Search NASA⌕ Search

SEARCH · Search NASA

Results for “analyzable 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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Entanglement rearrangement in self-consistent nuclear structure calculations

Background: Entanglement plays a central role in a diverse array of increasingly important research areas, including quantum computation, simulation, measurement, sensing, and communication. Extensive suites of investigations have been performed to better understand entanglement in atomic and molecular quantum many-body systems, while the exploration of entanglement in the structure of nuclei and their reactions is presently in its infancy. Purpose: The goal of this work is to begin investigating the entanglement properties of nuclei from first-principles nuclear many-body calculations. We attempt to identify common features and emergent structures of entanglement that could ultimately lead to new and natural many-body schemes. With an eye toward quantum accelerators in future hybrid-supercomputers, criteria for partitioning nuclear many-body calculations into quantum and classical components may provide advantages in future large-scale computations. Along the way we look for explanations of the relative success of phenomenological models such as the nuclear shell model, and for better ways to match to low-energy nuclear effective field theories and lattice QCD calculations to nuclear many-body techniques that are based upon entanglement. Method: We explore the entanglement between single-particle states in 4 He and 6 He. The patterns of entanglement emerging from different single-particle bases are compared, and possible links with the convergence of observables are explored, in particular, ground-state energies. The nuclear wave functions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases exhibiting different degrees of complexity are determined, in particular, harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases. Specifically, single-orbital entanglement entropy, two-orbital mutual information, and negativity are studied. Results: The entanglement structures in 4 He and 6 He are found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters we have worked with. In particular a core-valence structure clearly emerges from the full no-core calculation of 6 He. Here, the two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces. Conclusions: Measures of one- and two-nucleon entanglement are found to be useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

High‐Concentration Antibody Formulation via Solvent‐Based Dehydration

Abstract Although subcutaneous (SC) delivery is the preferred administration route for immunotherapies and other biologics for improved patient compliance and lower healthcare costs, it necessitates high‐concentration antibody formulations. However, high‐concentration antibody solutions face significant instabilities and prohibitively high viscosities. Other approaches for high‐concentration formulations have been developed, including non‐aqueous solutions, which can be irritating or painful, and antibody‐laden hydrogel microparticles, which require centrifugation and are limited to concentrations <300 mg mL −1 . This work presents a new formulation process wherein the antibody is concentrated and encapsulated into hydrogel microparticles via solvent‐based dehydration. The final dosage form is an aqueous particle suspension with a formulation concentration of 360 mg mL −1 . In this process, microparticles are synthesized continuously, and antibody precipitation is realized simultaneously to dehydration, which allows for higher antibody concentrations. Antibody phase behavior and precipitation–dehydration kinetics are analyzed. The antibody is structurally and functionally stable in the microparticle post‐processing and after 4 months. Injectability of the suspension meets clinical standards with glide force <20 N. For the first time, an aqueous antibody formulation at high concentrations comparable to non‐aqueous formulations is presented, ideal for subcutaneous administration. The process is envisioned to be generalizable as a platform for SC delivery in multiple clinical applications.

Zheng, Talia [Department of Chemical Engineering M↗
DOE OSTI2021

ThickBrick: optimal event selection and categorization in high energy physics. Part I. Signal discovery

We provide a prescription called ThickBrick to train optimal machine-learning-based event selectors and categorizers that maximize the statistical significance of a potential signal excess in high energy physics (HEP) experiments, as quantified by any of six different performance measures. For analyses where the signal search is performed in the distribution of some event variables, our prescription ensures that only the information complementary to those event variables is used in event selection and categorization. This eliminates a major misalignment with the physics goals of the analysis (maximizing the significance of an excess) that exists in the training of typical ML-based event selectors and categorizers. In addition, this decorrelation of event selectors from the relevant event variables prevents the background distribution from becoming peaked in the signal region as a result of event selection, thereby ameliorating the challenges imposed on signal searches by systematic uncertainties. Our event selectors (categorizers) use the output of machine-learning-based classifiers as input and apply optimal selection cutoffs (categorization thresholds) that are functions of the event variables being analyzed, as opposed to flat cutoffs (thresholds). These optimal cutoffs and thresholds are learned iteratively, using a novel approach with connections to Lloyd’s k-means clustering algorithm. We provide a public, Python implementation of our prescription, also called ThickBrick, along with usage examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Holographic thermal correlators: a tale of Fuchsian ODEs and integration contours

