Quantum mechanical treatment of the collinear H+ + H2 system. The uncoupled system

A fully converged close coupling study is performed of the collinear (H⁺ + H₂) system on the lower potential energy surface. The surface is derived by the DIMZO (diatomic in molecules-zero overlap) method. Transition probabilities for the reactions: H⁺ + H₂ (ν = 0, 1) → H₂ (ν′) + H⁺; ν′ = 0,..., 7 are given for a number of total energies in the range from 1 eV to 3 eV. It is found that for this energy region the transition ν = 0 → ν′ = 0 is the most preferential. This fact leads us to believe that addition of the upper surface will have a minor effect on the calculated probabilities of transitions from ν = 0 in the above-mentioned energy range.     

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.     

Multiphoton association reaction He + H+ → HeH+ steered by ultra‐short laser pulse

The multiphoton association reaction He + H⁺ → HeH⁺ in the electronic ground state is investigated using the time‐dependent quantum wave packet method. It is shown that the collision pairs He + H⁺ in continuum state transfer into ν = 0 state and then produce stable molecules HeH⁺ through emission of two or three photons. The multiphoton transition takes place via intermediate states, and the transfer probability is determined by the collision energy and the intermediate states. The populations of the intermediate states and ν = 0 state can be controlled by the laser duration. The three‐photon transition is more efficient than the two‐photon transition for producing the molecule HeH⁺ in ν = 0 state. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Determination of the quenching rates of N2+(B2Σu+, ν = 0,1) By N2 using laser-induced fluorescence

Time-resolved fluorescence laser-induced spectroscopy was used to examine the quenching of the vibrational levels ν = 0 and ν = 1 of N₂⁺(B²Σ_u⁺) by N₂. The rate coefficients of the quenching reactions are found to be constant over the temperature range 300–500 K. The quenching constant for the ν = 1 state was found to be approximately twice the value of the quenching constant of the ν = 0 state.     

A new method for the measurement of vibrational-state-selected ion-molecule reactions at thermal energies

A photoelectron-secondary-ion-coincidence method is described that allows us to determine the relative vibrational-energy-dependent cross sections for reactions of molecular ions with neutral atoms or molecules at thermal energies. Results for reactions of H₂⁺(ν) in vibrational states ν = 0–8 with H₂(H₃⁺), Ne(NeH⁺) and He(He⁺) are reported.     

Electronic nonadiabatic transitions in the reactive (Ar+ + H2, Ar + H+2, ArH+ + H) system. Numerical results for the collinear configuration

In this communication are presented exact quantum mechanical nonadiabatic electronic transition probabilities for the collinear reaction Ar⁺ + H₂(v_i = 0) → ArH⁺(v_f) + H. The calculations were performed using a potential surface calculated by the DIM method. It is established that large probabilities (≈ 1.0) can be obtained only if there is enough translational energy to overcome a potential barrier formed due to the crossing between v_i = 0 of the Ar⁺ + H₂ system and v_i = 2 of the Ar + H⁺₂ system. The threshold for the reaction is found to be 0.06 eV.     

A surface hopping quasiclassical trajectory study of the H2+ + H2 and (H2 + D2)+ systems

In this work we use a complete surface hopping quasiclassical trajectory method to determine cross sections for the reactions H₂⁺ + H₂ → H₃⁺ + H and the isotopic variants (H₂⁺ + D₂ and D₂⁺ + H₂). Initial translational energies ranged between 0.5 and 6 eV. The vibrational quantum number (v⁺) of the charged diatom is either 0 or 3. Comparing these results with our previous results with a partial treatment of surface hopping, we find essentially no change for v⁺ = 0 and reductions in cross sections of up to 30% for v⁺ = 3 trajectories.     

Vibrational energy transfer from N2 to CO on electron excitation of N2-CO solids at 4.2 K

Spectra emitted from 0.1% CO-N₂ solids excited with high energy electrons at 4 K show evidence for resonant transfer of vibrational energy from highly excited vibrational levels of N₂ to CO in the process N₂(X¹Σ_g⁺, ν) + CO(ν = 0) → N₂(X¹Σ_g⁺, ν - 1) + CO(ν = 1) + phonons. Energy transfer from levels with ν ? 9 has been observed.     

