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.     

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.     

A state-to-state dynamical study of the Br + H(2) reaction: comparison of quantum and classical trajectory results

We present a detailed theoretical investigation of the dynamics corresponding to the strongly endothermic Br + H(2) (v = 0-1, j = 0) → H + HBr reaction in the 0.85 to 1.9 eV total energy range. State-averaged and state-to-state results obtained through time-independent wave packet (TIWP) and time-independent quantum mechanical (TIQM) calculations and quasiclassical trajectories (QCT) are compared and analyzed. The agreement in the results obtained with both quantum mechanical results is very good overall. However, although QCT calculations reproduce the general features, their agreement with the QM results is sometimes only qualitative. The analysis of the mechanism based on state-averaged results turns out to be deceptive and conveys an oversimplified picture of the reaction consistent with a direct-rebound mechanism. Consideration of state-to-state processes, in contrast, unveils the existence of multiple mechanisms that give rise to a succession of maxima in the differential cross section (DCS). Such mechanisms correlate with different sets of partial waves and display similar collision times when analyzed through the time-dependent DCS.     

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.     

Time-dependent reactive scattering for the system H- + D2 <--> HD + D- and comparison with H- + H2 <--> H2 + H-

This work presents results of quantum mechanical calculations of reaction probabilities for the ion-neutral molecule collisions H- + D2 <--> HD + D-. Time-dependent wave packet propagations for total angular momentum J not equal to 0, including the full Coriolis coupling, are performed. The calculated state-to-state reaction probabilities using product Jacobi coordinates are compared with energy-resolved reaction probabilities calculated with the flux-operator using reactant Jacobi coordinates and with time-independent calculations. Differences between nearly converged integral cross sections and those using the J-shifting method and centrifugal sudden approximation and comparison with experimental results will be presented.     

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.     

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.     

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.     

State-to-state quantum dynamics of the H + HBr reaction: competition between the abstraction and exchange reactions

Quantum state-to-state dynamics for the H + HBr(υ(i) = 0, j(i) =0) reaction was studied on an accurate ab intio potential energy surface for the electronic ground state of BrH(2). Both the H + HBr → H(2) + Br abstraction reaction and the H' + HBr → H'Br + H exchange reaction were investigated up to a collision energy of 2.0 eV. It was found that the abstraction channel is dominant at lower collision energies, while the exchange channel becomes dominant at higher collision energies. The total integral cross section of the abstraction reaction at a collision energy of 1.6 eV was found to be 1.37 A?(2), which is larger than a recent quantum mechanical result (1.06 A?(2)) and still significantly smaller than the experimental value (3 ± 1 A?(2)). Meanwhile, similar to the previous theoretical study, our calculations also predicted much hotter product rotational state distributions than those from the experimental study. This suggests that further experimental investigations are highly desirable to elucidate the dynamic properties of the title reactions.     

Time dependent quantum dynamics study of the O++H2(v=0,j=0)-->OH++H ion-molecule reaction and isotopic variants (D2,HD)

The time dependent real wave packet method using the helicity decoupling approximation was used to calculate the cross section evolution with collision energy (excitation function) of the O++H2(v=0,j=0)-->OH++H reaction and its isotopic variants with D2 and HD, using the best available ab initio analytical potential energy surface. The comparison of the calculated excitation functions with exact quantum results and experimental data showed that the present quantum dynamics approach is a very useful tool for the study of the selected and related systems, in a quite wide collision energy interval (approximately 0.0-1.1 eV), involving a much lower computational cost than the quantum exact methods and without a significant loss of accuracy in the cross sections.     

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.     

Exact quantum scattering study of the H + HS reaction on a new ab initio potential energy surface H2S (3A")

We present an exact quantum dynamical study and quasi-classical trajectory (QCT) calculations for the exchange and abstraction processes for the H + HS reaction. These calculations were based on a newly constructed high-quality potential energy surface for the lowest triplet state of H(2)S ((3)A"). The ab initio single-point energies were computed using complete active space self-consistent field and multi-reference configuration interaction method with a basis set of aug-cc-pV5Z. The time-dependent wave packet (TDWP) method was used to calculate the total reaction probabilities and integral cross sections over the collision energy (E(col)) range of 0.0-2.0 eV for the reactant HS initially at the ground state and the first vibrationally excited state. It was found that the initial vibrational excitation of HS enhances both abstraction and exchange processes. In addition, a good agreement is found between QCT and TDWP reaction probabilities at the total momentum J = 0 as a function of collision energy for the H + HS (v = 0, j = 0) reaction.     

