Dynamics of the Rydberg electron in H*+D2-->D*+HD reactive collisions

Experimental crossed-beam studies carried out previously have indicated that the dynamics of the Rydberg-atom-molecule reaction H*+D2-->D*+HD are very similar to those of the corresponding ion-molecule reaction H++D2-->D++HD. The equivalence of the cross sections for these related systems would open up a new approach to the experimental study of ion-molecule reactions. However, a recent experimental and theoretical study has brought to light some important qualitative differences between the Rydberg-atom reaction and the ion-molecule reaction; in particular, the experimental cross section for the Rydberg-atom reaction exhibits a higher degree of forward-backward scattering asymmetry than predicted by a quasiclassical trajectory study of the ion-molecule reaction. In this paper, the authors consider the dynamics of the Rydberg-electron over the course of a reactive collision and the implications of these dynamics for the Rydberg-atom-molecule crossed-beam experiment. Using an approach based on perturbation theory, they estimate the attenuation of the experimental signal due to the Rydberg-electron dynamics as a function of the scattering angle. They show that at least part of the experimental asymmetry can be ascribed to this angle dependent attenuation. Their results offer general insight into the practical aspects of the experimental study of ion-molecule reactions by means of their Rydberg-atom counterparts.     

Guided ion beam and theoretical study of the reactions of Au+ with H2, D2, and HD

Reactions of the late third-row transition metal cation Au(+) with H(2), D(2), and HD are examined using guided ion beam tandem mass spectrometry. A flow tube ion source produces Au(+) in its (1)S (5d(10)) electronic ground state level. Corresponding state-specific reaction cross sections for forming AuH(+) and AuD(+) as a function of kinetic energy are obtained and analyzed to give a 0 K bond dissociation energy of D(0)(Au(+)-H) = 2.13 ± 0.11 eV. Quantum chemical calculations at the B3LYP∕HW+∕6-311+G(3p) and B3LYP∕Def2TZVPP levels performed here show good agreement with the experimental bond energy. Theory also provides the electronic structures of these species and the reactive potential energy surfaces. We also compare this third-row transition metal system with previous results for analogous reactions of the first-row and second-row congeners, Cu(+) and Ag(+). We find that Au(+) has a stronger M(+)-H bond, which can be explained by the lanthanide contraction and relativistic effects that alter the relative size of the valence s and d orbitals. Results from reactions with HD provide insight into the reaction mechanism and indicate that ground state Au(+) reacts largely via a direct mechanism, in concordance with the behavior of the lighter group 11 metal ions, but includes more statistical behavior than these metals as well.     

Influence of nuclear exchange on nonadiabatic electron processes in H(+)+H2 collisions

H(+)+H(2) collisions are studied by means of a semiclassical approach that explicitly accounts for nuclear rearrangement channels in nonadiabatic electron processes. A set of classical trajectories is used to describe the nuclear motion, while the electronic degrees of freedom are treated quantum mechanically in terms of a three-state expansion of the collision wavefunction. We describe electron capture and vibrational excitation, which can also involve nuclear exchange and dissociation, in the E = 2-1000 eV impact energy range. We compare dynamical results obtained with two parametrizations of the potential energy surface of H(3)(+) ground electronic state. Total cross sections for E > 10 eV agree with previous results using a vibronic close-coupling expansion, and with experimental data for E < 10 eV. Additionally, some prototypical features of both nuclear and electron dynamics at low E are discussed.     

Guided ion beam and theoretical study of the reactions of Os+ with H2, D2, and HD

