Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Density gradient 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 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

Effect of Interface Shape and Magnetic Field on the Microstructure of Bulk Ge:Ga

Thermal and compositional gradients induced during the growth process contribute significantly to the development of defects in the solidified boule. Thermal gradients and the solid-liquid interface shape can be greatly effected by ampoule material. Compositional gradients are strongly influenced by interface curvature and convective flow in the liquid. Results of this investigation illustrate the combined influences of interface shape and convective fluid flow. An applied magnetic field was used to reduce the effects of convective fluid flow in the electrically conductive melt during directional solidification. Several 8 mm diameter boules of Ga-doped Ge were grown at different field strengths, up to 5 Tesla, in four different ampoule materials. Compositional profiles indicate mass transfer conditions ranged from completely mixed to diffusion controlled. The influence of convection in the melt on the developing crystal microstructure and defect density was investigated as a function of field strength and ampoule material. Chemical etching and electron backscattered electron diffraction were used to map the crystal structure of each boule along the center plane. Dislocation etch pit densities were measured for each boule. Results show the influence of magnetic field strength and ampoule material on overall crystal quality.

Cobb, S. D.↗
NASA NTRS1990

Stability of an oscillated fluid with a uniform density gradient

Instabilities in a fluid with a constant density gradient that is subject to arbitrarily oriented oscillatory accelerations are considered. With the Boussinesq approximation and for the case of an unbounded fluid, transformation to Lagrangian coordinates allows the reduction of the problem to an ordinary differential equation for each three-dimensional wavenumber. The problem has three parameters: the nondimensional amplitude R of the base-state oscillation, the nondimensional level of background steady acceleration, which for some cases can be represented in terms of a local (in time) Richardson number Ri, and the Prandtl number Pr. Some general bounds on stability are derived. For Pr = 1 closed-form solutions are found for impulse (delta function) accelerations and a general asymptotic solution is constructed for large R and general imposed accelerations. The asymptotic solution takes advantage of the fact that at large R wave growth is concentrated at 'zero points'. These are times when the effective vertical wavenumber passes through zero. Kelvin-Helmholtz instabilities are found to dominate at low R, while Rayleigh-Taylor instabilities dominate at high R. At high R, the uniform shear of the Kelvin-Helmholtz case tends to distort and weaken instability waves. With unsteady flows, Ri = 1/4 is no longer an instability limit. Significant instabilities have been found for sinusoidal forcing for Ri up to 0.6.

Jacqmin, David↗
NASA NTRSDate not supplied

Fast Aircraft Separation Calculations for Gradient Based Optimization of Airspace Simulations

Simulations of airspace operational concepts can play a significant role in determining future paradigms that would allow for a safe increase in airspace density. In particular, airspace simulations which are capable of handling large numbers of aircraft act as an enabling capability for the testing of proposed airspace operational concepts. Simulations allowing for gradient based optimization methods are particularly attractive, since they would potentially allow for an efficient and empirical means to derive best operational practices. These could also allow for vehicle multidisciplinary design and optimization studies to include air traffic management considerations as a discipline. But any large scale simulation of airspace operations must include some methodology for addressing airspace separation requirements, which in the most direct sense would be tracked in a manner that computationally grows as a quadratic function of the number of simulated aircraft. Efficient indirect methods have been developed in certain contexts to address this limitation. However, any means of addressing separation requirements in a gradient based optimization context should be implemented by functions which provide analytic derivative information to maximize numerical precision and computational efficiency. In this paper, a fast and differentiable separation metric is described in application to gradient based optimization of airspace operations. Rather than computing the separation distance between every pair of aircraft in a simulation, this method effectively reduces the problem to a smaller relevant set using a geometric decomposition. This method guarantees that the smallest distance at all points in simulated time is determined exactly. When used in an optimization constraint context, this guarantees that a minimum separation is maintained between all pairs of aircraft. The presented metric has logarithmic computational growth with respect to the number of simulated aircraft, and is shown to perform well in a series of notional 2D airspace optimization problems when used to enforce specified airborne separation constraints. Results show that this is notably faster than a direct pairwise distance computing metric for optimizations involving both small and large numbers of aircraft, yet enforce separation requirements to the same tolerance. It is shown that this favorable scalability is an enabling capability for more sophisticated air traffic management conceptual studies.

