Statistical modeling of ion–molecule electrostatic capture

Multipole-moment effects in ion-molecule reactions at low temperatures: part II - charge-quadrupole-interaction-induced suppression of the He+ + N2 reaction at collision energies below kB·10 K

We report on an experimental and theoretical investigation of the He+ + N2 reaction at collision energies in the range between 0 and kB·10 K. The reaction is studied within the orbit of a highly excited Rydberg electron after merging a beam of He Rydberg atoms (He(n), n is the principal quantum number), with a supersonic beam of ground-state N2 molecules using a surface-electrode Rydberg-Stark decelerator and deflector. The collision energy Ecoll is varied by changing the velocity of the He(n) atoms for a fixed velocity of the N2 beam and the relative yields of the ionic reaction products N+ and N2+ are monitored in a time-of-flight mass spectrometer. We observe a reduction of the total reaction-product yield of ∼30% as Ecoll is reduced from ≈kB·10 K to zero. An adiabatic capture model is used to calculate the rotational-state-dependent interaction potentials experienced by the N2 molecules in the electric field of the He+ ion and the corresponding collision-energy-dependent capture rate coefficients. The total collision-energy-dependent capture rate coefficient is then determined by summing over the contributions of the N2 rotational states populated at the 7.0 K rotational temperature of the supersonic beam. The measured and calculated rate coefficients are in good agreement, which enables us to attribute the observed reduction of the reaction rate at low collision energies to the negative quadrupole moment, Qzz, of the N2 molecules. The effect of the sign of the quadrupole moment is illustrated by calculations of the rotational-state-dependent capture rate coefficients for ion-molecule reactions involving N2 (negative Qzz value) and H2 (positive Qzz value) for |J, M〉 rotational states with J ≤ 5 (M is the quantum number associated with the projection of the rotational angular momentum vector J⃑ on the collision axis). With decreasing value of |M|, J⃑ gradually aligns perpendicularly to the collision axis, leading to increasingly repulsive (attractive) interaction potentials for diatomic molecules with positive (negative) Qzz values and to reaction rate coefficients that decrease (increase) with decreasing collision energies.

Benchmarking an improved statistical adiabatic channel model for competing inelastic and reactive processes

Inelastic collisions and elementary chemical reactions proceeding through the formation and subsequent decay of an intermediate collision complex, with an associated deep well on the potential energy surface, pose a challenge for accurate fully quantum mechanical approaches, such as the close-coupling method. In this study, we report on the theoretical prediction of temperature-dependent state-to-state rate coefficients for these complex-mode processes, using a statistical quantum method. This statistical adiabatic channel model is benchmarked by a direct comparison using accurate rate coefficients from the literature for a number of systems (H₂ + H⁺, HD + H⁺, SH⁺ + H, and CH⁺ + H) of interest in astrochemistry and astrophysics. For all of the systems considered, an error of less than factor 2 was found, at least for the dominant transitions and at low temperatures, which is sufficiently accurate for applications in the above mentioned disciplines.

Influence of internal rotation on exothermic reactions between neutral molecules at low temperatures

A Langevin-type transition state model is developed to take account of the internal rotation energy in exothermic reactive collisions between neutral molecules. Energy and total angular momentum are both rigorously conserved. Reactive rate coefficients attain a maximum of a few 10(-10) cm(3)/s at temperatures in the range 10-30 K decreasing rapidly at higher temperatures. Results for a representative selection of well-studied systems, Si-O(2), CN-O(2), Si-NO, are in good agreement with experimental observations. At higher temperatures, typically around 100 K or greater, the rate coefficient exhibits a T(-1/3) dependence.

SACM/CT Study of Product Energy Distributions in the Dissociation of n-Propylbenzene Cations

The distribution of translational, rotational, and vibrational energies in the fragments (benzylium ions and ethyl radicals) of the dissociation of n-propylbenzene cations has been determined by statistical adiabatic channel model/classical trajectory (SACM/CT) calculations. The reaction was treated by CT calculations of capture processes for transitional modes, starting with specified fragment energies. A short-range valence/long-range ion-induced dipole potential model for the transitional modes was employed. The derived distributions approach the results from phase space theory (PST) at small energies and angular momenta. At larger energies and angular momenta, the shapes of the distribution functions remain similar to those from PST; however, the average translational, rotational, and vibrational energies of the fragments increasingly differ from PST predictions. The present results are consistent with separate SACM/CT calculations on the same potential of specific rate constants k(E,J) and thermally averaged rate constants k ∞(T) of the dissociation/recombination reaction.

Nonadiabatic transitions between lambda-doubling states in the capture of a diatomic molecule by an ion

The low-energy capture of a dipolar diatomic molecule in an adiabatically isolated electronic state with a good quantum number Omega (Hund's coupling case a) by an ion occurs adiabatically with respect to rotational transitions of the diatom. However, the capture dynamics may be nonadiabatic with respect to transitions between the pair of the Lambda-doubling states belonging to the same value of the intrinsic angular momentum j. In this work, nonadiabatic transition probabilities are calculated which define the Lambda-doubling j-specific capture rate coefficients. It is shown that the transition from linear to quadratic Stark effect in the ion-dipole interaction, which damps the T(-1/2) divergence of the capture rate coefficient calculated with vanishing Lambda-doubling splitting, occurs in the adiabatic regime with respect to transitions between Lambda-doubling adiabatic channel potentials. This allows one to suggest simple analytical expressions for the rate coefficients in the temperature range which covers the region between the sudden and the adiabatic limits with respect to the Lambda-doubling states.

