Exact quantum calculations of the kinetic isotope effect: cross sections and rate constants for the F+HD reaction and role of tunneling

In this paper we present integral cross sections (in the 5-220 meV collision energy range) and rate constants (in the 100-300 K range of temperature) for the F+HD reaction leading to HF+D and DF+H. The exact quantum reactive scattering calculations were carried out using the hyperquantization algorithm on an improved potential energy surface which incorporates the effects of open shell and fine structure of the fluorine atom in the entrance channel. The results reproduce satisfactorily molecular beam scattering experiments as well as chemical kinetics data for both the HF and DF channels. In particular, the agreement of the rate coefficients and the vibrational branching ratios with experimental measurements is improved with respect to previous studies. At thermal and subthermal energies, the rates are greatly influenced by tunneling through the reaction barrier. Therefore exchange of deuterium is shown to be penalized with respect to exchange of hydrogen, and the isotopic branching exhibits a strong dependence on translational energy. Also, it is found that rotational excitation of the reactant HD molecule enhances the production of HF and decreases the reactivity at the D end, obtaining insight on the reaction stereodynamics.     

A time-dependent wave packet quantum scattering study of the reaction HD+ (v = 0 - 3;j0 = 1) + He --> HeH+(HeD+) + D(H)

Time-dependent wave packet quantum scattering (TWQS) calculations are presented for HD(+) (v = 0 - 3;j(0)=1) + He collisions in the center-of-mass collision energy (E(T)) range of 0.0-2.0 eV. The present TWQS approach accounts for Coriolis coupling and uses the ab initio potential energy surface of Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. For a fixed total angular momentum J, the energy dependence of reaction probabilities exhibits quantum resonance structure. The resonances are more pronounced for low J values and for the HeH(+) + D channel than for the HeD(+) + H channel and are particularly prominent near threshold. The quantum effects are no longer discernable in the integral cross sections, which compare closely to quasiclassical trajectory calculations conducted on the same potential energy surface. The integral cross sections also compare well to recent state-selected experimental values over the same reactant and translational energy range. Classical impulsive dynamics and steric arguments can account for the significant isotope effect in favor of the deuteron transfer channel observed for HD(+)(v<3) and low translational energies. At higher reactant energies, angular momentum constraints favor the proton-transfer channel, and isotopic differences in the integral cross sections are no longer significant. The integral cross sections as well as the J dependence of partial cross sections exhibit a significant alignment effect in favor of collisions with the HD(+) rotational angular momentum vector perpendicular to the Jacobi R coordinate. This effect is most pronounced for the proton-transfer channel at low vibrational and translational energies.     

Differential Cross Sections of F+HD→DF+H Reaction at Collision Energies from 3.03 meV to 17.97 meV

The prototypical reaction of F+HD→DF+H was investigated at collision energies from 3.03 meV to 17.97 meV using a crossed molecular beam apparatus with multichannel Rydberg tagging time-of-flight detection. Significant contributions from both the Born-Oppenheimer (BO) forbidden reaction F^*(²P_1/2)+HD→DF+H and the BO-allowed reaction F(²P_3/2)+HD→DF+H were observed. In the backward scattering direction, the contribution from the BO-forbidden reaction F^*(²P_1/2)+HD was found to be considerably greater than the BO-allowed reaction F(²P_3/2)+HD, indicating the non-adiabatic effects play an important role in the dynamics of the title reaction at low collision energies. Collision-energy dependence of differential cross sections (DCSs) in the backward scattering direction was found to be monotonously decreased as the collision energy decreases, which does not support the existence of resonance states in this energy range. DCSs of both BO-allowed and BO-forbidden reactions were measured at seven collision energies from 3.03 meV to 17.97 meV. It is quite unexpected that the angular distribution gradually shifts from backward to sideway as the collision energy decreases from 17.97 meV to 3.03 meV, suggesting some unknown mechanisms may exist at low collision energies.     

High Resolution Crossed Beams Scattering Study of the F＋HD→DF＋H Reaction

Crossed beams scattering study was carried out on the F＋HD→DF＋H reaction using high- resolution H-atom Rydberg tagging time-of-flight technique. Vibrational state-resolved differential cross sections were measured, with partial rotational state resolution, at eight collision energies in the range of 2.51-5.60 kJ/mol. Experimental results indicated that the product angular distributions are predominantly backward scattered. As the collision energy increases, the backward scattered peak becomes broader gradually. Dependence of product vibration branching ratios on the collision energy was also determined. The experimental results show that the DF products are highly inverted in the vibrational state distribution and the DF （v＇=3） product is the most populated state. Furthermore, the DF （v＇=l） product has also been observed at collision energy above 3.97 kJ/mol.     

