SEARCH · Search NASA

Results for “Binding Energy”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Revisiting Competitive Adsorption of Small Molecules in the Metal–Organic Framework Ni-MOF-74

To precisely evaluate the potential of metal-organic frameworks (MOFs) for gas separation and purification applications, it is crucial to understand how various molecules competitively adsorb inside MOFs. In this paper, we combine in situ infrared spectroscopy with ab initio calculations to investigate the mechanisms associated with co-adsorption of a number of small molecules including CO, NO, and CO 2 inside the prototypical framework Ni-MOF-74. Surprisingly, we find that the displacement of CO bound inside Ni-MOF-74 (binding energy of 53 kJ/mol) is readily driven by CO 2 exposure, even though CO 2 has a noticeably weaker binding energy of only 41 kJ/mol; meanwhile, the significantly more strongly binding NO molecule (90 kJ/mol) is not able to easily displace bound CO inside Ni-MOF74. These results show that single-phase binding energies of a molecule inside the MOF cannot completely describe their interaction with the MOF in the presence of other guest molecules. Here, we unveil a number of crucial factors such as the kinetic barrier, partial pressure, secondary binding sites, and guest-host/lateral interactions that control the co-adsorption process and combined with the binding energy are better descriptors of the behavior and adsorption of gas mixtures inside MOFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Enhanced Configurational Sampling Approaches to Alchemical Ligand Binding Free Energy Simulations: Current Status and Challenges

In this study, ligand binding free energy simulations (LB-FES) have been routine tasks in modern drug discovery campaign. A long-standing challenge for LB-FES is the difficulty in adequately sampling nontrivial environmental reorganizations in response to ligand binding. Therefore, various enhanced configurational sampling (ECS) approaches were devised to speed up fluctuations of relevant slow degrees of freedom (SDOF) and ensure simulation convergence. However, in contrast to the achievements in parametrization, software performance, and workflow automation, efficient ECS methodology suitable for high throughput screening remains in an early stage of development. Here, a review of ECS developments with LB-FES is presented, revisiting current approaches and underlining the major technical pitfalls and challenges. This Perspective focuses on alchemical LB-FES on account of their predominant role in high throughput drug screening as well as the established partnership with ECS. The critical aspects of designing ECS approaches, from both theoretical and applied perspectives, are described. This work is intended to provide a contemporary review of the scientific, technical, and practical issues associated with the accelerating convergence of alchemical LBFES.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Solute-vacancy clustering in aluminum

In this study, we present an extensive first-principles database of solute-vacancy, homoatomic, heteroatomic solute-solute, and solute-solute-vacancy binding energies of relevant alloying elements in aluminum. We particularly focus on the systems with major alloying elements in aluminum, i.e., Cu, Mg, and Si. The computed binding energies of solute-vacancy, solute-solute pairs, and solute-solute-vacancy triplets agree with available experiments and theoretical results in literature. We consider physical factors such as solute size and formation energies of intermetallic compounds to correlate with binding energies. Systematic studies of the homoatomic solute-solute-vacancy and heteroatomic (Cu, Mg, or Si)-solute-vacancy complexes reveal the overarching effect of the vacancy in stabilizing solute-solute pairs. The binding energy database presented here elucidates the interaction between solute cluster and vacancy in aluminum, and it is expected to provide insight into the design of advanced Al alloys with tailored properties.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Recent progress in global optimizations of covariant energy density functionals

The recent progress on global optimizations of covariant energy density functionals (CEDFs) and global calculations of binding energies within the covariant density functional theory (CDFT) has been analyzed and reviewed. Recently developed anchor-based optimization approach of Ref. [1] allows global optimizations of CEDFs at a reasonable numerical cost. Moreover, it permits such optimizations in a very large fermionic basis with a proper extrapolation to an infinite one. This allows to accurately estimate global calculation errors due to use of truncated fermionic basis and neglect of some contributions to binding energies (such as total electron binding energy).

