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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Experimental Study of the Fundamental Properties of Warm Dense Mixtures

The aim of the proposed research was to provide a multi-scale study of the properties of warm dense hydrocarbons, by studying the thermodynamic properties through the equation of state and the microscopic properties by x-ray scattering. Understanding the fundamental properties of warm dense mixtures is an intellectual challenge due to the complexity of the system. Unlike liquids or gases, where constituent particle interactions occur through collisions or bonding between valence electrons, in these strongly coupled systems the atoms will be partially ionized and compressed so tightly together that interactions between the inner core electrons can play a role in the systems chemistry. Advances in computational capabilities and development of new theoretical models have been used to predict the properties of mixtures but there is currently no experimental data of the fundamental interaction between the particles in mixtures to test these predictions against. The proposed research was to experimentally investigate the interaction of the different species in hydrocarbons by measuring the compressibility of substances with different carbon and hydrogen ratios and the complexity of the microscopic interactions through elastic and inelastic x-ray scattering. To study the bulk properties of warm dense hydrocarbons we established the Warm Dense Matter Research Laboratory (WDMRL) in the Institute for Shock Physics at Washington State University. The goal was for experiments in the WDMRL to determine shock loading conditions of interest in the hydrocarbon mixtures. We planned on using Hugoniot EOS measurements and a range of carbon and hydrogen concentrations to determine conditions when the EOS of the mixture varied significantly from that of the classical mixing model. Even though shock transit measurements through aluminum foils suggested pressures upto 400GPa, the experiments in the WDMRL were unsuccessful in getting usable shockwave compression data above 100GPa in polystyrene which was below the pressure of interest for hydrocarbon mixtures (>200GPa). To complete the project, we tested a technique using x-ray phase contrast imaging to map the location of tracer layers in a test sample of polycarbonate to record the material motion in dynamically compressed samples. A technique that will be useful for future warm dense matter experiments. These experiments used <200nm gold layers in polycarbonate samples to measure the material velocity and shock speed using x-ray phase contrast imaging. These results were compared to continuum surface measurements performed at ISP and show that the tracer layer technique can measure hydrodynamic properties accurately in dynamically compressed materials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Using electron energy-loss spectroscopy to measure nanoscale electronic and vibrational dynamics in a TEM

Electron energy-loss spectroscopy (EELS) can measure similar information to x-ray, UV–Vis, and IR spectroscopies but with atomic resolution and increased scattering cross-sections. Recent advances in electron monochromators have expanded EELS capabilities from chemical identification to the realms of synchrotron-level core-loss measurements and to low-loss, 10–100 meV excitations, such as phonons, excitons, and valence structures. EELS measurements are easily correlated with electron diffraction and atomic-scale real-space imaging in a transmission electron microscope (TEM) to provide detailed local pictures of quasiparticle and bonding states. This perspective provides an overview of existing high-resolution EELS (HR-EELS) capabilities while also motivating the powerful next step in the field—ultrafast EELS in a TEM. Ultrafast EELS aims to combine atomic-level, element-specific, and correlated temporal measurements to better understand spatially specific excited-state phenomena. Ultrafast EELS measurements also add to the abilities of steady-state HR-EELS by being able to image the electromagnetic field and use electrons to excite photon-forbidden and momentum-specific transitions. We discuss the technical challenges ultrafast HR-EELS currently faces, as well as how integration with in situ and cryo measurements could expand the technique to new systems of interest, especially molecular and biological samples.

Chemistry↗
DOE OSTI2022

Neptunium (V) Solubility in the Presence and Absence of WIPP Relevant Ligands

CRA (Compliance Recertification Application)-2024 will update the oxidation state specific model used to calculate actinide solubility in the WIPP (Waste Isolation Pilot Plant). The pentavalent Np(V) ion is the most stable ion in solution within the An(V) series. This valence stability of Np(V) in aqueous solution makes Np a useful representative element for studying the aqueous complex chemistry of all An(V), but in the predicted WIPP scenario, this is the only TRU component that increases in the inventory with time as it is the main daughter product of 241 Am decay (alpha, n) so its relative importance increases throughout the 10,000-year performance period of the WIPP, it is only used to represent itself. This work is focused on confirming organic, borate and carbonate effects on solubility of Np(V) in WIPP simulated brines and 5 M NaCl and reassessing the predicted model speciation to strengthen the overall WIPP An(V) model.