Kinetics of the reactions OH (v = O) + NH3 →; H2O + NH2 and OH(v = O) + O3 → HO2 + O2 AT 298°K

The rate constants for the reactions OH(X₂Π, ν = O) + NH₃ → ^k1 H₂O + NH₂ and OH(X²Π, ν = O) + O₃^k2 → HO₂ + O₂ were measured at 298°K by the flash photolysis resonance fluorescence technique. The values of the rate constants thus obtained are K₁ = (4.1 ± 0.6) × 10^?14 and k₂ = (6.5 ± 1.0) × 10^?14 in units of cm³ molecule ^?1 sec¹. The results are discussed in terms of understanding the dynamics of the perturbed stratosphere.     

Quantum and quasiclassical study of the collinear reaction O(3P) + H2 → OH + H using a LEPS and fitted AB initio potential energy surface

Accurate quantum calculations of reaction probabilities P^T_ν′←ν have been carried out for the collinear reaction O(³P) + H₂ (ν = 0,1) → OH(ν′) + H using a LEPS and fitted ab initio potential energy surface. The energy dependence of the P^T_{ν′ ← ν} is similar for both surfaces. Collinear quasiclassical trajectory calculations have also been carried out, for comparison, on the LEPS surface for ν = 0, 1 and 2.     

Sensitization of the CN(B2Σ+ → X2Σ+) emission by Hg(63P0) metastables

The vibrational analysis of the CN(B²Σ⁺ → X²Σ⁺) emission sensitized by Hg(6³P₀) metastables has shown that the energy transfer process, Hg(6³P₀) + CN(X²Σ⁺) → Hg(6¹S₀) + CN(B²Σ⁺), populates the CN(B²Σ⁺) state in a non-Franck-Condon fashion. The relative vibrational populations for the ν = 0 to 4 states are 1.00, 0.56 ± 0.06, 0.26 ± 0.03, 0.11 ± 0.03 and 0.04 ± 0.01, respectively. Long-range attractive interaction between the Hg(6³P₀) atom and the CN(X²Σ⁺) radical is evidenced by the observed high rotational excitation of the CN(B²Σ⁺) radical following the energy transfer process.     

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.     

Chemiluminescent ion-molecule reactions in the system C+ + H2

The optical emission resulting from collisions between C⁺ ions and H₂ gas was measured in the energy range 2 to 20 eV_c.m.. The observed spectrum consists mainly of the CH⁺ A ¹Π → X ¹Σ⁺ band system; CH⁺ (A ^fΠ) is shown to be formed in the chemiluminescent reactio: C⁺(²P⁰) + H₂ → CH⁺(A ¹Π) + H(²S). The energy dependence of the emission cross section was measured. The occurrence of this reaction is discussed in terms of a electronic state correlation diagram for the system.     

Theoretical study of the reaction Ne + H+2 → NEH+ + H in the 2A′ ground state

A three-dimensional potential energy surface for the ²A′ ground state of the system (Ne? H₂)⁺ (²Σ⁺ in collinear geometry) has been calculated at SCF and CEPA levels. This surface describes the abstraction reaction which is endoergic by 0.57 eV (ΔH⁰₀) and has been studied recently by different experimental groups at low collision energies. Our CEPA calculations yield an endoergicity of 0.55 eV (ΔH⁰₀). The ²A′ surface has a minimum at collinear geometry with R_Ne—H = 2.29 a₀ and R_{H? H} = 2.08 a₀ and a well depth of 0.49 eV relative to Ne + H⁺₂. The effects of electron correlation on the shape of the surface and on the well depth are discussed. An analytic fit of the collinear part of the surface has been constructed based on Simon's proposal of using polynomials in the coordinates (R? R_e)/R instead of (R? R_e). The fitted potential is used for quantum mechanical scattering calculations with the finite element method (FEM ). Preliminary results for reaction probabilities for H⁺₂ in different vibrationally excited states are given and compared to the experimental results.     

