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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

Structures of FOX-4 Cephamycinase in Complex with Transition-State Analog Inhibitors

Boronic acid transition-state analog inhibitors (BATSIs) are partners with β-lactam antibiotics for the treatment of complex bacterial infections. Herein, microbiological, biochemical, and structural findings on four BATSIs with the FOX-4 cephamycinase, a class C β-lactamase that rapidly hydrolyzes cefoxitin, are revealed. FOX-4 is an extended-spectrum class C cephalosporinase that demonstrates conformational flexibility when complexed with certain ligands. Like other β-lactamases of this class, studies on FOX-4 reveal important insights into structure–activity relationships. We show that SM23, a BATSI, shows both remarkable flexibility and affinity, binding similarly to other β-lactamases, yet retaining an IC 50 value < 0.1 μM. Our analyses open up new opportunities for the design of novel transition-state analogs of class C enzymes.

59 BASIC BIOLOGICAL SCIENCES↗

Decoupling of catalysis and transition state analog binding from mutations throughout a phosphatase revealed by high-throughput enzymology

Using high-throughput microfluidic enzyme kinetics (HT-MEK), we measured over 9,000 inhibition curves detailing impacts of 1,004 single-site mutations throughout the alkaline phosphatase PafA on binding affinity for two transition state analogs (TSAs), vanadate and tungstate. As predicted by catalytic models invoking transition state complementary, mutations to active site and active-site-contacting residues had highly similar impacts on catalysis and TSA binding. Unexpectedly, most mutations to more distal residues that reduced catalysis had little or no impact on TSA binding and many even increased tungstate affinity. These disparate effects can be accounted for by a model in which distal mutations alter the enzyme’s conformational landscape, increasing the occupancy of microstates that are catalytically less effective but better able to accommodate larger transition state analogs. In support of this ensemble model, glycine substitutions (rather than valine) were more likely to increase tungstate affinity (but not more likely to impact catalysis), presumably due to increased conformational flexibility that allows previously disfavored microstates to increase in occupancy. These results indicate that residues throughout an enzyme provide specificity for the transition state and discriminate against analogs that are larger only by tenths of an Ångström. Thus, engineering enzymes that rival the most powerful natural enzymes will likely require consideration of distal residues that shape the enzyme’s conformational landscape and fine-tune active-site residues. Biologically, the evolution of extensive communication between the active site and remote residues to aid catalysis may have provided the foundation for allostery to make it a highly evolvable trait.

59 BASIC BIOLOGICAL SCIENCES↗

Tipiracil binds to uridine site and inhibits Nsp15 endoribonuclease NendoU from SARS-CoV-2

SARS-CoV-2 Nsp15 is a uridine-specific endoribonuclease with C-terminal catalytic domain belonging to the EndoU family that is highly conserved in coronaviruses. As endoribonuclease activity seems to be responsible for the interference with the innate immune response, Nsp15 emerges as an attractive target for therapeutic intervention. Here we report the first structures with bound nucleotides and show how the enzyme specifically recognizes uridine moiety. In addition to a uridine site we present evidence for a second base binding site that can accommodate any base. The structure with a transition state analog, uridine vanadate, confirms interactions key to catalytic mechanisms. In the presence of manganese ions, the enzyme cleaves unpaired RNAs. This acquired knowledge was instrumental in identifying Tipiracil, an FDA approved drug that is used in the treatment of colorectal cancer, as a potential anti-COVID-19 drug. Using crystallography, biochemical, and whole-cell assays, we demonstrate that Tipiracil inhibits SARS-CoV-2 Nsp15 by interacting with the uridine binding pocket in the enzyme’s active site. Our findings provide new insights for the development of uracil scaffold-based drugs.