Optimization↗
DOE OSTI2021

Atomic Gradient Structure Alters Electronic Structure in 3D across the Bulk and Enhances Photoactivity

Abstract Understanding structure–function relationships enables the design of materials with tailored functionalities. The long‐standing challenge is to design materials with high active volume to improve efficiency. Tailored grain boundaries and lattice defects are traditionally used to tune the electronic structure near interfaces or defects to promote electron and hole separation. However, the active volume of point defect sites or interfaces in these traditional photocatalysts is extremely low. This study reports a structure with continuous atomic positional deformation across the bulk, altering the electronic structure in 3D and creating a significantly higher active volume. Such a structure in anatase is obtained and tuned by phase transformation during the heating process. Transmission electron microscopy and density functional theory results reveal that atomic deformations result in continuous band bending across the particles, facilitating electron–hole separation, inhibiting their recombination, and inducing dramatically enhanced photoactivity. These findings enable a different materials design paradigm that can potentially be harnessed for a broad range of applications.

Ren, Peng↗
DOE OSTI2020

Tight-binding study of beryllium

In this work, we have applied the Naval Research Laboratory Tight-binding (NRL-TB) Method to the hcp alkaline-earth metal Beryllium. This approach consists of fitting to energy band and total energy data generated by the Linearized Augmented Plane Wave (LAPW) for the fcc, bcc, sc, and hcp structures as a function of volume. First, we found that using the Generalized Gradient Approximation (GGA) for the input data secures a better agreement to experimental volumes than the LDA. Second, we found that including small volumes to the fit is needed to get TB parameters that are transferable enough to successfully predict the energies of structures that were not fitted, and to perform molecular dynamics (MD) simulations. The non-orthogonal Hamiltonian obtained, is successful in correctly predicting the hcp lattice as the ground state of Be and finding eight other structures, that were not fitted to LAPW, positioned at higher energies. In addition, the NRL-TB produces accurate energy bands, densities of states, elastic constants, the Bain path and several quantities derived from MD simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Recovery of Forest Structure Following Large-Scale Windthrows in the Northwestern Amazon

The dynamics of forest recovery after windthrows (i.e., broken or uprooted trees by wind) are poorly understood in tropical forests. The Northwestern Amazon (NWA) is characterized by a higher occurrence of windthrows, greater rainfall, and higher annual tree mortality rates (~2%) than the Central Amazon (CA). We combined forest inventory data from three sites in the Iquitos region of Peru, with recovery periods spanning 2, 12, and 22 years following windthrow events. Study sites and sampling areas were selected by assessing the windthrow severity using remote sensing. At each site, we recorded all trees with a diameter at breast height (DBH) ≥ 10 cm along transects, capturing the range of windthrow severity from old-growth to highly disturbed (mortality > 60%) forest. Across all damage classes, tree density and basal area recovered to >90% of the old-growth values after 20 years. Aboveground biomass (AGB) in old-growth forest was 380 (±156) Mg ha -1 . In extremely disturbed areas, AGB was still reduced to 163 (±68) Mg ha -1 after 2 years and 323 (± 139) Mg ha -1 after 12 years. This recovery rate is ~50% faster than that reported for Central Amazon forests. The faster recovery of forest structure in our study region may be a function of its higher productivity and adaptability to more frequent and severe windthrows. These varying rates of recovery highlight the importance of extreme wind and rainfall on shaping gradients of forest structure in the Amazon, and the different vulnerabilities of these forests to natural disturbances whose severity and frequency are being altered by climate change.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1976

Stellar occultation spikes as probes of atmospheric structure and composition

The characteristics of spikes observed in occultation light curves of Beta Scorpii by Jupiter are discussed in terms of the gravity-gradient model. The occultation of Beta Sco by Jupiter on May 13, 1971, is reviewed, and the gravity-gradient model is defined as an isothermal atmosphere of constant composition in which the refractivity is a function only of the radial coordinate from the center of refraction, which is assumed to lie parallel to the local gravity gradient. The derivation of the occultation light curve in terms of the atmosphere, the angular diameter of the occulted star, and the occultation geometry is outlined. It is shown that analysis of the light-curve spikes can yield the He/H2 concentration ratio in a well-mixed atmosphere, information on fine-scale atmospheric structure, high-resolution images of the occulted star, and information on ray crossing. Observational limits are placed on the magnitude of horizontal refractivity gradients, and it is concluded that the spikes are the result of local atmospheric density variations: atmospheric layers, density waves, or turbulence.