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

Description for N = 126 Isotones 210 Po and 212 Rn with Particle-Hole Excited Nucleon-Pair Approximation and Realistic Effective Interaction

In this paper, we study yrast states of two N=126 isotones 210 Po and 212 Rn using the nucleon-pair approximation with particle–hole excitations and using a low-momentum interaction V low–k renormalized from the free CD-Bonn NN potential. An overall good agreement with experimental level structures, B(E2)s, and B(E3)s, is achieved. We also calculate the probabilities of neutron particle–hole excitations in these yrast states, with a focus on negative-parity states, which reflect the roles played by the neutron negative-parity configurations of one-particle-one-hole excitations across the N=126 shell gap and the negative-parity configurations of valence proton particles involving the 0i 13/2 orbit. The N=126 shell gap is discussed in terms of energies of neutron one-particle-one-hole excitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Dissociative recombination of the ground state of N2(+)

Large-scale calculations of the dissociative recombination cross sections and rates for the v = 0 level of the N2(+) ground state are reported, and the important role played by vibrationally excited Rydberg states lying both below and above the v = 0 level of the ion is demonstrated. The large-scale electronic wave function calculations were done using triple zeta plus polarization nuclear-centered-valence Gaussian basis sets. The electronic widths were obtained using smaller wave functions, and the cross sections were calculated on the basis of the multichannel quantum defect theory. The DR rate is calculated at 1.6 x 10 to the -7th x (Te/300) to the -0.37 cu cm/sec for Te in the range of 100 to 1000 K, and is found to be in excellent agreement with prior microwave afterglow experiments but in disagreement with recent merged beam results. It is inferred that the dominant mechanism for DR imparts sufficient energy to the product atoms to allow for escape from the Martian atmosphere.

Guberman, Steven L.↗
DOE OSTI2023

The Challenging World of Simple Inorganic Rings: Revisiting Roesky's Ketone and Roesky's Sulfoxide

Abstract The surprising differences between the experimental solid‐state and calculated gas‐phase structures of 5‐oxo‐1,3,2,4‐dithiadiazole (Roesky's ketone,1) and 1‐oxo‐1,2,4,3,5‐trithiadiazole (Roesky's sulfoxide,2), identified and studied in a series of papers published between 2004 and 2010 but then never satisfactorily explained, have been revisited, making use of the more advanced computational possibilities currently available. The previous calculations’ considerable overestimations of the C−S and S−S bond lengths in1and2, respectively, have been partly explained based on the results of periodic calculations and the application of Valence Bond (VB) Theory. In the case of1, the crystal environment appears to stabilize a structure with a highly polarized C=O bond, which features a C−S bond with considerable double‐bond character – an effect which does not exist for the isolated molecule – explaining the much shorter bond in the solid state. For2, a similar conclusion can be drawn for the S−S distance. For both compounds, though, packing effects are not the sole source of the differences: the inability of Density Functional Theory (DFT) to properly deal with the electronic structures of these apparently simple main‐group systems remains a contributing factor.

Chemistry↗
DOE OSTI2024

Sliceable, Moldable, and Highly Conductive Electrolytes for All-Solid-State Batteries

All-solid-state batteries (ASSBs) require solid electrolytes with high ionic conductivity, stability, and deformability for optimal energy and power density. Here, we developed lithium-deficient lithium yttrium bromide (LYB) solid electrolytes, Li 3–x YBr 6–x (0 ≤ x ≤ 0.50), using a comelting method with controlled lithium deficiency. These electrolytes exhibit favorable mechanical properties such as high moldability and sliceability. The Li 2.65 YBr 5.65 composition has an ionic conductivity of 4.49 mS cm –1 at 25 °C and an activation energy of 0.28 eV. Compared to Li 3 YBr 6 , Li 2.65 YBr 5.65 demonstrates improved rate performance and cycling stability in ASSBs. High-resolution X-ray diffraction confirms the formation of the LYB phase with a C2/m space group. Structural analysis reveals increased cation disorder and larger polyhedral volumes for x > 0 in Li 3–x YBr 6–x , contributing to reduced Li + migration energy barriers. Bond valence site energy calculations and molecular dynamics simulations reveal enhanced 3D lithium-ion transport. NMR spectroscopy further highlights increased Li + dynamics and impurity elimination.

