The centrifugally decoupled exponential distorted wave (CDEDW) approximation for the calculation of rotationally inelastic molecular collision cross se

A new approximate method is presented for the rapid calculation of rotationally inelastic molecular collision cross sections. The method is called the centrifugally decoupled exponential distorted wave (CDEDW) approximation and involves the combination of two well known approximations. The first approximation is the neglect of the off-diagonal coupling terms which arise from the orbital angular momentum operator in the coupled differential equations in the body-fixed axis system. The second approximation is to treat the remaining coupling terms, which arise from the interaction potential, using a unitary perturbation approximation. The CDEDW method is applied to the calculation of total and partial rotationally inelastic cross sections in the ArN₂ system, and detailed comparisons are made with exact and several other types of approximate calculations. Agreement with exact calculations is good and often comparable with the coupled states and p-helicity decoupled approximations. The CDEDW method requires a similar amount of computational effort to the infinite order sudden (IOS) approximation, and we show that for the present system the CDEDW method gives more reliable results.     

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.     

A quantum-mechanical study of chemical reaction and charge-transfer processes in the (Ar + H2)+ system

A three-dimensional quantum-mechanical study of the (Ar + H₂⁺ system within the reactive infinite-order sudden approximation is presented. All four possible channels for chemical reaction and charge transfer were treated simultaneously. The various cross sections deviate by at most 50% from recent trajectory surface hopping results.     

Quantum wave packet calculation of reaction probabilities,cross sections,and rate constants for H+ + LiH → Li + H reaction

The H⁺ + LiH → Li + H reactive scattering has been studied using a quantum real wave packet method. The state‐to‐state and state‐to‐all reaction probabilities for the entitled collision have been calculated at zero total angular momentum. The probabilities for J > 0 are estimated from the J = 0 results by using J‐shifting approximation based on the Capture model. The integral cross sections and thermal rate constants are then calculated. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

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.     

A coupled-states approximation study of Li+-H2 collisions

The recently developed coupled-states approximation for describing atom-molecule collisions is applied in a slightly modified form to the Li⁺-H₂ system. Due to the large anisotropy in the potential, a preferred orientation for rotational excitation exists which suggests the use of l = J-j rather than l = J as the angular momentum quantum number in approximating the eigenvalue of 1² by l(l + 1). Here, J and j are respectively the total and rotator angular momentum quantum numbers. The coupled-states integral and differential cross sections are compared with results of close-coupling calculations at 0.6, 0.9, and 1.2 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.     

Close-coupling elastic and inelastic integral and differential cross sections for Li+ + H2 collisions

The quantum mechanical close-coupling formalism is applied to the study of elastic and rotationally inelastic Li⁺ + H₂ collisions making use of the Kutzelnigg-Staemmler-Hoheisel potential energy surface. Integral and differential cross sections for j = 0 → 0 and j = 0 → 2 are obtained in the collision energy range 0.2 to 0.9 eV and for j = 1 → 1 and j = 1 → 3 at 0.6 eV. A rainbow structure is observed in both the elastic and inelastic angular distributions and a quenching of the fast oscillations is found in the cross sections for j = 1 initially compared to the case j = 0 initially. At 0.6 eV. the calculated quantum mechanical angular distributions are compared to those from a classical trajectory calculation using the same surface and to the experimental ones. The dynamics of rotational excitation in the Li⁺ + H₂ system is contrasted to rotational excitation in systems for which the atom-diatom interaction is predominantly repulsive.     

Exploring the reaction dynamics of O(3P)+ (X2 )→OH+(X3Σ−)+ H(2S) reaction with time‐dependent wave packet method

The O(³P)+ reaction has been investigated by employing time‐dependent quantum wave packet with split operator method on potential energy surface of the doublet ground‐state H₂O⁺(1²A″). The reaction probabilities and integral cross sections are calculated using centrifugal sudden approximation, which basically agree with the quasi‐classical results of Paniagua et al. [Phys. Chem. Chem. Phys. 2014, 16, 23594]. Moreover, the effect of vibrational and rotational excitation of reactant is investigated. The results show that the vibrational and rotational excitation effects on the integral cross section are not obvious. The little differences between Coriolis coupling results and centrifugal sudden approximation ones show that the cheaper centrifugal sudden calculations here reported are effective for this reaction.     

Time-dependent close coupling for vibrational excitation in three dimensions: Application to H+ - H2

Impact parameter calculations for the non-reactive H⁺ + H₂ (n_i = 0) → H⁺ + H₂ (n_f) collision are reported for energies 10 eV ? E_cm ? 200 eV describing the rotational motion of the molecule in the sudden limit. The time-dependent Schrödinger equation for the vibrational motion has been solved by close coupling techniques expanding the vibrational wavefunction into both harmonic and numerically exact H₂ bound states. The convergence in vibrational basis sets, where up to six vibrational levels are considered, becomes worse with decreasing energy and increasing inelasticity. Furthermore, the harmonic wavefunctions are not suitable over a large range of energies to calculate proper cross sections. The various integral and differential cross sections have been compared with the classical results of Giese and Gentry.     