Elliot, J. L.↗
NASA NTRS1977

The radial gradients and collisional properties of solar wind electrons

The plasma instrument on Mariner 10 carried out measurements of electron density and temperature in the interplanetary medium between heliocentric distances of 0.85 and 0.45 AU. Due to the stable coronal configuration and low solar activity during the period of observation, the radial variations of these quantities could be obtained. The power-law exponent of the core temperature was measured to be -0.3 + or - 0.04, and the halo temperature was found to be almost independent of heliocentric distance. The exponent of the power law for the density variation was 2.5 + or - 0.2 and the extrapolated value at 1 AU was consistent with measured values during the same period. Calculations of the core electron self-collision time, and the core-halo equipartition time were made as a function of radial distance. These measurements indicate a macroscale picture of a Coulomb-collisional core and a collisionless isothermal halo. Extrapolating back to the sun, core and halo temperatures become equal at a radial distance of approx. 2-15 radii.

Gilvie, K. W.↗
NASA NTRS2000

Diffusion Driven Combustion Waves in Porous Media

Filtration of gas containing oxidizer, to the reaction zone in a porous medium, due, e.g., to a buoyancy force or to an external pressure gradient, leads to the propagation of Filtration combustion (FC) waves. The exothermic reaction occurs between the fuel component of the solid matrix and the oxidizer. In this paper, we analyze the ability of a reaction wave to propagate in a porous medium without the aid of filtration. We find that one possible mechanism of propagation is that the wave is driven by diffusion of oxidizer from the environment. The solution of the combustion problem describing diffusion driven waves is similar to the solution of the Stefan problem describing the propagation of phase transition waves, in that the temperature on the interface between the burned and unburned regions is constant, the combustion wave is described by a similarity solution which is a function of the similarity variable x/square root of(t) and the wave velocity decays as 1/square root of(t). The difference between the two problems is that in the combustion problem the temperature is not prescribed, but rather, is determined as part of the solution. We will show that the length of samples in which such self-sustained combustion waves can occur, must exceed a critical value which strongly depends on the combustion temperature T(sub b). Smaller values of T(sub b) require longer sample lengths for diffusion driven combustion waves to exist. Because of their relatively small velocity, diffusion driven waves are considered to be relevant for the case of low heat losses, which occur for large diameter samples or in microgravity conditions, Another possible mechanism of porous medium combustion describes waves which propagate by consuming the oxidizer initially stored in the pores of the sample. This occurs for abnormally high pressure and gas density. In this case, uniformly propagating planar waves, which are kinetically controlled, can propagate, Diffusion of oxidizer decreases the wave velocity. In addition to the reaction and diffusion layers, the uniformly propagating wave structure includes a layer with a pressure gradient, where the gas motion is induced by the production or consumption of the gas in the reaction as well as by thermal expansion of the gas. The width of this zone determines the scale of the combustion wave in the porous medium.

Aldushin, A. P.↗
DOE OSTI2023

Melt-grown semi-insulating Mn:β-Ga 2 O 3 single crystals exhibiting unique visible absorptions and luminescence

In this study, several acceptor dopants have been explored in β-Ga 2 O 3 to produce semi-insulating substrates and epitaxial films. Fe and Mg make up the majority of research thus far; however, other transition metals provide potential alternatives for optimized performance. β-Ga 2 O 3 bulk single crystals were grown by the Czochralski and vertical gradient freeze methods with a nominal dopant concentration of 0.25 at. % Mn. Ultraviolet-visible-near infrared spectroscopy and photoluminescence revealed polarization- and orientation-dependent optical absorptions (pleochroism) coupled with an orange luminescence. All samples were electrically insulating, on the order of 10 9 –10 11 ohm cm at room temperature, indicative of acceptor doping. Actual dopant concentrations of the intentionally doped transition metal and background impurities were determined via glow discharge mass spectrometry, indicating the macroscale segregation behavior. High-temperature resistivity measurements indicated an experimental acceptor level of 1.7 ± 0.2 eV. Hydrogenation of samples resulted in an increase in the orange luminescence and O–H stretching modes observable in the infrared spectrum. Density functional theory calculations were performed to determine the likely site-occupancy and acceptor level of Mn in the bandgap.

