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At least 1,495 records · Page 83

Direct observation of electric field-induced magnetism in a molecular magnet

Abstract We report the direct observation of an electrically-induced magnetic susceptibility in the molecular nano- magnet [Fe 3 O(O 2 CPh) 6 (py) 3 ]ClO 4 · py, an Fe 3 trimer. This magnetoelectric effect results from the breaking of spatial inversion symmetry due to the spin configurations of the antiferromagnetic trimer. Both static and very low frequency electric fields were used. Fractional changes of the magnetic susceptibility of 11 ppb $$\pm 2$$ ± 2 per kVm -1 for the temperature range 8 . 5 < T < 13 . 5 K were observed for applied electric fields up to 62 kV m − 1 . The changes in susceptibility were measured using a tunnel diode oscillator operating at liquid helium temperatures while the sample is held at a higher regulated temperature.

30 DIRECT ENERGY CONVERSION↗

Domain wall enabled steep slope switching in MoS2 transistors towards hysteresis-free operation

Abstract The device concept of ferroelectric-based negative capacitance (NC) transistors offers a promising route for achieving energy-efficient logic applications that can outperform the conventional semiconductor technology, while viable operation mechanisms remain a central topic of debate. In this work, we report steep slope switching in MoS 2 transistors back-gated by single-layer polycrystalline PbZr 0.35 Ti 0.65 O 3 . The devices exhibit current switching ratios up to 8 × 10 6 within an ultra-low gate voltage window of $$V_{{{\mathrm{g}}}} = \pm \! 0.5$$ V g = ± 0.5 V and subthreshold swing (SS) as low as 9.7 mV decade −1 at room temperature, transcending the 60 mV decade −1 Boltzmann limit without involving additional dielectric layers. Theoretical modeling reveals the dominant role of the metastable polar states within domain walls in enabling the NC mode, which is corroborated by the relation between SS and domain wall density. Our findings shed light on a hysteresis-free mechanism for NC operation, providing a simple yet effective material strategy for developing low-power 2D nanoelectronics.

36 MATERIALS SCIENCE↗

Coulomb-free 1S0 p − p scattering length from the quasi-free p + d → p + p + n reaction and its relation to universality

Abstract The Coulomb-free 1 S 0 proton-proton ( p - p ) scattering length relies heavily on numerous and distinct theoretical techniques to remove the Coulomb contribution. Here, it has been determined from the half-off-the-energy-shell p - p scattering cross section measured at center-of-mass energies below 1 MeV using the quasi-free p + d → p + p + n reaction. A Bayesian data-fitting approach using the expression of the s-wave nucleon-nucleon scattering cross section returned a p - p scattering length $${a}_{pp}=-18.1{7}_{-0.58}^{+0.52}{| }_{stat}\pm 0.0{1}_{syst}$$ a p p = − 18.1 7 − 0.58 + 0.52 ∣ s t a t ± 0.0 1 s y s t fm and effective range r 0 = 2.80 ± 0.05 s t a t ± 0.001 s y s t fm. A model based on universality concepts has been developed to interpret this result. It accounts for the short-range interaction as a whole, nuclear and residual electromagnetic, according to what the s-wave phase-shift δ does in the description of low-energy nucleon-nucleon scattering data. We conclude that our parameters are representative of the short-range physics and propose to assess the charge symmetry breaking of the short-range interaction instead of just the nuclear interaction. This is consistent with the current understanding that the charge dependence of nuclear forces is due to different masses of up-down quarks and their electromagnetic interactions. This achievement suggests that these properties have a lesser than expected impact in the context of the charge symmetry breaking.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Abrupt reduction in shipping emission as an inadvertent geoengineering termination shock produces substantial radiative warming

Abstract Human activities affect the Earth’s climate through modifying the composition of the atmosphere, which then creates radiative forcing that drives climate change. The warming effect of anthropogenic greenhouse gases has been partially balanced by the cooling effect of anthropogenic aerosols. In 2020, fuel regulations abruptly reduced the emission of sulfur dioxide from international shipping by about 80% and created an inadvertent geoengineering termination shock with global impact. Here we estimate the regulation leads to a radiative forcing of $$+0.2\pm 0.11$$ + 0.2 ± 0.11 Wm −2 averaged over the global ocean. The amount of radiative forcing could lead to a doubling (or more) of the warming rate in the 2020 s compared with the rate since 1980 with strong spatiotemporal heterogeneity. The warming effect is consistent with the recent observed strong warming in 2023 and expected to make the 2020 s anomalously warm. The forcing is equivalent in magnitude to 80% of the measured increase in planetary heat uptake since 2020. The radiative forcing also has strong hemispheric contrast, which has important implications for precipitation pattern changes. Our result suggests marine cloud brightening may be a viable geoengineering method in temporarily cooling the climate that has its unique challenges due to inherent spatiotemporal heterogeneity.

