Vibrationally resolved charge transfer ofO3+with molecular hydrogen

Rotational energy transfer in collisions of nitrogen molecules has been studied theoretically, using the N2–N2 rigid-rotor potential of van der Avoird et al. [J. Chem. Phys. 84, 1629 (1986)]. For benchmarking purposes, converged close coupling (CC) calculations have been carried out to a total energy of about 200 cm−1. Coupled states (CS) approximation calculations have been carried out to a total energy of 680 cm−1, and infinite order sudden (IOS) approximation calculations have also been carried out. The CC and CS cross sections have been obtained both with and without identical molecule exchange symmetry, whereas exchange was neglected in the IOS calculations. The CS results track the CC cross sections rather well: between 113–219 cm−1 the average deviation is 14%, with accuracy improving at higher energy. Comparison between the CS and IOS cross sections at the high energy end of the CS calculations, 500–680 cm−1, shows that IOS is sensitive to the amount of inelasticity and the results for large ΔJ transitions are subject to larger errors. State-to-state cross sections with even and odd exchange symmetry agree to better than 2% and are well represented as a sum of direct and exchange cross sections for distinguishable molecules, an indication of the applicability of a classical treatment for this system. This result, however, does not apply to partial cross sections for given total J, but arises from a near cancellation of the interference terms between even and odd exchange symmetries on summing over partial waves. In order to compare with experimental data for rotational excitation rates of N2 in the n=1 excited vibrational level colliding with ground vibrational level (n=0) bath N2 molecules, it is assumed that exchange scattering between molecules in different vibrational levels is negligible and direct scattering is independent of n so that distinguishable molecule rigid rotor rates may be used. With these assumptions good agreement is obtained. Although the IOS approximation itself is found to provide only moderately accurate values for rate constants, IOS/ECS scaling methods, especially if based on fundamental rates obtained from coupled channel results, are found to provide generally good accuracy.

The distorted wave infinite order sudden (DWIOS) approximation for the calculation of vibrationally inelastic molecular collision cross sections

Vibrationally and rotationally elastic and inelastic collisions between He and I/sub 2/ in the total energy range of 0.044-0.5 eV are treated under the vibrational/rotational infinite-order sudden approximation (VRIOSA). In this method, one simultaneously makes the vibrational energy sudden, rotational energy sudden, and centrifugal sudden approximations and generates a completely uncoupled set of equations. The solution of these equations is discussed and the integral and differential cross sections, the integral and differential cross sections summed over final rotational states, the integral cross sections summed over final rotational and vibrational states, and a type of cross section which recently has been measured experimentally are presented and compared with vibrational close-coupled infinite-order sudden approximation results. The dependence of the accuracy of the VRIOSA upon the choice of the arbitrary vibrational quantum number parameters, n vector, is also investigated. Setting n vector equal to the final vibrational quantum number gives good results for the integral and experimental cross sections, while picking n vector equal to the average of the initial and final vibrational quantum numbers gives good results for the differential cross sections. The present comparisons involving a full three-dimensional system and quantities, such as the differential cross section, which are sensitive tomore » the phase of the S matrix extend earlier, more limited studies and show that the VRIOSA should be considered convenient and reliable for light atom-heavy diatomic molecule collisions at total energies up to a few electronvolts.« less

Classical trajectory calculations of effective cross sections have been carried out for the N2-Ne system using the recent HFD3(N2-Ne) potential surface of McCourt et al. Forty-five such cross sections governing a wide variety of transport and relaxation phenomena in binary gaseous mixtures have been calculated at a number of temperatures ranging from 77K to 1100K. Wherever possible, we have made comparisons with much cheaper infinite-order sudden approximation (IOSA) calculations in order to assess their reliability. For cross sections relating to diffusion and viscosity, IOSA errors are less than 5·4 per cent, but, for cross sections which vanish for isotropic interactions, the IOSA is much less reliable, with possible errors of up to a factor of two. At the same time, we have compared our classical trajectory results for this surface with available experimental results. We find that the HFD3(N2-Ne) surface is too anisotropic, by as much as 20 per cent.

A classical reactive study within the infinite order sudden approximation: integral cross sections for the reactions F + H 2vi = 0) → HF( vf = 0,1,2,3) + H

Test of the infinite-order sudden approximation for electron scattering at intermediate energy

A quantum mechanical study is made of the D+H2(vi=0,1)→ HD(vf=0,1,2)+H reactions within the infinite order sudden approximation (IOSA) for the total energy interval 0.28≤Et≤1.28 eV. Results at various stages of the calculation are given ranging from most detailed reactive transition probabilities through opacity functions and γ-dependent cross sections to total and state-to-state integral and differential cross sections, as well as rate constants. The cross sections and rate constants are compared with other available theoretical results and experiments. It is found that the IOSA total cross sections for vi=0,1 overlap very nicely with the corresponding quasiclassical trajectory cross sections, except for the tunneling region. A less satisfactory fit is obtained with the distorted wave born approximation results. The calculated rate constants are compared with experiment and a rather good fit is obtained, in particular for rate constants from the ground state.

Similarly to differential cross sections for one-electron photoionization, the doubly differential cross section for double photoionization (DPI) may be conveniently described by four parameters: the singly differential (with respect to energy sharing) cross section (σ0), the dipole asymmetry parameter (β), and two nondipole asymmetry parameters (Y and δ). Here we derive two model-independent representations for these parameters for DPI from a S01 atomic bound state: (i) in terms of one-dimensional integrals of the polarization-invariant DPI amplitudes and (ii) in terms of the exact two-electron reduced matrix elements. For DPI of He at excess energies, Eexc, of 100 eV, 450 eV, and 1 keV, we present numerical results for the asymmetry parameters within the framework of the convergent close-coupling theory and compare them with results of lowest-order (in the interelectron interaction) perturbation theory (LOPT). The results for Eexc=1keV exhibit a nondipole asymmetry that is large enough to be easily measured experimentally. We find excellent agreement between our LOPT results and other theoretical predictions and experimental data for total cross sections and ratios of double to single ionization cross sections for K-shell DPI from several multielectron atoms.

