Calculations Of Integral Cross Sections Research Articles

A transition-state based rotational sudden (TSRS) approximation for polyatomic reactive scattering.

A transition-state based rotational sudden (TSRS) approximation for the calculation of differential and integral cross sections is introduced. The TSRS approach only requires data obtained from reactive scattering calculations for the vanishing total angular momentum (J = 0). It is derived within the quantum transition state framework and can be viewed as a generalization and improvement of existing J-shifting schemes. The TSRS approach assumes a sudden decay of the activated complex and separability of the overall rotation and motion in the internal coordinates. Depending on the choice of the body fixed frame, different variants of the TSRS can be derived. The TSRS approach is applied to the calculation of integral cross sections of various isotopomers of the H2O+H→H2+OH reaction, the reverse reaction H2+OH→H2O+H, and the H2O+Cl→HCl+OH reaction. Comparison with accurate close-coupling calculations and established approximate schemes shows that a scattering frame based TSRS approximation yields more accurate results than the centrifugal sudden approximation and standard J-shifting for the H2O+H→H2+OH reaction and all isotopomers studied. For the H2+OH→H2O+H and the H2O+Cl→HCl+OH reactions, the TSRS results as well as the results of the other approximate schemes agree well with the exact ones. The findings are rationalized by an analysis of the different contributions to the moment of inertia matrix at the transition state geometry.

Quantum mechanical calculations of state-to-state cross sections and rate constants for the F + DCl → Cl + DF reaction.

We present accurate state-to-state quantum wave packet calculations of integral cross sections and rate constants for the title reaction. Calculations are carried out on the best available ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged state-to-state reaction cross sections have been calculated for collision energies up to 0.5 eV and different initial rotational and vibrational excitations, DCl(v = 0, j = 0 - 1; v = 1, j = 0). Also, initial-state resolved rate constants of the title reaction have been calculated in a temperature range of 100-400 K. It is found that the initial rotational excitation of the DCl molecule does not enhance reactivity, in contract to the reaction with the isotopologue HCl in which initial rotational excitation produces an important enhancement. These differences between the isotopologue reactions are analyzed in detail and attributed to the presence of resonances for HCl(v = 0, j), absent in the case of DCl(v = 0, j). For vibrational excited DCl(v = 1, j), however, the reaction cross section increases noticeably, what is also explained by another resonance.

F+DClCl+DF REAKSİYONU İÇİN DALGA PAKETİ METODU KULLANILARAK BAĞ DURUMLARININ VE BİREYSEL KUANTUM SEVİYELERİ ARASINDAKİ SAÇILMALARIN HESAPLANMASI

Accurate state-to-state quantum wave packet calculations of integral cross sections for the title reaction are presented. Calculations are carried out on the best available ground 12A' global adiabatic potential energy surface of Deskevich et. al.[1]. Converged state-to-state wave packet reaction cross sections with the DCl (v=0, j=0-1; v=1, j=0) reagent have been calculated for the collision energy range from threshold up to 0.5 eV. Accurate product vibrational and rotational distributions of cross sections have been calculated at selected collision energies. State-to-state and total initial-state resolved rate constants of the title reaction have been calculated in a temperature range of 100-300 K. The present accurate calculations at v=0, j=0, J=0 show noticeable differences with previous calculations for the F+HCl reaction. Assuming the reaction coordinate in the F-Cl distance and to estimate the zero point energy in the orthogonal coordinate we have calculated the bound states along the reaction path for frozen F-Cl distance to interpret the results.

Theoretical calculation of integral cross sections of rotational excitation for collisions in isotopes of He atom with Na2 molecule

Multiple hard-ellipsoid model is a theoretical model which can more accurately decribe collisions between He atom and Na2 molecule. In this paper, we adopted the multiple hard-ellipsoid model to calculate the integral cross sections of rotational excitation for collisions in 3He,4He,7He,10He-Na2 systems at different relative incidence energies. This study shows that we can improve the accuracy of the results by increasing the number of equipotential ellipsoid surfaces. Moreover, we find that the integral cross sections of rotational excitation change with the relative incidence energy and reduced mass of the system. Finally, at relative incidence energy of 100 meV, we investigate the influence of different regions of the intermolecular potential on integral cross sections of rotational excitation in 4He-Na2 collisions.

