Isotopic branching in (He, HD+) collisions

A three-dimensional time-dependent quantum mechanical approach is used to calculate the reaction probability (P(R)) and the integral reaction cross section (sigma(R)) for both channels of the reaction He + HD+(v = 0, 1, 2, 3; j = 0) --> HeH(D)+ + D(H), over a range of translational energy (E(trans)) on two different ab initio potential energy surfaces (McLaughlin-Thompson-Joseph-Sathyamurthy and Palmieri et al.). The reaction probability plots as a function of translational energy exhibit several oscillations, which are characteristic of the system. The vibrational enhancement of the reaction probability and the integral reaction cross section values are reproduced qualitatively by our calculations, in accordance with the experimental results. The isotopic branching ratio for the reaction decreases in going from v = 0 to v = 1 and then becomes nearly v-independent in going from v = 1 to v =3 on both the surfaces.     

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.     

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.     

Collision-induced dissociation in (He, H2(+)(v = 0-2; j = 0-3)) system: a time-dependent quantum mechanical investigation

The collision-induced process He + H(2)(+)(v = 0-2; j = 0-3) → He + H + H(+) has been investigated using a time-dependent quantum mechanical wave packet approach, within the centrifugal sudden approximation. The exchange reaction He + H(2)(+) → HeH(+) + H, which has a lower threshold, dominates over the dissociation process over the entire energy range considered in this study. The reaction cross section for both the exchange and dissociation channels and the branching ratio between the two channels have been computed on the McLaughlin-Thompson-Joseph-Sathyamurthy potential-energy surface and compared with the available experimental and quasiclassical trajectory results.     

Influence of reagent rotation on (H-, D2) and (D-, H2) collisions: a quantum mechanical study

Time-independent quantum mechanical (TIQM) approach (helicity basis truncated at k = 2) has been used for computing differential and integral cross sections for the exchange reaction H- + D2 (v = 0, j = 0-4) --> HD + D- and D- + H2 (v = 0, j = 0-3) --> HD + H- in three dimensions on an accurate ab initio potential energy surface. It is shown that the j-weighted differential reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder at four different relative translational energies (Etrans = 0.55, 0.93, 1.16 and 1.48 eV) for (H-, D2) and at one relative translational energy (Etrans = 0.6 eV) by Haufler et al. for both (H-, D2) and (D-, H2) collisions. The j-weighted integral reaction cross section values are in good agreement with the crossed beam measurements by Zimmer and Linder in the Etrans range 0.5-1.5 eV and close to the guided ion beam results by Haufler et al. for (H-, D2) in the range 0.8-1.2 eV. Time-dependent quantum mechanical (TDQM) results obtained using centrifugal sudden approximation are reported in the form of integral reaction cross section values as a function of Etrans in the range 0.3-3.0 eV for both reactions in three dimensions on the same potential energy surface. The TDQM reaction cross section values decline more sharply than the TIQM results with increase in the initial rotational quantum number (j) for the D2 molecules in their ground vibrational state (v = 0) for (H-, D2) collisions. The computed j-weighted reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder for (H-, D2) collisions and guided ion beam results by Haufler et al. for both (H-, D2) and (D-, H2) collisions for energies below the threshold for electron detachment channel.     

A quantum reaction dynamics study of the translational, vibrational, and rotational motion effects on the HD + H3+ reaction

Time-dependent, quantum reaction dynamics wavepacket approach is employed to investigate the impacts of the translational, vibrational, and rotational motion on the HD+H(3)(+) → H(2)D(+) + H(2) reaction using the Xie-Braams-Bowman potential energy surface [Z. Xie, B. J. Braams, and J. M. Bowman, J. Chem. Phys. 122, 224307 (2005)]. We treat this five atom reaction with a seven-degree-of-freedom model by fixing one Jacobi and one torsion angle related to H(3) (+) at the lowest saddle point geometry of the potential energy surface. The initial state selected reaction probabilities show that the rotational excitations of H(+)-H(2) greatly enhance the reactivity with the reaction probabilities increased double at high rotational states compared to the ground state. However, the vibrational excitations of H(3) (+) hinder the reactivity. The ground state reaction probability shows no reaction threshold for this exoergic reaction, and as the translational energy increases, the reaction probability decreases. Furthermore, reactive resonances and zero point energy play very important roles on the reaction dynamics. The obtained integral cross section has the character of an exoergic reaction without a threshold: it decreases with the translational energy increasing. The calculated thermal rate constants using this seven-degree-of-freedom model are in agreement with a later experiment measurement.     

