Anharmonicity in rotational and vibrational excitation of H2 by Li+ collisions

Integral cross sections for pure rotational and vibrational-rotational excitation of H₂(X¹Σ⁺_g) by Li⁺(¹S) impact are computed by close-coupling methods at 0.2, 0.6, and 1.2 eV in the c.m. system using vibrational functions that are numerical solutions of the one-dimensional radial Schrödinger equation for harmonic, Morse, and adiabatically corrected Kolos-Wolniewicz (KW) potential functions. Comparison of results employing KW and Morse functions shows excellent agreement for all transitions studied. Findings using harmonic oscillator functions, however, differ noticeably from KW and Morse values for vibrational (0 → 1) and very large rotational (Δj = 10) transitions, but are satisfactory for lower order (0 → 2, 4, 6, 8) rotational transitions.     

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.     

Measurements of differential cross sections for vibrational quantum transitions in scattering of Li+ on H2

A pulsed monoenergetic ⁷Li⁺ ion beam (lab. energy 10–40 eV) is scattered from a highly collimated (= 1.5°) H₂ nozzle beam. The time-of-flight spectrum of the ions scattered in the forward laboratory direction shows both a fast peak corresponding to forward center-of-mass scattering and a slow peak corresponding to wide-angle center-of-mass scattering. These peaks have been further resolved to show contributions from individual vibrational quantum transitions. From an analysis of the time-of flight spectra the differential inelastic cross sections for a wide range of angles and energies between 2 eV <E_cm < 9 eV have been determined. The spectra also contain information on rotational inelastic cross sections.     

Distorted-wave calculations for the three dimensional chemical reaction H + H2(v ⩽ 2, j = 0) → H2(v′ ⩽ 2, j′, mj) + H

Calculations of the vibrational—rotational product state population distributions and differential cross sections for the chemical reaction H + H₂(v ? 2, j = 0) → H₂(v′ ? 2, j′, m_j) + H have been carried out on the Porter—Karplus potential energy surface. The vibrationally-adiabatic-distorted-wave (VADW) method has been used. The relative rotational product distributions, differential cross sections and the helicity m_j, dependences of these quantities for the v = 0 reaction agree well with accurate close-coupling results. The absolute integral cross sections are considerably smaller than the accurate quantum values, however. The calculations for the v = 1 reaction agree with the findings of previous sudden quantum, limited close-coupling and quasiclassical theoretical studies and experiments that product H₂(v′ = 1) is more likely to be produced than H₂(v′ = 0). For the reaction with v = 2, it is found that at high translational energies product H₂(v′ = 2) is favoured over H₂(v′ = 1) or H₂(v′ = 0). The VADW differential cross sections for the v = 1 and v = 2 reactions have a similar shape to those of the v = 0 reaction, with backward peaking when summed over all m_j states. The relative rotational distributions for the v = 2, j = 0 → v′ = 2, j and v = 1, j = 0 → v′ = 1, j reactions are also similar to those obtained for the v = 0, j = 0 → v′ = 0, j reaction, with low rotational excitation.     

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.     

Effect of rotation on vibrational excitation of H2 by Li impact

Coupled channel calculations of integral cross sections for rotational and vibrational excitation of H₂(X¹Σ⁺_g by collision with Li⁺ are reported for 1.2 eV in the c.m. system employing an ab initio potential energy surface and numerical vibration—rotation functions of the Koo?s—Wolniewicz potential function including adiabatic correction. Pure rotational excitation is found to strongly dominate the inelastic scattering occurring at this energy. Preparation of H₂ in various allowed non-zero rotational states is seen to enhance the 0 → 1 vibrational cross section by approximately an order of magnitude.     

Classical trajectory study of rotationally inelastic scattering of two HF molecules

Classical trajectory calculations of the partial opacities and integral cross sections for rotationally inelastic collisions of HF—HF were carried out for the j₁ = 0,j₂ = 0 → (11), (02), (22) transitions at initial relative translational energies of 500, 1000, and 8000 cm^?1 and for the (11) → (02) transition at 1000 cm^?1. Three different methods of relating the initial and final quantum rotational levels to classical distributions were used. The results were compared to the quantum calculations of DePristo and Alexander. It was found that the classical method using a random distribution of initial rotational energies was in poor agreement with the quantum results, while the other two methods which assigned definite classical energies to the quantum levels were in good agreement with the quantum results.     