Afanasjev, A. V. [Mississippi State University, MS↗

DOE OSTI2020

Indirect Excitons and Trions in MoSe 2 /WSe 2 van der Waals Heterostructures

Indirect excitons (IX) in semiconductor heterostructures are bosons, which can cool below the temperature of quantum degeneracy and can be effectively controlled by voltage and light. In this work, IX quantum Bose gases and IX devices were explored in GaAs heterostructures where an IX range of existence is limited to low temperatures due to low IX binding energies. IXs in van der Waals transition-metal dichalcogenide (TMD) heterostructures are characterized by large binding energies giving the opportunity for exploring excitonic quantum gases and for creating excitonic devices at high temperatures. TMD heterostructures also offer a new platform for studying single-exciton phenomena and few-particle complexes. In this work, we present studies of IXs in MoSe 2 /WSe 2 heterostructures and report on two IX luminescence lines whose energy splitting and temperature dependence identify them as neutral and charged IXs. The experimentally found binding energy of the indirect charged excitons, that is, indirect trions, is close to the calculated binding energy of 28 meV for negative indirect trions in TMD heterostructures. We also report on the realization of IXs with a luminescence line width reaching 4 meV at low temperatures. An enhancement of IX luminescence intensity and the narrow line width are observed in localized spots.

2D materials↗

DOE OSTI2024

Deconvoluting XPS Spectra of La-Containing Perovskites from First-Principles

Perovskite-based oxides are used in electrochemical CO 2 and H 2 O reduction in electrochemical cells due to their compositional versatility, redox properties and stability. However limited knowledge exists on the mechanisms driving these processes. Toward this understanding, herein we probe the core level binding energy shifts of water-derived adspecies (H, O, OH, H 2 O) as well as the adsorption of CO 2 on LaCoO 3 and LaNiO 3 and we correlate the simulated peaks with experimental Temperature Programmed X-ray Photoelectron Spectroscopy (TPXPS) results. We find the strong adsorption of such chemical species can affect the antiferromagnetic ordering of LaNiO 3 . The adsorption of such adspecies is further quantified through Bader and differential charge analyses. We find the higher O 1s core level binding energy peak for both LaCoO 3 and LaNiO 3 corresponds to adsorption of water-related species and CO 2 , while the lower energy peak is due to lattice oxygen. We further correlate these DFT-based core level O 1s binding energies with the TPXPS measurements to quantify the decrease of the O 1s contribution due to desorption of adsorbates and the apparent increase of the lattice oxygen (both bulk and surface) with temperature. Finally, we quantify the influence of adsorbates on the La 4d, Co 2p and the Ni 3p core level binding energy shifts. This work demonstrates how theoretically generated XPS data can be utilized to predict species-specific binding energy shifts to assist in the deconvolution of the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Low-energy Scattering and Effective Interactions of Two Baryons at $m_{\pi}\sim$ 450 MeV from Lattice Quantum Chromodynamics

The interactions between two octet baryons are studied at low energies using lattice QCD (LQCD) with larger-than-physical quark masses corresponding to a pion mass of $m_{\pi}\sim 450$ MeV and a kaon mass of $m_{K}\sim 596$ MeV. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=-4$ and include the spin-singlet and triplet $NN$, $\Sigma N$ ($I=3/2$), and $\Xi\Xi$ states, the spin-singlet $\Sigma\Sigma$ ($I=2$) and $\Xi\Sigma$ ($I=3/2$) states, and the spin-triplet $\Xi N$ ($I=0$) state. The $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable, are extracted using L\"uscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $\Sigma N$ and $\Xi\Xi$ channels are found to be repulsive and do not support bound states. Using results from previous studies at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with experimental values and phenomenological predictions. The low-energy coefficients in pionless EFT relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the $SU(6)$ spin-flavor symmetry, predicted at large $N_c$. A remnant of an accidental $SU(16)$ symmetry found previously at a larger pion mass is further observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Tuning the Cation–Anion Interactions by Methylation of the Pyridinium Cation: An X-ray Photoelectron Spectroscopy Study of Picolinium Ionic Liquids

Here, X-ray photoelectron spectroscopy is used to investigate the impact of methylation on the electronic environment of pyridinium cations. Because of the electron-donating effect of the methyl group, there is a significant increase in electron density on the cationic nitrogen. The shift of the N 1s binding energy is inversely proportional to the anion basicity. The methylation position on the electronic environment of the cationic nitrogen is investigated. The N 1s binding energy follows the trend: 1-octylpyridinium > 1-octyl-3-picolinium > 1-octyl-4-picolinium > 1-octyl-2-picolinium, which is in good agreement with the cation acidity. The increase in the inductive effect subsequently weakens the cation–anion interactions through charge transfer from the anion to the cation, causing a subtle change in the electronic environment of the anion. Such an effect is noticeably reflected in the Br 3d binding energy. It shows that the Br 3d 5/2 binding energy of 1-octyl-2-picolinium bromide is 0.2 eV lower than that of 1-octylpyridinium bromide.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Biexcitons are bound in CsPbBr 3 perovskite nanocrystals

