Coupled-state Calculations Research Articles

Coupled states calculations on vibrational relaxation of N +2 in collisions with He

Coupled states calculations on the vibrational relaxation in collisions of N + 2 ( v=1) with He are carried out over a wide range of collision energies. The results are compared with previous semiclassical calculations and with experimental measurements.

New investigation of saturation effect in ion-atom excitation

Excitation cross sections of Kr34+ ions colliding with various target atoms, (Zt between 6 and 40) at nu =35 au have been investigated both experimentally and theoretically. The experimental cross sections were obtained from those for production of projectile He-like and H-like Lyman X-rays. The combined experimental and theoretical analysis of H-like emission allowed for a determination of the competitive capture-ionization process, whose contribution to the Lyman production cross sections is important for near-symmetric collision systems and has to be subtracted. A saturation effect of the experimental excitation cross sections with Zt is analysed from the theoretical point of view through atomic and molecular coupled-state calculations.

Single-centred calculations of excitation and electron removal in intermediate energy proton-hydrogen collisions

Single-centred expansion coupled states calculations are performed with basis sets large enough to achieve convergence. The particular collision system studied is p+H(1s) at energies of 15 keV and above. The results obtained establish the validity of this method for calculating excitation and electron removal cross sections even in situations where charge transfer is large. Cross sections for 1s to 2l', 3l' and 4l' excitation and for electron removal are presented and compared to experiment and to other theoretical calculations.

State-to-state cross sections for rotational excitation of ortho- and para-NH 3 by ortho- and para-H 2. Experiment versus theory

State-to-state cross sections for inversion-rotational excitation of ortho- and para-NH 3, colliding with para-H 2, have been obtained in a crossed molecular beam experiment. State preparation of the 0 + 0 state for ortho-NH 3 and 1 − 1 state for para-NH 3 is achieved by adiabatic expansion of ammonia followed by electrostatic state selection in a hexapole electric field. The NH 3 rotational state distribution is probed by (2+1) REMPI spectroscopy via the B state. From a comparison with previous NH 3—normal-H 2 scattering results relative cross sections are obtained for both NH 3—para-H 2 and NH 3—ortho-H 2 collisions. The experimental values are compared with the results from close coupling and coupled states calculations using ab initio potentials. It is demonstrated that the collisional behaviour of para-H 2 is strongly different from the scattering by He.

State-to-state differential cross sections for rotationally inelastic multiplet-conserving and multiplet-changing collisions of NO(2Π1/2, j=0.5) with Ar

Crossed, pulsed molecular beam measurements of state-to-state differential cross sections have been carried out for scattering of NO(2Π1/2, j=<cf10;1;2≳) by Ar, at a kinetic energy of 442 cm−1. Differential cross sections are presented (1) as functions of center-of-mass (c.m.) scattering angle for multiplet-conserving collisions 2Π1/2→2Π1/2 and final states j′=1.5, 12.5, and 14.5, and (2) as functions of final state j′ for both multiplet-conserving and multiplet-changing collisions 2Π1/2→2Π3/2, at a constant c.m. scattering angle of 50°. Rotational rainbow structure is seen in both types of data. Some of the results are compared with the coupled-states calculations of Joswig, Andresen, and Schinke, J. Chem. Phys. 85, 1904 (1986).

Line-by-line measurements of interference parameters for the 0–1 and 0–2 bands of CO in He, and comparison with coupled-states calculations

Here we present the first line-by-line measurements of interference parameters Y0k describing line-mixing effects in the weak overlapping regime for He-broadened CO lines in the 0–1 and 0–2 bands at 296 K. A detailed analysis of the line shape at intermediate perturber pressures (up to about 10 atm) has been performed, starting from previous theoretical calculations, which has demonstrated the possibility of an individual measurement of Yk parameters. The method is based on the existence of a component of the line shift, quadratic with the perturber pressure (density) and proportional to Y0k. Comparison of our measurements with results predicted from coupled-states calculations shows good overall agreement. Linear pressure shifts have also been simultaneously measured. The uncertainty on the data is important since linear shifts are very small; however, some features can be considered as significant although we have no clear understanding of them. Possible explanations are discussed.

L-shell ionization by antiprotons.

