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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Classical symmetries and the Quantum Approximate Optimization Algorithm

Here, we study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular, we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques toward predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Land Use in Computable General Equilibrium Models

Constant Elasticity of Transformation (CET) functions are widely used to allocate land across uses in Computable General Equilibrium (CGE) models. These models fail to maintain area of land in balance. Several ways have been used or offered to fix this problem. This paper first examines the extent to which the CET approach may generate imbalances in area of land and identifies determinants of such imbalances. It then evaluates the merits, properties, and welfare impacts of the available approaches that restore area of land in balance. We show that heterogeneity in land prices (land rents) is the main source of imbalance in area of land, not the curvature of the CET function. Furthermore, we show that the available approaches that restore area of land in balance either introduce ad hoc adjustments in land allocation or undermine the conventional welfare assessments of the CET results and ignore the opportunity costs of land transformation. The CGE models which applied stochastic productivity distribution functions to allocate land among uses maintain area of land in balance, but they suffer from important limitations and ignore costs of land transformation.

Taheripour, Farzad↗
DOE OSTI2026

Ab Initio Modeling of Aqueous Methanol Mixtures at DFT-SCAN Level Using Machine Learning Interatomic Potentials

Abstract Methanol–water mixtures find use in many applications, particularly catalytic energy conversion processes. Their importance has motivated numerous computational studies, most of which employed molecular dynamics based on classical force fields. These enable simulations of large systems on long time scales but do not reliably describe reactive dynamics involving bond breaking and bond formation. In contrast, ab initio molecular dynamics (AIMD) based on density functional theory (DFT) is generally more reliable for such applications but has a high computational cost, which discourages systematic studies of alcohol-water mixtures. To remedy this, we trained a machine learning interatomic potential capable of probing the properties of aqueous methanol mixtures at the DFT level using the SCAN functional. Our results show that SCAN qualitatively reproduces multiple key experimental features arising from the amphiphilic nature of methanol, including density, diffusion coefficients, X-ray structure factors, and Kirkwood–Buff integrals. We also find that structural correlations between water molecules are somewhat overestimated, leading to a stronger preferential association than that predicted by experiments. However, increasing the temperature by 30 K mitigates this effect and also recovers the correct mobilities of both methanol and water. These results indicate that SCAN provides an accurate description of methanol–water mixtures, making it a reliable choice for investigating the reactive dynamics in such systems.

Park, Sanghyun J. [Princeton University , , , ,]↗
DOE OSTI2022

Closing the loop between microstructure and charge transport in conjugated polymers by combining microscopy and simulation

A grand challenge in materials science is to identify the impact of molecular composition and structure across a range of length scales on macroscopic properties. We demonstrate a unified experimental–theoretical framework that coordinates experimental measurements of mesoscale structure with molecular-level physical modeling to bridge multiple scales of physical behavior. Here we apply this framework to understand charge transport in a semiconducting polymer. Spatially-resolved nanodiffraction in a transmission electron microscope is combined with a self-consistent framework of the polymer chain statistics to yield a detailed picture of the polymer microstructure ranging from the molecular to device relevant scale. Using these data as inputs for charge transport calculations, the combined multiscale approach highlights the underrepresented role of defects in existing transport models. Short-range transport is shown to be more chaotic than is often pictured, with the drift velocity accounting for a small portion of overall charge motion. Local transport is sensitive to the alignment and geometry of polymer chains. At longer length scales, large domains and gradual grain boundaries funnel charges preferentially to certain regions, creating inhomogeneous charge distributions. While alignment generally improves mobility, these funneling effects negatively impact mobility. The microstructure is modified in silico to explore possible design rules, showing chain stiffness and alignment to be beneficial while local homogeneity has no positive effect. This combined approach creates a flexible and extensible pipeline for analyzing multiscale functional properties and a general strategy for extending the accesible length scales of experimental and theoretical probes by harnessing their combined strengths.

42 ENGINEERING↗
DOE OSTI2019

Light Scattering by a Periodically Corrugated Boundary of a Hyperbolic Medium

The scattering features of radiation incident on a periodically modulated boundary of a hyperbolic medium (HM) are studied numerically. An optimal (in a certain class of functions)—sawtooth—profile shape is found that provides minimum reflection in a wide range of wavelengths. It is shown that, for a certain orientation of the optical axes of the HM, “hot points” appear on the sawtooth boundary, that are responsible for the subwavelength field localization. A generalization is implemented of the numerical method based on the Green’s second identity for the field calculation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Dynamical electron correlation and the chemical bond. I. Covalent bonds in AH and AF (A = B–F)

Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. This study focused on the effect of dynamical electron correlation on the spectroscopic constants ($R$ e , $ω$ e , $D$ e ), and potential energy curves, Δ$E$($R$), of the covalently bound AH and AF molecules, A = B–F. The changes in the spectroscopic constants (Δ$R$ e , Δ$ω$ e , Δ$D$ e ) caused by dynamical correlation are erratic and, at times, even surprising. These changes can be understood based on the dependence of the dynamical electron correlation energies of the AH and AF molecules as a function of the bond distance, i.e., Δ$E$ DEC ($R$). At large $R$, the magnitude of Δ$E$ DEC ($R$) increases nearly exponentially with decreasing $R$, but this increase slows as $R$ continues to decrease and, in many cases, even reverses at very short $R$. The changes in Δ$E$ DEC ($R$) in the region around $R$ e were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of Δ$E$ DEC ($R$) for the most polar molecules. The variations in Δ$E$ DEC ($R$) for $R$ ≲ $R$ e are directly correlated with major changes in the electronic structure of the molecules as revealed by a detailed analysis of the spin-coupled generalized valence bond wave function. In conclusion, the results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on chemical bonds and molecular properties and processes.

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

Analysis of over-magnetization of elemental transition metal solids from the SCAN density functional

Current investigations have revealed that the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation exchange-correlation functional significantly over-magnetizes elemental Fe, Co, and Ni solids. For the paradigmatic case, bcc Fe, the error relative to experiment is ≳ 20 % . A comparative analysis of magnetization results from SCAN and its deorbitalized counterpart, SCAN-L, leads to identification of the source of the discrepancy. It is not from the difference between Kohn-Sham (SCAN-L) and generalized Kohn-Sham (SCAN) procedures. The key is the iso-orbital indicator α (the ratio of the local Pauli and Thomas-Fermi kinetic energy densities). Its deorbitalized counterpart α L has more dispersion in both spin channels with respect to magnetization in an approximate region between 0.6 and 1.2 bohrs around an Fe nucleus. The overall effect is that the SCAN switching function evaluated with α L reduces the energetic disadvantage of the down channel with respect to up compared to the original α , which in turn reduces the magnetization. This identifies the origin of the SCAN magnetization error as insensitivity of the SCAN switching function to α values in the approximate range 0.5 ≲ α ≲ 0.8 and oversensitivity for α ≳ 0.8 .

36 MATERIALS SCIENCE↗
DOE OSTI2019

Solution of Periodic Boundary-Value Problems of the Spatial Theory of Elasticity in the Vector Form

We discuss boundary-value problems for the system of equations of the spatial theory of elasticity in the class of double-periodic functions and obtain a general solution of the system. We distinguish six types of elementary Floquet waves and examine their energy characteristics. We consider fundamental boundary-value problems in the half-space in the vector form. The diffraction problem for an elastic wave on a periodic system of defects in the vector form is reduced to the paired summator functional equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Cluster Configuration Spaces of Finite Type

For each Dynkin diagram $D$, we define a ''cluster configuration space'' ${\mathcal{M}}_D$ and a partial compactification ${\widetilde {\mathcal{M}}}_D$. For $D = A_{n-3}$, we have ${\mathcal{M}}_{A_{n-3}} = {\mathcal{M}}_{0,n}$, the configuration space of $n$ points on ${\mathbb P}^1$, and the partial compactification ${\widetilde {\mathcal{M}}}_{A_{n-3}}$ was studied in this case by Brown. The space ${\widetilde {\mathcal{M}}}_D$ is a smooth affine algebraic variety with a stratification in bijection with the faces of the Chapoton-Fomin-Zelevinsky generalized associahedron. The regular functions on ${\widetilde {\mathcal{M}}}_D$ are generated by coordinates $u_\gamma$, in bijection with the cluster variables of type $D$, and the relations are described completely in terms of the compatibility degree function of the cluster algebra. As an application, we define and study cluster algebra analogues of tree-level open string amplitudes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonadiabatic transition paths from quantum jump trajectories

We present a means of studying rare reactive pathways in open quantum systems using transition path theory and ensembles of quantum jump trajectories. This approach allows for the elucidation of reactive paths for dissipative, nonadiabatic dynamics when the system is embedded in a Markovian environment. Here, we detail the dominant pathways and rates of thermally activated processes and the relaxation pathways and photoyields following vertical excitation in a minimal model of a conical intersection. We find that the geometry of the conical intersection affects the electronic character of the transition state as defined through a generalization of a committor function for a thermal barrier crossing event. Similarly, the geometry changes the mechanism of relaxation following a vertical excitation. Relaxation in models resulting from small diabatic coupling proceeds through pathways dominated by pure dephasing, while those with large diabatic coupling proceed through pathways limited by dissipation. The perspective introduced here for the nonadiabatic dynamics of open quantum systems generalizes classical notions of reactive paths to fundamentally quantum mechanical processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Thermal exchange-correlation functionals: Capturing quantum electron behavior in warm, dense plasmas