54 ENVIRONMENTAL SCIENCES↗

Exploring the kinetics of actinyl–EDTA reduction by ferrous iron using quantum-mechanical calculations

Here, the reduction of An(VI) (An = U, Np, and Pu) to An(IV) significantly decreases its solubility and mobility. This reaction can be hindered by complexation with inorganic (e.g., carbonate) or organic ligands. Ethylenediaminetetraacetic acid (EDTA) is one such organic ligand that forms stable complexes with actinides. Therefore, it may enhance the mobility of actinides. However, the redox kinetics and mechanisms of actinyl (An(V/VI)O 2 +/2+ )–EDTA are not well characterized yet and are thus studied here using quantum-mechanical calculations. The principle is to approach the actinyl–EDTA and Fe 2+ (reductant) in small incremental steps and calculate the system energy at each distance. The overall reaction is then delineated into sub-processes (encounter frequency in bulk solution, formation of outer-sphere complex, transition from outer- to inner-sphere complex, and electron transfer), and reaction rates are determined for each sub-process. The formation of outer-sphere complexes occurs rapidly in microseconds to seconds over a wide range of actinyl concentrations (pM to μM); in contrast, the transition to the inner-sphere complex is relatively slow (milliseconds to a few seconds). Immediate electron transfer to form the pentavalent actinide is observed along the reaction path for Np(VI) and Pu(VI), but not for U(VI). Surprisingly, in acidic conditions, one of the carboxylic groups gets protonated in EDTA of [UO 2 (edta)] 2- rather than one of the amino groups. This process-based series of calculations can be applied to any redox reaction and allows the prediction of changes to the rate law and rate-limiting step in a more fundamental way for different environments

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Large second harmonic generation in a penta-CdO 2 sheet exfoliated from its bulk phase

Two-dimensional (2D) materials composed solely of pentagonal motifs are of particular interest due to their unique geometries and novel properties. Especially, the broken centrosymmetry and in-plane mirror symmetry in penta-graphene-like materials result in both in-plane and out-of-plane second harmonic generation (SHG). Transition metal cations with a filled d 10 shell (d 10 -TM) can significantly enhance the SHG response as found in many previously studied bulk materials. Here, in this study, based on first-principles calculations combined with independent particle approximation, we show that large SHG can also exist in some 2D d 10 -TM oxides, such as penta-CdO 2 , which can be chemically exfoliated from its bulk phase with its dynamical, thermal, and mechanical stability intact. We further find that penta-CdO 2 possesses extraordinary in-plane and out-of-plane SHG responses with large static SHG susceptibilities of χ sheet 14 (0) = χ sheet 25 (0) = χ sheet 36 (0) = 8.86 pm 2 V -1 due to the phase-matching between fundamental and second-harmonic light. In addition, the low thermal expansion and a large optical band gap of 3.24 eV endow the penta-CdO 2 sheet with a high laser-induced damage threshold. Discussions are also made on the penta-ZnO 2 sheet. This study expands the family of 2D materials with outstanding SHG performance.

36 MATERIALS SCIENCE↗

Tuning the optical and magnetic properties of lanthanide single-ion magnets using nitro-functionalized trispyrazolylborate ligands

We report the synthesis, crystal structures, photophysical and magnetic properties of 11 novel lanthanide complexes with the asymmetrically functionalized trispyrazolylborate ligand 4-nitrotrispyrazolylborate, 4-NO 2 Tp–: [Ln(4-NO 2 Tp) 3 ] (Ln = La–Dy, except Pm). In-depth photophysical characterization of the ligands via luminescence, reflectance and absorption spectroscopic techniques, decay lifetimes, quantum yields supported by time-dependent density functional theory (TD-DFT) and natural bond order (NBO) analysis reveal that n-NO 2 Tp– ligands are dominated by intra-ligand charge transfer (ILCT) transitions and that second-sphere interactions are critical to the stabilization of the T 1 state of n-NO 2 Tp– ligands and hence their ability to sensitize Ln 3+ emission. The luminescence properties of the complexes indicate that 4-NO 2 Tp– is a poor sensitizer of Ln 3+ emission, unlike 3-NO 2 Tp–. Moreover, [Nd(4-NO 2 Tp) 3 ] (crystallized as a hexane solvate) displays single-molecule magnet (SMM) properties, with longer relaxation times and larger barrier than the non-functionalized [NdTp 3 ], attributed to the addition of the NO 2 -group and subsequent rigidification of the molecular structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A comprehensive approach for elucidating the interplay between 4f n +1 and 4f n 5d 1 configurations in Ln 2+ complexes

