Scattering Angle Distribution Research Articles

Collision Energy Dependence of the Competing Mechanisms of Reaction of Chlorine Atoms with Propene.

Quasi-classical trajectory simulations examine the reaction of Cl with propene across a range of collision energies, from 7 to 28 kJ mol-1. The majority (70% at 7 kJ mol-1, 86% at 14 kJ mol-1, and 93% at 28 kJ mol-1) of reactive trajectories produce HCl by direct abstraction of a hydrogen atom from the methyl group of propene, but the remainder involve a variety of delayed mechanisms. Among these longer-lived trajectories, transient formation of an energized 1-chloropropyl radical intermediate is predominant, with only a minor contribution from the 2-chloropropyl radical and roaming pathways. The branching ratios between these intermediate states are largely invariant to collision energy, although the overall proportion of indirect trajectories increases at lower collision energies. The greater role for longer-lived trajectories is reflected in the computed product scattering angle distributions, which become more isotropic at lower energies. However, the distributions of population over vibrational and rotational states of the product HCl do not change with collision energy because they are controlled by the dynamics late along the reaction path.

Dynamics of proton transfer from ArH+ to CO

The reaction of ArH+ with CO is a fast proton transfer reaction that can form two different isomers, HCO+ and HOC+. It has been investigated in a crossed beam experiment and with direct dynamics simulations at collision energies ranging from 0.4 to 2.4 eV. Images of the differential cross sections reveal dominant forward scattering, which is evidence for direct dynamics. The measured product internal energies are primarily determined by the reaction enthalpy and only at large scattering angles depend noticeably on the collision energy. The computational results agree well with the measured internal energy and scattering angle distributions and with the previously measured total rate constant. The direct reaction dynamics with dominant forward scattering are well reproduced by the almost step like opacity functions. The HCO+/HOC+ branching is found to be close to 2:1 in the simulations at 0.83 eV and 2.37 eV collision energy. A mode-specific vibrational analysis provides further insight into the isomer specific distribution of the product internal excitation.

Direct Chemical Dynamics Simulations of H3+ + CO Bimolecular Reaction.

The proton transfer reaction H3+ + CO → HCO+/HOC+ + H2 has gained considerable attention in the literature due to its importance in interstellar chemistry. The reaction products-formyl cation (HCO+) and isoformyl cation (HOC+)-are known to initiate multiple chemical reaction networks, resulting in complex molecules found in space. Several experimental and theoretical studies probing the structure and energetics of the [H3CO]+ system, HCO+/HOC+ product branching ratios, reaction mechanisms, etc., have been reported in the literature. In the present work, we investigated the H3+ + CO bimolecular reaction in the gas phase using direct dynamics methodology. The simulation conditions were chosen to mimic recently reported velocity map imaging experiments on the same reaction. The calculations were performed using the density functional PBE0/aug-cc-pVDZ level of electronic structure theory. Internal energy and scattering angle distributions of reaction products found from the simulations are in qualitative agreement with the experiment. However, the product branching ratios at low collision energies were in contrast with the experimental predictions. Interesting dynamical features were observed in the simulations, and detailed atomic level mechanisms are presented.

Mode-Specific Quasiclassical Dynamics of the F- + CH3I SN2 and Proton-Transfer Reactions.

Mode-specific quasiclassical trajectory computations are performed for the F- + CH3I( v k = 0, 1) SN2 and proton-transfer reactions at nine different collision energies in the range of 1.0-35.3 kcal/mol using a full-dimensional high-level ab initio analytical potential energy surface with ground-state and excited CI stretching ( v3), CH3 rocking ( v6), CH3 umbrella ( v2), CH3 deformation ( v5), CH symmetric stretching ( v1), and CH asymmetric stretching ( v4) initial vibrational modes. Millions of trajectories provide statistically definitive mode-specific cross sections, opacity functions, scattering angle distributions, and product internal energy distributions. The excitation functions reveal slight vibrational SN2 inversion inhibition/enhancement at low/high collision energies ( Ecoll), whereas large decaying-with- Ecoll vibrational enhancement effects for the SN2 retention (double inversion) and proton-transfer channels. The most efficient vibrational enhancement is found by exciting the CI stretching (high Ecoll) for SN2 inversion and the CH stretching modes (low Ecoll) for double inversion and proton transfer. Mode-specific effects do not show up in the scattering angle distributions and do blue-shift the hot/cold SN2/proton-transfer product internal energies.