An irreducible tensor formalism is applied to isotropic collisions of diatomic molecules with 1S atoms. Explicit expressions of the generalized spectroscopic relaxation cross sections are given, including pressure broadening cross sections as well as collisional transfer and destruction cross sections of the k-component of the target density matrix. For applications in the high temperature limit, formulae within the infinite order sudden approximation (IOS) are given for 1Σ electronic state molecules and 2S+1Σ electronic state molecules in the Hund's case (b) limit. Application to collisions of CS by He atoms shows that a good agreement is found between close coupling and IOS results at moderate energies and that multipolar depolarizing rates within a j-level are of the same order of magnitude whatever the considered multipole order k whereas multipolar transfer rates are lower by an order of magnitude. Propensity rules in relation to the CS–He potential energy surface are given.

In this article is described a three-dimensional quantum mechanical study within the nonreactive infinite order sudden approximation (IOSA) of the title system. The study was performed using a recently introduced global potential energy surface [J. Chem. Phys. 102, 6696 (1995)]. Integral total cross sections for the two separate products, namely, N2O+H and N2+OH, were calculated as a function of kinetic energy in the range 0.05–0.50 eV. Our main findings are (a) the overall cross sections and the cross sections for N2O+H are only mildly dependent on the energy; (b) the cross sections for N2+OH, in conrast to those for N2O+H, depend on the energy and increase as the energy increases; (c) the yield of N2O+H is about 80–90 % of the total yield, in accordance with experiment; (d) the overall cross sections are about 1 to 3 times smaller than the quasiclassical-trajectory ones and about 5 to 15 times smaller than the experimental ones.

Charge transfer cross sections for collisions of ground state and excited state with atomic hydrogen are presented for energies less than . The cross sections are calculated in a diabatic representation using a fully quantum-mechanical, molecular-orbital, close-coupled method. Completely ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond method are incorporated. Inclusion of the and closed-channels results in oscillations in the charge transfer cross section for collision energies above the separated-atom energy of the lowest closed-channel . Rate coefficients for temperatures between 500 and 100 000 K and cross sections for collisions with isotopic D are presented. Results for the reverse process, charge transfer ionization, are also given.

Recent work is reviewed on the theory of angular momentum decoupling approximations in inelastic molecular scattering theory. It is shown that the failure of these approximations is more extensive than previously believed, particularly for completely state-selected m transitions. A systematic study of a number of centrifugal sudden approximations is made and discussed. A new method is presented for improving these approximations, which recouples the approximate solutions. Completely state-selected differential and integral cross sections are computed under the centrifugal decoupling approximation and its correction for Ne+HD scattering at a total energy of 31.5 meV. Five choices of the partial wave decoupling parameter (including the three known ones) are studied. The numerical results show that with the partial wave parameter chosen to be the arithmetic mean of the initial and final l-quantum numbers, the coupled states approximation gives excellent results for orientation averaged transitions, but fails dramatically for state-selected m transitions. The corrected centrifugal decoupling approximation gives significantly more accurate inelastic differential and integral state-selected cross sections than its uncorrected counterpart. The extension of this correction technique to the energy sudden and the infinite order sudden approximations is discussed.

Time independent quantum scattering calculations have been carried out on the SN2 Walden inversion reaction Cl−+CH3Cl(v,k)→ClCH3(v′,k′)+Cl−. The two C–Cl stretching degrees of freedom (quantum numbers v and v′) and the azimuthal angle describing the rotation of the CH3 group (quantum numbers k and k′) are treated explicitly. An infinite order sudden approximation has been introduced using Radau coordinates for the stretching modes. The potential energy surface of Vande Linde and Hase is used. The scattering problem is formulated in hyperspherical coordinates. For the reaction (k=0→k′=0) substitution is observed for initial vibrational excitation with v⩾2. If the system departs from the collinear reaction pathway (initial rotational excitation) the substitution cross sections are strongly decreased. The state-to-state cross sections σvk→v′k′ are large only for transitions with Δk=0. The total reaction cross sections σvk for given v vary only slightly at low values of the azimuthal quantum number k and rise for larger values of k. This is explained by multiple (avoided) crossings of the hyperspherical adiabats.

Differential and integral cross sections for the rotational excitation of Na2 in collisions with He at 0.1 eV are calculated in the coupled states and the rotationally sudden approximation. The final rotational state distribution at fixed scattering angle exhibits an interference structure similar to the usual rainbow pattern in potential scattering, namely, a broad main rainbow maximum for high Δj transitions and ’’supernumerary’’ oscillations on the bright side of the rotational rainbow for lower Δj transitions. This rainbow effect is explained in the stationary phase limit of the sudden approximation by interferences between’’trajectories’’ from different atom–molecule orientations. It is shown that the oscillations in the rotational distribution at fixed angle are equivalent to the oscillations vs scattering angle for a single rotational transition as reported by Schinke [Chem. Phys. 34, 65 (1978)]. The sudden cross sections are in satisfactory accord with the coupled-states results, when the average rotational state ? is choosen to reflect energy conservation.

The coupled-channels optical method is used to study the electron-magnesium scattering process at intermediate energies. Continuum optical potentials were included in the calculations. Differential and total cross sections are reported for the elastic and inelastic (31P and 33P) transitions at 10, 20 and 40 eV. The present calculations show fair agreement with experimental data for differential and total cross sections.