Nonadiabatic effects in the H+D2 reaction

The state-to-state dynamics of the H+D2 reaction is studied by the reactant-product decoupling method using the double many-body expansion potential energy surface. Two approaches are compared: one uses only the lowest adiabatic sheet while the other employs both coupled diabatic sheets. Rotational distributions for the reaction H+D2 (upsilon = 0, j = 0)-->HD(upsilon' = 3, j')+D are obtained at eight different collision energies between 1.49 and 1.85 eV; no significant difference are found between the two approaches. Initial state-selected total reaction probabilities and integral cross sections are also given for energies ranging from 0.25 up to 2.0 eV with extremely small differences being observed between the two sets of results, thus showing that the nonadiabatic effects in the title reaction are negligible at least for small energies below 2.0 eV.     

Accurate time dependent wave packet calculations for the N + OH reaction

We present accurate quantum calculations of state-to-state cross sections for the N + OH → NO + H reaction performed on the ground (3)A' global adiabatic potential energy surface of Guadagnini et al. [J. Chem. Phys. 102, 774 (1995)]. The OH reagent is initially considered in the rovibrational state ν = 0, j = 0 and wave packet calculations have been performed for selected total angular momentum, J = 0, 10, 20, 30, 40,...,120. Converged integral state-to-state cross sections are obtained up to a collision energy of 0.5 eV, considering a maximum number of eight helicity components, Ω = 0,...,7. Reaction probabilities for J = 0 obtained as a function of collision energy, using the wave packet method, are compared with the recently published time-independent quantum mechanical one. Total reaction cross sections, state-specific rate constants, opacity functions, and product state-resolved integral cross-sections have been obtained by means of the wave packet method for several collision energies and compared with recent quasi-classical trajectory results obtained with the same potential energy surface. The rate constant for OH(ν = 0, j = 0) is in good agreement with the previous theoretical values, but in disagreement with the experimental data, except at 300 K.     

Quantum and classical studies of the O(3P) + H2(v = 0-3,j = 0) --> OH + H reaction using benchmark potential surfaces

We present results of time-dependent quantum mechanics (TDQM) and quasiclassical trajectory (QCT) studies of the excitation function for O(3P) + H2(v = 0-3,j = 0) --> OH + H from threshold to 30 kcal/mol collision energy using benchmark potential energy surfaces [Rogers et al., J. Phys. Chem. A 104, 2308 (2000)]. For H2(v = 0) there is excellent agreement between quantum and classical results. The TDQM results show that the reactive threshold drops from 10 kcal/mol for v = 0 to 6 for v = 1, 5 for v = 2 and 4 for v = 3, suggesting a much slower increase in rate constant with vibrational excitation above v = 1 than below. For H2(v > 0), the classical results are larger than the quantum results by a factor approximately 2 near threshold, but the agreement monotonically improves until they are within approximately 10% near 30 kcal/mol collision energy. We believe these differences arise from stronger vibrational adiabaticity in the quantum dynamics, an effect examined before for this system at lower energies. We have also computed QCT OH(v',j') state-resolved cross sections and angular distributions. The QCT state-resolved OH(v') cross sections peak at the same vibrational quantum number as the H2 reagent. The OH rotational distributions are also quite hot and tend to cluster around high rotational quantum numbers. However, the dynamics seem to dictate a cutoff in the energy going into OH rotation indicating an angular momentum constraint. The state-resolved OH distributions were fit to probability functions based on conventional information theory extended to include an energy gap law for product vibrations.     