Direct Observation of Atom-Ion Nonequilibrium Sympathetic Cooling.

Sympathetic cooling is the process of energy exchange between a system and a colder bath. We investigate this fundamental process in an atom-ion experiment where the system is composed of a single ion trapped in a radio-frequency Paul trap and prepared in a classical oscillatory motion with total energy of ∼200 K, and the bath is an ultracold cloud of atoms at μK temperature. We directly observe the sympathetic cooling dynamics with single-shot energy measurements during one to several collisions in two distinct regimes. In one, collisions predominantly cool the system with very efficient momentum transfer leading to cooling in only a few collisions. In the other, collisions can both cool and heat the system due to nonequilibrium dynamics in the presence of the ion trap's oscillating electric fields. While the bulk of our observations agree well with a molecular-dynamics simulation of hard-sphere (Langevin) collisions, a measurement of the scattering angle distribution reveals forward-scattering (glancing) collisions which are beyond the Langevin model. This work paves the way for further nonequilibrium and collision dynamics studies using the well-controlled atom-ion system.

The optimal balance between quality and efficiency in proton radiography imaging technique at various proton beam energies: A Monte Carlo study

Proton radiography is a novel imaging modality that allows direct measurement of the proton energy loss in various tissues. Currently, due to the conversion of so-called Hounsfield units from X-ray Computed Tomography (CT) into relative proton stopping powers (RPSP), the uncertainties of RPSP are 3–5% or higher, which need to be minimized down to 1% to make the proton treatment plans more accurate.In this work, we simulated a proton radiography system, with position-sensitive detectors (PSDs) and a residual energy detector (RED). The simulations were built using Geant4, a Monte Carlo simulation toolkit. A phantom, consisting of several materials was placed between the PSDs of various Water Equivalent Thicknesses (WET), corresponding to an ideal detector, a gaseous detector, silicon and plastic scintillator detectors. The energy loss radiograph and the scattering angle distributions of the protons were studied for proton beam energies of 150MeV, 190MeV and 230MeV. To improve the image quality deteriorated by the multiple Coulomb scattering (MCS), protons with small angles were selected. Two ways of calculating a scattering angle were considered using the proton’s direction and position.A scattering angle cut of 8.7mrad was applied giving an optimal balance between quality and efficiency of the radiographic image. For the three proton beam energies, the number of protons used in image reconstruction with the direction method was half the number of protons kept using the position method.

Single-electron capture in 3-keV/uAr8+-He collisions

The electron transfer mechanism was investigated for the single-electron-capture process in 3-keV/u ${\mathrm{Ar}}^{8+}$-He collisions with cold target recoil ion momentum spectroscopy. The different state-selective electron capture processes were identified for one $1s$ electron of He capture into $4s$, $4p$, $4d\text{\ensuremath{-}}4f$, and $5s\text{\ensuremath{-}}5p$ states of ${\mathrm{Ar}}^{8+}$. We observed that $1s$ to $4s$ capture mainly happens at small transverse recoil ion momentum, while $1s$ to $4p$ capture mainly happens at large transverse recoil ion momentum. By comparing the measured projectile scattering angle distributions to the theoretical calculations, it is suggested that $1s$ to $4s$ and $1s$ to $4p$ state-selective capture processes are mainly caused by radial and rotational coupling effects, respectively, and the $4{p}_{\ifmmode\pm\else\textpm\fi{}1}$ quantum states are preferred.