Time-dependent wave packet quantum and quasi-classical trajectory study of He + H₂⁺, D₂⁺ → HeH⁺ + H, HeD⁺ + D reaction on an accurate FCI potential energy surface

The quantum scattering dynamics and quasi-classical trajectory (QCT) calculations have been carried out for the title reaction on an accurate potential energy surface (PES) computed using the full configuration interaction (FCI). On the basis of the PES, the integral cross-sections of He + H?? (v = 0-3, j = 1) → HeH? + H reaction have been calculated, and the results are generally agreed with the experimental cross-sections obtained by Tang et al. [J. Chem. Phys. 2005, 122, 164301] after taking into account the experimental uncertainties, which proves the reliability of implementing dynamics calculations on the FCI PES. The reaction probability of He + D?? (v = 0-2, j = 0) → HeD? + D reactions for total angular momentum J = 0 and the integral cross-section (ICS) have been calculated. The significant quantum effect has been explored by the comparison between the QCT reaction probabilities (or ICS) and the quantum mechanical (QM) reaction probabilities (or ICS), which may be attributed to the deep well in the PES of this light atoms system. Furthermore, the role of Coriolis coupling (CC) effects has also been found not important by the comparison between the CC calculation and the centrifugal sudden (CS) approximation calculation, except that the CC total cross-sections for the v = 1 and 2 states show the collision energy-dependent behaviors in the low-energy area, which are different from those based on the CS calculation.     

Time-dependent quantum mechanical wave packet study of the He+H(2) (+)(v,j)-->HeH(+)+H reaction

A detailed three-dimensional time-dependent quantum dynamical study of the He+H(2) (+)(v=0-3,j=0)-->HeH(+)+H reaction is reported for different vibrational v states of H(2) (+) in its ground rotational (j=0) state over a range of translational E(trans) energies on an accurate ab initio potential energy surface published by Palmieri et al. Plots of reaction probability as a function of total energy E reveal a large number of oscillations indicating the presence of a number of reactive scattering resonances. When averaged over total angular momentum J, some of the oscillations survive, indicating that they may be amenable to experimental observation. A comparison of our present results with our earlier results on the McLaughlin-Thompson-Joseph-Sathyamurthy surface and the experimental results from different research groups reveal a good deal of agreement as well as some discrepancies between theory and experiment at the level of state-selected gas phase dynamics.     

A new analytical potential energy surface for the singlet state of He2H+

The analytic potential energy surface (APES) for the exchange reaction of HeH(+) (X(1)Σ(+)) + He at the lowest singlet state 1(1)A(∕) has been built. The APES is expressed as Aguado-Paniagua function based on the many-body expansion. Using the adaptive non-linear least-squares algorithm, the APES is fitted from 15 682 ab initio energy points calculated with the multireference configuration interaction calculation with a large d-aug-cc-pV5Z basis set. To testify the new APES, we calculate the integral cross sections for He + H(+)He (v = 0, 1, 2, j = 0) → HeH(+) + He by means of quasi-classical trajectory and compare them with the previous result in literature.     

Observation of partial wave structures in the integral cross section of the S((1)D2) + H2(j = 0) reaction

The integral cross section of the S((1)D(2)) + H(2)(j = 0) → SH + H reaction has been measured for the first time at collision energies from 0.820 down to 0.078 kJ mol(-1) in a high-resolution crossed beam experiment. The excitation function obtained exhibits a non-monotonic variation with collision energy and compares well with the results of high-level quantum calculations. In particular, the structures observed in the lower energy part, where only a few partial waves contribute, can be described in terms of the sequential opening of individual channels, consistent with the theoretical calculations.     

Fully converged integral cross sections of collision induced dissociation, four-center, and single exchange reactions, and accuracy of the centrifugal sudden approximation in H2 + D2 reaction

The initial state selected time-dependent wave packet method was employed to calculate the integral cross sections for the H(2) + D(2) reaction with and without the centrifugal sudden (CS) approximation by including all important K (the projection of the total angular momentum on the body-fixed axis) blocks. With a full-dimensional model, the first fully converged coupled-channel (CC) cross sections for different competitive processes from the ground rotational state were obtained: collision induced dissociation (CID), four-center (4C) reaction and single exchange (SE) reaction. The effect of the total angular momentum J on the reaction dynamics of H(2) + D(2) and the accuracy of the CS approximation have also been studied. It was found that the CID and SE processes occur in a wide range of J values while the 4C process can only take place in a narrow window of J values. For this reason, the CC cross section for the 4C channel is merely comparable to the SE channel. A comparison of the integral cross sections from CC and CS calculations showed that the CS approximation works well for the CID process but not for the 4C and SE processes, and the discrepancy between the CC and CS cross sections grows larger as the translational energy and/or the vibrational energy increase(s).     