Here, we study the energetics of quasiparticle excitations in CsPbBr 3 perovskite nanocrystals using path integral molecular dynamics simulations. Employing detailed molecular models, we elucidate the interplay of anharmonic lattice degrees of freedom, dielectric confinement, and electronic correlation on exciton and biexciton binding energies of a range of nanocrystal sizes. We find generally good agreement with some experimental observations of binding energies and additionally explain the observed size-dependent Stokes shift. The explicit model calculations are compared with simplified approximations to rationalize the lattice contributions to binding. We find that polaron formation significantly reduces exciton binding energies, whereas these effects are negligible for biexciton interactions. While experimentally the binding energy of biexcitons is uncertain, based on our study, we conclude that biexcitons are bound in CsPbBr 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Atomistic simulations for investigation of substrate and salt effects on lipid in-source fragmentation in secondary ion mass spectrometry: A follow-up study

In-source fragmentation (ISF) poses a significant challenge in secondary ion mass spectrometry (SIMS). These fragment ions increase the spectral complexity and can lead to incorrect annotation of fragments as intact species. The presence of salt that is ubiquitous in biological samples can influence the fragmentation and ionization of analytes in a significant manner, but their influences on SIMS have not been well characterized. To elucidate the effect of substrates and salt on ISF in SIMS, we have employed experimental SIMS in combination with atomistic simulations of a sphingolipid on a gold surface with various NaCl concentrations as a model system. Our results revealed that a combination of bond dissociation energy and binding energy between N-palmitoyl-sphingomyelin and a gold surface is a good predictor of fragment ion intensities in the absence of salt. However, ion-fragment interactions play a significant role in determining fragment yields in the presence of salt. Additionally, the charge distribution on fragment species may be a major contributor to the varying effects of salt on fragmentation. This study demonstrates that atomistic modeling can help predict ionization potential when salts are present, providing insights for more accurate interpretations of complex biological spectra.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Dielectric Screening Modulates Semiconductor Nanoplatelet Excitons

The influence of external dielectric environments is well understood for 2D semiconductor materials but overlooked for colloidally grown II–VI nanoplatelets (NPLs). In this work, we synthesize MX (M = Cd, Hg; X = Se, Te) NPLs of varying thicknesses and apply the Elliott model to extract exciton binding energies—reporting values in good agreement with prior methods and extending to less studied cadmium telluride and mercury chalcogenide NPLs. Here, we find that the exciton binding energy is modulated both by the relative effect of internal vs external dielectric and by the thickness of the semiconductor material. An analytical model shows dielectric screening increases the exciton binding energy relative to the bulk by distorting the Coulombic potential across the NPL surface. We further confirm this effect by decreasing and recovering the exciton binding energy of HgTe NPLs through washing in polarizable solvents. Our results illustrate NPLs are colloidal analogues of van der Waals 2D semiconductors and point to surface modification as an approach to control photophysics and device properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Molecular dynamics study of interstitial He clusters in nickel

This study presents a molecular dynamics analysis focusing on the behavior of interstitial helium (He) clusters in nickel (Ni), examining their formation, stability, and migration energetics. Consistent with previous research, we found that the binding energies of interstitial helium within a helium cluster are positive and increase with the cluster size, indicating a preference for helium atoms to cluster together. However, our findings also reveal that while the formation energy increases monotonically with cluster size, the increase in binding energy is non-monotonic. Importantly, small He clusters were observed to be thermally unstable at reactor operational temperatures (approximately 600 K), with the He 2 cluster exhibiting instability even at room temperature. With a binding energy of 0.49 eV for a He 4 cluster, we hypothesize that for helium bubbles to form via homogeneous nucleation (i.e., through trap mutation) at reactor operating temperatures, the helium concentration must be high enough to facilitate the formation of helium clusters of at least size 4 or larger. As expected, interstitial helium and small helium clusters are highly mobile. This mobility was observed not only at room temperature but also at temperatures as low as approximately 200 K. Furthermore, the mean squared displacement method has been utilized to determine the migration barriers and the corresponding prefactors for clusters ranging from He 1 to He 6

