Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “DFT”

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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Testing the predictive power of theory for Pd x Ir (100-x) alloy nanoparticles for the oxygen reduction reaction

Here, density functional theory (DFT) calculations of O and OH binding energies on triatomic surface ensembles of Pd x Ir (100-x) nanoalloys successfully predicted the overall trend in experimental oxygen reduction reaction (ORR) activity as a function of nanoparticle (NP) composition. Specifically, triatomic Pd 3 ensembles were found to possess optimal O and OH binding energies and were predicted to be highly active sites for the ORR, rivaling that of Pt(111). However, DFT calculations suggest that the O binding energy increases at active sites containing Ir, thereby decreasing ORR activity. Pd x Ir (100-x) nanoalloys were synthesized using a microwave-assisted method and their activity towards the ORR was tested using rotating disk voltammetry (RDV). As predicted, the bimetallic electrocatalysts exhibited worse catalytic activity than the Pd-only NPs. The strong qualitative correlation between the theoretical and experimental results demonstrates that the activity of individual active sites on the surface of NPs can serve as a proxy for overall activity. This is a particularly useful strategy for applying DFT calculations to electrocatalysts that are too large for true first-principle analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Substituted SrFeO 3 as robust oxygen sorbents for thermochemical air separation: correlating redox performance with compositional and structural properties

Thermochemical air separation via cyclic redox reactions of oxide-based oxygen sorbents has the potential to achieve high energy efficiency. Although a number of promising sorbents have been investigated, further improvements in sorbent performance through a fundamental understanding of the structure–performance relationships are highly desirable. In this study, we systematically investigated the effects of A and B site dopants on the oxygen uptake/release properties (i.e., vacancy formation energy, reduction enthalpy, oxygen release temperature, and oxygen capacity) of the SrFeO 3 family of perovskites as oxygen sorbents. A monotonic correlation between DFT calculated oxygen vacancy formation energy and oxygen release temperature demonstrates the effectiveness of DFT for guiding sorbent selection. Combining vacancy formation energy with stability analysis, dopants such as Ba and Mn have been identified for tuning the redox property of SrFeO 3 sorbents, and increasing the oxygen capacity for temperature and pressure swings when compared to undoped SrFeO 3 . The Mn doped sample proved to be highly stable, with less than a 3% decrease in capacity over 1000 cycles. Although the dynamic nature of the redox process makes it difficult to use a single vacancy formation energy as the descriptor, a systematic approach was developed to correlate the oxygen storage capacities with the sorbents’ compositional properties and vacancy formation energies. The combination of DFT calculations with experimental studies from this study provides a potentially effective strategy for developing improved sorbents for thermochemical air separation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Hydrogen desorption from the surface and subsurface of cobalt

The influence of coverage on the diffusion of hydrogen into the subsurface of cobalt was studied using density functional theory (DFT) and temperature programmed desorption (TPD). DFT calculations show that as the hydrogen coverage on Co(0001) increases, the barrier for hydrogen diffusion into the bulk decreases by 20%. Additionally, subsurface hydrogen on a hydrogen covered surface was found to be more stable when compared to a clean cobalt surface. To test these theoretical findings experimentally, excited hydrogen was used in an ultra-high vacuum environment to access higher hydrogen coverages. Here, our TPD studies showed that at high hydrogen coverages, a sharp low temperature feature appeared, indicating the stabilization of subsurface hydrogen. Further DFT calculations indicate that this sharp low temperature feature results from associative hydrogen desorption from a hydrogen saturated surface with a population of subsurface hydrogen. Microkinetic modelling was used to model the TPD spectra for hydrogen desporption from cobalt with and without subsurface hydrogen, showing reasonable agreement with experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

CASPT2 molecular geometries of Fe( II ) spin-crossover complexes

Using fully internally contracted (FIC)-CASPT2 analytical gradients, geometry optimizations of spin-crossover complexes are reported. This approach is tested on a series of Fe(II) complexes with different sizes, ranging from 13 to 61 atoms. A combination of active space and basis set choices are employed to investigate their role in determining reliable molecular geometries. The reported strategy demonstrates that a wave function-based level of theory can be used to optimize the geometries of metal complexes in reasonable times and enables one to treat the molecular geometry and electronic structure of the complexes using the same level of theory. For a series of smaller Fe(II) SCO complexes, strong field ligands in the LS state result in geometries with the largest differences between DFT and CASPT2; however, good agreement overall is observed between DFT and CASPT2. For the larger complexes, moderate sized basis sets yield geometries that compare well with DFT and available experimental data. Here we recommend using the (10e,12o) active space since convergence to a minimum structure was more efficient than with truncated active spaces despite having similar Fe–ligand bond distances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Catlas: an automated framework for catalyst discovery demonstrated for direct syngas conversion