Poudel, Tej P. [Florida State Univ., Tallahassee, ↗
NASA NTRS2001

Band Anticrossing in Highly Mismatched Compound Semiconductor Alloys

Compound semiconductor alloys in which metallic anions are partially replaced with more electronegative isoelectronic atoms have recently attracted significant attention. Group IIIN(sub x)V(sub 1-x) alloys with a small amount of the electronegative N substituting more metallic column V elements has been the most extensively studied class of such Highly Mismatched Alloys (HMAs). We have shown that many of the unusual properties of the IIIN(sub x)V(sub 1-x) alloys can be well explained by the Band Anticrossing (BAC) model that describes the electronic structure in terms of an interaction between highly localized levels of substitutional N and the extended states of the host semiconductor matrix. Most recently the BAC model has been also used to explain similar modifications of the electronic band structure observed in Te-rich ZnS(sub x)Te(sub 1-x) and ZnSe(sub y)Te(sub 1-y) alloys. To date studies of HMAs have been limited to materials with relatively small concentrations of highly electronegative atoms. Here we report investigations of the electronic structure of ZnSe(sub y)Te(sub 1-y) alloys in the entire composition range, y between 0 and 1. The samples used in this study are bulk ZnSe(sub y)Te(sub 1-y) crystals grown by either a modified Bridgman method or by physical vapor transport. Photomodulated reflection (PR) spectroscopy was used to measure the composition dependence of optical transitions from the valence band edge and from the spin-orbit split off band to the conduction band. The pressure dependence of the band gap was measured using optical absorption in a diamond anvil cell. We find that the energy of the spin-orbit split off valence band edge does not depend on composition and is located at about 3 eV below the conduction band edge of ZnSe. On the Te-rich side the pressure and the composition dependence of the optical transitions are well explained by the BAC model which describes the downward shift of the conduction band edge in terms of the interaction between localized Se states and the conduction band. On the other hand we show that the large band gap reduction observed on the Se-rich side of the alloy system is a result of an interaction between the localized Te level and the valence bands. This interaction leads to the formation of a Te-like valence band edge that strongly interacts with the light hole valence band. Calculations based on a modified k(sup dot)p model account for the reduction of the band gap and the large increase of the spin-orbit splitting observed in Se-rich ZnSe(sub y)Te(sub 1-y) alloys. We will also discuss the importance of these new results for understanding of the electronic structure and band offsets in other highly mismatched alloy systems.

Yu, Kin Man↗
DOE OSTI2025

Universal Effective Charges in the 𝑠⁢𝑑 and 𝑓⁡𝑝 Shells

The 247-keV state in 54 Sc, populated in the 𝛽 decay of 54 Ca, is reported here as a nanosecond isomer with a half-life of 26.0(22) ns. The state is interpreted as the 1 + member of the 𝜋⁢𝑓 7/2 ⊗ 𝜈⁢𝑓 5/2 spin-coupled multiplet, which decays to the 3 + ,𝜋⁢𝑓 7/2 ⊗ 𝜈⁢𝑝 1/2 ground state. The new half-life corresponds to a pure 𝐸⁢2 transition with a strength of 1.93(16) W.u., providing the most precise, unambiguous 𝐵⁡(𝐸⁢2) value in the neutron-rich 𝑓⁡𝑝 region to date for a nucleus with valence protons above 𝑍 = 20. Notably, it is roughly 4 times larger than the 𝐵⁡(𝐸⁢2;1/2 − → 5/2 − ) value in 55 Ca. The results, as compared to semiempirical and ab initio shell-model calculations, indicate (1) a weak 𝑁 = 34 subshell gap relative to 𝑁 = 32, (2) a large 𝐸⁢2 enhancement in Sc as compared to Ca due to 1⁢𝑝 − 1⁢ℎ proton excitations across 𝑍 = 28, and (3) empirical effective proton and neutron charges 𝑒 𝜋 = 1.30⁢(8)⁢𝑒 and 𝑒 𝜈 = 0.452⁢(7)⁢𝑒, respectively, that are in contrast to reports of 𝑒 𝜋 ≈1.1–1.15⁢𝑒 and 𝑒 𝜈 ≈ 0.6–0.8⁢𝑒 for 𝑓⁡𝑝-shell nuclei near 𝑁 = 𝑍. Here, we demonstrate that these reports are erroneous and that, in fact, a universal set of effective charges can be used across the 𝑠⁢𝑑 and 𝑓⁡𝑝 shells.

Beta decay↗
DOE OSTI2024

Uncovering the spin ordering in magic-angle graphene via edge state equilibration

Abstract The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and–by studying the backscattering between counter-propagating edge states–the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Valley-spin polarization at zero magnetic field induced by strong hole-hole interactions in monolayer WSe 2

Monolayer transition metal dichalcogenides have emerged as prominent candidates to explore the complex interplay between spin and valley degrees of freedom. Their strong spin-orbit interaction and broken inversion symmetry lead to the spin-valley locking effect, in which carriers occupying theKandK′ valleys of the reciprocal space must have opposite spins. This effect is particularly strong for holes due to a larger spin-orbit gap in the valence band. By reducing the dimensionality of a monolayer of WSe 2 to 1D via electrostatic confinement, we demonstrate that spin-valley locking and strong hole-hole interactions lead to a ferromagnetic state where hole transport is spin-valley polarized, even without an applied magnetic field. A massive Dirac fermion model in the Hartree-Fock approximation reveals that many-body hole-exchange interactions lead to this polarized ground-state. This observation opens the possibility of implementing a robust and stable valley-polarized system, essential in valleytronic applications.