59 BASIC BIOLOGICAL SCIENCES↗

Structural snapshots of base excision by the cancer-associated variant MutY N146S reveal a retaining mechanism

Abstract DNA glycosylase MutY plays a critical role in suppression of mutations resulted from oxidative damage, as highlighted by cancer-association of the human enzyme. MutY requires a highly conserved catalytic Asp residue for excision of adenines misinserted opposite 8-oxo-7,8-dihydroguanine (OG). A nearby Asn residue hydrogen bonds to the catalytic Asp in structures of MutY and its mutation to Ser is an inherited variant in human MUTYH associated with colorectal cancer. We captured structural snapshots of N146S Geobacillus stearothermophilus MutY bound to DNA containing a substrate, a transition state analog and enzyme-catalyzed abasic site products to provide insight into the base excision mechanism of MutY and the role of Asn. Surprisingly, despite the ability of N146S to excise adenine and purine (P) in vitro, albeit at slow rates, N146S-OG:P complex showed a calcium coordinated to the purine base altering its conformation to inhibit hydrolysis. We obtained crystal structures of N146S Gs MutY bound to its abasic site product by removing the calcium from crystals of N146S-OG:P complex to initiate catalysis in crystallo or by crystallization in the absence of calcium. The product structures of N146S feature enzyme-generated β-anomer abasic sites that support a retaining mechanism for MutY-catalyzed base excision.

59 BASIC BIOLOGICAL SCIENCES↗

In-beam $$\gamma $$-ray spectroscopy of $$^{94}$$Ag

Abstract A recoil-beta-tagging experiment has been performed to study the excited $$T=0$$ T = 0 and $$T=1$$ T = 1 states in the odd–odd $$N=Z$$ N = Z nucleus $$^{94}$$ 94 Ag, populated via the $$^{40}$$ 40 Ca( $$^{58}$$ 58 Ni,1p3n) $$^{94}$$ 94 Ag reaction. The experiment was conducted using the MARA recoil separator and JUROGAM3 array at the Accelerator Laboratory of the University of Jyväskylä. Through correlating fast, high-energy beta decays at the MARA focal plane with prompt $$\gamma $$ γ rays emitted at the reaction target, a number of transitions between excited states in $$^{94}$$ 94 Ag have been identified. The timing characteristics of these transitions confirm that they fall within decay sequences that feed the short-lived $$T=1$$ T = 1 ground state of $$^{94}$$ 94 Ag. The transitions are proposed to proceed within and between the sets of states with $$T=0$$ T = 0 and $$T=1$$ T = 1 . Possible correspondence between some of these transitions from analog states in $$^{94}$$ 94 Pd has been discussed, and shell-model calculations including multipole and monopole electromagnetic effects have been presented, in order to enable predictions of the decay patterns between the $$T=0$$ T = 0 and $$T=1$$ T = 1 states and to allow a theoretical set of Coulomb energy differences to be calculated for the $$A = 94$$ A = 94 $$T=1$$ T = 1 analog states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reactivity descriptors in acid catalysis: acid strength, proton affinity and host–guest interactions

Brønsted acids mediate chemical transformations via proton transfer to bound species and interactions between the conjugate anion and bound cationic intermediates and transition states that are also stabilized by van der Waals forces within voids of molecular dimensions in inorganic hosts. This Feature Article describes the relevant descriptors of reactivity in terms of the properties of acids and molecules that determine their ability to donate and accept protons and to reorganize their respective charges to optimize their interactions at bound states. The deprotonation energy (DPE) of the acids and the protonation energy (Eprot) of the gaseous analogs of bound intermediates and transition states reflect their respective properties as species present at non-interacting distances. These properties accurately describe the reactivity of acids of a given type, such as polyoxometalates (POM) with a given type of addenda atom but different central atoms and heterosilicates, for different families of reactions. They do not fully capture, however, differences among acid types (e.g., Mo and W POM, heterosilicates, mineral acids) for diverse types of chemical transformations (e.g., elimination, isomerization, dimerization, condensation). The incompleteness of such descriptors reflects their inability to describe how protonated molecular species and conjugate anions restructure their respective charges when present as a binding pair at interacting distances. Such interaction energies represent electrostatic forces that depend on charge distributions in the cations and anions and the ability to reorganize the distributions to maximize the interactions. In the case of deprotonation, the electrostatic and charge reorganization components of DPE for various acids solely reflect the ability of the conjugate anion to accept and distribute the negative charge, a characteristic unique of each type of solid acid and specifically of the composition of its extended conjugate anion framework. The energy required to accept and rearrange the positive charge in bound intermediates and transition states reflects, in turn, their respective ability to recover the ionic and covalent components of DPE, the energy required to detach proton from conjugate anions. The DPE components and the recovery fractions together lead to a modified DPE, which captures only the part of DPE that remains unrecovered by the ion-pair interactions at bound intermediates and transition states, as the unifying descriptor for broad families of acids and reactions. The electrostatic and charge reorganization energies involved in these general descriptors are placed in historical context by assessing their connections to the heuristics of hard–soft acid–base displacements. Further development of these concepts requires benchmarking and extension of electrostatic and reorganization components of energies for a more diverse set of reaction types and acid families and advancement of methods for more efficient calculations of electrostatic interactions. Reactivity descriptors must also account for dispersive interactions between host cavities and guest molecules, requiring a framework analogous to the one described here for ion-pair interactions; these dispersive interactions depend on the fit between their shapes and sizes as well as their ‘‘structural stiffness’’ that determines the ability to modify the shapes of molecules and voids to minimize free energy. Entropy considerations and estimates of their dependence on properties of catalysts and molecules are also required for accurately determining Gibbs free energies that ultimately determine reaction rates.