Catalyst discovery is paramount to support access to energy and key chemical feedstocks in a post fossil fuel era. Exhaustive computational searches of large material design spaces using ab initio methods like density functional theory (DFT) are infeasible. We seek to explore large design spaces at relatively low computational cost by leveraging large, generalized, graph-based machine learning (ML) models, which are pretrained and therefore require no upfront data collection or training. We present Catlas, a framework that distributes and automates the generation of adsorbate-surface configurations and ML inference of DFT energies to achieve this goal. Catlas is open source, making ML assisted catalyst screenings easy and available to all. To demonstrate its efficacy, we use Catlas to explore catalyst candidates for the direct conversion of syngas to multi-carbon oxygenates. For this case study, we explore 947 stable/metastable binary, transition metal intermetallics as possible catalyst candidates. On this subset of materials, we are able to predict the adsorption energy of key descriptors, *CO and *OH, with good accuracy (0.16, 0.14 eV MAE, respectively). Using the projected selectivity towards C 2+ oxygenates from an existing microkinetic model, we identified 144 candidate materials. For 10 promising candidates, DFT calculations reveal a good correlation with our assessment using ML. Finally, among the top elemental combinations were Pt–Ti, Pd–V, Ni–Nb, and Ti–Zn, all of which appear unexplored experimentally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Engineering metal–metal oxide surfaces for high-performance oxygen reduction on Ag–Mn electrocatalysts

Understanding fundamental material–property relationships in mixed-element catalyst systems is crucial to advancing the viability of renewable electrochemical energy technologies, an important part of creating a more sustainable future. Herein, we report our insight on the nature and dynamics of highly active silver–manganese oxide (Ag–MnOx) catalyst surfaces for the oxygen reduction reaction (ORR) via a combined experimental–theoretical approach. Experimentally, we synthesize well-mixed Ag–Mn co-deposited thin films that are measurably flat and smooth, despite Mn surface migration and oxidation upon air exposure and electrochemical measurements. Cyclic voltammetry in 0.1 M KOH demonstrates up to 10-fold specific activity enhancements over pure Ag at 0.8 V vs. RHE for Ag-rich films (70–95% Ag in bulk). To further understand the Ag–Mn system, separate samples were synthesized with small amounts of Mn sequentially deposited onto the surface of a pure Ag thin film (Mn@Ag), ranging from partial to full surface coverage (down to 0.3 nm Mn $cm^{-2}_{geo}$ ~ 0.2 μg Mn $cm^{-2}_{geo}$). These sequentially deposited Mn@Ag films show analogous performance to their co-deposited counterparts indicating similar enhanced active sites. With density functional theory (DFT), we calculate that this enhancement arises from the tuned d-band of these material surfaces owing to the optimal hybridization of the electronic structures in specific Ag and MnO x geometries. Together, electrochemical measurements, DFT calculations, X-ray absorption spectroscopy, and valence-band X-ray photoelectron spectroscopy suggest synergistic electronic interactions between Ag and MnOx yield enhanced oxygen adsorption, and thus ORR activity, with DFT highlighting the Ag–MnO x interface sites as the most enhanced. This work demonstrates how combined experimental–theoretical methods can help design electrocatalysts with enhanced electrocatalytic properties and understand the nature of complex mixed metal–metal oxide surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Informing air–carbon ablation modeling with theoretical calculations of atomic oxygen and nitrogen interacting with carbon surfaces

To understand the gas–surface chemistry above the thermal protection system of a hypersonic vehicle, it is necessary to map out the kinetics of key elementary reaction steps. In this work, extensive periodic density functional theory (DFT) calculations are performed to elucidate the interaction of atomic oxygen and nitrogen with both the basal plane and edge sites of highly oriented pyrolytic graphite (HOPG). Reaction energies and barriers are determined for adsorption, desorption, diffusion, recombination, and several reactions. These DFT results are compared with the most recent finite-rate model for air–carbon ablation. Our DFT results corroborated some of the parameters used in the model but suggest that further refinement may be necessary for others. The calculations reported here will help to establish a predictive kinetic model for the complex reaction network present under hypersonic flight conditions.

