Scattering of neon atom by nitrogen molecule at thermal and subthermal energies

Collision of Ne atom with N₂ molecule in the thermal and subthermal energy regions (0.01–260 meV) has been thoroughly investigated. Centrifugally decoupled exponential distorted wave (CDEDW) method and the BSTT interaction potential have been used to calculate elastic as well as inelastic (rotational) scattering cross sections. The resonances in the very low energy region,R —Tenergy transfer mechanisms and nature of the rotational excitation cross sections near the threshold have been examined very critically. In general CDEDW method has been found to work quite well in this energy region.     

Distorted wave calculations of vibrational excitation in CO2+He and CO2+Ar collisions

Cross sections for the vibrational excitation and relaxation of CO₂ through collisions with He and Ar atoms have been computed using several approximate methods. They all employ the infinite-order sudden approximation for the rotational motion. The vibrational motion is treated using both exact close-coupling and distorted wave techniques. The latter approximate method permits the extension of the calculation to much higher collision energies. The validity of the distorted wave approximation is examined and is shown to be particularly good for the dominant inelastic processes in He+CO₂, leading to errors of the order of 7%. These become progressively greater for smaller cross sections. The excitation cross sections are reported for several vibrational transitions over an extended energy range up to 1.36 eV.     

Classical rotational and centrifugal sudden approximations for atom—molecule collisional energy transfer

The application of centrifugal and rotational sudden approximations to classical trajectory studies of rotational energy transfer in atom—molecule collisions to examined. Two different types of approximations are considered: a centrifugal sudden (CS) approximation, in which the orbital angular momentum is assumed to be constant during collisions, and a classical infinite order sudden (CIOS) approximation, in which the CS treatment is combined with an energy sudden approximation to totally decouple translational and rotational equations of motion. The treatment of both atom plus linear and nonlinear molecule collisions is described, including the use of rotational action-angle variables for the rotor equations of motion. Applications of both CS and CIOS approaches to rotational energy transfer in He + I₂ collisions are presented. We find the calculated CS and CIOS rotationally inelastic cross sections are in generally good agreement [errors of (typically) 10–50%] with accurate quasiclassical (QC) ones, with the CS results slightly more accurate than CIOS. Both methods are less accurate for small |Δj| transitions than for large |Δj| transitions. Computational savings for the CS and CIOS applications is about a factor of 3 (per trajectory) compared to QC. We also present applications using the CS method to rotational energy transfer in He, Ar, Xe + O₃ collisions, making comparisons with analogous QC results of Stace and Murrell (SM). The agreement between exact and approximate results in these applications is generally excellent, both for the average energy transfer at fixed impact parameters, and for rotationally inelastic cross sections. Results are better for He + O₃ and Ar + O₃ than for Xe + O₃, and better at low temperatures than at high. Since SM's quasiclassical treatment considered only total internal energy transfer without attempting a partitioning between vibration and rotation, while our CS calculation considers only rotational energy transfer, the observed good agreement between our and SM's cross sections indicates that most internal energy transfer in He, Ar, Xe + O₃ is rotational. The relation of this result to models of the activation process in thermal unimolecular rate constant determination is discussed.     

List of subjects

Elastic and inelastic cross sections for well specified m_j-states have been investigated in exact quantum mechanical calculations for H₂—inert gas systems using realistic potentials. The influence of different approximations like the neglect of closed channels and the distorted wave approximation is investigated, especially also in the orbiting resonances of H₂Ar. Compensations of effects of the repulsive and attractive part of the intermolecular potential are found in many cross sections. The diffraction pattern in the inelastic differential cross sections is shown to depend only on k′_j, the wave number of the final state.     

Body-fixed equations for atom-molecule scattering: Exact and centrifugal decoupling methods

We demonstrate an exact method for solving the close-coupled equations for rotationally inelastic scattering in the body-fixed (BF) coordinate representation, using a slight modification of the exponential method which allows application of the known boundary conditions for the space-fixed (SF) coordinate frame. The nature of the coupling in the BF frame suggests approximations which reduce the problem to a set of problems each of a smaller dimensionality. Using an atom-rigid rotor model potential, we have compared the decoupling approximation suggested by Pack and by McGuire and Kouri to the fully coupled problem. We find the centrifugal decoupling (CD) approximation to work best at low total angular momenta J, and for low rotor states j. Opacity functions for inelastic transitions are generally better than ones for elastic transitions, due to errors in the phases of elastic S-matrix elements. However, at high J, CD often severely underestimates the inelastic transition probabilities.     

