Low-energy Collisions Research Articles

The effect of multiple collisions on the electronic stopping losses

The paper considers the question of the dependence of electronic stopping dE/dx on the measurement technique. Usually, when using the transmission geometry, the value of electron stopping is defined as the ratio of the energy loss of the particle after passing through the film to the thickness of the film d. It is shown that this procedure provides overestimated results at low collision energies. Using the computer simulation, the dependence of the ratio of the particle mean trajectory length L in the film to its thickness d on the particle energy E has been obtained. Experimental values of inelastic loss dE/dx for transmission geometry were corrected for the L/d ratio and compared with the results of the “backscattering geometry” experiments. A good agreement of the corrected “transmission” data with the “backscattering” data has been demonstrated for the H-Cu, H-Ag and H-Au systems. The incident particle energies E0 ranged from 0.5 to 20 keV.

A new global potential energy surface for the BH2 molecule and dynamics studies of the B(2p2P) + H2 reaction

A new global potential energy surface (PES) for the ground state of the BH2 system was constructed using permutation invariant polynomial neural network. In ab initio calculation, the AVQZ basis set and multi-reference configuration interaction method was used. The topographic features of the new PES were discussed in detail. To further clarify the accuracy of PES, the dynamics studies of the B(2p2P) + H2 reaction were carried out using time-dependent wave packet method. The dynamics properties such as reaction probabilities, integral cross sections, differential cross sections (DCSs) and rate constants were reported. The DCSs indicated that the “complex-forming” reaction mechanism plays a dominant role at low collision energies and the forward abstraction mechanism dominates the reaction at high collision energies.

Inelastic scattering of Li＋ with CO: New ab initio potential energy surface and quantum dynamics

The interaction potential between Li＋ and CO has been investigated using quantum dynamical calculations. The ab initio ground electronic potential energy surface has been computed using the aug-cc-pVQZ basis set at MRCI level of accuracy. Quantum dynamics results within the VCC-RIOSA framework have been presented at collision energy Ec.m. = 3.64 eV. The computed differential cross sections (DCS) for the inelastic vibrational excitations have been found to be in qualitative agreement with those obtained in the experiments of Böttner et al. (1976). Other attributes like rotationally-summed state-to-state DCS, and integral cross sections, are also calculated. The rotational excitations are studied using rigid-rotor coupled-states methodology at Ec.m. = 4.23 eV showing excitations up to j′ = 40. Rotational excitations rates at very low collision energy range (Ec.m. = 0–300 cm−1) using rigid-rotor full close-coupling method have also been calculated in view of their astrophysical significance.

Comparison of log-derivative and renormalized Numerov methods in low-energy two-body collisions

The log-derivative (LOGD) and renormalized Numerov (RN) methods are popularly used in inelastic and reactive scattering calculations. The computational precision of two methods and their improved versions are compared in two-body diatomic and bimolecular collisions at low temperatures. In diatomic 40K-133Cs collision example the single-channel calculations show the solution-improved RN method has the advantage over others when large fixed propagating interval used. The relative error of local scattering length in different propagating sectors are explored. In multi-channel 40K-133Cs collisions the predicted positions of Feshbach resonances by using mapping grid points indicate strong potential-following character in LOGD methods, which is consistent with the analysis on local scattering length in single-channel calculations. In multiple open-channel calculations the elastic and inelastic scatterings and their dependence on collision energy are compared as well. In bimolecular 23Na87Rb-23Na87Rb long-range reactive scattering example the elastic and reactive rate coefficients are investigated. The original LOGD method displays surprisingly relatively high accuracy with less mapping grid points and a wide range of mapping parameters. By increasing the number of mapping grid points the improved LOGD exhibits definitely superiority on precision with proper mapping parameters. We demonstrate our consequent is applicable in other colliding systems.

Intramolecular interactions and the neutral loss of ammonia from collisionally activated, protonated ω-aminoalkyl-3-hydroxyfurazans.