Lanthanides (Ln) are typically found in the +3 oxidation state. However, in recent decades, their chemistry has been expanded to include the less stable +2 oxidation state across the entire series except promethium (Pm), facilitated by the coordination of ligands such as trimethylsilylcyclopentadienyl, C 5 H 4 SiMe 3 (Cp'). The [LnCp' 3 ] complexes have been the workhorse for the synthesis and theoretical study of the fundamental aspects of divalent lanthanide chemistry, where experimental and computational evidence have suggested the existence of different ground state (GS) configurations, 4f n+1 or 4f n 5d 1 , depending on the specific metal. Standard reduction potentials and 4f n+1 to 4f n 5d 1 promotion energies have been two factors usually considered to rationalize the occurrence of these variable GS configurations, however the driving force behind this phenomenon is still not clear. In this work we present a comprehensive theoretical approach to shed light on this matter using the [LnCp 3 ] - model systems. We begin by calculating 4f n+1 to 4f n 5d 1 promotion energies and successfully correlate them with existing experimental data. Furthermore, we analyze how changes in the GS charge distribution between the Ln ions, LnCp 3 and the reduced [LnCp 3 ] - complexes (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) correlate with experimental trends in redox potentials and the calculated promotion energies. For this purpose, a comprehensive theoretical work that includes relativistic ligand field density functional theory (LFDFT) and relativistic ab initio wavefunction methods was performed. This study will help the rational design of suitable environments to tune the different GS configurations as well as modulating the spectroscopic properties of new Ln 2+ complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unveiling the covalency of versatile Pu(iii)-N bonds in a unique plutonium(iii) complex

A trivalent plutonium–pyrazinyl–tetrazolate complex Na 2 [Pu(Hdtp)(dtp) 2 (H 2 O) 4 ]·9H 2 O (Pu_dtp, H 2 dtp = 2,3-di-1H-tetrazol-5-ylpyrazine) was synthesized through metathesis reaction of plutonium bromide and Na 2 (dtp)·2H 2 O in water. This structure is particularly notable among complexes formed by trivalent f-elements and the dtp 2− ligand in aqueous media. In contrast to other trivalent f-elements, including all Ln 3+ (with the exception of Pm 3+ ) and Cm 3+ , preferentially coordinated with eight water molecules rather than the nitrogen donors of the dtp 2− ligand, Pu 3+ exhibits a distinct affinity for nitrogen coordination. This observation provides strong evidence that the 5f electrons in Pu 3+ are more delocalized than other studied trivalent f-elements. In Pu_dtp, three distinct Pu(III)–N bonds are present: one Pu(III)–N5 from pyrazinyl, one Pu(III)–N4 from the least electronegative nitrogen in the tetrazolate, and three Pu(III)–N1/N2/N3 from the most electronegative nitrogens in the tetrazolate. Experimental Pu(III)–N bond lengths, Wiberg bond indices (WBI), natural localized molecular orbitals (NLMO), quantum theory of atoms in molecules (QTAIM), and energy decomposition analysis (EDA), reveal a covalency trend: Pu(III)–N from the most electronegative nitrogen in tetrazolate > Pu(III)–N from the least electronegative nitrogen in tetrazolate > Pu(III)–N from pyrazinyl. This trend arises from the increased negative charge on the most electronegative nitrogen atoms in the tetrazolate ring, enhancing electrostatic Pu–N1/N2/N3 interactions. These stronger electrostatic interactions lead to shorter bond lengths, thereby enhancing orbital overlap and greater covalency, compared to the less electronegative nitrogen in tetrazolate (Pu–N4) and the neutral pyrazinyl nitrogen (Pu–N5).