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Catalytic Resonance Theory: Experimental and Kinetic Interpretation of Programmable Catalysis

The complexity of programmable catalysts that change in the physical or electronic state on the time scale of a catalytic turnover results in uncertainty in the kinetic outcome of common measurements with dynamic catalyst experiments. To provide an interpretation of utility to experimentalists, a general programmable catalytic reaction exhibiting high turnover efficiency was simulated to understand the kinetic behavior of catalysts with varying frequency, binding energy, oscillation amplitude, and minimum oscillation binding energy at different temperatures and reactant gas pressures. The time-averaged catalytic rate for varying temperature in the form of an Arrhenius plot exhibited three distinct kinetic regimes, with the intermediate temperatures or applied frequencies exhibiting zero slope, indicative of barrier-free kinetic control. Transitions in experimentally measurable kinetic regimes with both temperature and applied catalyst oscillation frequency were associated with transitions in the sensitivity of reaction rate constants and degrees of rate control. Furthermore, these distinct kinetic macroscopic features specific to programmable catalysts were identified for observation in experimental dynamic kinetic measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei

Classes of two-nucleon (2N) contact interactions are developed in configuration space at leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N3LO) by fitting the experimental singlet np scattering length and deuteron binding energy at LO, and np and pp scattering data in the laboratory-energy ranges 0–15 MeV at NLO and 0–25 MeV at N3LO. These interactions are regularized by including two Gaussian cutoffs, one for T = 0 and the other for T = 1 channels. The cutoffs are taken to vary in the ranges R 0 = (1.5 –2.3) fm and R 1 = (1.5 –3.0) fm. The 780 (1100) data points up to 15 (25) MeV energy, primarily differential cross sections, are fitted by the NLO (N3LO) models with a χ 2 / datum about 1.7 or less (well below 1.5), when harder cutoff values are adopted. As a first application, we report results for the binding energies of nuclei with mass numbers A = 3 –6 and 16 obtained with selected LO and NLO 2N models both by themselves as well as in combination with a LO three-nucleon (3N) contact interaction. The latter is characterized by a single low-energy constant that is fixed to reproduce the experimental 3 H binding energy. The inclusion of the 3N interaction largely removes the sensitivity to cutoff variations in the few-nucleon systems and leads to predictions for the 3 He and 4 He binding energies that cluster around 7.8 and 30 MeV, respectively. However, in 16 O this cutoff sensitivity remains rather strong. Finally, predictions at LO only are also reported for medium-mass nuclei with A = 40 , 48, and 90.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Density functionals combined with van der Waals corrections for graphene adsorbed on layered materials

Standard density functionals like Perdew-Burke-Ernzerhof (PBE) or Strongly Constrained and Appropriately Normed (SCAN) need a correction to account for long-range van der Waals (vdW) interaction. The damped Zaremba-Kohn model (dZK) starts from a formula for the vdW interaction of a distant atom with a solid surface, both with known dielectric properties, damps this formula at short range, and then treats an adsorbed molecule or atomic layer as a collection of renormalized atoms. Here, we extend this model to graphene adsorbed on semiconducting layered materials [bulk graphite and hBN, and multilayer transition metal dichalcogenides (TMD)] by including the C 4 asymptotic term and multiple electrostatic image effects due to the two surfaces of the substrate slabs in the vdW calculations. The resulting SCAN-vdW-dZK and PBE-vdW-dZK give approximately the same results for the systems considered here, in agreement with available reference values. The predicted binding energies are roughly 25% lower than those from SCAN+rVV10 (revised Vydrov and Van Voorhis 2010), and ~15% lower than those from PBE+rVV10. Since SCAN+rVV10 usually overbinds, the predicted binding energies by SCAN-vdW-dZK and PBE-vdW-dZK are expected to be closer to the true values. The predicted equilibrium binding distances from SCAN-vdW-dZK and PBE-vdW-dZK are slightly larger (~ 0.1 Å) than those from SCAN+rVV10, and close to those from SCAN. The binding energy depends upon the number of substrate layers more strongly in vdW-dZK than in rVV10. The C 4 -term contributions can be 40% of the total vdW interactions, and the C 5 term contributes about 10%. The effects of images and the back surfaces of slabs can contribute about 4–10%. The vdW interaction energy power laws from the vdW-dZK model for graphene adsorbed on multilayer MoS 2 show slowly varying decay to the pairwise exponent –4 with increasing separation $\textit{D}$, very similar to those obtained from the random-phase approximation and renormalization group approaches by Ambrosetti et al. Both the PBE-vdW-dZK and SCAN-vdW-dZK give a greater increase in interlayer binding energy when the TMD substrate changes from monolayer to four-layer for the graphene/TMD adsorption systems. This is consistent with the relevant electron-energy-loss spectroscopy experimental results showing increased dielectric response from the substrate with increasing substrate layer number.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Helium interaction with solutes and impurities in neutron-irradiated nanostructured ferritic alloys: A first principles study