Gas phase fragmentation reactions of monoprotonated 4-(3-aminopropyl)- and 4-(4-aminobutyl)-3-hydroxyfurazan were investigated to examine potential interactions between functional groups. The two heterocyclic alkyl amines were ionized by electrospray ionization (ESI, positive mode) and fragmented using tandem mass spectrometry (MS/MS). The fragmentation pathways were characterized using pseudo MS3 experiments, precursor-ion scans, and density functional computations. For both heterocyclic ions, loss of ammonia was the only fragmentation process observed at low collision energies. Computational analysis indicated that the most feasible mechanism was intramolecular nucleophilic displacement of ammonia from the protonated ω-aminoalkyl side chain by N5 of the furazan ring. The alkylated nitrogen in the resulting bicyclic product ion facilitated N-O bond cleavage; subsequent neutral losses of nitric oxide (NO) and carbon monoxide (CO) occurred by homolytic bond cleavages. Next in the multistep sequence, neutral loss of ethylene from a radical cation was observed. A less favorable, competing fragmentation pathway of protonated 4-(3-aminopropyl)-3-hydroxyfurazan was consistent with cleavage of the 3-hydroxyfurazan ring and losses of NO and CO. Overall, the similar fragmentation behavior found for protonated 4-(3-aminopropyl)- and 4-(4-aminobutyl)-3-hydroxyfurazan differed from that previously characterized for furazan analogs with shorter alkyl chains. These observations demonstrate that a small change in the structure of multifunctional, heterocyclic alkyl amines may significantly influence interactions between distinct functional groups and the nature of the fragmentation process.

Correlation Study of the Spin-Orbit State-Resolved Scattering of Al(2P) in Oxidation Reaction and Nonreactive Collision.

Spin-orbit coupling plays an important role in chemical reactivity, especially in reactions that require the change of electron spin states. However, it is difficult to measure and analyze the reaction dynamics between spin-orbit splitting states, particularly for splitting states with a small energy difference. In this study, we find that nonreactive scattering of spin-orbit splitting states can provide complementary information that is overlooked in chemical reaction studies. Here, the oxidation reactivities of spin-orbit Al(2P1/2,3/2) states with small energy difference of 112 cm-1 are clearly distinguished in the high rotational AlO(v = 0 and 1, N) products at low collision energy of 507 cm-1 using a laser ablation crossed-beam and time-sliced ion velocity mapping technique, in conjunction with state-selected nonreactive scattering studies. For both the AlO(v = 0 and 1) channels, the spin-orbit relative reactivity σ3/2/σ1/2 increases with the increase of rotational level N of AlO products. However, for AlO(v = 0), the reactivity of the Al(2P3/2) excited state is consistently lower than that of the Al(2P1/2) ground state, whereas for AlO(v = 1), the reactivity of Al(2P3/2) is higher than that of Al(2P1/2) at a higher rotational state. The relative reactivity of spin-orbit split Al(2P) states at different scattering angles shows a more pronounced enhancement of forward scattering relative to side and backward scattering for Al(2P3/2) when a higher rotationally excited AlO is produced. Nonreactive scattering studies of Al(2P) suggest that the Al(2P3/2) state is deexcited to the ground Al(2P1/2) state at the sideways and backward scattering directions, and the deexcitation is supposed to reduce the reactivity of the excited Al(2P3/2) at the corresponding direction.

Theoretical cross sections for electron collisions relevant for ammonia discharges part 1: NH3, NH2, and NH

Besides being the worlds’ most important fertilizer precursor, ammonia could play an important role as hydrogen carrier in a decarbonized future. The efficient production and decomposition (or cracking) of ammonia are essential to this end. An electricity-driven technology of interest for both these processes are non-thermal plasmas. Plasma processes have the advantage of activating—even inert—molecules and initiating chemical reactions through electron collisions, rather than through conventional heating. However, a complete set of low-energy cross section data is not available for the electron collisions with ammonia (NH3) and its radicals, amidogen (NH2) and imidogen (NH). Here, we used the ab initio R-matrix method to determine theoretical cross sections for the low-energy electron collision processes with NH3, NH2, and NH. Additionally, we explored the contribution of the different processes towards dissociation (especially from electronic excited states). Where possible, we compared our theoretical cross section data with experimental data and/or previous recommendations. Lastly, our own recommended cross section data for the electron collisions are presented. Use of this complete set of electron collision data should contribute to a more accurate description of and better insights into the plasma-chemical kinetics behind plasma-assisted ammonia production and decomposition processes.