Bai, Zhuanling [Colorado School of Mines, Golden, ↗

Coherence imaging spectroscopy at Wendelstein 7-X for impurity flow measurements

In the last decade, Coherence Imaging Spectroscopy (CIS) has shown distinctive results in measuring ion flow velocities in the edge of magnetically confined plasma devices. Its 2D spatially resolved measurement capabilities and its high optical throughput are ideal for investigating the impurity behavior in the complex 3D magnetic island topology edge of Wendelstein 7-X (W7-X). However, a highly precise and stable calibration method is required for a reliable diagnostic operation. A new level of precision and stability has been achieved for the two CIS systems installed at W7-X with the use of a new calibration source, a continuous tunable laser commercially available only since 2015. A specific prototype model was successfully adapted to the challenging requirements of W7-X, granting high accuracy (±0.01 pm) and flexibility (spectral range: 450–650 nm) in the wavelength calibration required for measuring low-Z impurity ion flow velocities. These features opened up new investigation possibilities on temperature stability and wavelength response of the CIS components, allowing to fully characterize and validate the W7-X systems. The CIS diagnostic was operational throughout the last W7-X experimental campaign. Measured velocities on the order of ~20–30 km/s were observed, corroborated by comparisons with measurements with Mach probes.

47 OTHER INSTRUMENTATION↗

A compact electron source for the dielectric laser accelerator

In this work, we design and demonstrate a compact electron source that combines an integrated silicon nanotip photoemitter with a compact silicon-based electrostatic lens. The lens simultaneously accelerates electrons to 30 keV and focuses the resulting beam to a 0.4 μm (RMS) beam diameter with 62 pm-rad normalized emittance at a distance of 20 mm from the cathode. The compact nature of this lens provides a compelling source for dielectric laser accelerator (DLA) beamlines, ultrafast electron diffraction, or ultrafast electron microscopy. Driven by a 220 fs, 1960 nm pulsed laser beam, electron currents up to 28 electrons/pulse at 100 kHz are demonstrated. The electron bunch length is 540 ± 50 fs for photocurrents of <1 electron/pulse, increasing to 700 ± 80 fs for 28 electrons/pulse, as measured by cross correlation with a 220 fs pulsed laser beam. The maximum 5D peak brightness is measured to be 6.8 × 10 13 A/(m 2 rad 2 ) at 28 electrons/pulse. These results represent a significant step toward developing practical benchtop-sized linear accelerators based on DLA technology or compact ultrafast electron microscopy and diffraction applications.

47 OTHER INSTRUMENTATION↗

A Look Inside the Black Box: Using graph-theoretical descriptors to interpret a Continuous-Filter Convolutional Neural Network (CF-CNN) trained on the global and local minimum energy structures of neutral water clusters

A Continuous Filter Convolutional Neural Network (CF-CNN) was trained to predict the potential energy of water cluster networks \ce{(H2O)_{\textit{N}}}, \textit{N}=10--30, corresponding to local minima lying within 5 kcal/mol from the putative minima taken from a newly published database containing over 5 million unique networks. The chemical sampling space of the database was characterized using chemical descriptors derived from graph theory, which led to the identification of important trends in the topology, connectivity, polygon structures associated with the various networks as a function of cluster size. The resulting graphs are available alongside the original database at \url{https://sites.uw.edu/wdbase/}. The CF-CNN trained on a subset of 500,000 networks for (\textit{N}=10, 30) yielded a mean absolute error of 0.002$\pm$0.002 kcal/mol per water molecule, giving the trained CF-CNN the highest accuracy of any neural network-based surrogate model to date. In addition, clusters of sizes not included in the training set exhibited errors of the same magnitude, indicating that the CF-CNN ptotocol is general enough to accurately predict energies of networks for both smaller and larger sizes than those used during training. The graph-theoretical descriptors were developed in order to analyze the properties of the full database and interpret the predictive power of the CF-CNN. Using topology measures, such as the Wiener index and the average shortest path length along with two similarity measures, we showed that all networks from the test set were within the range of the ones from the training set, suggesting that the training set covered the chemical space of interest quite well. Our graph analysis suggests that the mean degree and number of polygons for networks with larger errors tend to lie further from the mean than those with lower errors. The generality of the used CF-CNN was thus demonstrated, while the use of the graph-theoretical descriptors assisted in interpreting the predicted results.