Reactions of the third-row transition metal cation Os(+) with H(2), D(2), and HD to form OsH(+) (OsD(+)) were studied using a guided ion beam tandem mass spectrometer. A flow tube ion source produces Os(+) in its (6)D (6s(1)5d(6)) electronic ground state level. Corresponding state-specific reaction cross sections are obtained. The kinetic energy dependences of the cross sections for the endothermic formation of OsH(+) and OsD(+) are analyzed to give a 0 K bond dissociation energy of D(0)(Os(+)-H) = 2.45 ± 0.10 eV. Quantum chemical calculations are performed here at several levels of theory, with B3LYP approaches generally overestimating the experimental bond energy whereas results obtained using BHLYP and CCSD(T), coupled-cluster with single, double, and perturbative triple excitations, levels show good agreement. Theory also provides the electronic structures of these species and the potential energy surfaces for reaction. Results from the reactions with HD provide insight into the reaction mechanism and indicate that Os(+) reacts via a direct reaction. We also compare this third-row transition metal system with the first-row and second-row congeners, Fe(+) and Ru(+), and find that Os(+) reacts more efficiently with dihydrogen, forming a stronger M(+)-H bond. These differences can be attributed to the lanthanide contraction and relativistic effects.     

Guided ion beam and theoretical study of the reactions of Hf+ with H2, D2, and HD

The kinetic energy dependences of reactions of the third-row transition metal cation Hf(+) with H(2), D(2), and HD were determined using a guided ion beam tandem mass spectrometer. A flow tube ion source produces Hf(+) in its (2)D (6s(2)5d(1)) electronic ground state level. Corresponding state-specific reaction cross sections are obtained. The kinetic energy dependences of the cross sections for the endothermic formation of HfH(+) and HfD(+) are analyzed to give a 0 K bond dissociation energy of D(0)(Hf(+)-H)=2.11±0.08 eV. Quantum chemical calculations at several levels of theory performed here generally overestimate the experimental bond energy but results obtained using the Becke-half-and-half-LYP functional show good agreement. Theory also provides the electronic structures of these species and the reactive potential energy surfaces. Results from the reactions with HD provide insight into the reaction mechanisms and indicates that Hf(+) reacts via a statistical mechanism. We also compare this third-row transition metal system with the first-row and second-row congeners, Ti(+) and Zr(+), and find that Hf(+) has a weaker M(+)-H bond. As most third-row transition metal hydride cation bonds exceed their lighter congeners, this trend is unusual but can be understood using promotion energy arguments.     

Guided ion beam and theoretical study of the reactions of Ir+ with H2, D2, and HD

We present the kinetic energy dependence of reactions of the late third-row transition metal cation Ir(+) with H(2), D(2), and HD measured using a guided ion beam tandem mass spectrometer. A flow tube ion source produces Ir(+) ions in its electronic ground state term and primarily in the ground spin-orbit level. Corresponding state-specific reaction cross sections are obtained. The kinetic energy dependence of the cross sections for forming IrH(+) and IrD(+) are analyzed to give a 0 K bond dissociation energy of D(0)(Ir(+)-H) = 3.12 +/- 0.06 eV. Ab initio calculations at the B3LYP/HW+/6-311+G(3p), BHLYP/HW+/6-311+G(3p), and QCISD(T)/HW+/6-311+G(3p) levels performed here show reasonable agreement with the experimental bond energies and with the previous theoretical values available. Theory also provides the electronic structures of these species and the reactive potential energy surfaces. We also compare this third-row transition metal system with those of the first-row and second-row congeners Co(+) and Rh(+). We find that Ir(+) has a stronger M(+)-H bond, which can be explained by the lanthanide contraction and relativistic effects that alter the relative size of the valence s and d orbitals. Results from reactions with HD provide insight into the reaction mechanisms and indicate that Ir(+) reacts largely via an insertion mechanism, in contrast with the lighter group 9 metal ions Co(+) and Rh(+) which react via direct mechanisms.     

Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.     

Probes of spin conservation in heavy metal reactions: experimental and theoretical studies of the reactions of Re+ with H2, D2, and HD