Reflection Characteristics of Oxygen Molecule on Ionomer Surface

The widespread utilization of polymer electrolyte fuel cells for transportation applications such as fuel cell vehicles requires high power density operation. However, as the current density increases, the diffusion polarization, which is attributed to the insufficient mass transport, degrades the cell performance. In particular, the oxygen transport resistance in catalyst layers (CLs) and micro porous layers (MPLs) at the cathode side is one of the major factors of the performance degradation. Therefore, the reduction in the oxygen transport resistance is important for the high power density operation. In the previous research, Kinefuchi et al. have investigated the oxygen diffusion resistance in MPLs and CLs using the direct simulation Monte Carlo (DSMC) method. They reported that the simulation well reproduces the experimental result in MPLs. However, the DSMC results underestimate the oxygen diffusion resistance in CLs. This discrepancy is caused by the drawback to a scattering model of gas molecules on surfaces, which plays a crucial role in DSMC analysis. In these calculations, the same scattering model is used for the scattering of oxygen molecules on surfaces regardless of the presence or absence of ionomer on micro porous carbons. An advanced scattering model that can reproduce the scattering and surface diffusion phenomena on ionomer surface, is required for more accurate analysis of the oxygen transport in CLs. The construction of the model needs the detailed understanding of the gas‒surface interaction. In this study, we have investigated the mechanics of oxygen scattering and surface diffusion on ionomer surface using molecular dynamics simulation. We modeled the solid surface in CLs as an ionomer film covering the carbon layers. The simulation domain was 51.1 × 44.2 × 100 Å3 in size. The ionomer film was composed of water molecules hydronium ions, and perfluorosulfonic acid molecules as typified by Nafion, water molecules, and hydronium ions. Oxygen molecules were directed to the ionomer surface and the trajectory calculations were performed for 20 ps. The initial translational energy and incident angle were the same for all the incident molecules, but the initial position and orientation were given randomly in order to obtain the sufficient statistics. If an oxygen molecule desorbed from the surface and reached the initial height, it was defined to be scattered. Firstly, we have evaluated the energy transfer between oxygen molecules and the ionomer surface by calculating between translational energy before and after the scattering. Oxygen molecules with low incident energy tend to receive energy when they leave the surface after the collisions. Next, we have evaluated the scattering phenomena of oxygen molecules on ionomer surface by examining the energy and angular probability distributions of scattered molecules. The energy distribution depends on the incident energy, and deviates from the distribution given by diffusive scattering model, that the incident molecules are assumed to accommodate completely with the surface. On the other hand, the scattering angle distribution is independent of the incident energy, and well-reproduced by the diffusive scattering model. These results suggest that oxygen molecules do not accommodate completely with the ionomer surface when they are reflected, however they are reflected following the diffusive scattering model because of the corrugation of the ionomer surface.

触媒層アイオノマー表面における酸素分子散乱・表面拡散現象の解析

Molecular dynamics simulations have been carried out to investigate the scattering phenomena and the surface diffusion of oxygen molecules on an ionomer surface, which play a crucial role in oxygen transport in catalyst layers of polymer electrolyte fuel cells. We evaluated the probability density functions of the translational energy and the scattering angle of the scattered molecules for a wide range of the incident condition and water content. We found that the translational energy distributions depend on the incident energy and the scattering angle distributions coincide with the cosine distribution, which shows a reflection in all angles with an equal probability, under any incident condition and water content. These results suggest that incident oxygen molecules do not accommodate completely with the ionomer surface during the collision and that oxygen molecules are reflected diffusely. We have also calculated the residence time of oxygen molecules on the ionomer surface. Increasing the normal component of the incident energy and the water content results in the longer residence time on the ionomer surface.

Comparison of optical methods for surface roughness characterization

We report a study of the correlation between three optical methods for characterizing surface roughness: a laboratory scatterometer measuring the bi-directional reflection distribution function (BRDF instrument), a simple commercial scatterometer (rBRDF instrument), and a confocal optical profiler. For each instrument, the effective range of spatial surface wavelengths is determined, and the common bandwidth used when comparing the evaluated roughness parameters. The compared roughness parameters are: the root-mean-square (RMS) profile deviation (Rq), the RMS profile slope (Rdq), and the variance of the scattering angle distribution (Aq). The twenty-two investigated samples were manufactured with several methods in order to obtain a suitable diversity of roughness patterns.Our study shows a one-to-one correlation of both the Rq and the Rdq roughness values when obtained with the BRDF and the confocal instruments, if the common bandwidth is applied. Likewise, a correlation is observed when determining the Aq value with the BRDF and the rBRDF instruments.Furthermore, we show that it is possible to determine the Rq value from the Aq value, by applying a simple transfer function derived from the instrument comparisons. The presented method is validated for surfaces with predominantly 1D roughness, i.e. consisting of parallel grooves of various periods, and a reflectance similar to stainless steel. The Rq values are predicted with an accuracy of 38% at the 95% confidence interval.