We analyze real-time thermal correlation functions of conserved currents in holographic field theories using the grSK geometry, which provides a contour prescription for their evaluation. We demonstrate its efficacy, arguing that there are situations involving components of conserved currents, or derivative interactions, where such a prescription is, in fact, essential. To this end, we first undertake a careful analysis of the linearized wave equations in AdS black hole backgrounds and identify the branch points of the solutions as a function of (complexified) frequency and momentum. All the equations we study are Fuchsian with only regular singular points that for the most part are associated with the geometric features of the background. Special features, e.g., the appearance of apparent singular points at the horizon, whence outgoing solutions end up being analytic, arise at higher codimension loci in parameter space. Using the grSK geometry, we demonstrate that these apparent singularities do not correspond to any interesting physical features in higher-point functions. We also argue that the Schwinger-Keldysh collapse and KMS conditions, implemented by the grSK geometry, continue to hold even in the presence of such singularities. For charged black holes above a critical charge, we furthermore demonstrate that the energy density operator does not possess an exponentially growing mode, associated with ‘pole-skipping’, from one such apparent singularity. Our analysis suggests that the connection between the scrambling physics of black holes and energy transport has, at best, a limited domain of validity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Correlators of four light-ray operators in CCFT

Building on results in arXiv:2203.04255, we compute the correlator of four gluon light-ray operators in celestial CFT. We find that it is described by Fox H-functions and generalized I-functions of multiple variables. We also analyze light-ray correlators for a scalar amplitude involving the exchange of a massive scalar.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Synthesis and Characterization of Nickel-Substituted Cobalt Ferrite Nanoparticles Using Sol–Gel Auto-combustion Method

In the present work, Co{sub 1−x}Ni{sub x}Fe{sub 2}O{sub 4} (x = 0.02, 0.04, and 0.06 M) is prepared by sol–gel auto-combustion method and its structural, functional, magnetic, and morphological characteristics are analyzed. The peaks corresponding to the plane observed from XRD matches with JCPDS data of CoFe{sub 2}O{sub 4} (22-1086) and NiFe{sub 2}O{sub 4} (10-0325). It is noted that the average crystallite size decreases from 31 to 27 nm when the nickel concentration increases from 0.02 to 0.06 M, indicative of the incorporation of Ni{sup 2+} ion in the cobalt ferrite lattice. FTIR analysis shows the presence of M↔O vibration at the tetrahedral and octahedral sites. Micro - Raman spectroscopy shows the stretching vibrations at 486.87 cm{sup − 1} (E{sub g}) and 696.96 cm{sup − 1} (A{sub 1g}), which are the characteristic vibrations of spinel ferrites. Magnetic studies show the variation in saturation magnetization (M{sub S} = 20.25, 9.41, 18.5 emu/g.) and coercivity (H{sub C} = 746.06, 953.03, 885.59 Oe) when the concentration of Ni{sup 2+} ion increases from 0.02 to 0.06 M. The prepared nanoparticles show a ferromagnetic nature which is attributed to the creation of an antiparallel spin and the magnetic moment created by the cation at tetrahedral and octahedral sites. The surface morphology of samples is imaged by a field emission scanning electron microscope.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2018

Overexpression of circular RNA circ{sub 0}01569 indicates poor prognosis in hepatocellular carcinoma and promotes cell growth and metastasis by sponging miR-411-5p and miR-432-5p