36 MATERIALS SCIENCE↗
NASA NTRS2014

Ballistic Performance Model of Crater Formation in Monolithic, Porous Thermal Protection Systems

Porous monolithic ablative systems insulate atmospheric reentry vehicles from reentry plasmas generated by atmospheric braking from orbital and exo-orbital velocities. Due to the necessity that these materials create a temperature gradient up to several thousand Kelvin over their thickness, it is important that these materials are near their pristine state prior to reentry. These materials may also be on exposed surfaces to space environment threats like orbital debris and meteoroids leaving a probability that these exposed surfaces will be below their prescribed values. Owing to the typical small size of impact craters in these materials, the local flow fields over these craters and the ablative process afford some margin in thermal protection designs for these locally reduced performance values. In this work, tests to develop ballistic performance models for thermal protection materials typical of those being used on Orion are discussed. A density profile as a function of depth of a typical monolithic ablator and substructure system is shown in Figure 1a.

Miller, J. E.↗
NASA NTRS2022

A Numerical Study of the Liquid Motion in Titan’s Subsurface Ocean

An ocean filled with liquid water lies beneath the icy surface of several Jovian and Saturnian moons. In such an ocean, the currents are driven by various phenomena such as the tidal forcing, the deformation of the ice shell lying at its top, the temperature gradient resulting from the surface and bottom heat fluxes…The flow induced by the first two forcings can be modelled by means of a 2D depth-averaged model, while the third one generates horizontal and vertical density variations whose effects can only be captured by a 3D baroclinic model. We study the tides of Titan’s subsurface ocean and the impact of the ice shell on the liquid motion by means of the Second-generation Louvain-la-Neuve Ice–ocean Model, SLIM (https://www.climate.be/slim). The impact of the ice shell lying at the top of the ocean is modelled by a surface friction term and surface pressure terms. The latter are a function of the difference between the ocean elevation and the vertical displacement of the shell and the time derivative of this difference. Because of Titan’s appreciable obliquity (0.306°), the tidal motion expected (and found) is similar to the Europa tidal scenario described by Tyler (2008): the surface elevation consists of two bulges rotating around Titan and the associated depth-averaged velocity field consists of two gyres, separated by an area of high speed flow, whose centre follows a sinusoidal path centred on the equator. The ice shell damps the surface motion, thus slowing down the flow, without significantly modifying the spatial patterns of these fields. The depth of the ocean and the mechanical characteristics of the ice shell being poorly constrained, a sensitivity analysis is conducted. The depth-averaged flow slows down when the depth is increased and a lag appears in the tidal phase but the tidal range remains similar. The ice shell mechanical characteristics influences both the elevation and depth-averaged velocity fields in terms of magnitude but does not modify the spatial patterns of these fields. The influence of the surface heat flux is studied by means of the 3D baroclinic version of SLIM. The heat flux derived from Titan’s topography by Kvorka et al. (2018) is used as surface boundary condition for the temperature equation while a uniform bottom heat flux is implemented. Its value is computed assuming that the heat budget of the ocean is at equilibrium. These boundary conditions cause density variations, which impact the hydrodynamics of the ocean. While the flow velocity induced by these variations is two orders of magnitude smaller than the tidal flow, its orientation is time-independent, hence impacting the orientation of the velocity field. Although the variations of ocean surface elevation and speed with respect to the shell mechanical properties can be larger than those induced by the surface heat flux, taking into account the latter results in large variations of the velocity field global patterns, which was not observed when modifying the shell mechanical properties. Future studies should therefore focus on modelling the surface and bottom heat fluxes while uncertainties about the mechanical characteristics of the shell can be tolerated.