Bilbrey, Jenna A.↗

Experimental equation of state of 11 lanthanide nitrides (NdN to LuN) and pressure induced phase transitions in NdN, SmN, EuN, and GdN

Through an extensive data analysis of powder X-ray diffraction data obtained at pressures up to at least 78 GPa, we report the experimental equations of state for all lanthanide nitrides between NdN and LuN, excluding the radioactive Pm. By fitting the obtained unit cell volumes as a function of pressure with the third order Birch–Murnaghan equation of state, we find that the bulk modulus increases with an increasing lanthanide number from K 0 = 146(12) GPa for NdN to 182(7) GPa in EuN. Hereafter, the bulk modulus reaches a plateau for the rest of the series except for TmN which has a lower bulk modulus. We find that the first derivative of the bulk modulus is around 4 for all compounds except TbN, which displays a significantly different compression behavior. In addition, we find a B1 to B10 pressure-induced phase transition in NdN, SmN, EuN, and GdN at increasingly higher pressures. In fact, we observe that the onset pressure of the phase transition increases linearly with Ln atomic number. From TbN and onwards, we do not observe any sign of a B1 to B10 transition indicating that the transition pressure exceeds the studied pressure range. Therefore, we believe that, for the heavier lanthanides, the linear relationship between the onset pressure and the lanthanide number does not hold and even higher pressures are needed to observe the transition. This coherent study of the series of lanthanide nitrides offers a unique opportunity for benchmark studies of computational methods applied to compounds with 4f electrons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evolution of structure and transport properties of the Ba 8 Cu 16 P 30 clathrate-I framework with the introduction of Ga

Two type-I clathrates were synthesized by introducing Ga into the framework of the Ba 8 Cu 16 P 30 type-I clathrate. The introduction of minute amounts of Ga, 1.9% Ga/M total (where M total = Cu + Ga), resulted in the disturbance of the completely ordered Pbcn superstructure of Ba 8 Cu 16 P 30 . Ba 8 Cu 15.43(2) Ga 0.3 P 30.26(3) crystallizes in a partially ordered orthorhombic Pmna clathrate-I superstructure with five out of 15 framework sites being jointly occupied by metal+phosphorus. Increasing the Ga content resulted in all framework sites being occupied by metal + phosphorus in the archetype cubic Pm n clathrate-I crystal structure of Ba 8 Cu 14.5(3) Ga 1.3 P 30.2(4) with 8.2% Ga/M total . A combination of energy dispersive x-ray spectroscopy, inductively coupled plasma mass spectroscopy, and single crystal x-ray diffraction was used to determine the structures alongside the compositions. The positional disorder was verified by 31 P solid state NMR spectroscopy. Characterization of the transport properties indicated that the Ga-substituted samples exhibit higher Seebeck coefficients and electrical resistivities compared to its pristine counterpart, in line with the expected reduction of the hole concentration due to Ga/Cu substitution. Moderate improvements in the thermoelectric power factor and overall figure-of-merit were observed for samples with 6.9% and 3.8% Ga/M total as compared to those for the pristine Ba 8 Cu 16 P 30 clathrate. Finally, band structure calculations shed light on how Ga substitution affects the electronic structure and thermoelectric properties of studied clathrates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Low Repetition-Rate, High-Resolution Femtosecond Transmission Electron Microscopy

Spatial and energy resolutions of state-of-the-art transmission electron microscopes (TEMs) have surpassed 50 pm and 5 meV. However, with respect to the time domain, even the fastest detectors combined with the brightest sources may only be able to reach the microsecond timescale. Thus, conventional methods are incapable of resolving myriad fundamental ultrafast (i.e., attosecond to picosecond) atomic-scale dynamics. The successful demonstration of femtosecond (fs) laser-based (LB) ultrafast transmission electron microscopy (UEM) nearly 20 years ago provided a means to span this nearly 10-order-of-magnitude temporal gap. While nanometer-picosecond UEM studies of dynamics are now well established, ultrafast Å-scale imaging has gone largely unrealized. Further, while instrument development has rightly been an emphasis, and while new modalities and uses of pulsed-beam TEM continue to emerge, the overall chemical and materials application space has been only modestly explored to date. In this Perspectives article, we argue that these apparent shortfalls can be attributed to a simple lack of data and detail. We speculate that present work and continued growth of the field will ultimately lead to the realization that Å-scale fs dynamics can indeed be imaged with minimally modified UEM instrumentation and with repetition rates (f rep ) below - and perhaps even well below - 1 MHz. We further argue that use of low f rep , whether for LB UEM or for chopped/bunched beams, significantly expands the accessible application space. Furthermore, this calls for systematically establishing modality-specific limits so that especially promising technologies can be pursued, thus ultimately facilitating broader adoption as individual instrument capabilities expand.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Probing C–I bond fission in the UV photochemistry of 2-iodothiophene with core-to-valence transient absorption spectroscopy

