Binary Encounter Bethe Method Research Articles

Electron impact partial ionization cross sections: R-carvone, 2-butanol, imidazole, and 2-nitroimidazole.

We calculate electron impact partial and total ionization cross sections of R-carvone (C10H14O), 2-butanol (C4H10O), imidazole (C3H4N2), and 2-nitroimidazole (C3H3N3O2). We have used the Binary Encounter Bethe (BEB) model to obtain total electron impact ionization cross sections (TICSs). The modified BEB method in combination with mass spectrum data of the molecules is used to calculate the partial ionization cross section (PICS) of the cationic fragments dissociating from the parent molecule. Our PICS data for R-carvone and 2-butanol are in good agreement with the experimental data for all the cation fragments along with the TICS data. For imidazole and 2-nitroimidazole, the estimates of the PICS are reported for the first time in the present study. We have found that both the modified BEB method and the mass spectrum dependence method work effectively to estimate PICS if we have information about the appearance energies and relative abundance data of the target under investigation.

Theoretical process for the investigation of dielectric characteristics of F3NO as an alternative gas for SF6

To examine the possibility of using a gas molecule as an SF6 alternative gas, the insulation properties of the molecule must be estimated. In this work, we present a theoretical approach to calculate geometry parameters, electron scattering cross sections, and transport properties of nitrogen fluoride oxide (F3NO), which we have selected as an alternative to SF6. The molecular minimum structure of F3NO was optimized using the ɷB97X-D functional combined with the aug-cc-pVTZ basis set. Using this initial geometry obtained by the molecular structure calculation, the R-matrix calculation was done to obtain the elastic and momentum transfer cross section. The BE-f method was used for electronic excitation cross section. For the ionization cross section, the binary encounter Bethe method was used. From the calculated cross section data, the electron transport coefficients and reaction coefficients were calculated by solving the two-term approximated Boltzmann equation to investigate the discharge and insulation characteristics.

Direct Ionization Cross Sections of Uranium Atom By Electron Impact

A theoretical model for electron impact ionization cross section has been found to be reliable for wide range of atoms is applied in this paper to the Uranium atom. A modified Kim binary encounter Bethe (BEB) method and modified Khare BEB method is employed for calculating electron impact ionization cross sections. The present results so obtained are compared with experimental as well as theoretical results known to the best of our knowledge.

Electron-impact ionization cross sections of new SF6 replacements: A method of combining Binary-Encounter-Bethe (BEB) and Deutsch-Märk (DM) formalism

Recently, much attention has been paid to some new carbon-fluoride gases, such as C2F4H2 (R134), C3F4H2 (HFO1234ze), C4F8, C4F7N, C5F10O, and C6F12O. All these gases present excellent dielectric strength and very low values of global warming potential and thus have potential to replace sulfur hexafluoride (SF6) as an insulating medium. However, the electron-impact ionization cross sections (Qion), which are the necessary basic data for the investigation of plasma discharges in these gases, are still unavailable. This work is devoted to the calculation of Qion for the above new SF6 replacements with incident electron energy of up to 5000 eV. We propose a method of combining the Deutsch-Märk (DM) formalism at low electron energy and the Binary-Encounter-Bethe (BEB) formalism at high electron energy by using a dual sigmoid function. The comparison between the calculated and experimental Qion for various molecules indicates that this new combined method yields 49.41% and 61.24% improvement by the Euclidean metric on average compared with the BEB and DM methods, respectively. We also investigate the effects of molecular orbitals and atomic shells on the Qion of new SF6 replacements. It is found that the BEB method conforms to the law that higher molecular orbitals have larger effect on electron-impact ionization of a molecule, while the DM method does not. Generally, the 2p shells of carbon, nitrogen, or oxygen atoms in a molecule play a dominant role in electron-impact ionization, whereas the shells of fluorine atoms do not affect the ionization process very significantly.