Theoretical study of inelastic processes in collisions of Y and Y+ with hydrogen atom

ABSTRACT Utilizing a simplified quantum model approach, the low-energy inelastic collision processes between yttrium atoms (ions) and hydrogen atoms have been studied. Rate coefficients corresponding to the mutual neutralization, ion-pair formation, excitation, and de-excitation processes for the above collision systems have been provided in the temperature range of 1000–10 000 K. Three ionic states and 73 covalent states are considered in calculations for the collisions of yttrium atoms with hydrogen atoms, which include six molecular symmetries and 4074 partial inelastic reaction processes. For the collisions of yttrium ions with hydrogen atoms, one ionic state and 116 covalent states are included, which are related to three molecular symmetries and 13 572 partial inelastic collision processes. It is found that the rate coefficients for the mutual neutralization process have a maximum at T = 6000 K, which is an order of magnitude higher than those of other processes. Notably, the positions of optimal windows for the collisions of yttrium atoms and ions with hydrogen atoms are found near electronic binding energy −2 eV (Y) and −4.4 eV (Y+), respectively. The scattering channels located in or near these optimal windows have intermediate-to-large rate coefficients (greater than 10−12 cm3 s−1). The reported data should be useful in the study of non-local thermodynamic equilibrium modelling.

Dynamics studies of the Si+(2P) + D2 reaction by using quantum and quasi-classical methods

The dynamics calculations of the Si+ + D2 (v0 = 0, j0 = 0) → SiD+ + D reaction were carried out by using time-dependent quantum wave packet and quasi-classical trajectory methods. The integral cross sections were calculated and compared with the experimental data in the collision energy range from 1.0 to 10.0 eV. The results indicated that present values are in good agreement with the experimental data. In addition, reaction probabilities, the distribution of the SiD+ product and differential cross sections are also calculated. The differential cross section indicated that the “complex-forming” mechanism plays a dominant role in the low collision energy range and the abstraction mechanism dominates the reaction at high collision energies.

Improved temperature dependence of rate coefficients for rotational state-to-state transitions in H2O + H2O collisions

Aims. We present an improved database of temperature-dependent rate coefficients for rotational state-to-state transitions in H2O + H2O collisions. The database includes 231 transitions between the lower para-states of H2O and 210 transitions between its lower ortho-states (up to j = 7) and can be employed in cometary and planetary applications up to the temperature of 1000 K. Methods. We developed and applied a new general method that allows the generation of rate coefficients for excitation and quenching processes that automatically satisfy the principle of microscopic reversibility and also helps to cover the range of low collision energies by interpolation of cross sections between the process threshold and the computed data points. Results. We find that in the range of intermediate temperatures, 150 < T < 600 K, our new rate coefficients are in good agreement with those reported earlier, but for higher temperatures, 600 < T < 1000 K, the new revised temperature dependence is recommended. The low temperature range, 5 < T < 150 K, is now covered by the above-mentioned interpolation of cross sections down to the process threshold.

Predicting head injury metrics during low- to moderate-speed frontal collisions using computational simulations

ObjectivesSubjective reports of mild traumatic brain injury (mTBI) are common following low-energy motor-vehicle collisions. Biomechanical analyses are useful in providing a quantitative means for determining the likelihood of sustaining mTBI. While occupant dynamics in low-speed rear impacts have been extensively investigated, peer-reviewed studies on occupant dynamics during low-speed frontal collisions are sparse. The objective of this study is to present a validated computational method to quantify the biomechanical response of the head in low- and moderate-speed frontal collisions. Data and methodsThis study used data from a previously-published series of four instrumented in-line front-to-rear staged collisions using 2014 Honda Accord sedans at closing velocities of approximately 7.4 kph (test L1), 12.7 kph (test L2), 21.7 kph (test L3), and 33.6 kph (test L4) kph. A model of the test vehicle occupant compartment was created using the MAthematical DYnamic MOdeling (MADYMO) software using methods previously described. Crash pulse data from L4 were applied to the MADYMO model. Seat belt parameters were optimized to achieve reasonable agreement between simulation results and test data for relevant head injury metrics (linear head acceleration [LHA], angular head acceleration [AHA], and HIC15). Crash pulses from the other tests in the series (L1, L2, and L3) were then applied to the model and peak values for LHA, AHA, and HIC15 were compared to the physical test data to demonstrate validation. ResultsThe optimization of seat belt and seat parameters within the MADYMO model resulted in accurate prediction of ATD dynamics demonstrated in Test L4. The simulation-predicted peak LHA was within 0.2 g of the test value, peak AHA was within 64 rad/s2, and HIC15 was within 0.46. When applied to the remainder of the tests (L1, L2, and L3), the optimized model showed excellent accuracy in predicting peak LHA and HIC15. When compared to the physical test data, the simulation-predicted values for LHA were within 0.4 g or less and the HIC15 values were within 0.4 or less across all tests. The model generally over-predicted AHA, particularly for the lower-severity collisions (L1 and L2). ConclusionsWe have demonstrated a reliable methodology for developing a biomechanical computational model to predict head injury metrics in low- to moderate-speed frontal collisions. This approach can be particularly valuable in forensic investigations of real-world crashes. Pre-existing crash test data can be used in conjunction with exemplar vehicle information to validate a MADYMO model. Appropriate crash pulse data from classical accident reconstruction techniques, event data recorders, or simulations can then be applied to the model to accurately predict head dynamics for real-world vehicle occupants without the need for full-scale staged crash tests.