SU‐E‐T‐673: Recent Developments and Comprehensive Validations of a GPU‐Based Proton Monte Carlo Simulation Package, GPMC

Purpose:A GPU‐based Monte Carlo (MC) simulation package gPMC has been previously developed and high computational efficiency was achieved. This abstract reports our recent improvements on this package in terms of accuracy, functionality, and code portability.Methods:In the latest version of gPMC, nuclear interaction cross section database was updated to include data from TOPAS/Geant4. Inelastic interaction model, particularly the proton scattering angle distribution, was updated to improve overall simulation accuracy. Calculation of dose averaged LET (LETd) was implemented. gPMC was ported onto an OpenCL environment to enable portability across different computing devices (GPUs from different vendors and CPUs). We also performed comprehensive tests of the code accuracy. Dose from electro‐magnetic (EM) interaction channel, primary and secondary proton doses and fluences were scored and compared with those computed by TOPAS.Results:In a homogeneous water phantom with 100 and 200 MeV beams, mean dose differences in EM channel computed by gPMC and by TOPAS were 0.28% and 0.65% of the corresponding maximum dose, respectively. With the Geant4 nuclear interaction cross section data, mean difference of primary proton dose was 0.84% for the 200 MeV case and 0.78% for the 100 MeV case. After updating inelastic interaction model, maximum difference of secondary proton fluence and dose were 0.08% and 0.5% for the 200 MeV beam, and 0.04% and 0.2% for the 100 MeV beam. In a test case with a 150MeV proton beam, the mean difference between LETd computed by gPMC and TOPAS was 0.96% within the proton range. With the OpenCL implementation, gPMC is executable on AMD and Nvidia GPUs, as well as on Intel CPU in single or multiple threads. Results on different platforms agreed within statistical uncertainty.Conclusion:Several improvements have been implemented in the latest version of gPMC, which enhanced its accuracy, functionality, and code portability.

Anisotropic Elastic Resonance Scattering Model for the Neutron Transport Equation

The resonance scattering transfer cross section has been reformulated to account for anisotropic scattering in the center of mass of the neutron-nucleus system. The main innovation over previous implementations is the relaxation of the ubiquitous assumption of isotropic scattering in the center of mass and the actual effective use of scattering angle distributions from evaluated nuclear data files in the computation of the angular moments of the resonant scattering kernels. The formulas for the high-order anisotropic moments in the laboratory system are also derived. A multigroup numerical formulation is derived and implemented into a module incorporated within the NJOY nuclear data processing code. An ultrafine-energy-mesh cross-section library was generated using these new theoretical models and then was used for fuel assembly calculations with the PARAGON lattice physics code. The results obtained indicate that this new model makes a significant difference to predictions of reactivity, multigroup fluxes, and isotopic inventory during depletion.

Quasiclassical trajectory study of the rotational mode specificity in the O((3)P) + CHD3(v1 = 0, 1, JK) → OH + CD3 reactions.

Quasiclassical trajectory computations on an ab initio potential energy surface reveal that rotational excitation can significantly enhance the reactivity of the ground-state and CH stretching-excited O((3)P) + CHD3(v1 = 0,1, JK) → OH + CD3 reactions. The state-specific rotational effects investigated up to J = 8 show that the K = 0 (tumbling rotation) enhancement factors can be as large as 1.5-3.5 depending on J and the collision energy, whereas the K = J (spinning rotation about the CH axis) excitations do not have any significant effect on the reactivity. The shapes of the opacity functions and scattering angle distributions depend on the initial vibrational state, but show virtually no JK dependence. The origin of the K = 0 rotational enhancements is that the tumbling rotation enlarges the range of the reactive initial attack angles, thereby increasing the reactivity.

Analysis of the multigroup model for muon tomography based threat detection

We compare different algorithms for detecting a 5 cm tungsten cube using cosmic ray muon technology. In each case, a simple tomographic technique was used for position reconstruction, but the scattering angles were used differently to obtain a density signal. Receiver operating characteristic curves were used to compare images made using average angle squared, median angle squared, average of the squared angle, and a multi-energy group fit of the angular distributions for scenes with and without a 5 cm tungsten cube. The receiver operating characteristic curves show that the multi-energy group treatment of the scattering angle distributions is the superior method for image reconstruction.