Electron impact ionisation cross-sections for complex molecules

The main goal of this work is to compute the total ionisation cross-section for electron scattering from various complex molecules. The targets chosen are pyridazine, alanine, glycine, benzoic acid, phenylacetylene, ethylbenzene and n-propylbenzene. There is no previous literature available for these molecules except for pyridazine, alanine and glycine, and hence we present the first report of their ionisation cross-section. We apply the complex scattering potential-ionisation contribution (CSP-ic) method to compute the cross-sections from the respective ionisation threshold to 5000 eV. The result for the pyridazine molecule shows an excellent agreement with the available experimental data and binary encounter-Bethe (BEB) cross-sections. In the absence of any experimental comparison for other molecules, we have also calculated their BEB ionisation cross-sections. These two methods are well known for giving reasonable estimates of the ionisation cross-sections. The CSP-ic method is based on the molecular structure and properties, while the BEB method deals with molecular orbitals. Thus, comparing the two results will check the accuracy of these theoretical models and further increase the credibility of the reported cross-section. In general, fairly good agreement is observed between the two results. However, any inconsistencies observed are backed by valid reasons.

Calculation of electron-impact ionization cross sections of perfluoroketone (PFK) molecules CxF2xO (x = 1–5) based on Binary-Encounter-Bethe (BEB) and Deutsch-Märk (DM) methods

Perfluoroketone (PFK) gases are widely used in industry, e.g. as an insulating medium in high-voltage apparatus and as a cleaning agent in chemical vapor deposition (CVD) chambers. A great deal of attention has been paid to them recently because of their low global warming potential (GWP). In order to describe the ionization processes in various plasmas resulting from PFK gases, the electron-impact ionization cross sections (Qion) of PFK molecules CxF2xO (x = 1–5) were calculated by the Binary-Encounter Bethe (BEB) and the Deutsch-Märk (DM) methods. The chemical structures of PFK molecules were optimized by the hybrid Density Functional Theory (DFT) method with the Austin-Petersson-Frisch functional including dispersion (APF-D). The binding and kinetic energies of electrons in molecular orbitals were also determined with the APF-D hybrid DFT method. The binding energies of valence electrons were then improved by the electron propagator theory (EPT) method. The ionization potentials of PFK molecules were calculated as the difference between the energy of a molecule and its cation using the complete basis set (CBS) method. The molecular orbital compositions were obtained by the natural atomic orbital (NAO) analysis. The results show that Qion determined by the BEB method are always larger than those by the DM method. The difference is reduced with the EPT corrections considered. The comparison between the theoretical and experimental Qion demonstrates that the EPT correction improves Qion considerably.

Electron impact ionisation cross sections of cis- and trans-diamminedichloridoplatinum(II) and its hydrolysis products

ABSTRACTWe report total electron-impact ionisation cross sections (EICSs) of cisplatin, its hydrolysis products and transplatin in the energy range from threshold to 10 keV using the binary-encounter-Bethe (BEB) and its relativistic variant (RBEB), and the Deutsch-Märk (DM) methods. We find reasonable agreement between all three methods, and we also note that the RBEB and the BEB methods yield very similar (almost identical) results in the considered energy range. For cisplatin, the resulting EICSs yield cross section maxima of 22.09 × 10−20 m2 at 55.4 eV for the DM method and 18.67 × 10−20 m2 at 79.2 eV for the (R)BEB method(s). The EICSs of monoaquated cisplatin yield maxima of 12.54 × 10−20 m2 at 82.8 eV for the DM method and of 9.74 × 10−20 m2 at 106 eV for the (R)BEB method(s), diaquated cisplatin yields maxima of 7.56 × 10−20 m2 at 118.5 eV for the DM method and of 5.77 × 10−20 m2 at 136 eV for the (R)BEB method(s). Molecular geometry does not affect the resulting EICS significantly, which is also reflected in very similar EICSs of the cis- and trans-isomer. Limitations of the work as well as desirable future directions in the research area are discussed.