Electron impact excitation of carbon monoxide in comet Hale‐Bopp

The fourth positive emissions of carbon monoxide in the coma of comet Hale‐Bopp have been assumed to be due mainly to fluorescence induced by sunlight. Based on this assumption they were used to deduce the abundance of carbon monoxide in the comet, giving a value higher than in other comets. Emissions produced by electron impact excitation of CO were not considered. Recent measurements and theoretical calculations of integral cross sections for electron impact excitation of CO allow the contribution of electron impact to be calculated, giving about 40% of the total. This implies that the abundance of CO in the outer coma of comet Hale‐Bopp was only 60% of that previously deduced. However, as the high proportion of CO in comet Hale‐Bopp was also seen in some other measurements, alternative explanations are considered. The method of calculation is tested by successfully predicting the O I emission at 1356 Å, supporting the belief that this line is due to electron impact excitation.

ASPIN: An all spin scattering code for atom–molecule rovibrationally inelastic cross sections

We present in this work a new computational code for the quantum calculation of integral cross sections for atom–molecule (linear) scattering processes. The atom is taken to be structureless while the molecule can be in its singlet, doublet, or triplet spin states and can be treated as either a rigid rotor or a rovibrational target. All the relevant state-to-state integral cross sections, and their sums over final states, can be calculated with the present code, for which we also describe in detail the various component routines. Program summary Program title: ASPIN Catalogue identifier: AEBO_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEBO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 99 596 No. of bytes in distributed program, including test data, etc.: 1 267 615 Distribution format: tar.gz Programming language: Fortran/MPI Computer: AMD OPTERON COMPUTING SYSTEMS, model TYAN GX28 (B2882) Operating system: SuSE LINUX Professional 9 RAM: 128 GB Classification: 2.6 External routines: LAPACK/BLAS Nature of problem: Scattering of a diatomic molecule in its Σ 1 , Σ 2 , or Σ 3 spin states with an atom in its S 1 state. Partial and integral cross sections. Solution method: The coupled channel equations that describe the scattering process are solved through the propagation of the reactance K matrix employing a modification of the Variable Phase Method [1–3]. Restrictions: Depending on the vib-rotational base used the problem may or may not fit into available RAM memory because all the runtime relevant quantities are stored on RAM memory instead of on disk. Additional comments: Both serial and parallel implementations of the program are provided. The CPC Librarian was not able to successfully run the parallel version. Running time: For simple and converged calculations a usual running time is in the order of a few minutes in the computer mentioned above, being shorter for the singlet and longer for the triplet.

Comment on ‘Electron scattering and ionization of NO, N2O, NO2, NO3 and N2O5 molecules: theoretical cross sections’

In their recent paper, Joshipura et al (2007 J. Phys. B: At. Mol. Opt. Phys. 40 199–210) inadvertently neglected to compare the results of their calculation of integral cross sections for excitation of the sum of all the electronic states in NO to existing experimental data (Brunger et al 2000 J. Phys. B: At. Mol. Opt. Phys. 33 809–19). In this comment such a comparison is now made, with the level of agreement between them found to be marginal.

Quantum mechanical and quasi-classical trajectory reaction probabilities and cross sections for the S(1D) + H2,D2,HD insertion reactions

Time-independent quantum mechanical (QM) and quasi-classical trajectory (QCT) calculations of reaction probabilities at total angular momentum J = 0 as a function of collision energy for the S(1D) + H2(v = 0, j = 0), S(1D) + D2(v = 0, j = 0) and S(1D) + HD(v = 0, j = 0) reactions have been performed on a recent ab initio potential energy surface. In addition, QCT calculations of integral cross sections as a function of collision energy (the excitation functions) have been carried out for the same reactions. The QCT excitation functions and those obtained by applying a capture model to the QM reaction probabilities are compared with the available experimental determinations. The QCT and QM methods reproduce the shape of the measured excitation functions quite satisfactorily. However, the theoretical intramolecular and intermolecular isotope effects are in disagreement with those obtained experimentally.