Low temperature capture of open shell dipolar molecules by ions: the capture of rotationally selected NO((2)Pi(1/2), j) by C(+)

The low-energy capture of dipolar diatomic molecules in an open electronic state by ions is usually considered to be induced by the first-order charge-permanent dipole interaction with other terms of the long-range potential playing a minor role. If the molecular dipole moment is anomalously small (as is the case for slightly asymmetrical molecules), however, the situation changes, and the capture dynamics is strongly affected by higher orders of the charge-permanent dipole, charge-permanent quadrupole, and charge-induced dipole interactions. The interplay of different terms in the interaction potential manifests itself in complicated temperature dependence of the rotationally state-specific capture rate coefficients. These features of the capture are studied by way of example for NO(X (2)Pi(1/2), j) + C(+) collisions in the temperature range 10(-2)-20 K where the dynamics is adiabatic with respect to rotational and fine-structure transitions and sudden with respect to transitions between Lambda doubling and hyperfine states. The theoretical rate coefficient, which depends on the translational and rotational temperature, agrees with the experimental one measured at T(tr) = 0.6 K and T(rot) = 20 K.

Microcanonical statistical study of ortho-para conversion in the reaction H3++H2→(H5+)*→H3++H2 at very low energies

The ortho-para conversion of H(3) (+) and H(2) in the reaction H(3) (+)+H(2)-->(H(5) (+))(*)-->H(3) (+)+H(2) in interstellar space is possible by scrambling the five protons via (H(5) (+))(*) complex formation. The product distribution of the ortho-para conversion reaction can be given by ratios of cumulative reaction probabilities (CRP) calculated by microcanonical statistical theory with conservation of energy, motional angular momentum, nuclear spin, and parity. A statistical method to calculate the state-to-state reaction probabilities for given initial nuclear spin species, rotational states, and collision energies is developed using a simple semiclassical approximation of tunneling and above-barrier reflection. A new calculation method of branching ratios for given total nuclear spins and scrambling mechanisms is also developed. The anisotropic long-range electrostatic interaction potential of H(2) in the Coulomb field of H(3) (+) is taken into account using the first-order perturbation theory in forming the complex. The CRPs and the product distribution of the ortho-para conversion reaction at very low energies with reactants in their ground vibronic and lowest rotational states for given initial nuclear spin species are presented as a function of collision energy assuming complete proton scrambling or incomplete proton scrambling. The authors show that the product distribution at very low energies (or very low temperatures) differs substantially from the high energy (or high temperature) limit branching ratios.

The temperature-dependence of rapid low temperature reactions: experiment, understanding and prediction

Despite the success of the CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme) method in measuring rate coefficients for neutral-neutral reactions of radicals down close to the very low temperatures prevalent in dense interstellar clouds (ISCs), there are still many reactions of potential importance in the chemistry of these objects for which there have been no measurements of low temperature rate coefficients. One important class of reactions is that between atomic and molecular free radicals and unsaturated hydrocarbons; that is, alkynes and alkenes. Based on semi-empirical arguments and correlations of 'room temperature' rate coefficients, k(298 K), for reactions of this type with the difference between the ionisation energy of the alkyne/alkene and the electron affinity of the radical, we suggest which reactions between the radicals, C(3P), O(3P), N(4S), CH, C2H and CN, and carbon chain molecules (Cn) and cyanopolyynes (HC2nCN and NCC2nCN) are likely to be fast at the temperature of dense ISCs. These reactions and rate coefficients have been incorporated into a purely gas-phase model (osu2005) of ISC chemistry. The results of these calculations are presented and discussed.

Rates of complex formation in collisions of rotationally excited homonuclear diatoms with ions at very low temperatures: Application to hydrogen isotopes and hydrogen-containing ions

State-selected rate coefficients for the capture of ground and rotationally excited homonuclear molecules by ions are calculated, for low temperatures, within the adiabatic channel classical (ACCl) approximation, and, for zero temperature, via an approximate calculation of the Bethe limit. In the intermediate temperature range, the accurate quantal rate coefficients are calculated for j = 0 and j = 1 states of hydrogen isotopes (H2, HD, and D2) colliding with hydrogen-containing ions, and simple analytical expressions are suggested to approximate the rate coefficients. For the ground rotational state of diatoms, the accurate quantal rate coefficients are higher compared to their ACCl counterparts, while for the first excited rotational state the reverse is true. The physical significance of quantum effects for low-temperature capture and the applicability of the statistical description of capture are considered. Particular emphasis is given to the role of Coriolis interaction. The relevance of the present capture calculations for rates of ortho-para conversion of H2 in collisions with hydrogen-containing ions at low temperatures is discussed.

Quantum scattering and adiabatic channel treatment of the low-energy and low-temperature capture of a rotating quadrupolar molecule by an ion

The capture rate coefficients of homonuclear diatomic molecules (H(2) and N(2)) in the rotational state j=1 interacting with ions (Ar+ and He+) are calculated for low collision energies assuming a long-range anisotropic ion-induced dipole and ion-quadrupole interaction. A comparison of accurate quantum rates with quantum and state-specific classical adiabatic channel approximations shows that the former becomes inappropriate in the case when the cross section is dominated by few partial contributions, while the latter performs better. This unexpected result is related to the fact that the classical adiabatic channel approximation artificially simulates the quantum effects of tunneling and overbarrier reflection as well as the Coriolis coupling and it suppresses too high values of the centrifugal barriers predicted by a quantum adiabatic channel approach. For H2(j=1)+Ar+ and N(2)(j=1)+He+ capture, the rate constants at T-->0 K are about 3 and 6 times higher than the corresponding values for H2(j=0)+Ar+ and N(2)(j=0)+He+ capture.