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.     

Resonance-enhanced multiphoton ionization of molecular hydrogen via the E,F1Σg+ state: Photoelectron energy and angular distributions

Photoelectron energy and angular distributions are measured for the 2+1 multiphoton ionization process H₂ X¹Σ_g⁺ (ν = 0,J) + 2hv → E,F¹Σ_g⁺(ν_E,J_E = J) + hν → H₂⁺X²Σ_g⁺ (ν⁺) + e^?, for ν_E = 0, 1, or 2 and for J_E = 0 or 1 of the inner well of the double-minimum E,F state. Although a strong preference is found for ν⁺ = ν_E, the detailed H₂⁺ vibrational distribution does not exhibit Franck-Condon behavior, and the photoelectron angular distributions vary markedly with both the J_E value of the intermediate state and the ν⁺ value of the ion.     

Mobilities of H+3 and HeH+ ions in helium gas and rate coefficient for HeH+ + H2 → H+3 + He

The mobilities of mass-identified H⁺₃ and HeH⁺ ions in helium and the reaction rate coefficient for HeH⁺ + H₂ → H⁺₃ + He have been measured by a drift-tube quadrupole mass spectrometer at 300 K. The zero-field reduced mobilities of H⁺₃ and HeH⁺ ions, corrected to 273 K, are 31.0 ± 0.8 and 23.4 ± 0.6 cm² V^?1 s^?1 respectively. The reaction rate coefficient was found to be (1.26 + 0.16) × 10^?9 cm³s^?1 and was observed to be independent of the mean ion kinetic energy in the range from 0.04 to 0.3 eV.     

Vibrational relaxation in atom exchange reactions: A classical trajectory study of H + H2(ν) and D + D2(ν) collisions using an accurate potential

A quasiclassical trajectory study has been carried out to investigate the dynamics of collisions between H + H₂(1 ? ν ? 4) and D + D₂(1 ? ν ? 4), using the accurate Yates-Lester potential. Reaction is selectively enhanced by the vibrational excitation of the diatomic reagent, as judged by information theory, but the degree of selectivity falls as the vibrational energy is successively increased. The calculated results are in fair agreement with experimental measurements on the removal of H₂(ν = 1) by H but not with those for D₂(ν = 1) by D.     

Electronic transitions in collinear H+ + D2 (ν = 0) → HD+ (ν = 0,1) + D via classical trajectories in complex time and complex phase space

A semiclassical treatment of electronic transitions in the collinear rearrangement H⁺ + D₂ (ν = 0) → HD⁺ (ν = 0,1) + D is presented. The treatment represents an extension of Stueckelberg's method for a single nuclear degree of freedom to collisions involving several nuclear degrees of freedom. The classical limit of scattering amplitudes (S-matrix elements) is calculated for the transition between the two adiabatic potential energy surfaces corresponding to the two lowest singlet states of HD⁺₂. S-matrix elements are constructed from trajectories propagating in complex time and complex phase space, which make localized transitions between the two surfaces by crossing their complex line of intersection. The action along each trajectory acquires an imaginary part, which contributes exponential damping to the corresponding amplitude for electronic transition.     

Vibration-rotation transition probabilities in CH+ and CD+

Vibrational dipole matrix elements and radiative transition probabilities have been evaluated from electric dipole moment functions for the X¹Σ⁺ states of CH⁺ and CD⁺, which were calculated from highly correlated electronic wavefunctions. The dipole moments in ν = 0 amount to 1.679 D (CH⁺) and 1.313 D (CD⁺), respectively. In comparison to other molecular ions the infrared transition probabilities are found to be rather small. For instance, the Einstein coefficient of spontaneous emission A¹₀ amounts to 1.63 s⁻¹ (CH⁺) and 0.19 s⁻¹ (CD⁺). Dipole moment functions of the neutral CH species in the X²Π and a⁴ Σ⁻ states have also been calculated and are compared with previous theoretical functions.