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

Revealing short- and long-range Li-ion diffusion in Li 2 MnO 3 from finite-temperature dynamical mean field theory

Li 2 MnO 3 is a key component of Li-excess layered cathodes of the form (1 − x), LiMO 2 + x, Li 2 MnO 3 (M = Mn, Ni, Co, …), yet its role in setting Li-ion transport limitations remains under debate. Here, in this study, we combine DFT+U, finite-temperature DFT+DMFT with a continuous-time quantum Monte Carlo impurity solver, and nudged-elastic-band (NEB) calculations to study Li + migration in paramagnetic Li 2 MnO 3 in the presence of a single Li vacancy. Evaluating DMFT total energies along the DFT+U NEB geometries reveals that dynamical correlations strongly renormalize the lowest-barrier processes, reducing the activation energies to E a = 0.18 eV for the shortest-range hop and E a = 0.50 eV for the next-lowest (transport-controlling) step. The 0.18 eV barrier quantitatively reproduces the short-range activation energy from µ+SR, while the 0.50 eV barrier is consistent with the long-range transport scale extracted from ac-impedance measurements. This single-vacancy, paramagnetic DMFT description thus provides a unified interpretation of local and macroscopic probes without invoking clustered vacancy configurations or strong extrinsic disorder, consistent with nearly stoichiometric Li 2 MnO 3 powders. More broadly, our results highlight finite-temperature dynamical correlations as an essential ingredient for predicting ionic migration energetics in correlated oxide electrodes.

Lee, Alex Taekyung [University of Illinois, Chicag↗
DOE OSTI2020

Molecular chemisorption of N 2 on IrO 2 (110)

We investigated the adsorption of N 2 on stoichiometric and O-rich IrO 2 (110) surfaces using temperature programmed desorption (TPD) experiments and density functional theory (DFT) calculations. TPD shows that N 2 desorbs predominantly from the stoichiometric-IrO 2 (110) surface in a well-defined peak at 270 K for N 2 coverages below about 0.5 ML, and that a shoulder centered near 235 K develops in the N 2 TPD traces as the coverage approaches saturation, indicating that adsorbed N 2 molecules become destabilized at high N 2 coverage. Experiments of N 2 adsorption onto O-rich IrO 2 (110) surfaces provide evidence that N 2 adsorbs exclusively on the coordinatively-unsaturated Ir atoms (Ircus) of the surface, and that pre-adsorbed O-atoms (“on-top” oxygen) stabilize adsorbed N 2 molecules, causing the main N 2 TPD peak to shift toward higher temperature with increasing oxygen coverage. Consistent with prior results, our DFT calculations predict that an N 2 molecule preferentially adsorbs into an upright configuration on an Ircus atom of the IrO 2 (110) surface and achieves a binding energy of about 100 kJ/mol. The computed binding energy agrees well with our experimental estimate of ~90 kJ/mol for low N 2 coverages on stoichiometric IrO 2 (110). Lastly, the DFT calculations also quantitatively reproduce the observed stabilization of N 2 by co-adsorbed on-top O-atoms and predict the destabilization of N 2 on IrO 2 (110) as the N 2 adlayer becomes crowded at high coverage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Electrode-molecule energy level offsets in a gold-benzene diamine-gold single molecule tunnel junction

One means for describing electron transport across single molecule tunnel junctions (MTJs) is to use density functional theory (DFT) in conjunction with a nonequilibrium Green’s function formalism. This description relies on interpreting solutions to the Kohn–Sham (KS) equations used to solve the DFT problem as quasiparticle (QP) states. Many practical DFT implementations suffer from electron self-interaction errors and an inability to treat charge image potentials for molecules near metal surfaces. For MTJs, the overall effect of these errors is typically manifested as an overestimation of electronic currents. Correcting KS energies for self-interaction and image potential errors results in MTJ current–voltage characteristics in close agreement with measured currents. An alternative transport approach foregoes a QP picture and solves for a many-electron wavefunction on the MTJ subject to open system boundary conditions. It is demonstrated that this many-electron method provides similar results to the corrected QP picture for electronic current. The analysis of these two distinct approaches is related through corrections to a junction’s electronic structure beyond the KS energies for the case of a benzene diamine molecule bonded between two gold electrodes.