A guided ion beam tandem mass spectrometer is used to examine the kinetic energy dependence of reactions of the third-row transition metal cation, Re(+), with molecular hydrogen and its isotopologues. A flow tube ion source produces Re(+) in its (7)S(3) electronic ground state. Reaction with H(2), D(2), and HD forms Re H(+)(Re D(+)) in endothermic processes. Modeling of the endothermic reaction cross sections yields the 0 K bond dissociation energy of D(0)(Re(+)-H)=2.29+/-0.07 eV (221+/-6 kJ/mol). The experimental thermochemistry is consistent with ab initio calculations, performed here and in the literature. Theory also provides the electronic structures of these species and is used to examine the reactive potential energy surfaces. Results from reactions with HD provide insight into the reaction mechanisms and indicate that the late metal ion, Re(+), reacts largely via a statistical mechanism. This is consistent with the potential energy surfaces which locate a stable Re H(2) (+)((5)B(2)) complex. Results for this third-row transition metal system are compared with the first-row congener (Mn(+)) and found to have much higher reactivity towards dihydrogen and stronger M(+)-H bonds. These differences can be attributed to efficient coupling among surfaces of different spin along with lanthanide contraction and relativistic effects.     

The spin-orbit transition of atomic chlorine in solid H2, HD, and D2

Essential to understanding the reaction dynamics of spin-orbit (SO) excited atomic chlorine (2P1/2) with molecular hydrogen is experimental measurements of the SO splitting of Cl in the van der Waals region of the entrance channel to reaction. Here we report high-resolution direct absorption studies of the SO transition (2P1/2<--2P3/2) of atomic chlorine isolated in solid molecular hydrogen (H2, HD, and D2).     

Low-energy H+ + H2 reactive collisions: mean-potential statistical model and role of permutation symmetry

Statistical theory based on a mean isotropic potential deduced from a full potential energy surface is applied to the complex-forming, reactive H(+) + H(2) system in the interval of collision energies E(c) = 10(-3) to 0.5 eV. We present expressions for the reaction probabilities that incorporate the full permutation symmetry of the protons and compare our results with other statistical models and full quantum mechanical approaches that take account this symmetry correctly, approximately, or erroneously for the exchange rearrangement mechanism of the reaction.     

Communication: the rotational excitation of D2 by H: on the importance of the reactive channels

We report fully-quantum time-independent calculations of cross sections and rate coefficients for the collisional excitation and dissociation of D(2) by H, two astrophysically relevant processes. Our calculations are based on the recent H(3) global potential energy surface of Mielke et al. [J. Chem. Phys. 116, 4142 (2002)]. Results of exact three-dimensional calculations, i.e., including the reactive channels, are compared to pure inelastic two-dimensional calculations based on the rigid rotor approximation. A reasonable agreement is found between the two sets of inelastic cross sections over the whole energy range 10-9000 cm(-1). At the highest collisional energies, where the reactive channels are significant, the rigid rotor approach slightly overestimates the cross sections, as expected. At moderate collisional energies, however, the opposite behaviour is observed. The rigid rotor approach is found to be reliable at temperatures below ~500 K, with a significant but moderate contribution from reactive channels.     

Corroboration of theory for H + D2 --> D + HD (v' = 3, j' = 0) reactive scattering dynamics

The differential cross section (DCS) for the reaction H + D2 --> D + HD (v' = 3, j' = 0) exhibits particularly rich dynamics; in addition to the expected direct recoil backscattering feature, a surprising time-delayed forward scattering feature appears that has been attributed to glory scattering arising from nearside and farside interference. This fact leads to a complex DCS that depends strongly on the collision energy. Its accurate calculation requires a fully quantum mechanical (QM) treatment. We report improved measurements of this DCS over the collision energy range 1.55 < or = E(coll) < or = 1.82 eV. Previous measurements using the core extraction method, while generally in agreement with theory, lacked sufficient resolution to capture all of the noteworthy behavior of the system; in the present work, we use ion imaging to observe many previously unresolved features of the DCS, particularly in the forward-scattered region. Agreement with QM calculations is found at all collision energies, reconciling an earlier discrepancy between experiment and theory near E(coll) = 1.54 eV.     

Classical rotational cross sections for H2—HD and HD—HD collisions

Classical trajectory calculations of integral cross sections for rotationally inelastic collisions of HD-para H₂ 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—H₂ 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 H₂ excitations at all energies.     