Science & Technology - Other Topics↗
NASA NTRS1978

Photon degradation effects in terrestrial solar cells

Reduction in cell output was observed in N(+)/P cells upon exposure to illumination or upon the application of a sufficiently high forward bias. Conversely, an enhancement in output was observed when P(+)/N cells were illuminated. Investigations performed on N(+)/P cells indicated that a recombination center located at E sub c - 0.37 eV in the forbidden band was responsible for the loss in output. The center was electrically inactive in its ground state but was activated either by raising the minority carrier quasi-Fermi level sufficiently close to the latent center energy level in the band gap, or by direct excitation of electrons from the valence band to the latent center level. The center was identified as a complex of a lattice defect and a silver atom or cluster of atoms.

Weizer, V. G.↗
NASA NTRS1992

Concerted hydrogen atom exchange between three HF molecules

We have investigated the termolecular reaction involving concerted hydrogen exchange between three HF molecules, with particular emphasis on the effects of correlation at the various stationary points along the reaction. Using an extended basis, we have located the geometries of the stable hydrogen-bonded trimer, which is of C(sub 3h) symmetry, and the transition state for hydrogen exchange, which is of D(sub 3h) symmetry. The energies of the exchange reation were then evaluated at the correlated level, using a large atomic natural orbital basis and correlating all valence electrons. Several correlation treatments were used, namely, configration interaction with single and double excitations, coupled-pair functional, and coupled-cluster methods. We are thus able to measure the effect of accounting for size-extensivity. Zero-point corrections to the correlated level energetics were determined using analytic second derivative techniques at the SCF level. Our best calculations, which include the effects of connected triple excitations in the coupled-cluster procedure, indicate that the trimer is bound by 9 +/- 1 kcal/mol relative to three separate monomers, in excellent agreement with previous estimates. The barrier to concerted hydrogen exchange is 15 kcal/mol above the trimer, or only 4.7 kcal/mol above three separated monomers. Thus the barrier to hydrogen exchange between HF molecules via this termolecular process is very low.

Komornicki, Andrew↗
NASA NTRS2001

Band Anticrossing in Highly Mismatched Compound Semiconductor Alloys

Compound semiconductor alloys in which metallic anions are partially replaced with more electronegative isoelectronic atoms have recently attracted significant attention. Group IIIN(x)V(1-x), alloys with a small amount of the electronegative N substituting more metallic column V elements has been the most extensively studied class of such Highly Mismatched Alloys (HMAs). We have shown that many of the unusual properties of the IIIN(x),V(1-x) alloys can be well explained by the Band Anticrossing (BAC) model that describes the electronic structure in terms of an interaction between highly localized levels of substitutional N and the extended states of the host semiconductor matrix. Most recently the BAC model has been also used to explain similar modifications of the electronic band structure observed in Te-rich ZnS(x)Te(l-x) and ZnSe(Y)Te(1-y) alloys. To date studies of HMAs have been limited to materials with relatively small concentrations of highly electronegative atoms. Here we report investigations of the electronic structure of ZnSe(y)Te(1-y) alloys in the entire composition range, 0 less than or equal to y less than or equal to 1. The samples used in this study are bulk ZnSe(y)Te(1-y) crystals grown by either a modified Bridgman method or by physical vapor transport. Photomodulated reflection (PR) spectroscopy was used to measure the composition dependence of optical transitions from the valence band edge and from the spin-orbit split off band to the conduction band. The pressure dependence of the band gap was measured using optical absorption in a diamond anvil cell. We find that the energy of the spin-orbit split off valence band edge does not depend on composition and is located at about 3 eV below the conduction band edge of ZnSe. On the Te-rich side the pressure and the composition dependence of the optical transitions are well explained by the BAC model which describes the downward shift of the conduction band edge in terms of the interaction between localized Se states and the conduction band. On the other hand we show that the large band gap reduction observed on the Se-rich side of the alloy system is a result of an interaction between the localized Te level and the valence bands. This interaction leads to the formation of a Te-like valence band edge that strongly interacts with the light hole valence band. Calculations based on a modified k p model account for the reduction of the band gap and the large increase of the spin-orbit splitting observed in Se-rich ZnSe(y)Te(l-y) alloys. We will also discuss the importance of these new results for understanding of the electronic structure and band offsets in other highly mismatched alloy systems.