Titan↗
NASA NTRS1971

Dynamic upper atmospheric force model on stabilized vehicles for a high-precision trajectory computer program

The upper atmosphere model draws heavily on the behavior of the earth's upper atmosphere which exhibits cyclic as well as irregular variations in density profile, temperature, pressure, and composition in unison with solar activities as deduced from the more recent land-based and satellite observations. The lift and drag model is designed specifically for inertially stabilized vehicles of the Mariner class, with possible extension to gravity gradient stabilized vehicles of the GEOS class. The model considers operation in the free molecular flow regimes with large Knudsen numbers. The vehicle is considered a composite structure with basic components having well-defined shapes, each with its own surface characteristics in terms of temperature, reflectivity, and accommodation of free stream molecules. The model takes into account both the calculation of precise aerodynamic force coefficients in terms of expansion of modified Bessel functions in speed ratios and angle of attack, and approximate force coefficients when the speed ratios approach infinity. Other considerations include specular and diffused reflectivity, shielding, and shadow effects.

Khatib, A. R.↗
NASA NTRS2012

Quantitative Infrared Image Analysis Of Thermally-Thin Cellulose Surface Temperatures During Upstream and Downstream Microgravity Flame Spread from A Central Ignition Line

Surface view calibrated infrared images of ignition and flame spread over a thin cellulose fuel were obtained at 30 Hz during microgravity flame spread tests in the 10 second Japan Microgravity Center (JAMIC). The tests also used a color video of the surface view and color images of the edge view using 35 millimeter 1600 Kodak Ektapress film at 2 Hz. The cellulose fuel samples (50% long fibers from lumi pine and 50% short fibers from birch) were made with an area density of 60 grams per square meters. The samples were mounted in the center of a 12 centimeter wide by 16 centimeter tall flow duct that uses a downstream fan to draw the air through the flow duct. Samples were ignited after the experiment package was released using a straight hot wire across the center of the 7.5 centimeter wide by 14 centimeter long samples. One case, at 1 atmosphere 35%O2 in N2, at a forced flow of 10 centimeters per second, is presented here. In this case, as the test progresses, the single flame begins to separate into simultaneous upstream and downstream flames. Surface temperature profiles are evaluated as a function of time, and temperature gradients for upstream and downstream flame spread are measured. Flame spread rates from IR image data are compared to visible image spread rate data. IR blackbody temperatures are compared to surface thermocouple readings to evaluate the effective emissivity of the pyrolyzing surface. Preheat lengths are evaluated both upstream and downstream of the central ignition point. A surface energy balance estimates the net heat flux from the flame to the fuel surface along the length of the fuel.

Olson, Sandra L.↗
DOE OSTI2023

Gradient synthesis of carbon quantum dots and activated carbon from pulp black liquor for photocatalytic hydrogen evolution and supercapacitor

Black liquor (BL) is a by-product of the chemical pulping industry and is mainly used as a low-value fuel; however, its potential to produce high-value products has not been fully exploited. In this study, a green and simple strategy is reported for the gradient production of Na + -functionalized carbon quantum dots (Na + -CQDs) for the first time, N and S co-doped CQDs (N/S-CQDs), and N and S co-doped KOH-activated carbon (N/S-KAC) from BL by dialysis, hydrothermal carbonization and activation-carbonization, respectively. Due to the good electron trapping ability, photoluminescence and promising up-conversion luminescence of CQDs, the hydrogen evolution efficiency of Na + -CQDs/TiO 2 and N/S-CQDs/TiO 2 photocatalysts was improved by 2.45 and 1.46 times, respectively, compared with pure TiO 2 . N/S-KAC with a high specific surface area of 2294 m 2 g -1 provides an excellent specific capacitance of 253 F g -1 at 0.5 A g -1 and a promising energy density of 26.92 Wh kg -1 under a power density of 566 W kg -1 for the fabricated symmetrical supercapacitor. Moreover, the electrode material has good cycling stability with a capacitance retention of ~ 93.91% after 5000 cycles. In conclusion, this pathway provides a versatile and scalable approach for the construction and co-production of nanostructured materials, photocatalysts and energy storage devices.