Electron induced ionization of plasma processing gases: C4Fx (x = 1–8) and the isomers of C4F6 and C4F8

The total ionization cross section (Qion) for C4Fx (x = 1–8) fluorocarbons and the isomers of C4F6 and C4F8 molecules are calculated from ionization threshold to 5 keV using the binary-encounter bethe method. The targets are fully optimized using the Hartree–Fock (HF) method and density function theory (DFT) for their minimum energy structure and orbital parameters. The present Qion with HF parameters showed good agreement with the experimental data for 1,3-C4F6, 2-C4F6, 2-C4F8 and 1-C4F8. On the other hand, the Qion with DFT parameters are in good accordance with the recent theoretical results for 1,3-C4F6 and 2-C4F6. The Qion for c-C4F8 showed much variation among the various results. The isomer effect in Qion is negligible for the isomers of C4F6 and C4F8 molecules. The calculation of Qion for C4F, C4F2, C4F3, C4F4, C4F5, c-C4F6, C4F7 and iso-C4F8 is a maiden attempt. The present cross section data are important quantities for low temperature plasma modeling especially related to the fluorocarbon plasmas.

Electron impact ionisation cross sections of iron oxides

We report electron impact ionisation cross sections (EICSs) of iron oxide molecules, FexOx and FexOx+1 with x = 1, 2, 3, from the ionisation threshold to 10 keV, obtained with the Deutsch-Märk (DM) and binary-encounter-Bethe (BEB) methods. The maxima of the EICSs range from 3.10 to 9 . 96 × 10-16 cm2 located at 59–72 eV and 5.06 to 14.32 × 10-16 cm2 located at 85–108 eV for the DM and BEB approaches, respectively. The orbital and kinetic energies required for the BEB method are obtained by employing effective core potentials for the inner core electrons in the quantum chemical calculations. The BEB cross sections are 1.4–1.7 times larger than the DM cross sections which can be related to the decreasing population of the Fe 4s orbitals upon addition of oxygen atoms, together with the different methodological foundations of the two methods. Both the DM and BEB cross sections can be fitted excellently to a simple analytical expression used in modelling and simulation codes employed in the framework of nuclear fusion research.Graphical abstract

Electron impact ionisation cross sections of iron hydrogen clusters

We computed electron impact ionisation cross sections (EICSs) of iron hydrogen clusters, FeH n with n = 1,2,...,10, from the ionisation threshold to 10 keV using the Deutsch-Mark (DM) and the binary-encounter-Bethe (BEB) formalisms. The maxima of the cross sections for the iron hydrogen clusters range from 6.13 × 10-16 cm2 at 60 eV to 8.76 × 10-16 cm2 at 76 eV for BEB-AE (BEB method based on quantum-chemical data from all-electron basis sets) calculations, from 4.15 × 10-16 cm2 at 77 eV to 7.61 × 10-16 cm2 at 80 eV for BEB-ECP (BEB method based on quantum-chemical data from effective-core potentials for inner-core electrons) calculations and from 2.49 × 10-16 cm2 at 43.5 eV to 7.04 × 10-16 cm2 at 51 eV for the DM method. Cross sections calculated via the BEB method are substantially higher than the ones obtained via the DM method, up to a factor of about two for FeH and FeH2. The formation of Fe-H bonds depopulates the iron 4s orbital, causing significantly lower cross sections for the small iron hydrides compared to atomic iron. Both the DM and BEB cross sections can be fitted perfectly against a simple expression used in modelling and simulation codes in the framework of nuclear fusion research. The energetics of the iron hydrogen clusters change substantially when exact exchange is present in the density functional, while the cluster geometries do not depend on this choice.