We summarize and give perspective upon recent progress in developing non-empirical constraint-based thermal (i.e., free energy) exchange-correlation (XC) density functionals essential for accurate description of the quantum behavior of electrons in warm, dense plasmas. After delineating the critical role of ground-state functionals for zero-temperature, time-dependent DFT, we outline the underpinnings of local density approximation, generalized gradient approximation (GGA), and meta-GGA XC free-energy functionals. Two basic thermalization principles for upgrading ground-state XC functionals to successful thermal ones are emphasized. Then, we turn to a long-standing challenge, assessment of the accuracy of well-founded functionals. Unlike the ground state, there are a few exact results for large T and P. An exception is path integral Monte Carlo (PIMC) data for dense H/D and He plasmas. For those, we did ab initio molecular dynamics simulations under selected thermodynamic conditions employing five thermal XC functionals: two approximate thermal GGAs, fully thermal GGA, an approximate meta-GGA, and fully thermal meta-GGA. Comparisons with the PIMC data show that functionals thermalized by augmenting a non-thermal functional with a lower-level thermal contribution are inferior to functionals with thermal XC and spatial inhomogeneity effects taken into account at the same level of refinement. We believe this and similar evidence should be convincing to the high-energy density physics community of the necessity of use of proper thermal XC functionals in simulation studies of finite-temperature quantum effects in warm, dense plasmas.

Ab-initio molecular dynamics↗
DOE OSTI2023

Efficient Reliability Analysis using Generalized Multifidelity Modeling and Explainable Active Learning

To assess the reliability of critical technologies like nuclear plants and infrastructure systems and improve the robustness of design, engineers have to quantify the uncertainties surrounding the system behavior accurately. However, the complexity of the problem can make standard reliability analysis algorithms prohibitively expensive, primarily due to the high computational cost of estimating the system response at each iteration. This cost can be greatly reduced by using multi-fidelity modeling and machine learning to build a surrogate model to replace the expensive response function. We propose a general and robust method for building surrogates from multiple Low Fidelity (LF) models coupled with machine learning to retain accuracy. Our framework first constructs “Corrected Low Fidelity models” (CLFs) by coupling a High Fidelity (HF) model inferred Gaussian Process correction term with each of the LF models. It then uses the correction terms to assign model probabilities to each of these CLFs in an explainable way before using them to assemble the final surrogate. No assumptions are made about the type of the LF models or their correlation with the HF model. The proposed surrogate modeling framework is used within the subset simulation algorithm (a variance-reduced MCMC-based reliability analysis algorithm) for enhanced efficiency. Additionally, an active learning step is added to the algorithm to adaptively decide when the surrogate is not sufficiently accurate, at which point the HF model is called and used to refine the surrogate. Through a frame buckling example, our method is shown to be highly efficient at reducing the expensive HF model calls while accurately estimating the failure probability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Analytical harmonic vibrational frequencies with VV10-containing density functionals: Theory, efficient implementation, and benchmark assessments

VV10 is a powerful nonlocal density functional for long-range correlation that is used to include dispersion effects in many modern density functionals, such as the meta-generalized gradient approximation (mGGA), B97M-V, the hybrid GGA, ωB97X-V, and the hybrid mGGA, ωB97M-V. While energies and analytical gradients for VV10 are already widely available, this study reports the first derivation and efficient implementation of the analytical second derivatives of the VV10 energy. The additional compute cost of the VV10 contributions to analytical frequencies is shown to be small in all but the smallest basis sets for recommended grid sizes. Here, this study also reports the assessment of VV10-containing functionals for predicting harmonic frequencies using the analytical second derivative code. The contribution of VV10 to simulating harmonic frequencies is shown to be small for small molecules but important for systems where weak interactions are important, such as water clusters. In the latter cases, B97M-V, ωB97M-V, and ωB97X-V perform very well. The convergence of frequencies with respect to the grid size and atomic orbital basis set size is studied, and recommendations are reported. Finally, scaling factors to allow comparison of scaled harmonic frequencies with experimental fundamental frequencies and to predict zero-point vibrational energy are presented for some recently developed functionals (including r2SCAN, B97M-V, ωB97X-V, M06-SX, and ωB97M-V).