Alternating Stereospecificity upon Central-Atom Change: Dynamics of the F- +PH2 Cl SN 2 Reaction Compared to its C- and N-Centered Analogues.

Central-atom effects on bimolecular nucleophilic substitution (SN 2) reactions are well-known in chemistry, however, the atomic-level SN 2 dynamics at phosphorous (P) centers has never been studied. We investigate the dynamics of the F- +PH2 Cl reaction with the quasi-classical trajectory method on a novel full-dimensional analytical potential energy surface fitted on high-level ab initio data. Our computations reveal intermediate dynamics compared to the F- +CH3 Cl and the F- +NH2 Cl SN 2 reactions: phosphorus as central atom leads to a more indirect SN 2 reaction with extensive complex-formation with respect to the carbon-centered one, however, the title reaction is more direct than its N-centered pair. Stereospecificity, characteristic at C-center, does not appear here either, due to the submerged front-side-attack retention path and the repeated entrance-channel inversional motion, whereas the multi-inversion mechanism discovered at nitrogen center is also undermined by the deep Walden-well. At low collision energies, 6 % of the PH2 F products form with retained configuration, mostly through complex-mediated mechanisms, while this ratio reaches 24 % at the highest energy due to the increasing dominance of the direct front-side mechanism and the smaller chance for hitting the deep Walden-inversion minimum. Our results suggest pronounced central-atom effects in SN 2 reactions, which can fundamentally change their (stereo)dynamics.

Crystallographic and temperature effects in low-energy collisions for plasma–material interactions

The interaction of plasma with materials is critical for the fundamental understanding of non-equilibrium processes and their wide application. Recent achievements in fusion energy research emphasize the importance of this problem. Because modelling and predicting plasma–material interactions (PMI) require considering a tremendous number of single plasma particle–surface interaction events, this type of modelling was, until recently, possible only within a binary collision approximation (BCA). The BCA approach considers materials as uniform temperature-insensitive media. The research presented here addresses the PMI problem within an atomistic-based approach for the first time at a statistically significant level. Approximately 105 molecular dynamics trajectories were generated for 100 eV deuterium ions interacting with a tungsten surface. The research demonstrated the critical importance of incorporating the discrete lattice structure of matter into the model. Deuterium penetration depth and fraction of backscattered deuterium ions strongly depend on the surface orientation, the impact incident ion directions, and the ions’ initial positions. On average, the BCA-based calculations underestimate the penetration depth by a factor of two or more, and the fraction of backscattered atoms is overestimated by a factor of two or more. Furthermore, increasing the material temperature from 500 to 3000 K reduces penetration depth by about 30% and increases the fraction of backscattered atoms by 250%.

Electron Scattering from Methyl Formate (HCOOCH3): A Joint Theoretical and Experimental Study.

Elastic low-energy electron collisions with methyl formate have been studied theoretically at the level of various theories. The elastic integral cross section was calculated using Schwinger multichannel and R-matrix methods, in the static-exchange and static-exchange plus polarization levels of approximations for energies up to 15 eV. The absolute total cross section for electron scattering from methyl formate has been measured in a wide energy range (0.2-300 eV) using a 127° electron spectrometer working in the linear transmission configuration. The integral elastic and the absolute total cross sections display a π* shape resonance at around 1.70-1.84 eV, which can be related to the resonance visible for formic acid, and a broad structure located at 7-8 eV, which can be associated to a superposition of σ* shape resonances. Our results were compared with theoretical and experimental results available in the literature and with the results of electron collisions with formic acid. The additivity rule was used to estimate the total cross section of methyl formate and the results agree well with the experimental data.