Szepieniec, Mark S.↗
DOE OSTI2020

Calculation of the detonation state of HN 3 with quantum accuracy

HN 3 is a unique liquid energetic material that exhibits ultrafast detonation chemistry and a transition to metallic states during detonation. We combine the Chebyshev interaction model for efficient simulation (ChIMES) many-body reactive force field and the extended-Lagrangian multiscale shock technique molecular dynamics method to calculate the detonation properties of HN 3 with the accuracy of Kohn–Sham density-functional theory. ChIMES is based on a Chebyshev polynomial expansion and can accurately reproduce density-functional theory molecular dynamics (DFT-MD) simulations for a wide range of unreactive and decomposition conditions of liquid HN 3 . We show that addition of random displacement configurations and the energies of gas-phase equilibrium products in the training set allows ChIMES to efficiently explore the complex potential energy surface. Schemes for selecting force field parameters and the inclusion of stress tensor and energy data in the training set are examined. Structural and dynamical properties and chemistry predictions for the resulting models are benchmarked against DFT-MD. We demonstrate that the inclusion of explicit four-body energy terms is necessary to capture the potential energy surface across a wide range of conditions. Our results generally retain the accuracy of DFT-MD while yielding a high degree of computational efficiency, allowing simulations to approach orders of magnitude larger time and spatial scales. The techniques and recipes for MD model creation we present allow for direct simulation of nanosecond shock compression experiments and calculation of the detonation properties of materials with the accuracy of Kohn–Sham density-functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Computational catalyst discovery: Active classification through myopic multiscale sampling

We report the recent boom in computational chemistry has enabled several projects aimed at discovering useful materials or catalysts. We acknowledge and address two recurring issues in the field of computational catalyst discovery. First, calculating macro-scale catalyst properties is not straightforward when using ensembles of atomic-scale calculations [e.g., density functional theory (DFT)]. We attempt to address this issue by creating a multi-scale model that estimates bulk catalyst activity using adsorption energy predictions from both DFT and machine learning models. The second issue is that many catalyst discovery efforts seek to optimize catalyst properties, but optimization is an inherently exploitative objective that is in tension with the explorative nature of early-stage discovery projects. In other words, why invest so much time finding a “best” catalyst when it is likely to fail for some other, unforeseen problem? We address this issue by relaxing the catalyst discovery goal into a classification problem: “What is the set of catalysts that is worth testing experimentally?” Here, we present a catalyst discovery method called myopic multiscale sampling, which combines multiscale modeling with automated selection of DFT calculations. It is an active classification strategy that seeks to classify catalysts as “worth investigating” or “not worth investigating” experimentally. Our results show an ~7–16 times speedup in catalyst classification relative to random sampling. These results were based on offline simulations of our algorithm on two different datasets: a larger, synthesized dataset and a smaller, real dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

First principles reactive simulation for equation of state prediction

The high cost of density functional theory (DFT) has hitherto limited the ab initio prediction of the equation of state (EOS). In this article, we employ a combination of large scale computing, advanced simulation techniques, and smart data science strategies to provide an unprecedented ab initio performance analysis of the high explosive pentaerythritol tetranitrate (PETN). Comparison to both experiment and thermochemical predictions reveals important quantitative limitations of DFT for EOS prediction and thus the assessment of high explosives. In particular, we find that DFT predicts the energy of PETN detonation products to be systematically too high relative to the unreacted neat crystalline material, resulting in an underprediction of the detonation velocity, pressure, and temperature at the Chapman–Jouguet state. The energetic bias can be partially accounted for by high-level electronic structure calculations of the product molecules. Furthermore we demonstrate a modeling strategy for mapping chemical composition across a wide parameter space with limited numerical data, the results of which suggest additional molecular species to consider in thermochemical modeling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Predicting Hugoniot equation of state in erythritol with ab initio and reactive molecular dynamics

Erythritol has been proposed as an inert surrogate for developing theoretical and computational models to study aging in energetic materials. In this work, we present a comparison of mechanical and shock properties of erythritol computed using the ReaxFF reactive force field and from ab initio calculations employing density functional theory (DFT). We screened eight different ReaxFF parameterizations, of which the CHO parameters developed for hydrocarbon oxidation provide the most accurate predictions of mechanical properties and the crystal structure of erythritol. Further validation of the applicability of this ReaxFF parameterization for modeling erythritol is demonstrated by comparing predictions of the elastic constants, crystal structure, vibrational density of states, and Hugoniot curves against DFT calculations. The ReaxFF predictions are in close agreement with the DFT simulations for the elastic constants and shock Hugoniot when the crystal is loaded along its c axis but show as much as 30% disagreement in the elastic constants in the ab plane and 12% difference in shock pressures when shocked along the a or b crystal axes. Last, we compare thermomechanical properties predicted from classical molecular dynamics with those calculated using the quasi-harmonic approximation and show that quantum mechanical effects produce large discrepancies in the computed values of heat capacity and thermal expansion coefficients compared with classical assumptions. Combining classical molecular dynamics predictions of mechanical behavior with phonon-based calculations of thermal behaviors, we show that predicted shock-induced temperatures for pressures up to 6.5 GPa do not exceed the pressure-dependent melting point of erythritol.

