HD Collisions Research Articles

Inelastic, exchange, and reactive processes in rovibrationally excited collisions of HD with H

ABSTRACT The HD molecule is an important coolant in early universe chemistry models and a tracer of H2 in star-forming regions. Rate coefficients for collisional excitation and de-excitation of HD rotational and vibrational levels form important ingredients in astrophysical models. While collisions with He, H2, and H are the most important, available data for H + HD collisions are largely limited to temperatures less than 1000 K for the vibrational ground state, low-lying rotational levels of the v = 1 HD vibrational level, or computed without reactive contributions. Here, through explicit quantum scattering calculations, we report extensive data for rovibrational transitions in HD induced by H atoms for a range of rotational levels in v = 1 and some v = 0 levels for temperatures up to 1000 K. The significance of the computed results for astrophysical modeling is discussed.

Stereodynamic control of cold rotationally inelastic CO + HD collisions.

Quantum control of molecular collision dynamics is an exciting emerging area of cold collisions. Co-expansion of collision partners in a supersonic molecular beam combined with precise control of their quantum states and alignment/orientation using Stark-induced Adiabatic Raman Passage allows exquisite stereodynamic control of the collision outcome. This approach has recently been demonstrated for rotational quenching of HD in collisions with H2, D2, and He and D2 by He. Here we illustrate this approach for HD(v = 0, j = 2) + CO(v = 0, j = 0) → HD(v' = 0, j') + CO(v' = 0, j') collisions through full-dimensional quantum scattering calculations at collision energies near 1 K. It is shown that the collision dynamics at energies between 0.01-1 K are controlled by an interplay of L = 1 and L = 2 partial wave resonances depending on the final rotational levels of the two molecules. Polarized cross sections resolved into magnetic sub-levels of the initial and final rotational quantum numbers of the two molecules also reveal a significant stereodynamic effect in the cold energy regime. Overall, the stereodynamic effect is controlled by both geometric and dynamical factors, with parity conservation playing an important role in modulating these contributions depending on the particular final state.

Stereodynamics of rotationally inelastic scattering in cold He + HD collisions

Stereodynamics of cold collisions has become a fertile ground for sensitive probe of molecular collisions and control of the collision outcome. A benchmark system for stereodynamic control of rotational transition is He + HD. This system was recently probed experimentally by Perreault et al. by examining quenching from j = 2 to j' = 0 state in the v = 1 vibrational manifold of HD. Here, through explicit quantum scattering calculations on a highly accurate ab initio interaction potential for He + H2, we reveal how a combination of two shape resonances arising from l = 1 and l = 2 partial waves controls the stereodynamic outcome rather than a single l = 2 partial wave attributed in the experiment. Furthermore, for collision energies below 0.5 cm-1, it is shown that stereodynamic preference for the integral cross section follows a simple universal trend.

Stereodynamic control of overlapping resonances in cold molecular collisions

Stereodynamic control of resonant molecular collisions has emerged as a new frontier in cold molecule research. Recent experimental studies have focused on weakly interacting molecular systems such as HD collisions with H$_2$, D$_2$ and He. We report here the possibility of such control in strongly interacting systems taking rotational relaxation in cold collisions of HCl and H$_2$. Using explicit quantum scattering calculations in full six dimensions it is shown that robust control of the collision dynamics is possible even when multiple (overlapping) shape-resonances coexist in a narrow energy range, indicating that cold stereochemistry offers great promise for many molecules beyond simple systems. We demonstrate a striking case where two prominent peaks in overlapping resonances are switched-off simultaneously by suitable alignment of the HCl molecule.

State-resolved rotational cross sections and thermal rate coefficients for [formula omitted] at low temperatures and HD + HD elastic scattering

Results for quantum-mechanical calculations of the integral cross sections and corresponding thermal rate coefficients for para-/ ortho- H 2 + HD collisions are presented. Because of significant astrophysical interest in regard to the cooling of primodial gas the low temperature limit of para-/ ortho- H 2 + HD is investigated. Shape resonances in the rotational state-resolved cross sections have been calculated at low energies. These resonances are important and significantly contribute to the corresponding rotational state-resolved thermal rate coefficients, particularly at low temperatures T ≲ 100 K . Additionally, the cross sections for elastic HD + HD have been calculated. As compared to the two other calculations for H 2 + HD we obtained mixed results, confirming one case but differing in the second case. In our treatment of HD + HD we obtained satisfactory agreement with both theoretical and experimental expectations.