Comparison of classical mechanics and the coupled states approximation for Li+-CO scattering on an ab initio calculated CI potential energy surface

The dynamics of rotational excitation on an ab initio calculated CI rigid rotor potential energy surface for Li⁺-CO are investigated using classical mechanics and the quantum mechanical coupled-states (CS) approximation. Transition probabilities out of the j = 0 initial level are calculated for various impact parameters between b = 0 and 40a_o for 1 eV collisions. The classical results agree well with the average of Δj-even and Δj-odd quantum transition probabilities except for a few lower impact parameters where CS seems to underestimate the large Δ transitions. No propensity rule is observed for the preference of the Δj-even versus Δj-odd transitions as might have been expected.     

Transfer of state multipoles in excited A 1Σ+u7Li2 following rotationally inelastic collisions with He: Experiment and theory

Circularly polarized dye laser radiation is used to prepare rotational levels j = 1 to j = 20 of the A ¹Σ⁺_u excited state of ⁷Li₂ with well defined values of the state multipoles K = 0, 1 and 2. Inelastic collisions with helium atoms populate other j levels and we have measured the circular polarisation ratio of emission, C, from these levels. C is plotted versus final j′ for each value of Δj from +2 to +18 and a family of curves is obtained which may be used as a critical test of current theories. The results are interpreted in terms of cross sections σ^K for transfer of the state multipoles under isotropic collision conditions. The observation of substantial polarisation following inelastic collision indicates that the σ^K are dominated by certain restricted scattering channels. Relative magnitudes of the multipole cross sections are calculated using the “l-dominant”, “restricted Δm_j channels” nd the Born approximation. These cross sections are then used to calculate C.     

Polarization in elastic scattering: close-coupling studies on ArN2

We present the results of close-coupling calculations of m_j-dependent differential and integral cross sections forj₁ = 2 → j₂ = 2 rotationally elastic ArN₂ collisions. Two potential surfaces were used with differing long-and short-range anisotropies. If the anisotropy is long-ranged the scattering of an isotropic beam results in a significant angle dependent polarization of the elastically scattered products. To a certain extent this reflects a selective loss of m_j-state population due to rotationally inelastic transitions. For quantization along the initial relative velocity vector or perpendicular to the scattering plane, the depolarization of an initially m_j-state selected beam vanishes in the forward direction and is significantly less than the statistical limit at all angles, which indicates a dynamical conservation of the direction of the molecular rotational angular momentum. By contrast, in the helicity frame depolarization is much more pronounced. The oscillatory structure present in the rotationally inelastic differential cross section does not appear to be quenched by the interference between various m → m′ transitions.     

The phase modulated semiclassical sudden approximation. Study of the transitions υ = 1, j → υ = 0 j′ in the pH2 + He4 system

A modified version of the semiclassical sudden approximation is presented. The expressions retain the attractive simplicity of the original sudden theory approximations but they take into account, due to a phase modulation, the adiabaticity modifications which are produced by the transitions between the rotational states. The comparison between the calculated total ro-vibrational and the close coupling cross sections for the couple pH₂ + He ⁴ gives satisfactory agreement. The influence of the non rigidity of the rotator and the role of the intramolecular anharmonicity are studied. The strong influenced of the υ = 2 state on the one quantum transitions (υ = 1, j) → (υ = 0, j′) can also be seen.     

A DWBA study of angular distributions for the state-to-state reactive scattering process of F + H2 → HF + H

Based on our earlier three-dimensional DWBA theory, we discuss angular distributions and the roles of various angular momenta. The theory predicts a relatively small number of partial waves, backward scattering, and broadening of angular distributions with increased energy, for the reaction F+ H₂ (v_a = 0, j_a = 0) → HF (v_b = 2 j_b = 0) + H     

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.     

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.     

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.     