Electron-scattering studies of carbonyl fluoride

The present article reports calculations of total, momentum transfer, differential, excitation, and ionization cross sections for electron scattering from the carbonyl fluoride (${\mathrm{F}}_{2}\mathrm{CO}$) molecule. Total cross sections (TCSs) are presented over an extensive energy range from 0.5 to 5000 eV. The ab initio R-matrix and spherical complex optical potential methods were used to perform low-energy computations and intermediate- to high-energy calculations, respectively. The TCSs computed through these two formalisms are in good agreement in the 24--26 eV energy range. The consistency of the data in this overlapping region has allowed us to predict total cross sections over an extensive energy range. Electronic excitation, momentum transfer, and differential cross sections were also calculated using the $R$-matrix method at low incident energies. In the present study, a low-energy resonance at 3.67 eV was detected with a $^{2}B_{1}$ symmetry, indicating the probability of anion formation by the dissociative electron attachment process and further decay to neutral and negative ion fragments. The total ionization cross section for ${\mathrm{F}}_{2}\mathrm{CO}$ was also evaluated using the complex scattering potential--ionization contribution method and the binary encounter Bethe method up to 5 keV.

Absolute cross sections for dissociative electron attachment to HCCCN

New absolute cross sections for dissociative electron attachment to HCCCN (cyanoacetylene or propiolonitrile) in the range of 0–10 eV electron energy are presented here, which have been determined from a new analysis of previously reported data (Graupner et al 2006 New J. Phys. 8 117). The highest cross sections are observed for the formation of CN− at 5.3 eV and CCCN− at 5.1 eV; approximately 0.06 Å2 and 0.05 Å2 respectively. As part of the re-analysis, it was necessary to determine absolute cross sections for electron-impact ionization of HCCCN with the binary-encounter Bethe method. These electron-impact ionization absolute cross sections for HCCCN are also presented here; the maximum value was found to be ∼6.6 Å2 at ∼80 eV.

Electron-impact total cross sections for phosphorous triflouride

Various total cross sections for scattering of electrons by phosphorous triflouride (${\mathrm{PF}}_{3}$) using the $R$-matrix method for incident energies from 0.1$--$15 eV and using spherical complex optical potential formalism beyond ionization threshold of target to 5000 eV are reported. We performed close-coupling calculations using static exchange plus polarization model. We employed different target models in order to study their relative dependence on the total cross sections. Three important structures are revealed in the total-cross-section curve: one that corresponds to the Ramsauer-Townsend minimum at 0.33 eV, the second is a strong maximum of 100 \AA{}${}^{2}$ at 1 eV, the third is around 11 eV corresponding to negative ion formation as predicted by earlier study. The total ionization cross sections are computed using the complex scattering potential ionization contribution method and the binary encounter Bethe method. The electronic-excitation cross sections, momentum-transfer cross sections, and differential and ionization cross sections are our maiden efforts for this system. We have compared our total-cross-section results with available theoretical and experimental results.