An experimental and quasiclassical trajectory study of the rovibrationally state-selected reactions: HD+(v=0-15,j=1)+He-->HeH+(HeD+)+D(H)

The absolute integral cross sections for the formation of HeH+ and HeD+ from the collisions of HD+(v,j=1)+He have been examined over a broad range of vibrational energy levels v=0-13 at the center-of-mass collision energies (ET) of 0.6 and 1.4 eV using the vacuum ultraviolet (VUV) pulsed field ionization photoelectron secondary ion coincidence method. The ET dependencies of the integral cross sections for products HeH+ and HeD+ from HD+(v=0-4)+He collisions in the ET range of 0-3 eV have also been measured using the VUV photoionization guided ion beam mass spectrometric technique, in which vibrationally selected HD+(v) reactant ions were prepared via excitation of selected autoionization resonances of HD. At low total energies, a pronounced isotope effect is observed in absolute integral cross sections for the HeH++D and HeD++H channels with significant favoring of the deuteron transfer channel. As v is increased in the range of v=0-9, the integral cross sections of the HeH++D channel are found to approach those of HeD++H. The observed velocity distributions of products HeD+ and HeH+ are consistent with an impulsive or spectator-stripping mechanism. Detailed quasiclassical trajectory (QCT) calculations are also presented for HD+(v,j=1)+He collisions at the same energies of the experiment. The QCT calculations were performed on the most accurate ab initio potential energy surface available. If the zero-point energy of the reaction products is taken into account, the QCT cross sections for products HeH+ and HeD+ from HD+(v)+He are found to be significantly lower than the experimental results at ET values near the reaction thresholds. The agreement between the experimental and QCT cross sections improves with translational energy. Except for prethreshold reactivity, QCT calculations ignoring the zero-point energy in the products are generally in good agreement with experimental absolute cross sections. The experimental HeH+/HeD+ branching ratios for the HD+(v=0-9)+He collisions are generally consistent with QCT predictions. The observed isotope effects can be rationalized on the basis of differences in thermochemical thresholds and angular momentum conservation constraints.     

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.     

Differential cross sections for H + D2 → HD(v' = 2, j' = 0,3,6,9) + D at center-of-mass collision energies of 1.25, 1.61, and 1.97 eV

We have measured differential cross sections (DCSs) for the reaction H + D(2) → HD(v' = 2,j' = 0,3,6,9) + D at center-of-mass collision energies E(coll) of 1.25, 1.61, and 1.97 eV using the photoloc technique. The DCSs show a strong dependence on the product rotational quantum number. For the HD(v' = 2,j' = 0) product, the DCS is bimodal but becomes oscillatory as the collision energy is increased. For the other product states, they are dominated by a single peak, which shifts from back to sideward scattering as j' increases, and they are in general less sensitive to changes in the collision energy. The experimental results are compared to quantum mechanical calculations and show good, but not fully quantitative agreement.     

Role of the F spin-orbit excited state in the F+HD reaction: contributions to the dynamical resonance

We report quantum mechanical calculations of excitation functions (relative reaction cross sections) for the F+HD reaction. We include three potential energy surfaces and an accurate treatment of all couplings (non-adiabatic, spin-orbit, and Coriolis). Comparison with experimental results [Dong, Lee, and Liu, J. Chem. Phys., 113, 3633 (2000)] show excellent agreement for the DF product channel and an improved but not perfect agreement for the HF product channel. In the former case, when weighted by the (16%) fractional population of the spin-orbit excited state (F(*)) in the beam, the overall reactivity of the F(*) is small (approximately 5%). For the HF product channel and with the same (16%) fractional weight, F(*) reactivity makes a contribution of approximately 12% in the high-energy tail of the resonance peak. As a result, averaging over the population of F spin-orbit states in the beam changes the shape of the resonance. The greater the fraction of F(*) in the beam, the less pronounced will be the resonance modulation of the reaction excitation function.     