Yu, Kin Man↗
DOE OSTI2025

Controlled Synthesis of SnO 2 Nanocrystals with Tunable Band Gaps

Tin(IV) oxide nanocrystals (SnO 2 NCs) have significant potential in various applications, with their performance closely related to their band gap. The band gap is influenced by the size and shape of the NCs, which can be precisely controlled by adjusting reaction conditions. In this study, we present deliberately designed synthesis protocols to produce high-quality SnO 2 NCs with tunable band gaps using different methods. Key factors affecting the synthesis include control of the oxidizing agent, reaction temperature, solvent selection, and reaction time optimization. The resulting NCs were characterized by using TEM, XRD, XPS, and optical spectroscopy. Notably, SnO 2 NCs synthesized by controlling the oxidizing agent (air injection) in a hot organic solution were smaller in size and exhibited abundant oxygen vacancies. In contrast, extending the reaction time or using ethanol as a solvent in hydrothermal systems facilitated larger spherical or rod-like SnO 2 NCs with fewer oxygen vacancies. Further analysis of the band gap and valence band maximum energy revealed that the abundant vacancies in SnO 2 NCs synthesized with the air-controlled hot organic solution method resulted in a narrower band gap and an upshifted valence band. These synthetic strategies illustrate the potential for deliberately designing SnO 2 NCs with optimized electronic structures for various applications.

band gap↗
DOE OSTI2026

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

High-precision Penning trap mass measurements of neutron-rich chlorine isotopes at the 𝑁 = 28 shell closure

Although it is known that the N = 28 spherical shell closure erodes, the strength of the closure with decreasing proton number Z < 20 is an open question in nuclear structure. Here, in this region of interest, high-precision mass measurements of neutron-rich 43-45 Cl isotopes were performed at the Low Energy Beam and Ion Trap (LEBIT) when coupled to the National Superconducting Cyclotron Lab. The resulting mass excesses (MEs) are ME(⁴³Cl) = -24114.4(1.7) keV, ME(⁴⁴Cl) = -20450.8(10.6) keV, and ME(⁴⁵Cl) = -18240.1(3.7) keV, and improve the uncertainty of these masses by up to a factor of ∼40 compared to the previous values reported in the 2020 Atomic Mass Evaluation. Comparison to ab initio calculations using the Valence-Space In-Medium Similarity Renormalization Group (VS-IMSRG) shows good agreement up to and including the closure.

Erington, H. [Michigan State Univ., East Lansing, ↗
DOE OSTI2023

Probing the Potential Energy Profile of the I + (H 2 O) 3 → HI + (H 2 O) 2 OH Forward and Reverse Reactions: High Level CCSD(T) Studies with Spin-Orbit Coupling Included

Three different pathways for the atomic iodine plus water trimer reaction I + (H 2 O) 3 → HI + (H 2 O) 2 OH were preliminarily examined by the DFT-MPW1K method. Related to previous predictions for the F/Cl/Br + (H 2 O) 3 reactions, three pathways for the I + (H 2 O) 3 reaction are linked in terms of geometry and energetics. To legitimize the results, the “gold standard” CCSD(T) method was employed to investigate the lowest-lying pathway with the correlation-consistent polarized valence basis set up to cc-pVQZ(-PP). According to the CCSD(T)/cc-pVQZ(-PP)//CCSD(T)/cc-pVTZ(-PP) results, the I + (H 2 O) 3 → HI + (H 2 O) 2 OH reaction is predicted to be endothermic by 47.0 kcal mol -1 . The submerged transition state is predicted to lie 43.7 kcal mol -1 above the separated reactants. The I···(H 2 O) 3 entrance complex lies below the separated reactants by 4.1 kcal mol -1 , and spin-orbit coupling has a significant impact on this dissociation energy. The HI···(H 2 O) 2 OH exit complex is bound by 4.3 kcal mol -1 in relation to the separated products. Compared with simpler I + (H 2 O) 2 and I + H 2 O reactions, the I + (H 2 O) 3 reaction is energetically between them in general. It is speculated that the reaction between the iodine atom and the larger water clusters may be energetically analogous to the I + (H 2 O) 3 reaction. The iodine reaction I + (H 2 O) 3 is connected with the analogous valence isoelectronic bromine/chlorine reactions Br/Cl + (H 2 O) 3 but much different from the F + (H 2 O) 3 reaction. Significant difference with other halogen systems, especially for barrier heights, are seen for the iodine systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