A further test of the shape and anisotropy of the F---H2 interaction potential

A recently proposed anisotropic potential model for the interaction of a fluorine atom with a hydrogen molecule treated as a rigid rotor analysed by carrying out exact quantum calculations of elastic and rotationally inelastic differential cross sections for comparison with previoully reported F---H₂ and newly measured F---D₂ state selected measurements. The sensitivity of the cross sections to changes of the potential anisotropy and to isotopic substitution is examined. The results provide specific indications on the features of the best potential energy surface in terms of its average ‘size’ and its most likely anisotropy responsible for inelastic rotational excitations occuring at collision energies of about 85 meV.     

Analytic approximations to distorted wave integrals,for inelastic molecular collision cross sections

Several methods-for approximating distorted wave integrals using analytic formulae are presented and compared. The various methods are applied to the calculation of rotationally and vibrationally inelastic HeH₂ collisions and the resulting integrals compared with their exact counterparts. Some of the methods involve the use of the modified wave number approximation. This approximation is shown to break down seriously at large values of the orbital angular momentum. A further important point which is demonstrated is the importance of the region around the outer classical turning point of the two channels involved in the calculation. Among all the methods examined, a recently proposed one based on a generalisation of the well-known Mies formula is found to be the most reliable. A slightly improved version of this method is also developed and tested. Comparison of this improved method with exact calculations establishes its reliability over a large range of energies and total angular momentum quantum numbers.     

Validity of the coupled states approximation for molecular collisions

The process of rotational excitation in the body-fixed frame is examined in detail. Physical arguments are presented to justify the coupled states approximation which involves a diagonalization of the body-fixed centrifugal potential. Cross sections for rotational transitions in HeHCN and in ArN₂ collisions are reported and are compared to exact close coupling cross sections. The coupled states method is found to maintain its high accuracy for the extremely strong-coupling HeHCN system and also for the large Δj transitions in the ArN₂ system even when many partial waves are required. General rules are given for the applicability of this approach in terms of the strength and the position of the anisotropy in the potential energy surface.     

Classical rotational cross sections for H2—HD and HD—HD collisions

Classical trajectory calculations of integral cross sections for rotationally inelastic collisions of HD-para H₂ 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—H₂ 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 H₂ excitations at all energies.     

Elastic and inelastic angular distributions in the jz-conserving coupled states approximation for molecular collisions

An approximation scheme is described which allows the decoupling of molecular rotational j and l angular momenta in molecular collisions. With a particular choice of the interaction potential, the potential matrix couples only the molecular states of the system and in particular those in which the z-axis projection of j is conserved. Test calculations on He + H₂ for the elastic j = O → O and rotationally inelastic j = O → 2 differential cross sections are presented in the energy range 0.1 to 0.9 eV. These results are compared with the full coupled-channel cross sections and are found to be extremely accurate.     

Inelastic collisions between 4He and H2: Study of dynamical approximations

We report a detailed study of the convergence and accuracy of HeH₂ rotationally and ro-vibrationally inelastic cross sections, determined within both the coupled states (CS) and effective potential (EP) formalisms. Two different potential surfaces were used. CS total cross sections appear insensitive to the specific choice of centrifugal barrier. Although the CS results are more accurate, the EP method reproduces the important qualitative features of the various inelastic processes. In addition, with the counting-of-states correction, the EP cross sections for ro-vibrationally inelastic transitions out of low-lying rotational levels agree with the CS values to within a factor of two, with only few exceptions.     

Three dimensional atom-diatom quantum reactive scattering calculations using absorbing potential: speed up of the propagation scheme

In this paper a new propagation scheme is proposed for atom-diatom reactive calculations using a negative imaginary potential (NIP) within a time independent approach. It is based on the calculation of a rotationally adiabatic basis set, the neglected coupling terms being re-added in the following step of the propagation. The results of this approach, which we call two steps rotationally adiabatic coupled states calculations (2-RACS), are compared to those obtained using the adiabatic DVR method (J. C. Light and Z. Bazic, J. Chem. Phys., 1987, 87, 4008; C. Leforestier, J. Chem. Phys., 1991, 94, 6388), to the NIP coupled states results of the team of Baer (D. M. Charutz, I. Last and M. Baer, J. Chem. Phys., 1997, 106, 7654) and to the exact results obtained by Zhang (J. Z. H. Zhang and W. H. Miller, J. Chem. Phys., 1989, 91, 1528) for the D + H(2) reaction. The example of implementation of our method of computation of the adiabatic basis will be given here in the coupled states approximation, as this method has proved to be very efficient in many cases and is quite fast.     