Emerging evidence indicated that abnormally expressed circular RNAs (circRNAs) are critically involved in tumorigenesis and development of several cancers. However, the study relevant to the relationship between circRNAs and hepatocellular carcinoma (HCC) is rare. In this study, the expression of circ{sub 0}01569 in HCC tissue specimens and cells were determined by qRT-PCR. The clinical relevance of circ{sub 0}01569 was also analyzed. In addition, loss-of-function and gain-of-function assays were conducted to explore the biological functions of circ{sub 0}01569. Furthermore, tumor formation and lung metastasis studies were induced to confirm the in vitro data. Mechanistically, bioinformatics analysis and luciferase reporter assays were conducted to illustrate the underlying mechanism of circ{sub 0}01569. The results indicated that circ{sub 0}01569 was overexpressed in HCC tissue samples and cells. This overexpression is correlated with larger tumor size, advanced TNM stages and unfavorable prognosis in the patients with HCC. Additionally, circ{sub 0}01569 significantly facilitated HCC cell growth, migration and invasion. The animal studies further confirmed the in vitro results. More importantly, circ{sub 0}01569 could directly sponge miR-411-5p and miR-432-5p. The oncogenic functions of circ{sub 0}01569 is partially dependent on its regulation on miR-411-5p and miR-432-5p. In summary, circ{sub 0}01569/miR-411-5p/miR-432-5p regulatory signaling might be a rational HCC-related therapeutic target.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Amorphous and crystalline TiO 2 nanoparticle negative electrodes for sodium-ion batteries

Titanium dioxide (TiO 2 ) is a promising negative electrode for sodium ion batteries (SIBS). Although TiO 2 materials with amorphous (A-TiO 2 ) and single-phase crystalline structures (C-TiO 2 ) have been separately explored, the study to compare the fundamental electrochemistry of A-TiO 2 and C-TiO 2 is limited. In this work, we investigated A-TiO 2 and C-TiO 2 nanoparticles with identical chemical composition and morphology. C-TiO 2 exhibits enhanced electrochemical performance than A-TiO 2 in terms of rate capability and cycle life. Cyclic voltammetry (CV) analysis suggests reversible Na ion insertion/extraction in C-TiO 2 . However, such process is irreversible in the case of A-TiO 2 . The charge storage mechanisms in both samples were studied to show that diffusion-controlled intercalation process becomes significant in C-TiO 2 sample. The C-TiO 2 sample has a better Na + diffusivity measured through the galvanostatic intermittent titration technique (GITT) compared to A-TiO 2 , which corroborates well with the rate capability study. Furthermore, the evolution of local structure of the TiO 2 samples was analyzed by ex situ pair distribution function (PDF) to understand the variation in electrochemical properties. In conclusion, it reveals that the corner-shared Ti-Ti distance along Na ion diffusion pathway increases with the increase of crystallinity, leading to the expanded diffusion channels and therefore more active sites and faster diffusion.

25 ENERGY STORAGE↗
DOE OSTI2021

A new coupled multiphase flow–finite strain deformation–fault slip framework for induced seismicity

Production of hydrocarbons and water from subsurface reservoirs are known to cause permanent deformation of the reservoir and seismicity along faults both of which are detrimental to sustainable development of natural resources. Most of the prior studies on understanding fluid flow-induced plasticity and seismicity have focused on one or the other phenomenon due to the numerical difficulty associated with simultaneous modeling of the two failure phenomena because stress and deformation evolve non-linearly in both plasticity and seismicity. However, in reservoirs undergoing long-term production, plastic failure can alter the stress paths of points on a fault such that the onset, location, and magnitude of actual seismic events can no longer be predicted by a poroelastic simulation due to inaccurate stress and deformation history. We present a computational framework for coupled multiphase flow, finite strain poroplastic deformation, and dynamic fault slip and use it to understand the impact of plastic deformation on the onset, location, and magnitude of induced fault slip events. We evaluate the impact of plasticity on reservoir pressure, deformation, induced stress, and fault slip by comparing infinitesimal strain elastic and finite strain poro-elastoplastic models. For real-world applications, we consider different scenarios where the reservoir is either mechanically weaker or stronger than the caprock. We analyze the stress evolution as a function of the change in reservoir pressure to understand the role of contrast in reservoir and caprock elastic moduli on geomechanical stability. The results show that the poroplastic reservoir exhibits larger vertical deformation and delayed slip than the poroelastic reservoir after the same amount of oil production. For the same amount of pressure drop, a reservoir with a smaller modulus than the caprock displays a larger vertical displacement and an earlier onset of both plastic failure and fault slip. For a reservoir with a larger modulus than the caprock, vertical displacement is larger on the reservoir top boundary and smaller on the ground surface, and a higher pressure drop is needed to induce plastic failure and fault slip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Comparison of volatiles evolving from selected highland and mare lunar regolith simulants during vacuum sintering