Deshlahra, Prashant↗

Experimental and modeling study of the autoignition behavior of a saturated heterocycle: Pyrrolidine

Experiments are conducted in both rapid compression machine (RCM) and shock tube (ST) to better quantify autoignition behavior (e.g., ignition delay, heat release) and understand heteroatomic effects in heterocyclic compounds, which are important reference components for the combustion of biomass-derived liquid fuels. These tests focus on the nitrogen-containing, five-membered saturated ring, pyrrolidine, at diluted conditions covering pressures of 20 and 50 bar, temperatures of 720–1450 K and a range of stoichiometries (ϕ = 0.5–2). A chemical kinetic model is developed and coupled to an existing combustion kinetics framework describing key nitrogen containing intermediates (e.g. pyrrole, ammonia and NOx). H-abstraction reactions by OH, H, CH 3 and HO 2 , are determined using ab-initio transition state theory methods, while analogies to cyclopentane are adopted for many other reactions, such as ring-opening. Here, the autoignition measurements reveal the lack of negative temperature coefficient (NTC) behavior and low-temperature chemistry for pyrrolidine, as opposed to its saturated hydrocarbon analogue, cyclopentane. Interestingly, at the lowest temperatures (T < 750 K), the reactivity of cyclopentane is greater than pyrrolidine, while at higher temperatures, pyrrolidine becomes more reactive. Agreement between the experimental measurements and the model is good, and it is found that H-abstraction reactions by HO 2 and ensuing chemistry play key roles in controlling the reactivity of this cyclic amine. Most of the fluxes, i.e., >70 %, are predicted to move through 1- or 2-pyrroline (C 4 H 7 N) and then the cyclic C 4 H 6 N radical, at both lower and higher temperatures, to form either CH 2 CHCHCHNH via ring-opening or pyrrole via β-scission. It appears that the ring opens more easily at lower temperature whereas the C–H β-scission dominates at higher temperature and lower pressure, such that the reaction of the fuel radical intermediate carrying an unpaired electron on the nitrogen atom with HO 2 is the next most notable in promoting oxidation. When comparing pyrrolidine and cyclopentane, which exhibits distinct pathways in different temperature regimes, the pyrrolidine pathways and sensitivity analysis align more closely to the high temperature case of cyclopentane where the important role of HO 2 radicals is seen to provide chain branching through HO 2 reaction with the fuel, accompanied by H 2 O 2 formation and decomposition to OH. The formation of 5-membered diene rings and ring opening reactions are also found to be highly relevant. Of particular note, it is found that there is little influence of small molecule nitrogen-chemistry, e.g., NH 2 , HCN, NO/NO 2 on the reactivity of the pyrrolidine mixtures investigated here where no recirculated combustion gases are included.