A study of the nearly thermoneutral reactions of N+ with H2, HD and D2

The rate coefficients k for the nearly thermoneutral atom abstraction reactions of N⁺ ions with H₂, HD and D₂ have been determined as a function of ion-molecule centre-of-mass energy, KE_cm, in a SIFDT apparatus, over the range of KE_cm from thermal energy at 300 K to ≈ 0.5 eV. From Arrhenius-type plots of ln k versus (KE_cm)⁻¹, values of the thermicities of the reactions, ΔE, have been determined. The differences in the values of ΔE obtained for the reactions are accounted for by differences in the vibrational zero-point energies of the reactant and product molecules. From the data, the absolute proton affinity of the N atom is found to be 3.531 eV.     

Modelling light diatomics trapped in rare gas matrices: H2, HD and D2 in Ar,Kr and Xe

The different models allowing the calculations of the rovibrational frequency shifts with respect to the free molecule of a molecular impurity embedded in a rare gas crystal are reviewed. It is shown that models which account for the translational motion of the impurity yield reliable results, the effects of the rare-gas translation seem to be less important. The different models currently used are described in detail and the computational procedures are discussed. Finally, it is shown that for heteronuclear diatomics, the translation-rotation coupling could play an important role.     

Vibrational inelastic and charge transfer processes in H(+)+H2 system: an ab initio study

State-resolved differential cross sections, total and integral cross sections, average vibrational energy transfer, and the relative probabilities are computed for the H(+)+H2 system using the newly obtained ab initio potential energy surfaces at the full CI/cc-pVQZ level of accuracy which allow for both the direct vibrational inelastic and the charge transfer processes. The quantum dynamics is treated within the vibrational close-coupling infinite-order-sudden approximation approach using the two ab initio quasidiabatic potential energy surfaces. The computed collision attributes for both the processes are compared with the available state-to-state scattering experiments at E(c.m.)=20 eV. The results are in overall good agreement with most of the observed scattering features such as rainbow positions, integral cross sections, and relative vibrational energy transfers. A comparison with the earlier theoretical study carried out on the semiempirical surfaces (diatomics in molecules) is also made to illustrate the reliability of the potential energy surfaces used in the present work.     

Quantum statistical and wave packet studies of insertion reactions of S(1D) with H2, HD, and D2

A thorough theoretical investigation of the reactions between S(1D) and various hydrogen isotopomers (H2, D2, and HD) has been carried out using a recent ab initio potential energy surface. State-resolved integral and differential cross sections, thermal rate constants, and their dependence on energy or temperature were obtained from quantum mechanical capture probabilities within a statistical model. For comparison, the J=0 reaction probabilities were also computed using an exact wave packet method. The statistical results are in excellent agreement with available exact differential and integral cross sections. The comparison with experimental results shows that the agreement is reasonably good in general, but some significant differences exist, particularly for the SD/SH branching ratio in the S(1D)+HD reaction.     

H2, HD, and D2 inside C60: coupled translation-rotation eigenstates of the endohedral molecules from quantum five-dimensional calculations

We have performed rigorous quantum five-dimensional (5D) calculations of the translation-rotation (T-R) energy levels and wave functions of H(2), HD, and D(2) inside C(60). This work is an extension of our earlier investigation of the quantum T-R dynamics of H(2)@C(60) [M. Xu et al., J. Chem. Phys. 128, 011101 (2008)] and uses the same computational methodology. Two 5D intermolecular potential energy surfaces (PESs) were employed, differing considerably in their well depths and the degree of confinement of the hydrogen molecule. Our calculations revealed pronounced sensitivity of the endohedral T-R dynamics to the differences in the interaction potentials, and to the large variations in the masses and the rotational constants of H(2), HD, and D(2). The T-R levels vary significantly in their energies and ordering on the two PESs, as well as from one isotopomer to another. Nevertheless, they all display the same distinctive patterns of degeneracies, which can be qualitatively understood and assigned in terms the model which combines the isotropic three-dimensional harmonic oscillator, the rigid rotor, and the coupling between the orbital and the rotational angular momenta of H(2)/HD/D(2). The quantum number j associated with the rotation of H(2), HD, and D(2) was found to be a good quantum number for H(2) and D(2) on both PESs, while most of the T-R levels of HD exhibit strong mixing of two or more rotational basis functions with different j values.