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

Prediction of a Dynamically Stable New Half-Metallic Phase for the BaN and BaC Compounds

The structural, magnetic, elastic, mechanical, and thermodynamic properties of BaC and BaN compounds in different phases were studied using first-principle calculations based on spin-polarized density functional theory within the generalized gradient approximation (GGA-PBEsol) and the modified Becke–Johnson approach (mBJ-GGA-PBEsol) for the exchange-correlation energy and potential. The following phases—rock-salt (NaCl), CsCl, zinc blende (ZB), NiAs- and WZ-type hexagonal, tetragonal (P4/nmm), and orthorombic (Pnma) phases of BaC and BaN compounds—were considered. We obtained that Pnma phase has the lowest energy configuration as a function of the volume for both the BaN and BaC compounds. The ferromagnetic phase is energetically favored with respect to the non-magnetic phase in the BaN and BaC compounds, except for the CsCl phase in the BaC compound. Considering the phonon dynamics of BaN and BaC compounds in the Pnma, NaCl, ZB, and WZ phases, we observed that the BaN and BaC compounds in the Pnma, NaCl, and ZB phases are dynamically stable. The calculated elastic properties for the Pnma, NaCl, and ZB phases show that they are elastically stable. The Pnma phase for the BaN and BaC compounds, which is a new phase was found to be dynamically and elastically stable. The BaN and BaC compounds exhibit half-metallic behavior in the Pnma, NaCl, and ZB phases. The half-metallic and magnetic character found in the BaN and BaC compounds are attributed to the presence of spin-polarized 2p orbitals of the nitrogen and carbon atoms, respectively. We found that BaN and BaC compounds are half-metallic ferromagnets with magnetic moment of 1 μ{sub B} and 2 μ{sub B} per formula unit, respectively. Using the GGA-PBEsol (mBJ-GGA-PBEsol) approach, our calculated half-metallic gaps for BaN and BaC compounds are 0.22 eV (0.54 eV) and 0.32 eV (0.44 eV) in the Pnma phase, 0.23 eV (1.32 eV) and 0.35 eV (1.00 eV) in the NaCl phase, and 0.38 eV (1.54 eV) and 0.50 eV (1.57 eV) in the ZB phase, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

A minimum assumption approach to MEG sensor array design

Objective. Our objective is to formulate the problem of the magnetoencephalographic (MEG) sensor array design as a well-posed engineering problem of accurately measuring the neuronal magnetic fields. This is in contrast to the traditional approach that formulates the sensor array design problem in terms of neurobiological interpretability the sensor array measurements. Approach. We use the vector spherical harmonics (VSH) formalism to define a figure-of-merit for an MEG sensor array. We start with an observation that, under certain reasonable assumptions, any array of m perfectly noiseless sensors will attain exactly the same performance, regardless of the sensors' locations and orientations (with the exception of a negligible set of singularly bad sensor configurations). We proceed to the conclusion that under the aforementioned assumptions, the only difference between different array configurations is the effect of (sensor) noise on their performance. We then propose a figure-of-merit that quantifies, with a single number, how much the sensor array in question amplifies the sensor noise. Main results. We derive a formula for intuitively meaningful, yet mathematically rigorous figure-of-merit that summarizes how desirable a particular sensor array design is. We demonstrate that this figure-of-merit is well-behaved enough to be used as a cost function for a general-purpose nonlinear optimization methods such as simulated annealing. We also show that sensor array configurations obtained by such optimizations exhibit properties that are typically expected of 'high-quality' MEG sensor arrays, e.g. high channel information capacity. Significance. Our work paves the way toward designing better MEG sensor arrays by isolating the engineering problem of measuring the neuromagnetic fields out of the bigger problem of studying brain function through neuromagnetic measurements.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Transition Metal Dichalcogenide MoS 2 : Oxygen and Fluorine Functionalization for Selective Plasma Processing

Low-temperature plasma processing is a promising technique for tailoring transition metal dichalcogenides (TMDs). For chalcogen substitution processing, a key challenge is to identify the ion energy window that enables selective chalcogen removal while preserving the metal lattice. Using ab initio molecular dynamics (AIMD), we demonstrate that oxygen and fluorine functionalization widen the processing window by significantly lowering the sulfur sputtering energy threshold (E sputt,S ) of MoS 2 from ∼30 to ∼10 eV via formation of sputtering products such as SO 2 and SF n . Additionally, we show that experimentally relevant cryogenic temperatures strongly affect E sputt,S (T). The dependence is confirmed via AIMD and also predicted by a mechanistic parameter-free theory, suggesting that E sputt (T) generalizes to other TMDs, functionalizations, and surface impact conditions. Our results highlight oxygen/fluorine functionalization, ionic impact angle, and material temperature to be key control parameters for selective, damage-controlled chalcogen removal in TMD processing.