Close-coupling calculations of rotational energy transfer in p-H 2 + HD

We report quantum-mechanical close-coupling calculations for rotational state resolved cross-sections for p-H 2 + HD collisions. The low temperature limit of p-H 2 + HD is investigated, which is of significant astrophysical interest in regard to the cooling of primordial gas and the interstellar media. Sharp resonances have been reproduced in the cross-sections of some transition states at very low kinetic energies, E kin ∼ (10 −4–10 −5) eV.

Low‐Temperature Experiments on the Formation of Deuterated C3H+3

Manydeuteratedmoleculeshavebeendiscoveredininter-andcircumstellarregions.Insomecases,theobserved abundances can be explained with simple thermodynamic models; often, however, isotope enrichment is more complicated. This has been seen recently in detailed low-temperature experiments performed for the fundamental systemsH þ =H2D þ andCH þ =CHn� 1D þ .An unsolvedproblem is toexplainthelarge abundanceofC3H2andlarger hydrocarbons and their deuterated variants observed in cold, dark interstellar clouds. In this work a variabletemperature22poletrapisutilizedforcloselyscrutinizingvariousion-moleculereactionsthatmaycontributetothe formation of C3H2D þ or C3HD þ and, via dissociative recombination, C3HD. The experimental study of the promising candidate C3H þ þ HD ! C3H2D þ þ H2, which has already been excluded by theory, corroborates that this exothermic H-D exchange does not occur at all. A careful analysis of the data reveals that the 15 K rate coefficient is smaller than 4 ; 10 � 16 cm 3 s � 1 . In contrast, quite efficient routes have been found in the lowtemperature experiments, starting with C þ and proceeding via deuterated C3H þ to C3H þ and C3H þ . Formation of C3D þ in C þ þ HD collisions is 6 times faster than assumed in astrochemical models (k ¼ 9:3 ; 10 � 10 cm 3 s � 1 ). Surprisingly, direct production of C3HD þ via radiative association has also been observed (kr ¼ 6:0 ; 10 � 11 cm 3 s � 1 ).ReactionsofpartlyorfullydeuteratedC3H þ þ H2 collisionsystemarestronglydependentontemperatureand thehydrogenorthotopararatio.Inaddition,itshowsverycomplicatedisotopeeffects.Forexample,inC3H þ þ HD collisions the formation of C3HD þ (k ¼ 4:6 ;10 � 10 cm 3 s � 1 ) dominates over the H-D exchange (k ¼ 5:6 ; 10 � 11 cm 3 s � 1 ) and radiative association C3H2D þ (kr ¼ 3:2 ;10 � 11 cm 3 s � 1 ). The reactions of C3H þ þ H2 are very slow for all isotope combinations. Although several questions remain open and more low-temperature experiments are needed, it is recommended that the new values are included in astrochemical databases, since they are fundamental to the correct description of the carbon chemistry in interstellar clouds.

Interference effects in the spectrum of HD: VI: HD–HD, and HD–Kr at room temperature

The absorption spectrum of the fundamental band of hydrogen deuteride (λ ≈ 2.7 μm) has been studied in pure HD and in mixtures with krypton at moderate densities (1–45 amagat) and room temperature, using a high-resolution Fourier transform infrared spectrometer. The effects that arise from interference between the allowed dipole transition moments of free HD and the dipoles induced during collisions were studied. For HD–HD collisions, the eight transitions from P1(3) to R1(4) were analyzed to determine line positions, intensities, shift and broadening coefficients, and the phase shift parameters that govern the interference effects. Thus the interference phenomenon was studied over a wider range of initial- and final-J values than previously possible, and the systematic dependence of the phase shifts on transition was determined. For HD–Kr collisions, the R1(0) and R1(1) transitions were examined in detail. The spectrum in the region of R1(1) exhibited a realtively broad underlying "plateau" feature that was shown to be due to the presence of impurity CF4 molecules in the Kr sample.

Angular momentum dependence of unimolecular decay in a triatomic system

Classical trajectory calculations were performed to determine the lifetime τ of long-lived collision complexes in H+-D2 or D+-HD collisions. For the same complex characterized by total energy and total angular momentum, the lifetimes are independent of (a) the kind of energy supply (i.e. translational or vibrational), and (b) the distribution of the three masses into projectile and target. It was found that τ(J) increases monotonously with J, first linearly, then faster, finally proportional to (J max - J)-1. The shape of τ(J) can be understood in terms of statistical theory if the overall rotation is included in the assumed quasi-equilibrium.