Density functional theory calculations are performed to explore the binding between He and alloying solutes, impurities, and transmutation products expected in neutron irradiated nanostructured ferritic alloys (NFAs), here 14YWT is taken as an example. Elements that exhibit significant binding (attraction) with an interstitial He are Y (binding energy = 0.46 eV), Mg (0.32), O (0.33), Ti (0.16), and C (0.15). Those that provide significant binding to a substitutional He are O (1.44), Y (1.24), N (0.73), H (0.56), Mg (0.52), Ti (0.34), Si (0.34), C (0.33), Al (0.32), Ni (0.26), Ta (0.23), and Mn (0.16). The presence of these elements in Fe matrix could reduce the transport of He towards oxide particles, dislocations, and internal boundaries, and could promote He bubble nucleation in the matrix. For convenience, we compile existing binding energy data of He with He n and He n V (He-vacancy) clusters. Dissociation pathway analysis reveals that, in general, the most likely dissociation of a He n V cluster is by a sequential emission of individual He atoms. Furthermore, larger bubbles are more prone to dissociation than smaller ones. In addition, we estimate the binding energy (segregation energy) of He in bulk Y 2 Ti 2 O 7 (YTO) single crystal, YTO/Fe interface, and YTO particle embedded in Fe, with respect to interstitial He in Fe, from existing formation energies of He in these structures. We also compile available data of He binding with Fe self-interstitial atom (SIA), SIA clusters, and edge and screw dislocations. Note that given the absence of DFT data, the binding with SIA clusters and dislocations are gathered from simulations with empirical potentials. Finally, the data presented in this paper is important to inform multiscale simulations of He bubble accumulation.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Electrical Control and Transport of Tightly Bound Interlayer Excitons in a MoSe 2 /hBN/MoSe 2 Heterostructure

Controlling interlayer excitons in Van der Waals heterostructures holds promise for exploring Bose-Einstein condensates and developing novel optoelectronic applications, such as excitonic integrated circuits. Despite intensive studies, several key fundamental properties of interlayer excitons, such as their binding energies and interactions with charges, remain not well understood. Here we report the formation of momentum-direct interlayer excitons in a high-quality MoSe 2 /hBN/MoSe 2 heterostructure under an electric field, characterized by bright photoluminescence (PL) emission with high quantum yield and a narrow linewidth of less than 4 meV. These interlayer excitons show electrically tunable emission energy spanning ~1⁢8⁢0 meV through the Stark effect, and exhibit a sizable binding energy of ~8⁢1 meV in the intrinsic regime, along with trion binding energies of a few millielectronvolts. Remarkably, we demonstrate the long-range transport of interlayer excitons with a characteristic diffusion length exceeding 1⁢0 μ⁢m, which can be attributed, in part, to their dipolar repulsive interactions. Further, spatially and polarization-resolved spectroscopic studies reveal rich exciton physics in the system, such as valley polarization, local trapping, and the possible existence of dark interlayer excitons. Furthermore, the formation and transport of tightly bound interlayer excitons with narrow linewidth, coupled with the ability to electrically manipulate their properties, open exciting new avenues for exploring quantum many-body physics, including excitonic condensate and superfluidity, and for developing novel optoelectronic devices, such as exciton and photon routers.

2-dimensional systems↗

DOE OSTI2020

Self-interaction error overbinds water clusters but cancels in structural energy differences

Here, we gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/ H 2 O from about 42 meV/ H 2 O for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These findings suggest that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