Ar＋TlF体系的转动非弹性散射

本文用一种新的方法求解A+BC体系的转动非弹性散射问题,即在径向耦合方程的势能耦合项中只取对角项,并用Morse势拟合Lennard-Jones势,从而可得去耦合径向方程的两个解集。渐近分析表明,此两个解集分别相应于入射波和出射波。将总波函数按总角动量的本征函数展开,展开系数为常数乘以上述得到的径向函数。再将总波函数代入Schrdinger方程,则可得到散射矩阵。计算结果表明,本法比IOS法更接近CC法,但计算量比后者少得多,且方法严谨。     

On the possibility of orienting rotationally cooled polar molecules in an electric field

We have investigated the effects of initial rotational stateJ and the gas temperature (T) on the rotationally elastic, inelastic and summed processes in CH₄ and SiH₄ molecules by low-energy electron impact. While rotationally summed differential, integral, momentum transfer and energy-loss cross sections are independent of initial stateJ (and hence independent onT), it is found that the same rotationally inelastic differential and integral cross sections, when averaged over rotational distribution function, show a qualitative improvement over the unaveraged results when compared with experimental results. Various theorems regarding the dependence of scattering parameters on the rotational distribution, as described in a series of papers by Shimamura, are discussed by presenting actual calculations on the two spherical tops, namely the CH₄ and SiH₄ molecules.     

Physical analysis of atom-symmetric top collisions

Presented is a study of the general features of rotationally inelastic atom-symmetric top collision systems. This was made possible by employing a newly-developed exponential distorted wave procedure to calculate cross sections rapidly and accurately. It is demonstrated that consideration of the symmetry properties of symmetric tops leads to a reduction in the dimensionality of scattering equations and significant labor savings. Physical trends observed in cross sections and rate constants are shown to be understandable in terms of energetic and coupling concepts.     

The role of rotation in the vibrational relaxation of water by hydrogen molecules

Vibrational relaxation cross sections of the H(2)O(upsilon(2) = 1) bending mode by H(2) molecules are calculated on a recent high-accuracy ab initio potential-energy surface using quasiclassical trajectory calculations. The role of molecular rotation is investigated at a collisional energy of 3500 cm(-1) and it is shown that initial rotational excitation significantly enhances the total (rotationally summed) vibrational relaxation cross sections. A strong and complex dependence on the orientation of the water angular momentum is also observed, suggesting the key role played by the asymmetry of water. Despite the intrinsic limitations of classical mechanics, these exploratory results suggest that quantum approximations based on a complete decoupling of rotation and vibration, such as the widely used vibrational close-coupling (rotational) infinite-order-sudden method, would significantly underestimate rovibrationally inelastic cross sections. We also present some rationale for the absence of dynamical chaos in the scattering process.     

Coriolis coupling effects in the dynamics of deep well reactions: application to the H(+) + D2 reaction

We present exact and estimated quantum differential and integral cross sections as well as product state distributions for the title reaction. We employ a time-dependent wavepacket method including all Coriolis couplings and also an adapted code where the helicity quantum number and with this the Coriolis couplings have been truncated. Results from helicity truncated as well as helicity conserving (HC) calculation are presented. The HC calculations fail to reproduce the exact results due to the influence of the centrifugal barrier. While the truncated calculation overestimate the exact integral cross sections they reproduce the features of the integral cross section very well. We also find that the product rotational state distributions are well reproduced if the maximum helicity state is chosen carefully. The helicity truncated calculations fail to give a good approximation of differential cross sections.     

Model discrimination for rotational energy transfer in the Ar-N2 system

The jackknife test of Rothstein et al. is applied to discrimination between several different models used to compute the rotationally inelastic cross sections for the Ar-N₂ system. The modified exponential models are the best models, except for the case where the energy gap is small, when power laws are best.     

On the decoupling of angular momenta in molecular collisions

It is pointed out that the more exact treatment of the j_z-conserving coupled states (R?-helicity) approximation is quite closely related to the P?-helicity method of Tamir and Shapiro, and the two methods lead to approximate equations identical in form. The difference in interpretation of the magnetic quantum numbers in the two methods is used to understand the accuracy of the crudest approximations obtained by neglecting the transformation from rotating to space-fixed coordinate frames. Further it is expected that the two approaches lead to similar results in the case where the exact diagonal elements of the l² operator are retained and the correct transformations to non-helicity frames are used. Finally, the two methods should lead to identical results for integral cross sections and opacities.     

Inelastic scattering of low-energy electrons by metastable atoms

Cross sections for inelastic collisions of low-energy electrons with metastable atoms in the case of close coupling between different atomic states are obtained in the quasi-statistical approximation. Processes with metastable C, N, O and rare-gas atoms are considered. The calculated cross sections and rate constants are compared with experimental and numerical calculations.