Measurement of rotational energy transfer rates for HD (v=1) in collisions with thermal HD

We report state-to-state rotational energy transfer rates for HD excited to the first excited vibrational level of the ground electronic state. Stimulated Raman scattering is used to produce the rotationally selected, vibrationally excited HD. Subsequent collisional energy transfer from the prepared state, upon collision with a thermal distribution of HD, is monitored by multiphoton ionization through the E,F electronic state. The data are analyzed by solving the rate equations coupling the lowest six rotational states of the first excited vibrational level. In this manner, both the absolute rate constants and the shape of the energy transfer probability density function are determined. The best fit of the data to trial probability density functions indicates that the HD–HD collisions preserve the magnetic sublevel, mj. The total rotational energy transfer rate out of a particular rotational level is compared to high resolution Raman linewidth measurements in order to determine the degree to which the rotational energy transfer rate contributes to the linewidth.

Classical rotational cross sections for H 2—HD and HD—HD collisions

Classical trajectory calculations of integral cross sections for rotationally inelastic collisions of HD-para H 2 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—H 2 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 H 2 excitations at all energies.

State-Resolved Rotational Excitation in HD + HD Collisions

A novel pulsed--molecular-beam technique has been used to measure differential cross sections for state-resolved rotational transitions in HD + HD collisions. Inelastic transition probabilities are reported for the rotation-energy--level transitions J/sub A/J/sub B/ = 00 ..-->.. J/sub A/'J/sub B/' = (10,01), 11, and (20,02) at a center-of-mass scattering angle at 90/sup 0/ and at several collision energies. A brief description of the apparatus is provided.

The born approximation as a simple diagnostic method for direct molecular collisions with applications to Cl + HI and F + H 2 reactions

Born approximation computations are presented and discussed for the Cl + HI → I + HCl and F + H 2 → H + HF reactions and their isotopic analogues. Most aspects of the role of reagent energy or the energy disposal in the products previously deduced from experiment or trajectory computations can be accounted for the Born approximation. The procedure used here neglects the interaction between non-bonded atoms. It does thereby provide a very simple computational scheme which requires as input only the spectroscopic constants of the reactants and products. In addition it offers simple qualitative interpretations of the trends in the results. The overall satisfactory agreement between the present results and past studies lends credibility to the basic propensity rule provided by the Born approximation: The most probable transitions are those that minimize the momentum transfer to the nuclei. The principle is discussed with special reference to exothermic ( E′ T ⪢ E T) and endothermic transitions. The computations for Cl + HI indicate a decline of the reaction cross section with increasing kinetic energy and a strong enhancement by HI rotational energy. The surprisal analysis confirms the absence of vibrational population inversion for endothermic transitions. For the F + H 2 (and isotopic variants) reactions, the product-rotational state distribution extends nearly to the energy cut-off. The vibrational state distribution is somewhat different for para- and normal H 2 and, in general, the collision outcome is very sensitive to the initial rotational state of H 2 particularly at low translational energies. The HF/DF branching ratio is F + HD collisions is increasing with increase of the HD rotational state. The vibrational surprisal is essentially isotopically invariant.

Dynamics of the O+–H2 reaction. II. Reactive and nonreactive scattering of O+(4S3/2) at relative energies above 13 eV

We report velocity vector distributions for the reactive and nonreactive scattering of O+ by H2, D2, and HD in the relative energy range 13–50 eV. Essentially no very small angle reactive scattering is observed for any of these systems. In the lower and intermediate parts of the energy range, the product of the O+(D2, D)OD+ reaction reaches a maximum intensity near 50°, and decreases somewhat at larger angles. This shape is maintained but with decreasing intensity from 15–30 eV relative energy. At higher energies, the distribution moves to larger angles and the intensity continues to drop. From 13–20 eV, OH+ from O+–HD collisions peaks near 35°, and has little intensity at larger angles, while the corresponding OD+ product rises to a broad miximum near 90°, and is only slightly less intense at larger angles. At relative energies above 13 eV the nonreactive scattering of O+ has a major component that corresponds to the elastic impulsive scattering of O+ from one atom of the target. Nonreactive scattering from HD shows two peaks which correspond to impulsive O+–H or O+–D collisions. The experimental results are compared to the predictions of a model in which reaction occurs as the result of those sequences of two-body hard sphere interactions which lead to bound product molecules. The general forms of the product angular distributions and their dependence on the isotopic composition of the target are fairly well represented by the model. For other features such as the experimental energy dependence of the total cross section (σ ∝ Erel−7/2) and the corresponding isotope effect, the model is less successful. A convenient velocity vector diagram method is given which allows a simple, edifying analysis of product angular distributions to be made with a compass and straightedge.