Dissociative chemisorption of H2 on the Cu(110) surface: a quantum and quasiclassical dynamical study

Six-dimensional quantum dynamical and quasiclassical trajectory (QCT) calculations are reported for the reaction and vibrationally inelastic scattering of (v = 0,1,j = 0) H(2) scattering from Cu(110), and for the reaction and rovibrationally elastic and inelastic scattering of (v = 1,j = 1) H(2) scattering from Cu(110). The dynamics results were obtained using a potential energy surface obtained with density functional theory using the PW91 functional. The reaction probabilities computed with quantum dynamics for (v = 0,1,j = 0) were in excellent agreement with the QCT results obtained earlier for these states, thereby validating the QCT approach to sticking of hydrogen on Cu(110). The vibrational de-excitation probability P(v=1,j = 0 --> v = 0) computed with the QCT method is in remarkably good agreement with the quantum dynamical results for normal incidence energies E(n) between 0.2 and 0.6 eV. The QCT result for the vibrational excitation probability P(v = 0,j = 0 --> v = 1) is likewise accurate for E(n) between 0.8 and 1 eV, but the QCT method overestimates vibrational excitation for lower E(n). The QCT method gives probabilities for rovibrationally (in)elastic scattering, P(v = 1,j = 1 --> v('),j(')), which are in remarkably good agreement with quantum dynamical results. The rotationally averaged, initial vibrational state-selective reaction probability obtained with QCT agrees well with the initial vibrational state-selective reaction probability extracted from molecular beam experiments for v = 1, for the range of collision energies for which the v=1 contribution to the measured total sticking probability dominates. The quantum dynamical probabilities for rovibrationally elastic scattering of (v = 1,j = 1) H(2) from Cu(110) are in good agreement with experiment for E(n) between 0.08 and 0.25 eV.     

Accurate quantum mechanical calculations of differential and integral cross sections and rate constant for the O+OH reaction using an ab initio potential energy surface

The authors report accurate quantum mechanical studies of the O+OH reaction on the improved Xu-Xie-Zhang-Lin-Guo potential energy surface. The differential cross section was obtained at several energies near the reaction threshold using a time-independent method. The dominant forward and backward peaks in the angular distribution are consistent with a complex-forming mechanism, which is also confirmed by the extensive rotational excitation in the O2 product. However, the asymmetry of these peaks suggests a significant nonstatistical component. The initial state (upsilon i=0, j i=0) specified integral cross section, which was calculated up to 1.15 eV of collision energy using the Chebyshev wave packet method, shows no energy threshold and decreases with the increasing collision energy, consistent with the barrierless nature of the reaction. The resulting rate constant exhibits a negative temperature dependence for T>100 K and decays as the temperature is lowered, in qualitative agreement with available experimental data.     

New, unexpected, and dominant mechanisms in the hydrogen exchange reaction

A quasiclassical trajectory study of the state specific H+D(2)(upsilon = 0,j = 0) --> HD(upsilon' = 0,j' = 0) + D reaction at a collision energy of 1.85 eV (total energy of 2.04 eV) found that the scattering is governed by two unexpected and dominant new mechanisms, and not by direct recoil as is generally assumed. The new mechanisms involve strong interaction with the sloping potential around the conical intersection, an area of the potential energy surface not previously considered to have much effect upon reactive scattering. Initial investigations indicate that more than 50% of reactive scattering could be the result of these new mechanisms at this collision energy. Features in the corresponding quantum mechanical results can be attributed to these new (classical) reaction mechanisms.     

A quantum wave packet dynamics study of the N(2D) + H2 reaction

We report a dynamics study of the reaction N((2)D) + H(2) (v=0, j=0-5) --> NH + H using the time-dependent quantum wave packet method and a recently reported single-sheeted double many-body expansion potential energy surface for NH(2)(1(2)A' ') which has been modeled from accurate ab initio multireference configuration-interaction calculations. The calculated probabilities for (v=0, j=0-5) are shown to display resonance structures, a feature also visible to some extent in the calculated total cross sections for (v=0, j=0). A comparison between the calculated centrifugal-sudden and coupled-channel reaction probabilities validate the former approximation for the title system. Rate constants calculated using a uniform J-shifting scheme and averaged over a Boltzmann distribution of rotational states are shown to be in good agreement with the available experimental values. Comparisons with other theoretical results are also made.