Quantum dynamics of Br + HD reaction

In this article we report the results of three-dimensional time-dependent quantum wavepacket calculations carried out for the Br + HD( v = 0, j = 0) reaction in the collision energy range 0.0-1.2 eV. An accurate potential energy surface computed by Kurosaki was used for the dynamical calculations. Both reactive channels, BrH + D and BrD + H, show vibrational enhancement of the reaction cross sections. For the three initial vibrational states considered, the production of BrD channel dominates over that of BrH for the considered collision energy range. The two arrangement channels exhibit different initial rotational state dependence. The cross section for the formation of BrD is almost independent of j whereas the same for the formation of BrH increases with increase in j. A comparison with the results on an e-LEPS surface shows that the two surfaces behave very differently with respect to the cross section for the initial rotational states.     

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.     

Overlapping resonances and Regge oscillations in the state-to-state integral cross sections of the F+H2 reaction

A Regge pole analysis is employed to explain the oscillatory patterns observed in numerical simulations of integral cross section for the F+H(2)(v=0,j=0)-->HF(v(')=2,j(')=0)+H reaction in the translational collision energy range 25-50 meV. In this range the integral cross section for the transition, affected by two overlapping resonances, shows nearly sinusoidal oscillations below 38 meV and a more structured oscillatory pattern at larger energies. The two types of oscillations are related to the two Regge trajectories which (pseudo) cross near the energy where the resonances are aligned. Simple estimates are given for the periods of the oscillations.     

An investigation of nonadiabatic interactions in Cl(2Pj) + D2 via crossed-molecular-beam scattering

We have determined limits on the cross section for both electronically nonadiabatic excitation and quenching in the Cl((2)P(j)) + D(2) system. Our experiment incorporates crossed-molecular-beam scattering with state-selective Cl((2)P(12,32)) detection and velocity-mapped ion imaging. By colliding atomic chlorine with D(2), we address the propensity for collisions that result in a change of the spin-orbit level of atomic chlorine either through electronically nonadiabatic spin-orbit excitation Cl((2)P(32)) + D(2)-->Cl(*)((2)P(12)) + D(2) or through electronically nonadiabatic spin-orbit quenching Cl(*)((2)P(12)) + D(2)-->Cl((2)P(32)) + D(2). In the first part of this report, we estimate an upper limit for the electronically nonadiabatic spin-orbit excitation cross section at a collision energy of 5.3 kcal/mol, which lies above the energy of the reaction barrier (4.9 kcal/mol). Our analysis and simulation of the experimental data determine an upper limit for the excitation cross section as sigma(NA)< or =0.012 A(2). In the second part of this paper we investigate the propensity for electronically nonadiabatic spin-orbit quenching of Cl(*) following a collision with D(2) or He. We perform these experiments at collision energies above and below the energy of the reaction barrier. By comparing the amount of scattered Cl(*) in our images to the amount of Cl(*) lost from the atomic beam we obtain the maximum cross section for electronically nonadiabatic quenching as sigma(NA)< or =15(-15) (+44) A(2) for a collision energy of 7.6 kcal/mol. Our experiments show the probability for electronically nonadiabatic quenching in Cl(*) + D(2) to be indistinguishable to that for the kinematically identical system of Cl(*) + He.     

Adiabatic and non-adiabatic quantum dynamics calculation of O(1D) + D2 → OD + D reaction

Adiabatic (1A' or 1A' state) and non-adiabatic (2A'/1A' states) quantum dynamics calculations have been carried out for the title reaction (O((1)D) + D(2) → OD + D) to obtain the initial state-specified (v(i) = 0, j(i) = 0) integral cross section and rate constant using the potential energy surfaces of Dobbyn and Knowles. A total of 50 partial wave contributions have been calculated using the Chebyshev wave packet method with full Coriolis coupling to achieve convergence up to the collision energy of 0.28 eV. The total integral cross section and rate constant are in excellent agreement with experimental as well as quasi-classical trajectory results. Contributions from the adiabatic pathway of the 1A' state and the non-adiabatic pathway of the 2A'/1A' states, increase significantly with the collision energy. Compared to the O((1)D) + H(2) system, the kinetic isotope effect (k(D)/k(H)) is found to be nearly temperature independent above 100 K and its value of 0.77 ± 0.01 shows excellent agreement with the experimental result of 0.81.     

