data results in a bulk modulus of B 0 = 215(27) GPa and B' = 5(2).

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effect of Zn Addition on Phase Evolution in AlCrFeCoNiZn High–Entropy Alloy

The addition of Zn to AlCrFeCoNi high-entropy alloy (HEA) poses intriguing questions as to how it would affect phase evolution. Herein, the phase evolution in AlCrFeCoNiZn is studied using a combination of experimental techniques (X-ray diffraction, scanning electron microscopy, energy-dispersive spectroscopy, and differential scanning calorimetry) and computational (density-functional theory [DFT], calculation of phase diagrams, and machine-learning) methods. Mechanically alloyed and spark-plasma-sintered AlCrFeCoNiZn assumes a metastable single-phase, body-centered-cubic (BCC) structure that undergoes diffusion-controlled phase separation upon subsequent heat treatment to form separate (Al, Cr)-rich, (Fe, Co)-rich, and (Zn, Ni)-rich phases. The formation of (Al, Cr)-rich phase, not reported previously in AlCrFeCoNi-based HEAs, is attributed to strong clustering tendency of Cr–Zn and Cr–Ni pairs, combined with the strong ordering of Zn–Ni pair, driving out Cr that in turn combines with Al to form a (Al, Cr)-rich phase. In the DFT results, the formation of thermodynamically stable L1 2 phase is shown wherein Cr–Fe–Zn [Al–Ni-Co] preferably occupy1a (000) [3c (0 ½ ½)] positions. Furthermore, the sluggish diffusional transformation to L1 2 phase from BCC precursors is attributed to the small stacking-fault energy of AlCrFeCoNiZn. The equilibrated HEA exhibits a high microhardness of 8.24 GPa with an elastic modulus of 184 GPa.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Simulating Electron Impact Ionization using a General Particle Tracer (GPT) Custom Element

A new C++ custom element has been developed with the framework of General Particle Tracer (GPT) to simulate electron impact ionization of residual gas molecules. The custom element uses Monte-Carlo routines to determine both the ion production rate and the secondary electron kinetic energy based on user-defined gas densities and theoretical values for the ionization cross section and the secondary electron differential cross section. It then uses relativistic kinematics to track the secondary electron, the scattered electron, and the newly formed ion after ionization. The ion production rate and the secondary electron energy distribution determined by the custom element have been benchmarked against theoretical calculations and against simulations made using the simulation package IBSimu. While the custom element was originally built for particle accelerator simulations, it is readily extensible to other applications. The custom element will be described in detail and examples of applications at the Thomas Jefferson National Accelerator Facility will be presented for ion production in a DC high voltage photo-gun.

Yoskowitz, J. T.↗
DOE OSTI2021

Highly accurate and constrained density functional obtained with differentiable programming

Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain a highly accurate neural network–based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. Here we evaluate our model against different families of XC approximations and show that at the meta-GGA level our functional exhibits unprecedented accuracy for both energy and density predictions. For nonempirical functionals, there is a strong linear correlation between energy and density errors. We use this correlation to define an XC functional quality metric that includes both energy and density errors, leading to an improved way to rank different approximations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Evolution of Chain Dynamics and Oxidation States with Increasing Chain Length for a Donor–Acceptor-Conjugated Oligomer Series

While it is known that the chain length strongly affects the properties of π-conjugated polymers, the effects of chain length on the molecular structure, chain conformation, and oxidation state properties in donor–acceptor-type conjugated structures remain unclear. This limits our understanding of how the polymer molecular weight impacts material properties. Here, a discrete and monodisperse oligomer series (n = 3, 5, 7, 9, 15, and 21) and polymers (nPB), composed of the donor 3,4-propylenedioxythiophene (ProDOT), the acceptor benzothiadiazole (BTD), and methylthio end-capping groups, are synthesized by C–H-activated cross-coupling. The molecular structure, molecular weight, and dispersity of each oligomer/polymer are thoroughly characterized by nuclear magnetic resonance spectroscopy, mass spectrometry, and gel permeation chromatography. This series reveals a rod-to-coil transition at n = 15 and coil formation at polymer length scales of ~28 units via solution small-angle neutron scattering characterization. The oxidation states are deciphered via cyclic voltammetry, differential pulse voltammetry, spectroelectrochemistry, and density functional theory calculations. Oligomers 3–9 undergo successive one-electron oxidation steps, while 15 and higher undergo multielectron oxidations per step in CH 2 Cl 2 –TBAPF6 at a Pt ultramicroelectrode. The electronic transition of each oxidation state (1+, 2+, 3+, etc.) is tracked by absorption spectroscopy, revealing a “bipolaron to di-polaron” transition at n = 7 at which shorter oligomers prefer bipolaron formation and longer oligomers prefer di-polaron formation in their dication states. Furthermore, oxidized 15 has a lower electronic transition energy compared to its polymer homologue, as shown by spectroelectrochemistry, revealing a synergy between the chain length and the oxidation state properties. This study proves that the convergence limit between small molecule and polymer behavior occurs at approximately 15 units and highlights the property transitions that occur as a function of chain length for a donor–acceptor class of conjugated organic materials.