ACCOUNT OF EXCITATION OF ATOM Ba BY ELECTRONIC IMPACT FROM MAIN AND METASTABLE STATES: R-MATRIXES METHOD WITH PSEUDOSTATES

The recently developed R-matrix method with pseudo-states (in a 37-state closecoupling approximation, 37CC) has been applied in the calculation of integral cross sections for electron-impact excitation of neutral Ba. Results are obtained for transitions from the (6s 2 1 S e ) ground state and the (5d6s 1,3 D е ) excited states to the 16 lowest-excited target states (with principal quantum numbers n = 3, 4, 5), as well as elastic cross sections. Incident electron energies range from threshold to 13.6 eB. In this work the results of integral cross sections calculations from both the elastic scattering (6s 2 1 S e ) - (6s 2 1 S e ) and the resonance transition (6s 2 1 S e ) - (6s6p 1 P 0 ) in the near-threshold region are presented.

Formula for the calculation of integral cross sections in a Fourier expansion method

A method has been developed to calculate the integral cross sections from the measured generalized oscillator strengths that are fitted by a Fourier expansion. The method has been applied to the e-Xe and e-N{sub 2} scattering problems. Excellent agreement has been obtained with existing measured values for the transitions to 5p{sup 5}({sup 2}P{sub 3/2})6s and 5p{sup 5}({sup 2}P{sub 1/2})6s of Xe at 100 and 500 eV. For the vibrational states, v=1{endash}4, of the b{sup 1}{Pi}{sub u} electronic state of N{sub 2} at 300 eV, good agreement with the data calculated by the Lassettre expansion has also been achieved. {copyright} {ital 1997} {ital The American Physical Society}

Calculation of integral cross sections for vibrationally inelastic electron-methane scattering

Integral cross sections are presented for vibrationally inelastic electron-methane scattering. They were calculated by a method which is an extension of the single-centre expansion approach previously applied by us to elastic electron-molecule scattering. The scattering wavefunction is first calculated within the adiabatic nuclei approximation, and is then substituted once into the Lippmann-Schwinger equation in order to correct for non-adiabaticity. This yields inelastic cross sections in good overall agreement with experiment. Threshold peaks are found in the cross sections for excitation of the infrared active modes. The results show that our method is a promising approach with which to investigate the inelastic scattering of electrons from polyatomic molecules.

Theoretical studies of He(1S)+CH(X 2Π). II. Fully ab initio cross sections for the inelastic scattering and comparison with experiment

We report a series of full close-coupling calculations of integral cross sections for fine structure resolved, rotationally inelastic transitions of CH induced by collisions with He. These calculations use the necessary two CH(X 2Π)+He potential energy surfaces as determined by a variety of ab initio techniques described in the preceeding paper. The calculated N=1→N=2−7 cross sections confirm a previous prediction of preferential population of final state levels in which the electronic wave function of the CH molecule is antisymmetric with respect to reflection in the plane of rotation of the molecule. A generally good overall agreement is found between the energy-dependent cross sections determined in earlier experiments of Macdonald and Liu and appropriate averages of the calculated cross sections. However, small, systematic, qualitative discrepancies persist between theory and experiment. Diagnostic calculations were carried out to identify the cause of these discrepancies. These calculations explored the influence of restrictions in basis set, configuration interaction, and functional forms used in fitting the potential energy surfaces. They also explored the consequences of the dynamical approximations of CH as a rigid rotor and the independence of the CH spin–orbit constant on the approach of the He partner. All these diagnostic calculations generally confirm the anticipated marginal influence of these approximations.

Theoretical studies on the electron-impact excitation of neutral magnesium.

We used the distorted-wave approximation (DWA) and first-order many-body theory (FOMBT) for the calculation of integral cross sections (ICS's), differential cross sections (DCS's), and electron-impact coherence parameters (EICP's) for electron-impact excitation of neutral magnesium for several transitions. In the case of 3${\mathrm{}}^{1}$P excitation, we studied the basis-set dependence of the ICS's, DCS's, and EICP's, we investigated the effect of unitarization on these quantities, and we compared the DWA with FOMBT. We also studied the principal-quantum-number dependence of the EICP's for ${\mathit{n}}^{1}$P (n=3,4,5,6) excitation.