Autoignition↗

Computational discovery of two-dimensional rare-earth iodides: promising ferrovalley materials for valleytronics

Two-dimensional Ferrovalley materials with intrinsic valley polarization are rare but highly promising for valley-based nonvolatile random access memory and valley filter devices. These ferromagnetic materials exhibit valleys at or near the Fermi level with intrinsic magnetism. The strong coupling between magnetism and spin–orbit coupling induces intrinsic valley polarization. Using Kinetically Limited Minimization, an unconstrained crystal structure prediction algorithm, and prototype sampling based on first-principles calculations, we have discovered new Ferrovalley materials, rare-earth iodides RI 2 , where R is a rare-earth element belonging to Sc, Y, or La-Lu, and I is Iodine. The rare-earth iodides are layered and demonstrate either 2H, 1T, or 1T d phase as the ground state in bulk, analogous to transition metal dichalcogenides (TMDCs). The calculated exfoliation energy of monolayers (MLs) is comparable to that of graphene and TMDCs, suggesting possible experimental synthesis. The MLs in the 2H phase exhibit ferromagnetism due to unpaired electrons in d and f orbitals. Throughout the rare-earth series, d bands have valley polarization at K and $\overline{K}$ points in the Brillouin zone in the vicinity of the Fermi level. Large intrinsic valley polarization in the range of 15–143 meV without external stimuli is observed in these Ferrovalley materials, which can be enhanced further by applying an in-plane bi-axial strain. These valleys can selectively be probed and manipulated for information storage and processing, potentially offering superior performance beyond conventional electronics and spintronics. Here we further show that the 2H ferromagnetic phase of RI 2 MLs possesses non-zero Berry curvature and exhibits anomalous valley Hall effect with considerable anomalous Hall conductivity. Our work will incite exploratory synthesis of the predicted Ferrovalley materials and their application in valleytronics and beyond.

2D materials↗

New Covariant Density Functionals of Nuclear Matter for Compact Star Simulations

We generate three families of extended covariant density functionals of nuclear matter that have varying slope of symmetry energy and skewness at nuclear saturation density, but otherwise share the same basic parameters (symmetry energy, compressibility, saturation parameters, etc.) with the standard DDME2, DD2, and MPE functionals. Tables of the parameters of these new density functionals are given, which can be straightforwardly used in DDME2, DD2, and MPE parameterization-based codes. Furthermore, we provide tables of a large number of equations of state (81 for each family) that can be used in astrophysical simulations to assess the impact of variations of the not-well-known slope of symmetry energy and skewness of nuclear systems on the astrophysics of compact objects. We also provide tables of computed integral parameters (mass, radius, and tidal deformability) that can be used, e.g., for modeling gravitational waveforms. Finally, for the extended DDME2-based parameterization, we implement a first-order phase transition to quark matter to obtain a family of equations of state that accommodates a phase transition to quark matter. Analogous tables of the equations of state and integral parameters are provided for this case as well.

79 ASTRONOMY AND ASTROPHYSICS↗

Coherent Many-Body Oscillations Induced by a Superposition of Broken Symmetry States in the Wake of a Quantum Phase Transition

It is now widely accepted that quenches through the critical region of quantum phase transitions result in post-transition states populated with topological defects—analogs of the classical topological defects. However, consequences of the very nonclassical fact that the state after a quench is a superposition of distinct, broken-symmetry vacua with different numbers and locations of defects have remained largely unexplored. Here, we identify coherent quantum oscillations induced by such superpositions in observables complementary to the one involved in symmetry breaking. These oscillations satisfy Kibble-Zurek dynamical scaling laws with the quench rate, with an instantaneous oscillation frequency set primarily by the gap of the system. In addition to the obvious fundamental significance of a superposition of different broken symmetry states, quantum coherent oscillations can be used to verify unitarity and test for imperfections of the experimental implementations of quantum simulators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Effect of network connectivity on behavior of synthetic Broborg hillfort glasses