The UV photochemistry of small heteroaromatic molecules serves as a testbed for understanding fundamental photo-induced chemical transformations in moderately complex compounds, including isomerization, ring-opening, and molecular dissociation. Here, a combined experimental-theoretical study of 268 nm UV light-induced dynamics in 2-iodothiophene (C 4 H 3 IS) is performed. The dynamics are experimentally monitored with a femtosecond extreme ultraviolet (XUV) probe that measures iodine N-edge 4d core-to-valence transitions. Experiments are complemented by density functional theory calculations of both the pump-pulse induced valence excitations and the XUV probe-induced core-to-valence transitions. Possible intramolecular relaxation dynamics are investigated by ab initio molecular dynamics simulations. Furthermore, gradual absorption changes up to ~0.5 to 1 ps after excitation are observed for both the parent molecular species and emerging iodine fragments, with the latter appearing with a characteristic rise time of 160 ± 30 fs. Comparison of spectral intensities and energies with the calculations identifies an iodine dissociation pathway initiated by a predominant π → π* excitation. In contrast, initial excitation to a nearby n ⟂ → σ* state appears unlikely based on a significantly smaller oscillator strength and the absence of any corresponding XUV absorption signatures. Excitation to the π → π* state is followed by contraction of the C–I bond, enabling a nonadiabatic transition to a dissociative π→σ C-I * state. For the subsequent fragmentation, a relatively narrow bond-length region along the C–I stretch coordinate between 230 and 280 pm is identified, where the transition between the parent molecule and the thienyl radical + iodine atom products becomes prominent in the XUV spectrum due to rapid localization of two singly occupied molecular orbitals on the two fragments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of a central barrier potential on asymmetry-induced transport in a coaxial Malmberg–Penning trap

Experiments are presented measuring the radial particle flux produced when a central barrier potential is applied to the central ring of a coaxial Malmberg-Penning trap at the same time as the voltages producing the main asymmetry potential $\phi_1(r)\cos{(kz)}\cos{(l\theta-\omega t)}$. When a negative DC voltage is applied to the entire central ring, the peak flux produced by the main asymmetry is reduced by a factor $e^{(V_{eff}/1.2)}$ where $V_{eff}$ is the effective applied potential in volts. This barrier potential also increases the frequency of this peak flux. When asymmetric $\pm$ voltages are applied to the two azimuthally-divided halves of the central ring, DC voltages increase the radial flux while AC voltages decrease it. It is shown that these asymmetric barrier voltages produce their own transport and that the resulting modification of the plasma may be a factor in changing the observed flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Extending Badger's rule. I. The relationship between energy and structure in hydrogen bonds

Here, we derive a new expression for the strength of a hydrogen bond (V HB ) in terms of the elongation of the covalent bond of the donor fragment participating in the hydrogen bond (Δr HB ) and the intermolecular coordinates R (separation between the heavy atoms) and θ (deviation of the hydrogen bond from linearity). The expression includes components describing the covalent D–H bond of the hydrogen bond donor via a Morse potential, the Pauli repulsion, and electrostatic interactions between the constituent fragments using a linear expansion of their dipole moment and a quadratic expansion of their polarizability tensor. We fitted the parameters of the model using ab initio electronic structure results for six hydrogen bonded dimers, namely, NH 3 –NH 3 , H 2 O–H 2 O, HF–HF, H 2 O–NH 3 , HF–H 2 O, and HF–NH 3 , and validated its performance for extended parts of their potential energy surfaces, resulting in a mean absolute error ranging from 0.07 to 0.31 kcal/mol. The derived expression describes the energy–structure relationship in terms of a single structural parameter, namely, the elongation of the donor’s covalent bond (Δr HB ), and suggests the novel relationship of 8.0 kcal/mol pm −1 (or 0.8 kcal/mol per 0.001 Å elongation). This structural parameter is easily obtained from theory and can serve as the single descriptor of the strength of individual hydrogen bonds.

Santis, Garrett D. [Univ. of Washington, Seattle, ↗