Electron-impact ionization ofPbq+ions forq=1–10

Theoretical calculations and experimental crossed-beam measurements are compared for electron-impact single ionization of ${\mathrm{Pb}}^{q+}$ ions for $q=1--10$. We compare with two main theoretical methods. First, we check against configuration-average distorted-wave calculations, which include both direct-ionization and indirect excitation-autoionization contributions. Second, for ion stages ${\mathrm{Pb}}^{+}$ through to ${\mathrm{Pb}}^{5+}$, we calculate the dominant excitation-autoionization channels using level-resolved distorted-wave theory to evaluate the excitation cross sections. We find that for ion stages ${\mathrm{Pb}}^{+}$, ${\mathrm{Pb}}^{2+}$, and ${\mathrm{Pb}}^{3+}$, distorted-wave theory significantly overestimates the total-ionization cross section, due to an overestimation of the direct-ionization cross section from the $5d$ subshell. For ion stages ${\mathrm{Pb}}^{4+}$ through to ${\mathrm{Pb}}^{10+}$ there is good agreement between theory and experiment. We find evidence for significant metastable fraction in the ion beam of the experiment for ion stages ${\mathrm{Pb}}^{2+}$, ${\mathrm{Pb}}^{3+}$, ${\mathrm{Pb}}^{4+}$, ${\mathrm{Pb}}^{5+}$, and ${\mathrm{Pb}}^{6+}$. For ion stage ${\mathrm{Pb}}^{3+}$ we find that the level-resolved distorted-wave calculation of the excitation autoionization results in a slight reduction of the configuration-average theoretical results, due to splitting of levels within the autoionizing configurations. We also investigate two semiempirical methods of calculating the direct-ionization cross sections: namely, the Lotz method and the binary encounter Bethe method. We find that both methods provide results which are significantly lower than the distorted-wave method for the $5d$-subshell direct ionization of ${\mathrm{Pb}}^{+}$, ${\mathrm{Pb}}^{2+}$, and ${\mathrm{Pb}}^{3+}$. For the higher ion stages, both methods are lower than the distorted-wave direct-ionization cross-section results, trending towards the distorted-wave results as the ion stage increases.

Absolute electron impact ionization cross-sections for CO,CO2, OCSand CS2

Absolute total electron impact ionization cross-sections have been measured for CO,CO2, OCSand CS2 from near threshold to 250 eV. Experimental data are compared with previously reportedmeasurements and with calculations using the additivity method of Margreiter, Deutschand Märk (DM) and the binary encounter Bethe method (BEB). Bond components to thetotal cross-section, previously deduced from systematic studies of perfluorocarbons, mixedhalocarbons, nitriles, chlorocarbons and alcohols, have been shown to reproduce andpredict maximum electron impact cross-sections to a high level of confidence.C = O and C = S bond cross-sections are now reported from the maximum cross-sections forCO2 andCS2, andshown to predict the measured maximum ionization cross-section for OCS to within 4%. The data for OCSand CS2 are shown to be in good accord with the expectations of previously derived relationshipsbetween the maximum ionization cross-section, the molecular volume polarizability and themolecular ion appearance energy (ionization threshold energy).

Absolute electron impact ionization cross-sections for the C1 to C4 alcohols

Absolute total positive-ion electron impact ionization cross-sections from a few eV above threshold to over 200 eV are reported for the C1 to C4 alcohols, including the isomers of propanol and butanol. Correlations between measured ionization cross-sections, ionization potential and molecular polarisability volume are explored and compared with data reported previously for perfluorocarbons, nitriles and mixed halocarbons. Small, but reproducible, differences between the isomers of the C3 and C4 alcohols have been used to estimate molecular volume polarisabilities for iso- and tertiary butanol. A C–OH functional group contribution to the total ionization cross-section has been deduced in line with bond contributions determined for a range of C–X (where X = C, H, F, Cl, Br, I, CN) bond types previously reported. The reproducibility of the measured cross-sections over the full energy range is better than ±2% and in some cases ±1%. Absolute cross-sections measured with the instrument are in excellent agreement with measurements for the inert gases and N2 made by several other groups claiming accuracies of around ±5%. Experimental data are compared with calculations using the Deutsch–Märk additivity method, the Binary Encounter Bethe method, and the polarisation model.

Electron-impact total ionization cross sections of SF x( x = 1–5)

Total cross sections for electron impact ionization are necessary quantities for numerical modeling of plasma chemistry and for quantitative mass-spectrometric gas analysis. Theoretical cross sections for SF, SF 2, SF 3, SF 4, and SF 5 are calculated by the recently developed binary-encounter-Bethe (BEB) model. The BEB model combines a modified form of the Mott cross section and the Bethe cross section. The results are compared with experimental cross sections for SF 3 and SF 5 free radicals. In view of the success of the BEB method for SF 6 and many other molecules, it is expected that the results presented here will provide reliable total ionization cross sections for SF x ( x = 1–5).