Hu, Jing↗
DOE OSTI2021

Structure prediction of epitaxial inorganic interfaces by lattice and surface matching with Ogre

We present a new version of the Ogre open source Python package with the capability to perform structure prediction of epitaxial inorganic interfaces by lattice and surface matching. In the lattice matching step, a scan over combinations of substrate and film Miller indices is performed to identify the domain-matched interfaces with the lowest mismatch. Subsequently, surface matching is conducted by Bayesian optimization to find the optimal interfacial distance and in-plane registry between the substrate and the film. For the objective function, a geometric score function is proposed based on the overlap and empty space between atomic spheres at the interface. The score function reproduces the results of density functional theory (DFT) at a fraction of the computational cost. The optimized interfaces are pre-ranked using a score function based on the similarity of the atomic environment at the interface to the bulk environment. Final ranking of the top candidate structures is performed with DFT. Ogre streamlines DFT calculations of interface energies and electronic properties by automating the construction of interface models. The application of Ogre is demonstrated for two interfaces of interest for quantum computing and spintronics, Al/InAs and Fe/InSb.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Reaction processes at step edges on S-decorated Cu(111) and Ag(111) surfaces: MD analysis utilizing machine learning derived potentials

We report a variety of complexation, reconstruction, and sulfide formation processes can occur at step edges on the {111} surfaces of coinage metals (M) in the presence of adsorbed S under ultra-high vacuum conditions. Given the cooperative many-atom nature of these reaction processes, Molecular Dynamics (MD) simulation of the associated dynamics is instructive. However, only quite restricted Density Functional Theory (DFT)-level ab initio MD is viable. Thus, for M = Ag and Cu, we instead utilize the DeePMD framework to develop machine-learning derived potentials, retaining near-DFT accuracy for the M–S systems, which should have broad applicability. These potentials are validated by comparison with DFT predictions for various key quantities related to the energetics of S on M(111) surfaces. The potentials are then utilized to perform extensive MD simulations elucidating the above diverse restructuring and reaction processes at step edges. Key observations from MD simulations include the formation of small metal–sulfur complexes, especially MS 2 ; development of a local reconstruction at A-steps featuring an S-decorated {100} motif; and 3D sulfide formation. Additional analysis yields further information on the kinetics for metal–sulfur complex formation, where these complexes can strongly enhance surface mass transport, and on the propensity for sulfide formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry

Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d 1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d 1 MOPs to be suitable for nearly eliminating all energetic delocalization and static correlation errors. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization and static correlation errors within a non-empirical framework.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Atomistic insight into the effects of electrostatic fields on hydrocarbon reaction kinetics

Reactive Molecular Dynamics (MD) and Density Functional Theory (DFT) computations are performed to provide insight into the effects of external electrostatic fields on hydrocarbon reaction kinetics. By comparing the results from MD and DFT, the suitability of the MD method in modeling electrodynamics is first assessed. Results show that the electric field-induced polarization predicted by the MD charge equilibration method is in good agreement with various DFT charge partitioning schemes. Then, the effects of oriented external electric fields on the transition pathways of non-redox reactions are investigated. Results on the minimum energy path suggest that electric fields can cause catalysis or inhibition of oxidation reactions, whereas pyrolysis reactions are not affected due to the weaker electronegativity of the hydrogen and carbon atoms. MD simulations of isolated reactions show that the reaction kinetics is also affected by applied external Lorentz forces and interatomic Coulomb forces since they can increase or decrease the energy of collision depending on the molecular conformation. In addition, electric fields can affect the kinetics of polar species and force them to align in the direction of field lines. These effects are attributed to energy transfer via intermolecular collisions and stabilization under the external Lorentz force. The kinetics of apolar species is not significantly affected mainly due to the weak induced dipole moment even under strong electric fields. The dynamics and reaction rates of species are studied by means of large-scale combustion simulations of n-dodecane and oxygen mixtures. Results show that under strong electric fields, the fuel, oxidizer, and most product molecules experience translational and rotational acceleration mainly due to close charge transfer along with a reduction in their vibrational energy due to stabilization. This study will serve as a basis to improve the current methods used in MD and to develop novel methodologies for the modeling of macroscale reacting flows under external electrostatic fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