Statistical Phase-Space Theory of the Reaction C+ + D2 Including Threshold Behavior

The quantum-mechanical statistical phase-space theory of Pechukas, Light, and Nikitin is used to calculate the cross sections for the endothermic reaction C+ + D2→CD+ + D in the energy range 0–4 eV. The calculated cross section is about two times larger than the experimental results of Maier (1967) and has almost the same energy dependence below 2 eV. The statistical-theory threshold law is predicted to be valid only for a region less than 0.1 eV from threshold. Two different types of dependence of the reaction probability on incident impact parameter are emphasized, and one is used to explain the magnitude of the predicted cross section in this case. The intramolecular isotope effect in C+ + HD collisions is studied and the CH+ / CD+ product ratio is predicted to be 0.92 at 1 eV.

Inelastic collisions between excited alkali atoms and molecules. V. Sensitized fluorescence in mixtures of sodium with N2, H2, HD, and D2

3 2P1/2 ↔ 3 2P3/2 excitation transfer in sodium, induced in inelastic collisions with ground-state N2, H2, HD, and D2 molecules, has been investigated in a series of sensitized fluorescence experiments. Mixtures of sodium vapor at a pressure of 5 × 10−7 Torr, and the gases, were irradiated with each NaD component in turn, and the fluorescence which contained both D components was monitored at right angles to the direction of the exciting beam. Measurements of the relative intensities of the NaD fluorescent components yielded the following collision cross sections for excitation transfer. For Na–N2 collisions: Q12(2P1/2 → P3/2) = 144 Å2, Q21(2P1,2 ← 2P3/2) = 76 Å2 for Na–H2 collisions: Q12 = 80 Å2, Q21 = 42 Å2. For Na–HD collisions: Q12 = 84 Å2, Q21 = 44 Å2. For Na–D2 collisions: Q12 = 98 Å2, Q21 = 52 Å2. The cross sections Q21 exhibit a slight resonance effect between the atomic and molecular rotational transitions.

Inelastic collisions between excited alkali atoms and molecules. IV. Sensitized fluorescence and quenching in mixtures of cesium with N2, H2, HD, and D2

6 2P1/2 ↔ 6 2P3/2 mixing and 6 2S1/2 ← 6 2P1/2,3/2 quenching in cesium, induced in collisions with ground state N2, H2, HD, and D2 molecules, have been investigated using techniques of sensitized fluorescence. Mixtures of cesium vapor and the gases, in which the cesium vapor pressure was kept very low to avoid multiple scattering, were irradiated with each component of the cesium resonance doublet in turn. The fluorescence which contained both components of the doublet was observed in a direction perpendicular to that of the exciting beam. Measurements of the relative intensities of the fluorescent components yielded the following cross sections for mixing and quenching. For Cs–N2 collisions: Q12(2P1/2 → 2P3/2) = 4.7 Å2, Q21(2P1/2 ← 2P3/2) = 25 Å2, Q10(2S1/2 ← 2P1/2) = 77 Å2, Q20(2S1/2 ← 2P3/2) = 69 Å2. For Cs–H2 collisions: Q12 = 6.7 Å2, Q21 = 44 Å2, Q10 = 7 Å2, Q20 = 5 Å2. For Cs–HD collisions: Q12 = 4.8 Å2, Q21 = 32 Å2, Q10 = 4 Å2, Q20 = 3 Å2. For Cs–D2 collisions: Q12 = 4.2 Å2, Q21 = 28 Å2, Q10 = 8 Å2, Q20 = 7 Å2. The Cs–N2 and Cs–H2 cross sections supersede the values published previously (McGillis and Krause 1967). The cross sections Q21 appear to exhibit resonances with molecular rotational transitions.