Volatiles evolving from JSC-1A, NU-LHT-4M and CSM-LHT-1G lunar regolith simulants during in vacuo thermal processing were analyzed using mass spectrometry as a function of temperature. Two high-fidelity simulants, JSC-1A (mare) and NU-LHT-4M (highland), were compared to a newly developed CSM-LHT-1G highland simulant, modified to closely match lunar geochemistry. Large autogenous gas loads were observed for all investigated materials. Mineralogical knowledge was used to identify and attribute individual volatile species to reacting, transforming, or decomposing constituents (hydrates, carbonates, sulfates, sulfides, clays, etc.) of the respective regolith simulant in the self-generated gas environment. Cumulative mass losses for individual simulant components as a function of temperature were quantified using mass spectrometry in conjunction with thermogravimetric analysis. Investigation of the four components of CSM-LHT-1G – anorthosite, basalt, augite, and glass – aided the attribution of volatile species to specific compounds and their respective sources. The results showed significant decomposition of non-lunar phases present in the man-made regolith simulants below the typical glass crystallization temperatures, which paves the way to devising methods for enhancing the fidelity of the simulants. Finally, high gas loads and corrosive gases (HF and HCl) were recognized as potential hazards, pertaining to the development of large testbed facilities.

42 ENGINEERING↗
DOE OSTI2020

Kβ X-ray Emission Spectroscopy as a Probe of Cu(I) Sites: Application to the Cu(I) Site in Preprocessed Galactose Oxidase

Cu(I) active sites in metalloproteins are involved in O 2 activation, but their O 2 reactivity is difficult to study due to the Cu(I) d 10 closed shell which precludes the use of conventional spectroscopic methods. Kβ X-ray emission spectroscopy (XES) is a promising technique for investigating Cu(I) sites as it detects photons emitted by electronic transitions from occupied orbitals. Here, we demonstrate the utility of Kβ XES in probing Cu(I) sites in model complexes and a metalloprotein. Using Cu(I)Cl, emission features from double-ionization (DI) states are identified using varying incident X-ray photon energies, and a reasonable method to correct the data to remove DI contributions is presented. Kβ XES spectra of Cu(I) model complexes, having biologically relevant N/S ligands and different coordination numbers, are compared and analyzed, with the aid of density functional theory (DFT) calculations, to evaluate the sensitivity of the spectral features to the ligand environment. While the low-energy Kβ 2,5 emission feature reflects the ionization energy of ligand np valence orbitals, the high-energy Kβ 2,5 emission feature corresponds to transitions from molecular orbitals (MOs) having mainly Cu 3d character with the intensities determined by ligand-mediated d–p mixing. A Kβ XES spectrum of the Cu(I) site in preprocessed galactose oxidase (GO pre ) supports the 1Tyr/2His structural model that was determined by our previous X-ray absorption spectroscopy and DFT study. Finally, the high-energy Kβ 2,5 emission feature in the Cu(I)-GO pre data has information about the MO containing mostly Cu 3d x 2 –y 2 character that is the frontier molecular orbital (FMO) for O 2 activation, which shows the potential of Kβ XES in probing the Cu(I) FMO associated with small-molecule activation in metalloproteins.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Atomistic Insights into Lithium–Glyme Solvate Ionic Liquids: Effects of Chain Length and Anion Coordination