Oxidized and Reduced Dimeric Protein Complexes Illustrate Contrasting CID and SID Charge Partitioning.

Charge partitioning during the dissociation of protein complexes in the gas phase is influenced by many factors, such as interfacial interactions, protein flexibility, protein conformation, and dissociation methods. In the present work, two cysteine-containing homodimer proteins, β-lactoglobulin and α-lactalbumin, with the disulfide bonds intact and reduced, were used to gain insight into the charge partitioning behaviors of collision-induced dissociation (CID) and surface-induced dissociation (SID) processes. For these proteins, we find that restructuring dominates with CID and dissociation with symmetric charge partitioning dominates with SID, regardless of whether intramolecular disulfide bonds are oxidized or reduced. CID of the charge-reduced dimeric protein complex leads to a precursor with a slightly smaller collision cross section (CCS), greater stability, and more symmetrically distributed charges than the significantly expanded form produced by CID of the higher charged dimer. Collision-induced unfolding plots demonstrate that the unfolding-restructuring of the protein complexes initiates the charge migration of higher charge-state precursors. Overall, gas collisions reveal the charge-dependent restructuring/unfolding properties of the protein precursor, while surface collisions lead predominantly to more charge-symmetric monomer separation. CID's multiple low-energy collisions sequentially reorganize intra- and intermolecular bonds, while SID's large-step energy jump cleaves intermolecular interfacial bonds in preference to reorganizing intramolecular bonds. The activated population of precursors that have taken on energy without dissociating (populated in CID over a wide range of collision energies, populated in SID for only a narrow distribution of collision energies near the onset of dissociation) is expected to be restructured, regardless of the activation method.

Li + HF and Li + HCl Reactions Revisited I: QCT Calculations and Simulation of Experimental Results.

The Li + HF and Li + HCl reactions share some common features. They have the same kinematics, relatively small barrier heights, bent transition states, and are both exothermic when the zero point energy is considered. Nevertheless, the pioneering crossed beam experiments by Lee and co-workers in the 80s (Becker et al., J. Chem. Phys. 1980, 73, 2833) revealed that the dynamics of the two reactions differ significantly, especially at low collision energies. In this work, we present theoretical simulations of their results in the laboratory frame (LAB), based on quasiclassical trajectories and obtained using accurate potential energy surfaces. The calculated LAB angular distributions and time-of-flight spectra agree well with the raw experimental data, although our simulations do not reproduce the experimentally derived center-of-mass (CM) differential cross section and velocity distributions. The latter were derived by forward convolution fitting under the questionable assumption that the CM recoil velocity and scattering angle distribution were uncoupled, while our results show that the coupling between them is relevant. Some important insights into the reaction mechanism discussed in the article by Becker et al. had not been contrasted with those that can be extracted from the theoretical results. Among them, the correlation between the angular momenta involved in the reactions has also been examined. Given the kinematics of both systems, the reagent orbital angular momentum, , is almost completely transformed into the rotation of the product diatom, j'. However, contrary to the coplanar mechanism proposed in the original paper, we find that the initial and final relative orbital angular momenta are not necessarily parallel. Both reactions are found to be essentially direct, although about 15% of the LiFH complexes live longer than 200 fs.

Gas-phase stability and thermodynamics of ligand-bound, binary complexes of chloramphenicol acetyltransferase reveal negative cooperativity.