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

VLBI Data Processing on Coronal Radio-sounding Experiments of Mars Express

The ESA’s Mars Express solar corona experiments were performed at two solar conjunctions in the years 2015 and 2017 by a number of radio telescopes in the European VLBI Network. This paper presents the methods to measure the frequency and phase fluctuations of the spacecraft radio signal, and the applications to study the characteristics of the plasma turbulence effects on the signal at a single station and at multiple stations via cross correlation. The power spectra of the frequency fluctuations observed between 4.9 and 76.3 R {sub s} have a power-law shape close to a Kolmogorov spectrum over the frequency interval ν {sub lo} < ν < ν {sub up}, where the nominal value of ν {sub lo} is set to 3 mHz and ν {sub up} is in the range of 0.03–0.15 Hz. The rms of the frequency fluctuations is presented as a function of the heliocentric distance. Furthermore, we analyze the variations of the electron column density fluctuations at solar offsets 4.9 R {sub s} and 9.9 R {sub s} and the cross-correlation products between the VLBI stations. The power density of the differential fluctuations between different stations decreases at ν < 0.01 Hz. Finally, the fast flow speeds of solar wind >700 km s{sup -1} are derived from the cross correlation of frequency fluctuations at ν < 0.01 Hz. The fast flow speeds of solar wind correspond to the high heliolatitude of the coronal region that the radio rays passed. The VLBI observations and analysis methods can be used to study the electron column density fluctuations and the turbulence at multiple spatial points in the inner solar wind by providing multiple lines of sight between the Earth and the spacecraft.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Coal-based Bricks & Blocks (CBBs): Process Development to Prototype Fabrication Coupled with Techno-Economic Analysis and Market Survey

The decline of coal use for energy production provides an abundance of local feedstock for new innovative uses and value-added products. Expanding the U.S. coal-value chain to manufacture high-value carbon products can strengthen the nation’s energy and mineral security, enhance the U.S. national defense security, increase the United States’ economic prosperity, while achieving U.S. environmental objectives. The primary project goal is a relatively light-weight composite product with superior (or comparable) compressive strength. Both virgin and, where available, post-consumer recycled thermoplastic versions are tested for each thermoplastic species. A useful attribute of thermoplastics as binders is that they can be heated to their melting point, cooled, and reheated again without significant degradation. A key advantage of thermoset CBBs is that they require only mixing and molding. CBB advantages include low cost, availability, binding ability and processability. Coal-based bricks and blocks (CBBs) weigh about 50% less than clay bricks and can be manufactured with an interlocking design to promote ease of use for the novice builder. CBB formulation is evaluated according to a design-of-experiments (DoE) approach. DoE variables are a) relative weight fractions of binder, b) relative proportions of large versus small (milled) anthracite size fractions, and c) additive percentage. Fabrication methods include hot-press molding and extrusion, the later being the most commercially viable. CBBs are tested for compressive strength, modulus of rupture (by flexure test) and water absorption per ASTM C67, with density determined by the Archimedes drainage method. Fractured interfaces are examined by SEM (Scanning Electron Microscopy) to resolve fracture dynamics and interior microstructure uniformity. Differential scanning calorimetry (DSC) is used to compare plastic transition temperatures i.e., glass and melting temperatures to contrast virgin with post-consumer recycled thermoplastics and optimize their usage. These results are used in the DoE analysis to identify the binder and relative weight percentages for optimum strength, density, and porosity. Overall, CBBs possess strength comparable to clay-based bricks but are non-permeable and hydrophobic, and hence resistant to degradation by freeze-fracturing, corrosion, and efflorescence. The strongest composites have been made with the following thermoplastic binders (in order of strength): thermoset, high-density polyethylene crosslink resin, high-density polyethylene, nylon 6/6, and polypropylene. Results from a techno-economic analysis TEA show economy of scale for CBBs by modularization and reveal the binder as the cost driver for material costs. Ideally, the incorporation of post-consumer recycled thermoplastic will decrease material acquisition costs and increase product sustainability. Notably, CBBs do not require the high temperature calcination needed to produce cement, nor do they require firing in the 1600-2400 °F range for three days using natural gas, as do clay brick equivalents. Instead, CBBs are heated to a modest <600 °F according to the melt flow index of the thermoplastic binder. Existing anthracite mines can be expanded to produce CBBs to reduce aggregate transportation costs and emissions that exist for clay bricks. TEA reflects this reduced energy cost while a comparative CO2 emission analysis quantifies the reduced environmental footprint. The market survey identifies several commercialization opportunities, dependent upon the brick classification.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2026