Energy dependence of rotational and vibrational distributions of N2(C) for the Ar*(3P0,2) + N2(X) excitation transfer reaction

The Ar* + N₂(X) → N₂(C, v′, N′) + Ar excitation transfer reaction has been investigated experimentally in two different atomic beam experiments. The inelastic cross sections Q_{v′ = 0}(E) and Q_{v′ = 1}(E) to the v′ vibrational level have been measured in the energy range 0.06 ⩽ E(eV) ⩽ 6, using a crossed beam machine. Both cross sections show a behaviour typical for a curve crossing mechanism, with maximum values Q₀ = 8.0 Ų and Q₁ = 1.2 Ų at E = 0.16 eV and E = 0.13 eV, respectively. The oscillatory behaviour of the ratio Q₁(E)/Q₀(E), as first observed by Cutshall and Muschlitz, is also present in our data. Within the model of Gislason et al. the results indicate a decreasing bond stretching with increasing energy. As an alternative we discuss the possibility that the oscillation is due to a different energy dependence of the cross sections for the Ar*(³P₀) and Ar*(³P₂) fine structure states in the mixed beam of metastable Ar*. The vibrational and rotational distributions have also been measured at E = 0.065 eV in a small scale atomic beam-scattering cell experiment, which can be considered as an intermediate between a bulk experiment and a crossed beam experiment. The relative vibrational populations are n_v′ = 100, 16.0, 3.03 and 0.31 for v′ = 0 through 3, with rotational “temperatures” of T_rot,v′ = 1960, 1010, 370 and 130 K. Pronounced deviations (“hump”) of the Boltzmann rotational distributions occur at N′ ≈ 27 for v′ = 0, 1 and 2, with a fractional population of 1, 3 and 11%. For v′ = 0 the “hump” is largely obscured by overlap with the v′ = 1 bandhead. These bimodal distributions are in qualitative agreement with the results of Nguyen and Sadeghi for v′ = 0. The results are discussed within the framework of a curve crossing mechanism with the Ar⁺-N⁻₂ diabatic potential as an intermediate. By assuming equal charges on both N atoms the Coulomb potential of the collinear orientation lies lower (0.45 eV at R = 2.5 Å) than the perpendicular orientation, with the consequence of different transfer probabilities for both orientations. Within a classical model or rotational excitation the final N′ values can be calculated for both orientations, resulting in much higher N′ values for the perpendicular orientation. This mechanism supplies a qualitative explanation for the observed bimodal rotational distributions.     

Monte Carlo simulation of O(1D) + H2 and O(1D) + HCl — rotational excitation of product OH radicals

Experimental studies with molecular beam and LIF techniques have independently shown that the reaction O(¹D) + H₂ → OH + H passes through a long-lived complex and gives products with small translational and large rotational excitation. We have previously published a statistical algorithm, based on ordinary RRKM theory with angular momentum restrictions included, which was designed to simulate molecular beam experiments. It has now been modified and applied to simulate the experimental rotational OH distributions from O(¹D)+H₂, measured by Luntz et al. The present study also includes simulation of similar results by Luntz for O(¹D) + HCI → OH + Cl. The purely statistical algorithm successfully simulates the apparently non-statistical experimental rotational distributions. For these reactions the total angular momentum conservation. which is applied at the transition state, proves to be decisive for the product energy distributions.     

A coupled states quantum reactive scattering study of H + D2 → HD + D ATErel(υ = j = 0) = 0.55 eV

In this paper we present the results of accurate quantum coupled states calculations for the H + D₂ → HD + D reaction at 0.55 eV translational energy (relative to υ = 0, j = 0) using the accurate LSTH potential surface.     

The rotational excitation and population distribution of OH(A2Σ+) produced by electron impact on water

The rotational excitation and population distributions in OH(A²Σ⁺, υ′ = 0) have been determined by analyzing the OH(A²Σ⁺ → X²Π_i) emission spectrum. The spectrum results from the impact of mon-energetic electrons (0–100 eV) on water vapour. It is shown that these rotational distributions of the OH(A²Σ⁺) state depend on the electron impact energy and have contributions from singlet and triplet states of water. The contribution from each dissociative state of water can be described by a Boltzmann distribution, both in the case of rotational excitation and population.Three distribution parameters (“temperatures”) for rotational excitation are obtained, namely 13800 K and 2900 K for the singlet contributions and 4000 K for the triplet contribution. The corresponding distribution parameters for the rotational population are 30000, 3300, and 4800 K, respectively. The results are discussed in view of recent theoretical calculations on water energy levels.