The biological role of the bacterial chloramphenicol (Chl)-resistance enzyme, chloramphenicol acetyltransferase (CAT), has seen renewed interest due to the resurgent use of Chl against multi-drug-resistant microbes. This looming threat calls for more rationally designed antibiotic derivatives that have improved antimicrobial properties and reduced toxicity in humans. Herein, we utilize native ion mobility spectrometry-mass spectrometry (IMS-MS) to investigate the gas-phase structure and thermodynamic stability of the type I variant of CAT from Escherichia coli (EcCATI) and several EcCATI:ligand-bound complexes. EcCATI readily binds multiple Chl without incurring significant changes to its gas-phase structure or stability. A non-hydrolyzable acetyl-CoA derivative (S-ethyl-CoA, S-Et-CoA) was used to kinetically trap EcCATI and Chl in a ternary, ligand-bound state (EcCATI:S-Et-CoA:Chl). Using collision-induced unfolding (CIU)-IMS-MS, we find that Chl dissociates from EcCATI:S-Et-CoA:Chl complexes at low collision energies, while S-Et-CoA remains bound to EcCATI even as protein unfolding occurs. Gas-phase binding constants further suggest that EcCATI binds S-Et-CoA more tightly than Chl. Both ligands exhibit negative cooperativity of subsequent ligand binding in their respective binary complexes. While we observe no significant change in structure or stability to EcCATI when bound to either or both ligands, we have elucidated novel gas-phase unfolding and dissociation behavior and provided a foundation for further characterization of alternative substrates and/or inhibitors of EcCATI.

Structural Elucidations of derivatized Sterols using Electrospray Ionization/Atmospheric Pressure Chemical Ionization-Quadrupole Ion Trap-Mass spectrometry

Free sterols are neutral molecules that are difficult to ionize by Electrospray Ionization (ESI) or Atmospheric Pressure Chemical Ionization (APCI). Therefore, in order to increase their ionization efficiency, sterols were converted into their corresponding picolinyl esters. In this study we examined the possibility of analyzing picolinyl ester of sterols derivatives using flow injection ESI-quadrupole ion trap (QIT) MS and APCI-QIT MS and we investigated their fragmentation pathways using low energy collision induced dissociation-tandem mass spectrometry (CID-MS2). This study also aimed to examine the possibility of using ESI-QIT MS3 to identify sterol isomers. The picolinyl esters readily formed protonated molecular ions ([M+H]+) in ESI and APCI sources except for the picolinyl ester of 7-dehydrocholesterol which was detected as the radical cation ion [M].+ using APCI-QIT MS. The ester bonds of picolinyl esters cleaved during CID MS2, resulting in diagnostic fragments corresponding to steryl cation moieties [M+H-C6H5NO2]+. The CID MS3 of [M+H]+ → [M+H-C6H5NO2]+ of picolinyl esters was found to be useful for structural elucidation and for distinguishing among steryl isomers.

Rotational Dynamics Induced by Low-Energy Binary Collisions of Quantum Droplets

A theoretical analysis of the rotational dynamics induced by off-axis binary collisions of quantum droplets constituted by ultracold atoms is reported. We focus on quantum droplets formed by degenerate dilute Bose gases made from binary mixtures of alkaline atoms under feasible experimental conditions. The stability of the ground state is known to be longer for the chosen heteronuclear gases than for the homonuclear ones. In both cases, we find that the dynamics seem to privilege high similarity of the density of each atomic species. However, the evolution of the phase of the corresponding order parameter differs significantly for heteronuclear admixtures. We evaluate the fidelity as a figure of merit for the overlap between the order parameters of each atomic species. Dynamical evidence of the differences between the phases of the order parameters is predicted to manifest in their corresponding linear and angular momenta. We numerically verify that the total angular and linear momenta are both conserved during the collision. Some direct correlations between the Weber number and the impact parameter with the distribution of the dynamical variables are established.

An improved model for predicting the erosion within the DEM framework

For investigating the erosion caused by particle impact, an erosion model based on the particle impact energy has been proposed in our previous study, which can be called IEEM (Impact Energy Erosion Model). By incorporating IEEM with DEM (Discrete Element Method), the erosion caused by particle impact can be numerically predicted. However, IEEM assumes that all particle impacts lead to erosion, which contradicts the reality where gentle particle impacts with low collision energy do not cause erosion. Therefore, an improved erosion model called FIEEM (Filtering Impact Energy Erosion Model) is devised by introducing the concept of filtration into IEEM. In FIEEM, the low-energy particle collisions are filtered by comparing the contact stress with the flow stress of the target material so that these collisions cannot cause erosion, and the Hertz contact theory is employed to determine the accurate contact stress. Subsequently, the DEM simulations of the charge behaviors and liner wear in an industrial-scale SAG (Semi-Automatic Grinding) mill are conducted and then compared with the experimental data for validating the accuracy and effectiveness of FIEEM. Additionally, the discussion regarding the difference of the predicted erosion between IEEM and FIEEM is also presented from the point of effective collision energy.