Quantum Dynamics of Li+HF/DF Reaction Investigated by a State-to-State Time-dependent Wave Packet Approach

Using the reactant coordinate based time-dependent wave packet method, on the APW potential energy surface, the differential and integral cross sections of the Li+DF/HF(v=0, j=0, 1) reactions were calculated over the collision energy range from the threshold to 0.25 eV. The initial state-specified reaction rate constants of the title reaction were also calculated. The results indicate that, compared with the Li+DF reaction, the product LiF of Li+HF reaction is a little more rotationally excited but essentially similar. The initial rotational excitation from j=0 to 1 has little effect on the Li+DF reaction. However, the rotational excitation of DF does result in a little more rotationally excited product LiF. The different cross section of both reactions is forward biased in the studied collision energy range, especially at relatively high collision energy. The resonances in the Li+HF reaction may be identifiable as the oscillations in the product ro-vibrational state-resolved integral cross sections and backward scattering as a function of collusion energy. For the Li+HF reaction, the rate constant is not sensitive to the temperature and almost has no change in the temperature range considered. For the Li+DF reaction, the rate constant increase by a factor of about 10 in the temperature range of 100?300 K. Brief comparison for the total reaction probabilities and integral cross section of the Li+HF reaction has been carried out between ours and the values reported previously. The agreement is good, and the difference should come from the better convergence of our present calculations.     

Differential cross section for the H+D(2)-->HD(v(')=1,j(')=2,6,10)+D reaction as a function of collision energy

We have measured differential cross sections (DCSs) for the HD (v(')=1,j(')=2,6,10) products of the H+D(2) exchange reaction at five different collision energies in the range 1.48< or =E(coll)< or =1.94 eV. The contribution from the less energetic H atoms formed upon spin-orbit excitation of Br in the photolysis of the HBr precursor is taken into account for two collision energies, E(coll)=1.84 and 1.94 eV, allowing us to disentangle the two different channels. The measured DCSs agree well with new time-dependent quantum-mechanical calculations. As the product rotational excitation increases, the DCSs shift from backward to sideward scattering, as expected. We also find that the shapes of the DCSs show only a small overall dependence on the collision energy, with a notable exception occurring for HD (v(')=1,j(')=2), which appears bimodal at high collision energies. We suggest that this feature results from both direct recoil and indirect scattering from the conical intersection.     

Coherence parameters for He+(2p) capture and H(2p) excitation in He2+-H(1s) collisions

Semiclassical coupled channel calculations have been carried out for the collision system He²⁺-H(1s) in the velocity range 0.15–3.0 a.u. (impact energies 0.5–225 keV/amu) in order to study capture probabilities and alignment and orientation parameters for the dominant He⁺(n=2) channels. A 14-state AO basis set calculation has been combined with an analytical treatment of the asymptotic collision region. For impact velocities about and abovev=0.6 a.u. a strong propensity for resonance capture into an oriented He⁺(2p) state with the same sense of rotation as the collisional rotation of the internuclear axis is predicted together with a very smooth behaviour of the alignment angle as function of impact parameter. Eikonal method calculations of differential capture cross sections predict that the left/right orientation asymmetry will prevail in differential scattering experiments. The resulting total cross sections for capture into specificnl-substates (n=2, 3) and the total light polarisation parameter for He⁺(2p) capture compare well with previous work. Finally we report H(2s,2p) excitation cross sections, probabilties and H(2p) alignment and orientation parameters, following the established propensity rule for orientation in H(2p) excitation.     

Quantum dynamics study of Li + HF reaction

We report rigorous quantum dynamics studies of the Li + HF reaction using the time-dependent wavepacket approach. The dynamics study is carried out on a recent ab initio potential energy surface, and state-selected reaction probabilities and cross sections are calculated up to 0.4 eV of collision energy. Many long-lived resonances (as long as 10 ps) at low collision energies (below 0.1 eV) are uncovered from the dynamics calculation. These long-lived resonances play a dominant role in the title reaction at low collision energies (below 0.1 eV). At higher energies, the direct reaction process becomes very important. The reaction probabilities from even rotational states exhibit a different energy dependence than those from odd rotational states. Our calculated integral cross section exhibits a broad maximum near the collision energy of 0.26 eV with small oscillations superimposed on the broad envelope which is reminiscent of the underlying resonance structures in reaction probabilities. The energy dependence of the present CS cross section is qualitatively different from the simple J-shifting approximation, in which a monotonic increase of cross section with collision energy was obtained. Received: 8 January 1997 / Accepted: 14 January 1997     