36 MATERIALS SCIENCE↗
NASA NTRS1990

Growth hormone aggregates in the rat adenohypophysis

Although it has been known for some time that GH aggregates are contained within the rat anterior pituitary gland, the role that they might play in pituitary function is unknown. The present study examines this issue using the technique of Western blotting, which permitted visualization of 11 GH variants with apparent mol wt ranging from 14-88K. Electroelution of the higher mol wt variants from gels followed by their chemical reduction with beta-mercaptoethanol increased GH immunoassayability by about 5-fold. With the blot procedure we found 1) that GH aggregates greater than 44K were associated with a 40,000 x g sedimentable fraction; 2) that GH aggregates were not present in glands from thyroidectomized rats, but were in glands from the thyroidectomized rats injected with T4; 3) that GH aggregates were uniquely associated with a heavily granulated somatotroph subpopulation isolated by density gradient centrifugation; and 4) that high mol wt GH forms were released from the dense somatotrophs in culture, since treatment of the culture medium with beta-mercaptoethanol increased GH immunoassayability by about 5-fold. Taken together, the results show that high mol wt GH aggregates are contained in secretory granules of certain somatotrophs and are also released in aggregate form from these cells in vitro.

NASA Discipline Cell Biology↗
DOE OSTI2020

Photoelectron spectroscopy and computational investigations of the electronic structures and noncovalent interactions of cyclodextrin-closo-dodecaborate anion complexes x-CD·B12X122- (x = a, ß, y; X = H, F)

We report a joint negative ion photoelectron spectroscopy (NIPES) and computational study on the electronic structures and noncovalent interactions of a series of cyclodextrin-closo-dodecaborate dianion complexes, ?-CD·B12X122- (? = a, ß, ?; X = H, F). The measured vertical / adiabatic detachment energies (VDEs / ADEs) are 1.15/0.93, 3.55/3.20, 3.90/3.60, and 3.85/3.60 eV for B12H122- and its a-, ß-, ?-CD complexes, respectively; while the corresponding values are 1.90/1.70, 4.00/3.60, 4.33/3.95, and 4.30/3.85 eV for the X = F case. These results show that the inclusion of B12X122- into the CD cavities greatly increase the electronic stability of the dianions. The effect of electronic stabilization for ß-CD is roughly the same as for ?-CD, both being considerably stronger than that for a-CD. Density functional theory (DFT) based geometry optimization reveals that B12X122- are inserted into CDs increasingly deeper from a-CD to ?-CD. The calculated VDEs and ADEs agree with the experiments well, particularly, reproducing the electron binding energy (EBE) trends. The molecular orbital analyses indicate that the most loosely bound photodetached electrons origin from the guest B12X122- moieties. In addition to a shift of all signals to larger EBE, significant changes in the signal patterns are observed. At low EBE, this is due to the splitting of highly degenerate B12X122- orbitals, while at high EBE, photodetachment from CD oxygens contributes to the new bands. The guest B12X122- and host CD nocovalent, size-specific interaction based on the independent gradient model (IGM) and energy decomposition analysis (EDA), is dominated by electrostatic interactions. The analysis further unravels unambiguiously the existence of dihydrogen bonding and how it affects the total energy that stabilizes the host-guest complexes of CDs·B12H122- compared to the general hydrogen bonding interaction in CDs·B12F122-. This work clearly exhibits strong influences on the electronic structures of dodecaborates upon clustering with CDs, with both size (a-, ß-, ?-) and molecular (X = H or F) specificities, thus providing critical molecular-level information on the cyclodextrin-closo-dodecaborate interactions of interest to medical applications, e.g. Boron neutron capature therapy. The NIPES experiments done at PNNL were supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Bioscience (X.-B.W.) and was performed at the EMSL, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. H.S. and Z.S. acknowledge the funding support of National Natural Science Foundation of China (Nos.11727810, 61720106009 and 21603074), the Science and Technology Commission of Shanghai Municipality (Nos. 19JC1412200), and the Program of Introducing Talents of Discipline to Universities 111 project (B12024). Z. L. thanks the China Scholarship Council (CSC) for financial support. We acknowledge the ECNU Multifunctional Platform for Innovation (001) and HPC Research Computing Team for providing computational and storage resources. J.W. acknowledges support from the Alexander von Humboldt foundation (Feodor Lynen Fellowship and Rückkehrerstipendium), a Freigeist fellowship of the Volkswagenfoundation and Prof. Vladimir A. Azov for helpful discussions.

Li, Zhipeng↗