Polyachenko, Yury [Princeton Plasma Physics Labora↗
DOE OSTI2024

Magnetism in the two-dimensional dipolar XY model

Here, motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar XY model [C. Chen et al., Nature (London) 616, 691 (2023)], we numerically study the model's equilibrium properties. We obtain the phase diagram, critical properties, entropies, variance of the magnetization, and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and pseudo-Majorana functional renormalization group techniques, generalizing the latter to a U⁡(1) symmetric setting. Our simulations perform extensive thermometry in dipolar Rydberg atom arrays and establish conditions for adiabaticity and thermodynamic equilibrium. On the ferromagnetic side of the experiment, we determine the entropy per particle S/N≈0.5, close to the one at the critical temperature, S c /N=0.585⁢(15). The simulations suggest the presence of an out-of-equilibrium plateau at large distances in the correlation function, thus motivating future studies on the nonequilibrium dynamics of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Atomic Layer Deposition for Materials-Based H2 Storage: Opportunities and Limitations

The transportation demands in our growing hydrogen (H2) economy requires robust storage systems. The current commercially implemented technology in fuel cell cars relies on the well-established technology of hydrogen gas compressed to 350-700 bar, depending on the application. The compressed gas tanks in use today are bulky and cost intensive. To address this challenge, material-based storage is one of the long-term alternatives considered and constitutes the focus of this talk. Material-based storage is broadly defined as hydrogen bound to solid materials, with its binding strength varying from physisorption to porous materials, such as zeolites and metal organic frameworks, to chemisorption in (complex) metal hydrides. The ultimate targets set by the U.S. Department of Energy for this technology include a system gravimetric capacity of 6.5 wt% and volumetric capacity of 40 g/L at 100 bar, operating temperatures ranging between -40 C and +40 C and adsorption/desorption timescales of < 5 min. Storage in the form of physisorbed or chemisorbed hydrogen has guided the materials research, which metal- organic framework and (complex) metal hydrides being the most promising materials classes. A variety of these materials have met one or more of the targets, but it has remained elusive for a single material system to meet all these stringent requirements. Nano-encapsulation and low-concentration chemical additives have previously been employed separately to overcome such challenges. Functionalization via atomic layer deposition (ALD), however, offers unique characteristics that make it suitable for both, nano-encapsulation and "doping" with low-concentration additives. This deposition technique has sub-monolayer thickness control, is highly conformal in high-surface area materials and is self-limiting, i.e., once the gas-phase precursor reacts with the available surface sites, the surface reactions stop. In this presentation, we will showcase examples where ALD, more generally vapor-phase functionalization, on (complex) metal hydrides and organic frameworks has improved the material properties for H2 storage. In our first study, Al2O3 was deposited on magnesium borohydride, Mg(BH4)2, at room temperature using trimethylaluminum (TMA) and water. From our findings, encouraging initial results were obtained: the H2 desorption temperature was lowered by 60-120 degrees C, the desorbed gravimetric H2 capacity at temperatures < 250 degrees C was doubled, and the desorption kinetics increased by a factor of ~6 compared to uncoated Mg(BH4)2. However, hydrolysis reactions caused by residual surface -OH groups from the ALD water-pulse degraded the sample substantially. Through this study, the use of TMA was observed to be highly reactive with the Mg(BH4)2 surface species, leading to the strategy of exposing the sample only to TMA. The relative mole fraction of the vapor-phase additive can be precisely controlled with the number of TMA pulses and pulse duration. By tuning these parameters, we show in our second study that 10 pulses of TMA at ambient conditions were able to decrease the H2 desorption temperature by ~100 degrees C while retaining <95 % of its H2 capacity. We applied this approach with other additives such as BBr3, TiCl4 and tetrahydrofuran, and demonstrate that this unique approach opens the door to a new class of molecular additives and catalysts which cannot easily be introduced with conventional mechano-chemical or solvent-based techniques for (complex) metal-hydrides. In the case of metal organic frameworks, ALD is a promising technique to functionalize the pores with metal atoms or functional groups able to tune the gas selectivity and binding energy, for which ~15 kJ/mol has been established as the optimal value for H2 storage in sorbent materials. Vapor-phase techniques such as ALD have numerous benefits over other functionalization tools for H2 storage materials opening innumerable opportunities to the field. To exploit these opportunities, the current limitations on room temperature and water-less ALD processes needs to be overcome which will greatly expand the possibilities of encapsulation and incorporation of additives for organic frameworks and (complex) metal hydrides.

atomic layer deposition↗