There is wide industrial interest in developing robust models of long-term (>100 years) glass durability. Archeological glass analogs, glasses of similar composition, and alteration conditions to those being tested for durability can be used to evaluate and inform such models. Two such analog glasses from a 1500-year-old vitrified hillfort near Uppsala, Sweden have previously been identified as potential analogs for low concentration Fe-bearing aluminosilicate nuclear waste glasses. However, open questions remain regarding the melting environment from which these historic glasses were formed and the effect of these conditions on their chemical durability. A key factor to answering the previous melting and durability questions is the redox state of Fe in the starting and final materials. Past work has shown that the melting conditions of a glass-forming melt may influence the redox ratio value (Fe +3 /ΣFe), a measure of a glass's redox state, and both melting conditions and the redox ratio may influence the glass alteration behavior. Synthetic analogs of the hillfort glasses have been produced using either fully oxidized or reduced Fe precursors to address this question. In this study, the melting behavior, glass transition temperature, oxidation state, network structure, and chemical durability of these synthesized glass analogs is presented. Resulting data suggests that the degree of network connectivity as impacted by the oxidation state of iron impacted the behavior of the glass-forming melt but in this case does not affect the chemical durability of the final glass. Glasses with a lower degree of melt connectivity were found to have a lower viscosity, resulting in a lower glass transition temperature and softening temperature, as well as in a lower temperature of foam onset and temperature of foam maximum. This lower degree of network connectivity most likely played a more significant role in accelerating the conversion of batch chemicals into glass than the presence of water vapor in the furnace's atmosphere. Future work will focus on using the results from this work with outcomes from other aspects of this project to evaluate long-term glass alteration models.

36 MATERIALS SCIENCE↗

Validating Protection System Behavior with Machine Learning in a Master State Overseer

As power system protection devices continue the widespread transition from analog to digital, they become increasingly intricate. The internal functions and communication between critical grid components must now be significantly more complex to keep up with the demands of the modern smart grid. This brings increased difficulty in maintenance and monitoring, making it harder to identify potential misoperation, power anomalies, and cyber threats. Such issues are often only pinpointed after an exhaustive and costly post-mortem analysis, when a major outage or damage has already occurred. A solution is needed for validating protection systems as they operate, independently evaluating grid state and confirming whether the protection system is behaving accordingly. As opposed to incident response, this acts as a constant verification mechanism that raises a flag when subtler issues are noticed, catching them earlier and preventing larger incidents. This work presents the implementation of such a system, expanding on the prototype developed by the authors in a previous paper. This is accomplished with a machine learning (ML) system capable of validating the performance of protection systems by classifying anomalous events and characterizing protection system responses based solely on available current and voltage measurements. Additionally, this system is contextualized within a larger, modular Master State awareness Overseer (MSO) framework, responsible for monitoring, analyzing, and managing an electric grid.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

Analog-antianalog isospin mixing in 47 K 𝛽−decay

Here, we have measured the isospin mixing of the 𝐼 𝜋 =1/2 + , 𝐸 𝑥 = 2.599 MeV state in nearly doubly magic 47 Ca with the isobaric analog 1/2 + state of 47 K . Using the TRIUMF atom trap for 𝛽 decay, we have measured a nonzero asymmetry of the progeny 47 Ca with respect to the initial 47 K spin polarization, which together with the 𝛽 asymmetry implies a nonzero ratio of Fermi to Gamow-Teller matrix elements 𝑦 = 0.098 ± 0.037 for the 1/2 + → 1/2 + transition. Interpreting 𝑦 as mixing between this state and the isobaric analog state implies a Coulomb matrix element magnitude 101 ± 37 keV. This relatively large matrix element supports a model from the literature of analog-antianalog isospin mixing, which predicts large matrix elements in cases involving excess neutrons over protons occupying more than one major shell. The result supports pursuing a search for time-reversal odd, parity-even, isovector interactions using a correlation in 47 K 𝛽 decay.

beta decay↗

High-Pressure Rate Rules for Ether Alkylperoxy Radical Isomerization

The first isomerization reaction of an alkylperoxy (RO 2 ) radical holds significant importance in low-temperature oxidation, as it governs the branching ratios of the hydroperoxyalkyl (QOOH) radicals, which influence the competition between the chain-propagation and chain-branching reactions. In this study, we systematically calculated high-pressure rate rules for the RO 2 isomerization reaction of monoethers, exploring 5-, 6-, 7-, and 8-membered ring transition states. Primary, secondary, and tertiary carbon sites, where both the abstracting peroxy group and the abstracted hydrogen are located, were considered, with particular emphasis on distinguishing between secondary carbons adjacent (alpha) and nonadjacent to the ether functional group. Using the G4//B3LYP/6-311++G(2df,2pd) level of theory and the transition state theory, we estimated the rate constants and the Arrhenius coefficient for over 120 possible isomerization reactions. We examined the effect of ring size and ring atoms, revealing that 6- and 7-membered ring isomerizations were generally the fastest. The impact of the ether functional group on transition states was investigated by comparing reactions with identical ring size, peroxy, and radical positions, but with the ether functional group positioned either outside (i.e., out) or inside (i.e., in) the transition state ring, leading to differences in the rate constants. When comparing to analogous alkane rate constants, differences of up to an order of magnitude were observed, underscoring the need for caution when assigning rate rules by analogy. We applied our rate constants in the di-iso-butyl ether kinetic model and evaluated their influence on low-temperature chemistry finding that they altered the branching ratios by up to a factor of 9, highlighting the significance of site-specific rate constants for more accurate low-temperature modeling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dimensionality-Induced Change in Topological Order in Multiferroic Oxide Superlattices