Direct Dynamics Simulations of the Product Channels and Atomistic Mechanisms for the OH–+ CH3I Reaction. Comparison with Experiment

Electronic structure and direct dynamics calculations were used to study the potential energy surface and atomic-level dynamics for the OH(-) + CH3I reactions. The results are compared with crossed molecular beam, ion imaging experiments. The DFT/B97-1/ECP/d level of theory gives reaction energetics in good agreement with experiment and higher level calculations, and it was used for the direct dynamics simulations that were performed for reactant collision energies of 2.0, 1.0, 0.5, and 0.05 eV. Five different pathways are observed in the simulations, forming CH3OH + I(-), CH2I(-) + H2O, CH2 + I(-) + H2O, IOH(-) + CH3, and [CH3--I--OH](-). The SN2 first pathway and the proton-transfer second pathway dominate the reaction dynamics. Though the reaction energetics favor the SN2 pathway, the proton-transfer pathway is more important except for the lowest collision energy. The relative ion yield determined from the simulations is in overall good agreement with experiment. Both the SN2 and proton-transfer pathways occur via direct rebound, direct stripping, and indirect mechanisms. Except for the highest collision energy, 70-90% of the indirect reaction for the SN2 pathway occurs via formation of the hydrogen-bonded OH(-)---HCH2I prereaction complex. For the proton-transfer pathway the indirect reaction is more complex with the roundabout mechanism and formation of the OH(-)---HCH2I and CH2I(-)---HOH complexes contributing to the reaction. The majority of the SN2 reaction is direct at 2.0, 1.0, and 0.5 eV, dominated by stripping. At 0.05 eV the two direct mechanisms and the indirect mechanisms have nearly equal contributions. The majority of the proton-transfer pathway is direct stripping at 2.0, 1.0, and 0.5 eV, but the majority of the reaction is indirect at 0.05 eV. The product relative translational energy distributions are in good agreement with experiment for both the SN2 and proton-transfer pathways. For both, direct reaction preferentially transfers the product energy to relative translation, whereas transfer to product vibration is more important for the indirect reactions. For the proton-transfer reactions the velocity scattering angle distribution is peaked in the forward direction and in quite good agreement with experiment. However, for the SN2 reaction, the experimental scattering is isotropic in nature whereas forward scattering dominates the simulation distributions. The implication is that the simulations give too much stripping, which leads to forward scattering. The dynamics for the OH(-) + CH3I SN2 pathway are similar to those found previously for the F(-) + CH3I SN2 reaction.

Simulation studies of the Cl− + CH3I SN2 nucleophilic substitution reaction: Comparison with ion imaging experiments

In the previous work of Mikosch et al. [Science 319, 183 (2008)], ion imaging experiments were used to study the Cl(-) + CH3I → ClCH3 + I(-) reaction at collision energies E(rel) of 0.39, 0.76, 1.07, and 1.9 eV. For the work reported here MP2(fc)/ECP/d direct dynamics simulations were performed to obtain an atomistic understanding of the experiments. There is good agreement with the experimental product energy and scattering angle distributions for the highest three E(rel), and at these energies 80% or more of the reaction is direct, primarily occurring by a rebound mechanism with backward scattering. At 0.76 eV there is a small indirect component, with isotropic scattering, involving formation of the pre- and post-reaction complexes. All of the reaction is direct at 1.07 eV. Increasing E(rel) to 1.9 eV opens up a new indirect pathway, the roundabout mechanism. The product energy is primarily partitioned into relative translation for the direct reactions, but to CH3Cl internal energy for the indirect reactions. The roundabout mechanism transfers substantial energy to CH3Cl rotation. At E(rel) = 0.39 eV both the experimental product energy partitioning and scattering are statistical, suggesting the reaction is primarily indirect with formation of the pre- and post-reaction complexes. However, neither MP2 nor BhandH/ECP/d simulations agree with experiment and, instead, give reaction dominated by direct processes as found for the higher collision energies. Decreasing the simulation E(rel) to 0.20 eV results in product energy partitioning and scattering which agree with the 0.39 eV experiment. The sharp transition from a dominant direct to indirect reaction as E(rel) is lowered from 0.39 to 0.20 eV is striking. The lack of agreement between the simulations and experiment for E(rel) = 0.39 eV may result from a distribution of collision energies in the experiment and/or a shortcoming in both the MP2 and BhandH simulations. Increasing the reactant rotational temperature from 75 to 300 K for the 1.9 eV collisions, results in more rotational energy in the CH3Cl product and a larger fraction of roundabout trajectories. Even though a ClCH3-I(-) post-reaction complex is not formed and the mechanistic dynamics are not statistical, the roundabout mechanism gives product energy partitioning in approximate agreement with phase space theory.