For this study, mixtures of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) in diglyme (G2), triglyme (G3) and tetraglyme (G4) at solvate ionic liquid (SIL) concentrations were investigated using classical molecular dynamics (cMD) simulations with a physically motivated force-field specifically developed for modeling these systems. The structural and dynamical properties of the mixtures were computed and analyzed. Lithium solvation shells, radial distribution functions, and X-ray structure factors were studied across the different SIL systems. Translational diffusion and rotational relaxation times were also evaluated, exhibiting similar trends with increasing glyme chain length. The results are consistent with experimental data and in good agreement with previous computational studies on G3 and G4. These findings validate the accuracy of the force field in modeling glyme systems and its use for describing the [Li(G2) 4/3 ][TFSI] mixture. Additionally, the thermal and electrochemical stability of these electrolytes were systematically examined. The thermal stability appears to be governed by cooperative interactions among glyme molecules, while the electrochemical stability is primarily influenced by Li + -anion interactions, which vary significantly with glyme chain length. Overall, the study sheds light on the crucial role of the anion in these glyme-based SILs and offers valuable insights into Li + -glyme systems at SIL concentrations, highlighting their promise as potential Li-ion battery electrolytes.

anions↗
DOE OSTI2021

How the Size and Density of Charge-Transfer Excitons Depend on Heterojunction’s Architecture

We have characterized the size, intensity, density, and distribution of charge-transfer (CT) excitons as a function of the acceptor–donor architecture of prototypical organic interfaces. This characterization was done by computational analysis of 17 models of varying numbers, positions, and orientations of the donor and acceptor molecules. The models’ building blocks were phenyl-C61-butyric acid methyl ester (PCBM) fullerene acceptors and dual-band donor polymers composed of thiophene, benzothiadiazole, and benzotriazole subunits. The electronic structure of the donor–acceptor complexes was computed with the time-dependent long-range-corrected density-functional tight-binding method and analyzed with the fragment-based one-electron transition density matrix. In all models, the complexes with edge-on orientation have denser spectra of low-energy CT states lying below the absorption bands compared to the complexes with face-on orientation. This CT-state distribution in edge-on complexes provides a gate to efficiently populate cold CT excitons. Moreover, the cold CT excitons have a higher degree of charge separation in the edge-on than in the face-on complexes. The CT amount and the CT exciton size generally increase with the energy of the CT states, although the electron remains localized on a single molecule in cold CT states. Delocalization over two PCBM molecules was observed for high-energy CT states. The exciton size also depends on the orientation. Larger excitons are produced by the delocalization of the electrons perpendicularly to the interface. When the delocalization is parallel, the smaller electron–hole distances yield moderately sized CT excitons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

The Impact of Coordination Environment on the Thermodynamic Stability of Uranium Oxides

Amorphous uranium oxides are acknowledged to arise via industrial processes relevant to the nuclear fuel cycle yet evade rigorous structural characterization. An encouraging approach is to develop statistical relationships between uranium–oxygen coordination environments and thermodynamic stability from which general statements about the likelihood of observing particular U–O arrangements can be made. The number of known crystalline uranium oxides is insufficient to build statistical relationships. We have developed a database of theoretical compounds using genetic algorithms with the density functional theory as a foundation to analyze coordination geometries in the uranium–oxygen phase space. We draw fundamental insights into the nature of uranium–oxygen interactions by correlating total energy with the coordination environment. The most stable configuration of U cations with O anions is in an environment with coordination numbers 5–8 in a cubic configuration. Higher and lower coordination numbers are observed only in metastable phases. General trends are observable in the relationships between the coordination number, density, and uranium fraction in each structure. The new insight into uranium coordination enabled by these analyses is foundational for further studies into the characteristic properties of individual uranium oxide materials and for elucidation of potential oxidation pathways for uranium metal.