Variational calculation of integral cross sections for the reaction F+H 2→HF+H

Accurate reactive scattering calculations of integral cross sections for the reaction F+H 2 were carried out by utilizing the latest basis contraction techniques developed for the S matrix Kohn variational method. Convergence with respect to increasing the number of K states ( K max) for high J calculations were tested. Calculations using K max2 gave accurate integral cross sections. Computed cross sections using variational CS approximation ( K maxO) were also shown and are correct semi-quantitatively

Quasiclassical trajectory calculations of integral cross sections for highly vibrationally excited Li 2He, Kr systems

On the basis of recently published, bond-distance dependent semiempirical potentials total cross sections have been calculated for Li 2He and Li 2Kr collisions as functions of collision energy and initial vibrational state ν 1 = 0–20 of the molecule, using either the vibrational adiabatic quantum-mechanical infinite-order-sudden (IOS) approximation or vibration-dependent quasiclassical trajectories (QCT). Via the QCT calculations the experimentally observed non-monotonic change of total cross section with changing initial vibrations state could be reproduced and explained. For Li 2 (ν 1)He at E tr = 0.08 eV the vibrational and rotational inelastic cross sections at ν 1 = 20 are significantly larger than for ν 1 = 0.

Quantum-mechanical calculation of integral cross sections for the reaction F+H 2( v=0, j=0)→FH( v′ j′)+H by the hyperspherical method

A close-coupling calculation of integral cross sections for the reaction F+H 2( v=0, j=0)→FH( v′ j′)+H has been performed in the threshold energy range using hyperspherical coordinates. The convergence of partial reaction probabilities with respect to Ω m, the maximum magnitude of the total angular momentum projection onto the axis of least inertia, has been studied. Production runs have been done with Ω m=3. A limited comparison with experimental data is performed.

Hyperspherical close-coupling calculation of integral cross sections for the reaction H+H 2→H 2+H

A close-coupling calculation of integral cross sections for the reaction H + H 2( v=0, j=0) → H 2( v′, odd j′) + H has been performed in the energy range E tot=0.9–1.4 eV using hyperspherical coordinates. It is in satisfactory agreement with recent calculations using ▪ methods, showing no resonance structure, in contrast with recent experiments. The quantization axis for the internal motion is chosen as the axis of least inertia and the basis set used to describe internal motions does not depend on total angular momentum J. The convergence of the results with respect to Ω m, the maximum projection of the total angular momentum, has been studied. A calculation with Ω m=1 produces semi-quantitative v′=1 cross sections using a small amount of computer time and a calculation with Ω m=3 is sufficient to converge v′=1 cross sections.

Reduced dimensionality quantum calculations of integral cross sections for H + H 2(υ = 1) → H 2(υ′ = 0), H 2(υ′ = 1) + H

Reduced dimensionality quantum, rotationally energy averaged integral cross sections for the H + H 2(υ = 1) → H 2(υ′ = 0), H 2(υ′ = 1) + H reactions are presented and compared to the recent centrifugal sudden results of Schatz, for the Porter-Karplus surface. A simple adiabatic analysis is also presented which accounts for the threshold behavior of the total cross section summed over υ′.

Calculation of integral cross sections for electronic excitation

A method is presented to calculate the energy dependence of integral excitation cross sections for energies between 10 and 100 eV in the close coupling approximation. Especially the cross sections which are resolved with respect to the fine structure and the respective projection quantum numbers are obtained. The problem of the computing time for these systems has been solved by a Monte Carlo summation of the partial wave sum for the cross section. Results are presented for the alkali–mercury interaction.

Classical rotational cross sections for H 2—HD and HD—HD collisions

Classical trajectory calculations of integral cross sections for rotationally inelastic collisions of HD-para H 2 and HD—HD were carried out for a wide variety of transitions over a wide range of initial relative translational energies. The results of the HD—H 2 calculations were compared with the quantum effective potential calculations of Chu. It was found that the classical method is in reasonably good agreement with the quantum method for the calculation of rotational transitions of HD at the higher initial translational energies, but the classical method is in poor agreement with quantum results for HD excitation at low energies and for H 2 excitations at all energies.