Crossed Beam Study on the F+D2→DF+D Reaction at Hyperthermal Collision Energy of 23.84 kJ/mol

We presented an experimental apparatus combining the H-atom Rydberg tagging time-of-flight technique and the laser detonation source for studying crossed beam reactions athyperthermal collision energies. The preliminary study of the F+D₂→DF+D reaction at hyperthermal collision energy of 23.84 kJ/mol was performed. Two beam sources were used in this study: one is the hyperthermal F beam source produced by a laser detonation process, and the other is D₂ beam source generated by liquid-N₂ cooled pulsed valve. Vibrational state-resolved di erential cross sections (DCSs) of product for the title reaction were determined. From the product vibrational state-resolved DCS, it can be concluded that products DF(v'=0, 1, 2, 3) are predominantly distributed in the sideway and backward scattering directions at this collision energy. However, the highest vibrational excited product DF(v'=4), is clearly peaked in the forward direction. The probable dynamical origins for these forward scattering products were analyzed and discussed.     

The investigation of spin-orbit effect for the F((2)P)+HD reaction

In this paper, we employ the time-dependent quantum wave packet method to study the reaction of F((2)P(3/2), (2)P(1/2)) with HD on the Alexander-Stark-Werner potential energy surface. The reaction probabilities and total integral cross sections of the spin-orbit ground and excited states for the two possible products of the system are calculated. Because the reaction channel of the excited spin-orbit state is closed at the resonance energy, the resonance feature does not appear in the reaction probabilities and cross section for the F((2)P(1/2))+HD(v=j=0)-->HF+D reaction, in contrast with that found for the ground spin--orbit state. We also compare the average cross sections of the two possible products with the experimental measurement. The resonance peak in the present average cross section for the HF+D product is slightly larger than the experimental result, but much smaller than that of the single-state calculations on the potential energy surface of Stark and Werner. It seems that the spin--orbit coupling would play a relatively important role in this reaction. Moreover, the isotope effects of the ground and excited spin--orbit states and the reactivity of the two product channels from the excited spin--orbit state are presented.     

Differential Cross Sections for the H+D2O→HD+OD Reaction: a Full Dimensional State-to-State Quantum Dynamics Study

The time-dependent wave-packet method was employed to calculate the first full-dimensional state-to-state differential cross sections (DCS) for the title reaction with D₂O in the ground and the first symmetric (100) and asymmetric stretching (001) excited states. The calculated DCSs for these three initial states are strongly backward peaked at low collision energies. With the increase of collision energy, these DCSs become increasingly broader with the peak position shifting gradually to a smaller angle, consistent with the fact that the title reaction is a direct reaction via an abstraction mechanism. It is found that the (100) and (001) states not only have roughly the same integral cross sections, but also have essentially identical DCS, which are very close to that for the ground state at the same total energy of reaction. The reaction produces a small fraction of OD in the v=1 state, with the population close to the relative reactivity between the ground and vibrationally excited states, therefore confirming the experimental result of Zare et al. and the local mode picture[J. Phys. Chem. 97 , 2204 (1993)]. Unexpectedly, the stretching excitation reduces the rotation excitation of product HD at the same total energy.     

Ab initio investigation of the autoionization process Ar*(4s3P2, 3P0)+Hg --> (Ar-Hg)+ + e-: potential energy curves and autoionization widths, ionization cross sections, and electron energy spectra

Multireference configuration interaction (MRCI) calculations have been performed for the Ar*(4s3P2,0) + Hg collision complex. Feshbach projection based on orbital occupancy defines the entrance channel resonance states and provides their potential energy curves as well as resonance-continuum coupling matrix elements, which are turned into an autoionization width function by Stieltjes imaging. Coupled cluster calculations with singles, doubles, and pertubative triples [CCSD(T)] give the exit channel potential of ArHg+. The Hg20+ core is treated by a scalar-relativistic effective core potential, reparametrized to reproduce experimental excitation and ionization energies. Spin-orbit interaction is included for the Ar* open 3p shell. The nuclear motion is treated within the local complex potential approximation. Ionization occurs for 85% (3P0) and 98% (3P2) of the symmetry allowed close collisions. Calculated ionization cross sections show good agreement with experimental data. The difference potential of the collision complex is remarkably flat down to internuclear separations of 8a0 and leads to very sharp peaks in theoretical electron energy spectra for single collision energies. After accounting for the experimental energy distribution and the resolution function of the spectrometer, a very satisfying agreement with experimental electron energy spectra is found, including subtle differences due to spin-orbit coupling. Theoretical input appears indispensable for an analysis of the measured data in terms of potential energy curves and autoionization width functions.     