We construct ferroelectric (LuFeO 3 ) m /(LuFe 2 O 4 ) superlattices with varying index m to study the effect of confinement on topological defects. We observe a thickness-dependent transition from neutral to charged domain walls and the emergence of fractional vortices. In thin LuFeO 3 layers, the volume fraction of domain walls grows, lowering the symmetry from P6 3 cm to P3c1 before reaching the nonpolar P6 3 /mmc state, analogous to the group-subgroup sequence observed at the high-temperature ferroelectric to paraelectric transition. Our study shows how dimensional confinement stabilizes textures beyond those in bulk ferroelectric systems.

36 MATERIALS SCIENCE↗

Optical polarization analogs in inelastic free-electron scattering

Advances in the ability to manipulate free-electron phase profiles within the electron microscope have spurred development of quantum-mechanical descriptions of electron energy loss (EEL) processes involving transitions between phase-shaped transverse states. Here, we elucidate an underlying connection between two ostensibly distinct optical polarization analogs identified in EEL experiments as manifestations of the same conserved scattering flux. Our work introduces a procedure for probing general tensorial target characteristics including global mode symmetries and local polarization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-pressure phase transition of olivine-type Mg 2 GeO 4 to a metastable forsterite-III type structure and their equations of state

Germanates are often used as structural analogs of planetary silicates. We have explored the high-pressure phase relations in Mg 2 GeO 4 using diamond-anvil cell experiments combined with synchrotron X-ray diffraction and computations based on density functional theory. Upon room temperature compression, forsterite-type Mg 2 GeO 4 remains stable up to 30 GPa. At higher pressures, a phase transition to a forsterite-III type (Cmc2 1 ) structure was observed, which remained stable to the peak pressure of 105 GPa. Using a third-order Birch Murnaghan fit to the experimental data, we obtained V 0 = 305.1(3) Å3, K 0 = 124.6(14) GPa, and $K'_0$ = 3.86 (fixed) for forsterite-type Mg 2 GeO 4 and V 0 = 263.5(15) Å 3 , K 0 = 175(7) GPa, and $K'_0$ = 4.2 (fixed) for the forsterite-III type phase. The forsterite-III type structure was found to be metastable when compared to the stable assemblage of perovskite/post-perovskite + MgO, as observed during laser-heating experiments. Understanding the phase relations and physical properties of metastable phases is crucial for studying the mineralogy of impact sites, understanding metastable wedges in subducting slabs, and interpreting the results of shock compression experiments.

58 GEOSCIENCES↗

The contribution of Compton ionization to ultrafast x-ray scattering

We investigate the role of Compton ionization in ultrafast non-resonant x-ray scattering using a molecular model system, which includes the ionization continuum via an orthonormalized plane wave ansatz. Elastic and inelastic components of the scattering signal, as well as coherent-mixed scattering that arises from electron dynamics, are calculated. By virtue of a near-quantitative distinction between scattering related to electronic transitions into bound and continuum states, we demonstrate how Compton ionization contributes to the coherent-mixed component. Analogous to inelastic scattering, the contribution to the coherent-mixed signal is significant and particularly manifests at intermediate and high-momentum transfers. Strikingly, for molecules with inversion symmetry, the exclusion of bound or continuum transitions may lead to the prediction of spurious coherent-mixed signals. We conclude that qualitative and quantitative accuracies of predicted scattering signals on detectors without energy resolution require that elements of the two-electron density operator are used. This approach inherently accounts for all accessible electronic transitions, including ionization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