Semiclassical coupled-state model calculations have been performed for L-shell ionization of gold induced by protons and antiprotons in the energy range 0.15--3 MeV. The results of the calculations have been compared with the predictions of a simple approach suggested by Brandt and Basbas for description of antiparticle excitation of atomic inner shells. Apart from the range of very low collision velocities, a reasonable agreement has been found between the two models. In addition to the binding and Coulomb-distortion effects discussed by Brandt and Basbas [Phys. Rev. A 27, 578 (1983); 28, 3142(E) (1983)], for the L shell a further effect due to dynamical couplings between the L-substate ionization amplitudes also contributes to the particle-antiparticle differences. While the latter processes have only a negligible effect on the energy dependence of the cross sections, their inclusion has been shown to be unavoidable when ratios of the subshell ionization cross sections are analyzed for the two kinds of excitation.

The torsional energy levels of ethylene: Interpretation in terms of two internal modes

A recently proposed explanation of an apparent discrepancy between the spectroscopically and thermodynamically determined torsional potential of the ethylene molecule is examined and found to be inadequate. Elaboration of the model, which involves coupling between two internal low-frequency large-amplitude degrees of freedom is carried out in terms of the generalized Jacobi vector (GJV) model to a point which involves a coupled states calculation.

Close-coupling and coupled states calculation of low energy He–CH4 and Ne–CH4 collisions

Exact close-coupling calculations are used to evaluate the effectiveness of the coupled states approximation in the interpretation of low energy, noble gas methane collisions. The effect of the higher order angle dependent terms of the potential on the inelastic rotational transition was investigated. Calculations using only open channel basis functions were clearly different from converged calculations, but the differences were small enough to be negligible in comparison with experiment. It was shown that open channel coupled states calculations are of sufficient accuracy to evaluate the agreement of the potential model with experiment. The use of the coupled states approximation does not fully account for discrepancies between theory and experiment observed earlier.

State-to-state rotational phase coherence effect on the vibration–rotation band shape: An accurate quantum calculation for CO–He

Accurate coupled state calculations of line coupling are performed for infrared lines of carbon monoxide perturbed by helium. Such calculations lead to both real and imaginary line couplings. For the first time, the effect of this imaginary line couplings, connected with state-to-state rotational phase coherences, on infrared band shape, is analyzed. An extension of detailed balance principle to the complex plane is suggested from the present computed off-diagonal cross sections. This allows us to understand the physical mechanism underlying the weak effect of phase coherences on CO–He infrared band shape.

Triple-center determination of differential cross sections for electron transfer and elastic scattering in alpha -H collisions.

Differential cross sections have been calculated for electron transfer and elastic scattering of 20- to 125-keV ..cap alpha.. particles on H(1s) atoms. The transition amplitudes in the eikonal expression for the scattering amplitude are those recently determined in a large triple-center, coupled-state calculation with up to 34 states on the centers, including a third center at the saddle point of the electronic potential. The differential cross sections are compared at 20 and 70 keV with recently reported results using a coupled--molecular-state approach. There is very good agreement at the lower energy, but significant disagreement at the higher energy, particularly in the smaller, more sensitive elastic differential cross section.

Vibrational levels of HD+near dissociation

The transformed Schrodinger equation, in which the g/u symmetry breaking terms appear in the potential energy, is solved in an adiabatic approximation to give vibration-rotation energies and vibrationally averaged Fermi contact parameters near dissociation for the ground and first excited states of HD+. The electronic part of the equation is solved variationally, using basis functions modelled on the Hylleraas expansion. These results are found to be in close agreement with those from a coupled states calculation, for which improved values for other hyperfine parameters are also given. By extending the range of integration in the numerical solution of the vibration-rotation equation, the highest bound levels of HD+ are found to be v=22, J=1 for the ground electronic state and v=1, J=0 for the first excited state.

Inelastic collisions of CaF(A 2Π) with He and Ar: Quantum calculations and adiabatic analysis

We present coupled-states (CS) calculations for collisions of CaF(A 2Π) with He and Ar. These calculations are based on potential energy surfaces determined by use of the Gordon–Kim electron–gas method [J. Chem. Phys. 56, 3122 (1972)]. The theoretical CS cross sections for rotationally inelastic transitions are compared with the experimental results of Dufour and co-workers [Chem. Phys. 98, 315 (1985)]. We obtain theoretical cross sections significantly greater than the experimental values. In order to discuss and interpret the results of our scattering calculations, we make use of a fully adiabatic description of the collision dynamics. This adiabatic analysis shows that the long-range part of the potential plays a key role in determining the sizes of the theoretical cross sections, and in underlying the failure of the energy sudden scaling relation to describe the calculated cross sections.

Coupled state calculations of vacancy transfer probabilities from 2p and 3d rotational coupling in Ar-Mg collisions

For heavy ion-atom collisions at low energies, rotational coupling of the 2pπ-2pσ molecular Orbitals is known to be responsible for K-vacancy production in the lighter collision partner, while 3dδ-3dπ-3dσ rotational coupling is responsible for L-vacancy production in both collision partners. We use the screened classical-path impact parameter formalism to set up and solve the coupled-state equations for the vacancy transfer probability amplitudes in these two cases.