Electron transfer and ionization in collisions of He-like ions with Na(3s) and Na(3p)

Single electron transfer and ionization in collisions of He-like ions (N5+, O6+, Ne8+) and Na has been investigated both experimentally and theoretically at energies around the matching velocity of the valence electron (2 to 10 keV/amu). State selective cross sections and scattering angle distributions were obtained using recoil-ion momentum spectroscopy in combination with a magneto-optically cooled Na atom target. A strong dependence of the relative cross sections on the collision energy is observed. The results are compared with Classical-Trajectory Monte Carlo (CTMC) calculations and show an overall very good agreement.

On the determination of absolute vibrational excitation probabilities in molecule-surface scattering: Case study of NO on Au(111)

We describe a method to obtain absolute vibrational excitation probabilities of molecules scattering from a surface based on measurements of the rotational state, scattering angle, and temporal distributions of the scattered molecules and apply this method to the vibrational excitation of NO scattering from Au(111). We report the absolute excitation probabilities to the v = 1 and v = 2 vibrational states, rotational excitation distributions, and final scattering angle distributions for a wide range of incidence energies and surface temperatures. In addition to demonstrating the methodology for obtaining absolute scattering probabilities, these results provide an excellent benchmark for theoretical calculations of molecule-surface scattering.

Classical dynamics study of atomic oxygen over graphite (0 0 0 1) with new interpolated and analytical potential energy surfaces

Two adiabatic potential energy surfaces (PESs) based on density functional theory data are constructed for the interaction of atomic oxygen with graphite (0001) surface: an analytical FPLEPS PES and an interpolated Modified Shepard one. A classical trajectory study has been performed for the two PESs for different initial conditions: collision energy (0.1⩽Ecol⩽1.3eV), surface temperature (100⩽Tsurf⩽900K) and two incident angles (θv=0°, 45°), and also for thermal conditions (T=TOxygen=Tsurf=300–1500K). In addition, hyperthermal experimental conditions corresponding to a hot atom distribution (〈Ecol〉=5.2eV) were also considered. All the properties studied for the two PESs were in close agreement in almost the major part of the explored conditions, although some differences were obtained for low Ecol due to the presence of a physisorption minimum in the MS PES that was not included into the FPLEPS one. The adsorption process occurs mainly over bridge sites. Adsorption probabilities are lower than reflection ones in practically all the conditions explored and increase quickly with Ecol until a maximum and then decrease smoothly. Polar scattering angle distributions present a peak centred around the specular angle position and broaden when increasing Ecol or Tsurf. A good agreement respect this peak position was found in comparison with the experimental hyperthermal data. The transfer of energy is mainly from the atom to the surface and increases when initial collision energy does.

Grazing scattering of 1–2 MeV HeH + ions from KCl(0 0 1): Effect of surface track potential

Three dimensional (3D) distributions (energy E, scattering angle θ and azimuth angle φ) of the fragment protons dissociated from HeH + during grazing angle scattering from a KCl(0 0 1) are measured using a magnetic spectrometer in order to study the effect of the surface track potential. The distributions of the fragment protons scattered from a SnTe(0 0 1) are also measured as a reference. Although the observed distributions for KCl(0 0 1) and SnTe(0 0 1) are basically the same, there is small differences, especially in the scattering angle distribution. While the fragment protons are scattered at the specular angle from SnTe(0 0 1), the protons are scattered at slightly larger angles from KCl(0 0 1). The observed angular shift is more pronounced for the trailing protons than the leading protons. It is also found that the angular shift increases with decreasing ion energy. The observed angular shift can be qualitatively explained by the surface track potential induced by the partner He ions using a simple model of the surface track potential.