Strong long-wavelength electron-phonon coupling in Ta 2 ⁢Ni⁡(Se,S) 5

The search for intrinsic excitonic insulators (EI) has long been confounded by coexisting electron–phonon coupling in bulk materials. Although the ground state of an EI may be difficult to differentiate from density-wave orders or other structural instabilities, excited states offer distinctive signatures. One way to provide clarity is to directly inspect the phonon spectral function for long wavelength broadening caused by phonon interaction with the high velocity EI phason. Here, in this study, we report that the quasi-one-dimensional (quasi-1D) EI candidate Ta 2 NiSe 5 shows extremely anisotropic phonon broadening and softening in the semimetallic normal state. In contrast, such behavior is completely absent in the broken symmetry state of Ta 2 NiSe 5 and in the isostructural Ta 2 NiS 5 , where the latter has a fully gapped normal state. By contrasting the expected phonon lifetimes in the BCS and BEC limits of a putative EI, our results suggest that the phase transition in Ta 2 Ni(Se,S) 5 family is closely related to strong interband electron–phonon coupling. We experimentally determine the dimensionless coupling $\frac{g}{ω_0}$ ∼ 10, revealing Ta 2 Ni(Se,S) 5 as a rare “ultrastrong coupling” material.

Kang, Zhibo [Yale University, New Haven, CT (Unite↗
DOE OSTI2023

Differentiating Between Simultaneous Loss Drivers in Earth's Outer Radiation Belt: Multi‐Dimensional Phase Space Density Analysis

Abstract We analyzed the contribution of electromagnetic ion cyclotron (EMIC) wave driven electron loss to a flux dropout event in September 2017. The evolution of electron phase space density (PSD) through the dropout showed the formation of a radially peaked PSD profile as electrons were lost at high L* , resembling distributions created by magnetopause shadowing. By comparing 2D Fokker Planck simulations of pitch angle diffusion to the observed change in PSD, we found that the μ and K of electron loss aligned with maximum scattering rates at dropout onset. We conclude that, during this dropout event, EMIC waves produced substantial electron loss. Because pitch angle diffusion occurred on closed drift paths near the last closed drift shell, no radial PSD minimum was observed. Therefore, the radial PSD gradients resembled solely magnetopause shadowing loss, even though the local pitch angle scattering produced electron losses of several orders of magnitude of the PSD.

Staples, F. A.↗
DOE OSTI2026

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗
DOE OSTI2020

Correlation strength and orbital differentiation across the phase diagram of plutonium metal

We compare the trends on the strength of electronic correlations across the different phases of elemental Pu focusing on its site and orbital dependence, using a combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) calculations within the vertex corrected one crossing approximation. We find that Pu-5f states are more correlated in δ -Pu, followed by some crystallographic sites in α and β phases. In addition, we observe that Pu-5f 5/2 and Pu-5f 7/2 orbital differentiation is a general feature of this material, as is site differentiation in the low-symmetry phases. The Pu-5f 5/2 states show Fermi liquid like behavior, whereas the Pu-5f 7/2 states remaining incoherent down to very low temperatures. We correlate the correlation strength in the different phases to their structure and the Pu-5 f occupancy of their crystallographic sites.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Metal–Ligand Covalency in the Valence Excited States of Metal Dithiolenes Revealed by S 1s3p Resonant Inelastic X-ray Scattering

Metallo dithiolene complexes with biological and catalytic relevance are well-known for having strong metal–ligand covalency, which dictates their valence electronic structures. We present the resonant sulfur Kβ (1s3p) X-ray emission spectroscopy (XES) for a series of Ni and Cu bis(dithiolene) complexes to reveal the ligand sulfur contributions to both the occupied and unoccupied valence orbitals. While S K-edge X-ray absorption spectroscopy played a critical role in identifying the covalency of the unoccupied orbitals of metal dithiolenes, the present focus on XES explores the occupied density of states. For a series of [Cu(mnt) 2 ] n– and [Ni(mnt) 2 ] n– anions and dianions, a comparison of the nonresonant and resonant S Kβ XES spectra highlights the dramatic improvement in spectral resolution and corresponding ability to differentiate subtle changes in occupied electronic structure across the series. Furthermore, the use of resonant inelastic X-ray scattering (RIXS) probes the valence excited states and the core–valence couplings of the complexes. By employing a theoretical approach based on time-dependent density functional theory to interpret the RIXS spectra, we reveal how metal–ligand covalency influences the excited state energies and covalencies. We identify the low energy excited states as having the same symmetry as the nominal “ligand field” or “d–d” states that typically dominate the photophysics of 3d metal complexes but with significant metal– ligand charge transfer character dictated by their covalency. These results suggest that strong metal–ligand covalency can be used to influence the charge-transfer photochemistry of first row transition metal complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