Coupled states calculations on vibrational relaxation in He+CO2(0110) and He+CO

Computations of vibrational relaxation rate coefficients for He+CO2 (0110) and He+CO (ν=1) over the temperature range 100–300 K are reported. The calculations used the quantum mechanical coupled-channel method for vibrations and the coupled states approximation (CSA) for rotations. These calculations were used to test the accuracy of the vibrationally close coupled, rotationally infinite order sudden approximation (VCC-IOSA) and a semiclassical method. For He+CO2, the VCC-IOSA results compare very well with those obtained using the CSA, while the agreement is not so good for He+CO. This is because CO has a much larger rotational constant and vibrational frequency than CO2.

Low-energy electron scattering by the NO molecule

Eigenphase sums and resonance positions and widths are calculated for low-energy elastic impact of electrons on NO molecules using the R-matrix method with numerically defined continuum orbitals. Calculations are performed using both the simple close-coupling and the close-coupling plus short-range polarisation models using up to six electronic states or pseudostates of the NO target. The open-shell, 2 Pi , target is found to show increased sensitivity to polarisation effects which are better represented by coupled-states calculations than by a one-state model with an optical potential. Comparison is made with the available experimental data on e-NO scattering.

Rotational excitation of OH by H2: a comparison between theory and experiment

Comparison is made between close-coupling calculations of cross sections for the rotational excitation of OH by H2 and crossed-beam measurements. Good agreement is obtained for transitions within the 2 Pi 3/2 ladder, although discrepancies remain for inter-ladder (2 Pi 3/2-2 Pi 1/2) transitions. Differences with earlier coupled-states calculations by Schinke and Andresen (1984) are found and discussed.

Convergence of coupled-state calculations for electron capture by bare ions from atomic hydrogen.

We show that the remarkably rapid convergence of the molecular expansion allows an accurate and fast determination of capture cross sections by multicharged ions.Received 18 March 1986DOI:https://doi.org/10.1103/PhysRevA.34.4436©1986 American Physical Society

A coupled states calculation of accurate quantum rate constants for H + H2

AbstractIn this article we present the results of converged quantum reactivescattering calculations of thermal rate constants for H + H2 using the Liu‐Siegbahn‐Truhlar‐Horowitz (LSTH) potential energy surface. These calculations are based on the coupled states (CS) approximation wherein rotational states having different body fixed angular momentum projection quantum numbers are decoupled. By comparision with accurate coupled channel results on the Porter‐Karplus No. 2 (PK2) potential surface, we estimate that the maximumerror in thermal rate constants arising from both this approximation and from other numerical approximations in the calculation is less than 25%. We also show that the sum over projection quantum numbers Ω associated with the CS calculation may be approximated quite accurately in terms of the Ω = 0 rate constants by assuming that the |Ω| > 0 rate constants differ from Ω = 0 by a shift in activation energy, which reflects the vibrationally adiabatic bending energy associated with each Ω.Comparison of the LSTH rate constants with experiment indicates average errors of 16% and 24% relative to the two modern measurementsof the rate constants for H + H2. These errors are reduced to 18% and 9% if the CS rate constants are multiplied by exp(0.0065 eV/kT). The expected error (based on recent quantum structure calculations) associated with the 0.425 eV barrier of theLSTH potential surface is 0.0065 eV. Overall, the agreement of either the LSTH or modified LSTH rate constants with experiment is within the 32% maximum disagreement between the two experimental measurements at all butthe lowest temperature that has been studied.Comparison of our CS rate constants with the results from simpler theories is considered using both the LSTH and PK2 potential surfaces. The best overall agreement is with transition state theories that use accurate dynamical methods to calculate tunnelling factors. These include reduced dimensionality quantum dynamics methods and variational transition state theory using either the Marcus‐Coltrin or least action ground‐state tunnelling paths. Comparison with the results of quasiclassical trajectory calculations indicates substantial errors at low temperatures.

A coupled states reactive scattering study of bending excited resonances in three-dimensional H + H2

Abstract Reaction probabilities from coupled states calculations on the Liu-Siegbahn-Truhlar-Horowitz surface for H+H 2 are calculated for the energy range 0.90–1.30 eV. Peaks in the vibrationally inelastic reaction probabilities near 1.10, 1.20 and 1.22–1.24 eV suggest that bending excited resonances labelled by the quantum numbers (11 1 0), (12 0 0) and (12 2 0) exist.