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

Wavelet methods for studying the onset of strong plasma turbulence

Recent simulations have demonstrated that coherent current sheets dominate the kinetic-scale energy dissipation in strong turbulence of magnetized plasma. Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed turbulence from a laminar state. Originally applied to neutral fluid turbulence, an iterative wavelet technique decomposes the field into coherent and incoherent contributions. In contrast to Fourier power spectra, finite time Lyapunov exponents, and simple measures of intermittency such as non-Gaussian statistics of field increments, the wavelet technique is found to provide a quantitative measure for the onset of turbulence and to track the transition to fully developed turbulence. The wavelet method makes no assumptions about the structure of the coherent current sheets or the underlying plasma model. Temporal evolution of the coherent and incoherent wavelet fluctuations is found to be highly correlated (a Pearson correlation coefficient of >0.9) with the magnetic field energy and plasma thermal energy, respectively. The onset of turbulence is identified with the rapid growth of a background of incoherent fluctuations spreading across a range of scales and a corresponding drop in the coherent components. This is suggestive of the interpretation of the coherent and incoherent wavelet fluctuations as measures of coherent structures (e.g., current sheets) and dissipation, respectively. The ratio of the incoherent to coherent fluctuations Ric is found to be fairly uniform in the turbulent state across different plasma models and provides an empirical threshold of ~0.1 for turbulence onset. The utility of this technique is illustrated through examples. First, it is applied to the Kelvin–Helmholtz instability from different simulation models including fully kinetic, hybrid (kinetic ion/fluid electron), and Hall MHD simulations. Second, the wavelet diagnostic is applied to the development of turbulence downstream of the bowshock in a global magnetosphere simulation. Finally, the wavelet technique is also shown to be useful as a de-noising method for particle simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Polarization-dependent resonant inelastic x-ray scattering of β-Ga2O3: An experimental and computational study

The bulk electronic structure of β-Ga2O3 single crystals was investigated using oxygen K-edge x-ray emission and absorption spectroscopy as well as resonant inelastic soft x-ray scattering. Spectra were obtained for different orientations of the crystal planes with respect to the polarization vector of the incident x-ray beam. The spectra are analyzed with calculations based on density functional theory and using the Bethe–Salpeter equation in the ocean code to take the core–hole interaction into account. These calculations correctly capture all the main features in the experimental spectra, demonstrating the potential of the approach to predict the electronic properties of similar compounds. We find a pronounced anisotropy as a function of the excitation polarization vector and significant differences in the spectral contributions from the inequivalent oxygen atoms of β-Ga2O3.

Pyatenko, Elizaveta↗
DOE OSTI2025

Action painting under spectroscopic light: Excited-state exchange interactions behind the vibrant blue in Jackson Pollock’s Number 1A, 1948

Number 1A, 1948 by Jackson Pollock is a quintessential example of his action painting technique where ropes of color, drips of black, and pools of white coalesce into the layered dynamism that defines his style. While past work has identified the red and yellow pigments that form part of his core palette, the vibrant blue in the painting has remained unassigned. In this study resonance Raman spectroscopy is used to assign the blue in the painting as manganese blue. This assignment offers critical context for the conservation of his works. Importantly, assignment of this pigment enables spectroscopic investigation of the electronic structure origin of the pure hue of manganese blue and the chemical phenomena that produce its color. To probe these phenomena, resonance Raman data are coupled to magnetic circular dichroism spectroscopy and density functional theory calculations to assign and analyze the two electronic transitions that create the blue color. This study reveals these bands are split by excited-state exchange interactions; the gap between them contains the reflected light that gives manganese blue its appearance. This sheds light on distinct advantages of molecular inorganic pigments: their ability to leverage ligand field effects in charge transfer states to create multiple intense visible absorption features and the ability to fine-tune pigment color through host lattice electrostatics.

DFT↗