Evidence for excited spin-orbit state reaction dynamics in F+H2: theory and experiment

We describe fully quantum, time-independent scattering calculations of the F+H2-->HF+H reaction, concentrating on the HF product rotational distributions in v'=3. The calculations involved two new sets of ab initio potential energy surfaces, based on large basis set, multireference configuration-interaction calculations, which are further scaled to reproduce the experimental exoergicity of the reaction. In addition, the spin-orbit, Coriolis, and electrostatic couplings between the three quasidiabatic F+H2 electronic states are included. The calculated integral cross sections are compared with the results of molecular beam experiments. At low collision energies, a significant fraction of the reaction is due to Born-Oppenheimer forbidden, but energetically allowed reaction of F in its excited (2P 1/2) spin-orbit state. As the collision energy increases, the Born-Oppenheimer allowed reaction of F in its ground (2P 3/2) spin-orbit state rapidly dominates. Overall, the calculations agree reasonably well with the experiment, although there remains some disagreement with respect to the degree of rotational excitation of the HF(v'=3) products as well as with the energy dependence of the reactive cross sections at the lowest collision energies.     

O+HCl→OH+Cl反应的立体动力学的准经典轨线研究

运用准经典轨线方法, 基于Peterson从头计算势能面对O+HCl→OH+Cl反应的立体动力学性质进行了研究. 讨论了在31.77和51.04 kJ/mol两种碰撞能情况下极化依赖的微分反应截面(2π/σ)(dσ₀₀/dω_t), (2π/σ)(dσ₂₀/dω_t), (2π/σ)(dσ₂₂₊/dω_t)和(2π/σ)(dσ_21-/dω_t)以及描述k-j′两矢量相关和k-k′-j′三矢量相关的分布函数P(θ_r)和P(φ_r). 计算得到的P(θ_r)分布表明, 产物分子的转动角动量j′具有强烈的取向分布, 并且产物转动角动量的取向效应对散射能的变化比较敏感. 而P(φ_r)的分布表明, 产物分子虽然具有沿着y轴的取向效应, 但是没有明显的定向效应.     

Exact state-to-state quantum dynamics of the F + HD --> HF(v' = 2) + D reaction on model potential energy surfaces

In this paper, we present the results of a theoretical investigation on the dynamics of the title reaction at collision energies below 1.2 kcal/mol using rigorous quantum reactive scattering calculations. Vibrationally resolved integral and differential cross sections, as well as product rotational distributions, have been calculated using two electronically adiabatic potential energy surfaces, developed by us on the basis of semiempirical modifications of the entrance channel. In particular, we focus our attention on the role of the exothermicity and of the exit channel region of the interaction on the experimental observables. From the comparison between the theoretical results, insight about the main mechanisms governing the reaction is extracted, especially regarding the bimodal structure of the HF(v = 2) nascent rotational state distributions. A good overall agreement with molecular beam scattering experiments has been obtained.     

On the role of scattering resonances in the F+HD reaction dynamics

We study scattering resonances in the F+HD-->HF+D reaction using a new method for direct evaluation of the lifetime Q-matrix [Aquilanti et al., J. Chem. Phys. 2005, 123, 054314]. We show that most of the resonances are due to van der Waals states in the entrance and exit reaction channels. The metastable states observed in the product reaction channel are assigned by calculating the energy levels and wave functions of the HF...D van der Waals complex. The behavior of resonance energies, widths, and decay branching ratios as functions of total angular momentum is analyzed. The effect of isotopic substitution on resonance energies and lifetimes is elucidated by comparison with previous results for the F+H2 reaction. It is demonstrated that HF(v'=3) products near threshold are formed by decay of the narrow resonances supported by van der Waals wells in the exit channel. State-to-state differential cross sections in the HF(v'=3) channel exhibit characteristic forward-backward peaks due to the formation of a long-lived metastable complex. The role of the exit-channel resonances in the interpretation of molecular beam experiments is discussed.