Quantum Dynamics Study on D+OD+ Reaction: Competition between Exchange and Abstraction Channels

Quantum dynamics for the D+OD⁺ reaction at the collision energy range of 0.0-1.0 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstrac-tion (D+OD⁺→O⁺+D₂) and thermoneutral exchange (D+OD⁺→D+OD⁺) channels were investigated from the same set of time-dependent quantum wave packets method under cen-trifugal sudden approximation. The reaction probability dependence with collision energy, the integral cross sections, and the thermal rate constant of the both channels are calculated. It is found that there is a convex structure in the reaction path of the exchange reaction. The calculated time evolution of the wave packet distribution at J=0 clearly indicates that the convex structure significantly influences the dynamics of the exchange and abstraction channels of title reaction.     

Three dimensional quantum dynamics of (H-, H2) and its isotopic variants

We present the results of a time-dependent quantum mechanical investigation using centrifugal sudden approximation in the form of reaction probability as a function of collision energy (E(trans)) in the range 0.3-3.0 eV for a range of total angular momentum (J) values and the excitation function sigma(E(trans)) for the exchange reaction H(-) + H(2) (v = 0, j = 0) --> H(2) + H(-) and its isotopic variants in three dimensions on an accurate ab initio potential energy surface published recently (J. Chem. Phys. 2004, 121, 9343). The excitation function results are shown to be in excellent agreement with those obtained from crossed beam measurements by Zimmer and Linder for H(-) + D(2) collisions for energies below the threshold for electron detachment channel and somewhat larger than the most recent results of Haufler et al. for (H(-), D(2)) and (D(-), H(2)) collisions.     

Guided-ion beam and theoretical study of the potential energy surface for activation of methane by W+

A guided-ion beam tandem mass spectrometer is used to study the reactions, W(+) + CH(4) (CD(4)) and [W,C,2H](+) + H(2) (D(2)), to probe the [W,C,4H](+) potential energy surface. The reaction W(+) + CH(4) produces [W,C,2H](+) in the only low-energy process. The analogous reaction in the CD(4) system exhibits a cross section with strong differences at the lowest energies caused by zero-point energy differences, demonstrating that this reaction is slightly exothermic for CH(4) and slightly endothermic for CD(4). The [W,C,2H](+) product ion reacts further at thermal energies with CH(4) to produce W(CH(2))(x)(+) (x = 2-4). At higher energies, the W(+) + CH(4) reaction forms WH(+) as the dominant ionic product with smaller amounts of WCH(3)(+), WCH(+), and WC(+) also formed. The energy dependent cross sections for endothermic formation of the various products are analyzed and allow the determination of D(0)(W(+)-CH(3)) approximately 2.31 +/- 0.10 eV, D(0)(W(+)-CH(2)) = 4.74 +/- 0.03 eV, D(0)(W(+)-CH) = 6.01 +/- 0.28 eV, and D(0)(W(+)-C) = 4.96 +/- 0.22 eV. We also examine the reverse reaction, [W,C,2H](+) + H(2) (D(2)) --> W(+) + CH(4) (CH(2)D(2)). Combining the cross sections for the forward and reverse processes yields an equilibrium constant from which D(0)(W(+)-CH(2)) = 4.72 +/- 0.04 eV is derived. Theoretical calculations performed at the B3LYP/HW+/6-311++G(3df,3p) level yield thermochemistry in reasonable agreement with experiment. These calculations help identify the structures and electronic states of the species involved and characterize the potential energy surface for the [W,C,4H](+) system.     

The excitation function for Li + HF → LiF + H at collision energies below 80 meV

We have measured the dependence of the relative integral cross section of the reaction Li + HF → LiF + H on the collision energy (excitation function) using crossed molecular beams. By varying the intersection angle of the beams from 37° to 90° we covered the energy range 25 meV ≤ E(tr) ≤ 131 meV. We observe a monotonous rise of the excitation function with decreasing energy over the entire energy range indicating that a possible translational energy threshold to the reaction is significantly smaller than 25 meV. The steep rise is quantitatively recovered by a Langevin-type excitation function based on a vanishing threshold and a mean interaction potential energy ∝R(-2.5) where R is the distance between the reactants. To date all threshold energies deduced from ab initio potentials and zero-point vibrational energies are at variance with our results, however, our findings support recent quantum scattering calculations that predict significant product formation at collision energies far below these theoretical thresholds.