Fully converged sudden rotation total integral cross sections for 4He + H2 (ν = 0, j = 0) → 4He + H2 (ν′ = 1, j′)

Total integral cross sections for ⁴He + H₂ (ν = 0, j = 0) → ⁴He + H₂ (ν′ = 1, j′ = 0, 2) have been calculated in the total energy range 1.2 to 5.5 eV, according to a quantal sudden approximation for the H₂ rotational degrees of freedom and a close coupling expansion of the vibrational degree of freedom. Convergence of the above cross sections is investigated by employing four vibration basis sets in the close coupling calculations, i.e., ν = 0,1, ν = 0,1, 2, ν = 0, 1, 2, 3 and ν = 0, 1, 2, 3, 4. Between 4.2 and 5.5 eV calculations were done with three vibration basis sets; ν = 0.–4, ν = 0–5, and ν = 0–6. It is found that at least four vibrational basis functions are needed to converge (to within 5–10%) these cross sections in the above energy range. Comparison of breathing sphere calculations and summed sudden rotation results shows good agreement for the (weakly anisotropic) Mies-Krauss potential. However, as expected the former results underestimate the vibrational 0 → 1 total integral cross sections.     

Collisions at thermal energy between metastable hydrogen atoms and hydrogen molecules: total and differential cross sections

A metastable hydrogen (deuterium) atom source in which groundstate atoms produced by a RF discharge dissociator are bombarded by electrons, provides a relatively large amount of slow metastable atoms (velocity 3–5 km/s). Total integral cross sections for H*(D*)(2s) + H₂(X ¹Σ _g ⁺ ,v=0) collisions have been measured in a wide range of relative velocity (2,5–30 km/s), by using the attenuation method. A significant improvement of accuracy is obtained, with respect to previous measurements, at low relative velocities. Total cross sections for H* and D*, as functions of the relative velocity, are different, especially in the low velocity range. H* + H₂ total differential cross sections have also been measured, with an angular spread of 3.6°, for two different collision energy distributions, centered respectively at 100 meV and 390 meV. A first attempt of theoretical analysis of the cross sections, by means of an optical potential, is presented.     

Computational tests of the factorization of cross sections in the sudden approximation

The factorization expressions for cross sections reported by Goldflam, Green and Kouri and independently by Khare are tested using accurate close coupling input for e^? + H₂, H + H₂, He + (HF, DF, HCl, DCl) and Ar + N₂. The results at the degeneracy averaged cross section level are used to illustrate accuracy criteria given for the factorization. Effects studied include variation of the projectile reduced mass, influence of initial and final rotor state, collision energy and potential anisotropy.     

Quantum wave packet and quasiclassical trajectory studies of the reaction H(2S) + CH(X2Π; v = 0, j = 1) → C(1D) + H2(X1 ): Coriolis coupling effects and stereodynamics

The quantum mechanics (QM) and quasiclassical trajectory (QCT) calculations have been carried out for the title reaction with the ground minimal allowed rotational state of CH (j = 1) on the 1 ¹A′ potential energy surface. For the reaction probability at total angular momentum J = 0, a similar trend of the QM and QCT calculations is observed, and the QM results are larger than the latter almost in the whole considered energy range (0.1–1.5 eV). The QCT integral cross sections are larger than the QM results with centrifugal sudden approximation, while smaller than those from QM method including Coriolis coupling for collision energies bigger than 0.25 eV. The quantum wave‐packet computations show that the Coriolis coupling effects get more and more pronounced with increasing of J. In addition to the scalar properties, the stereodynamical properties, such as the average rotational alignment factor <P₂( j′?k )>, the angular distributions P(θ_r), P(?_r), P(θ_r,?_r), and the polarization‐dependent generalized differential cross sections have been explored in detail by QCT approach. © 2013 Wiley Periodicals, Inc.     

Exponential perturbation theories for inelastic scattering

An Exponential Perturbation Theory (EPT) is derived whereby one calculates a phase-shift matrix by an nth order perturbation theory and then exponentiates it to obtain the scattering matrix. The theory has been developed to include high-order terms, closed channels and resonances. The radial wavefunctions used are WKB solutions which are generalized to cases where there are multiple turning points. The orbital angular momentum may be treated exactly or in the classical or sudden limits. Calculations are done for the rotationally inelastic scattering in He + H₂, Ar + N₂ and Ar + HCl. The first two systems give fair to good agreement with accurate calculations; the last case gives poor agreement. The first-order EPT is very much better than the first-order distorted-wave approximation.     

Integral and differential cross sections for the heavy-light-heavy cihci reaction. A quantum mechanical study within the infinite order sudden approximation

In this communication we present quantum mechanical integral and differential cross sections for the reaction HCl(ν_i = 0) + Cl′ → HCl′ + Cl. The calculations employed the the infinite order sudden approximation. The characteristic oscillations encountered in collinear calculations were still apparent in three dimensions.     

Energy dependence of reaction cross sections at high energy

The energy dependence of the total reaction cross sections for the reaction A + BC → AB + C is obtained in the sufficiently high energy regime, based on the Born approximation and the stationary phase approximation. The total reaction cross section (σ_t) which is a sum over all final vibrational and rotational states of the integral of the angular distribution over angles, is found to be in the form

where Q is the maximum exoergicity and positive. It is shown that, when adjusted to an experimental value, (σ_t) fits remarkably well the cross sections for the reaction K + CH₃I → Kl + CH₃, past the maximum of the cross sections reported by Gersch and Bernstein.     

Differential cross sections for fine-structure inelastic collisions of K(42P) with Ar,Kr and N2

We report measurements of differential cross sections for fine-structure inelastic collisions of potassium (4²P_3/2-4²P_1/2 with Ar, Kr and N₂. The experiment uses crossed molecular beams and a method to detect scattering angles by the analysis of Doppler shifts in laser induced fluorescence. The experimental results for KAr are compared with calculations.