Quasiclassical Trajectory Cross Sections Research Articles

A Quasiclassical Trajectory Study of the Reaction of H Atoms with O2((1)Δg).

The kinetic and dynamic characteristics of the reaction of H atoms with electronically excited O2 were studied using the quasiclassical trajectory (QCT) method and the potential energy surface of Li et al. ( J. Chem. Phys. 2010 , 133 , 144306 - 144314 ). The reaction takes place via a deep potential well that can be entered by climbing a barrier in the reactant valley and can be left without a barrier on the product side. In this reaction, the basic assumptions of statistical rate theories are not fulfilled: (i) 80% of the trajectories cross the barrier region twice and are nonreactive; (ii) the energy is not equilibrated in the HO2 potential well. The QCT cross sections agree well with those from the existing exact quantum-mechanical data and extend them to vib-rotationally excited reactants. The thermal rate coefficients agree well with measurements of pure reactive quenching of O2((1)Δg) and are lower than those involving both reactive and electronic quenching. The temperature dependence is described as k2 = 5.81 × 10(-16) T(1.45) exp(-2270/T) cm(3) molecule(-1) s(-1). On the basis of a comparison of the QCT data with the two kinds of experiments, we estimate that electronic quenching is faster than reaction by a factor of about 10 at low and 2 at high flame temperatures.

Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies: II. Quasiclassical trajectory analysis

Recent calculations on the hydrogen-exchange reaction [Bouakline et al., J. Chem. Phys. 128, 124322 (2008)], have found strong geometric phase (GP) effects in the state-to-state differential cross-sections (DCS), at energies above the energetic minimum of the conical intersection (CI) seam, which cancel out in the integral cross-sections (ICS). In this article, we explain the origin of this cancellation and make other predictions about the nature of the reaction mechanisms at these high energies by carrying out quasiclassical trajectory (QCT) calculations. Detailed comparisons are made with the quantum results by splitting the quantum and the QCT cross-sections into contributions from reaction paths that wind in different senses around the CI and that scatter the products in the nearside and farside directions. Reaction paths that traverse one transition state (1-TS) scatter their products in just the nearside direction, whereas paths that traverse two transition states (2-TS) scatter in both the nearside and farside directions. However, the nearside 2-TS products scatter into a different region of angular phase-space than the 1-TS products, which explains why the GP effects cancel out in the ICS. Analysis of the QCT results also suggests that two separate reaction mechanisms may be responsible for the 2-TS scattering at high energies.

Relaxation of NH(a1Δ, v = 1) in Collisions with H(2S): An Experimental and Theoretical Study

Collisions of electronically and vibrationally excited NH(a(1)Delta, v = 1) with H atoms were investigated by experimental, quantum mechanical (QM) wavepacket, and quasiclassical trajectory (QCT) methods. The NH(a(1)Delta, v = 1) total loss rate constant, corresponding to the sum of the NH vibrational relaxation, N((2)D)+H(2) formation, and electronic quenching to NH(X(3)Sigma(-)), was measured at room temperature. Most of the calculations were performed within the Born-Oppenheimer approximation, neglecting electronic quenching due to Renner-Teller coupling because QCT calculations showed that for the loss of NH(a(1)Delta, v = 1) the contribution of quenching is negligible. The QM study included Coriolis couplings, and the QCT study counted only trajectories ending close to a vibrational quantum level of the product diatom. The collisions are dominated by long-lived intermediate complexes, and QM probabilities and cross sections thus exhibit pronounced resonances. QM and QCT cross sections and rate coefficients of the various processes are in very good agreement. The measured rate constant is (9.1 +/- 3.3) x 10(-11) cm(3) s(-1), compared with (14.4 +/- 0.5) x 10(-11) and (15.6 +/- 1.6) x 10(-11) cm(3) s(-1), as obtained from QM and QCT calculations, respectively. The reason for the theoretical overestimation is unknown.

An experimental and quasiclassical trajectory study of the rovibrationally state-selected reactions: HD+(v=–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 pulsed-field ionization photoelectron secondary ion coincidence study of the H2+(X,υ+=–15,N+=1)+He proton transfer reaction

The endothermic proton transfer reaction, H2+(upsilon+)+He-->HeH+ + H(DeltaE=0.806 eV), is investigated over a broad range of reactant vibrational levels using high-resolution vacuum ultraviolet to prepare reactant ions either through excitation of autoionization resonances, or using the pulsed-field ionization-photoelectron-secondary ion coincidence (PFI-PESICO) approach. In the former case, the translational energy dependence of the integral reaction cross sections are measured for upsilon+=0-3 with high signal-to-noise using the guided-ion beam technique. PFI-PESICO cross sections are reported for upsilon+=1-15 and upsilon+=0-12 at center-of-mass collision energies of 0.6 and 3.1 eV, respectively. All ion reactant states selected by the PFI-PESICO scheme are in the N+=1 rotational level. The experimental cross sections are complemented with quasiclassical trajectory (QCT) calculations performed on the ab initio potential energy surface provided by Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. The QCT cross sections are significantly lower than the experimental results near threshold, consistent with important contributions due to resonances observed in quantum scattering studies. At total energies above 2 eV, the QCT calculations are in excellent agreement with the present results. PFI-PESICO time-of-flight (TOF) measurements are also reported for upsilon+=3 and 4 at a collision energy of 0.6 eV. The velocity inverted TOF spectra are consistent with the prevalence of a spectator-stripping mechanism.

Quantum reactive scattering calculations of cross sections and rate constants for the N(2D)+O2(X 3Σg−)→O(3P)+NO(X 2Π) reaction

Time-dependent quantum wave packet calculations have been performed on the two lowest adiabatic potential energy surfaces (2 2A′ and 1 2A″) for the N(2D)+O2(X 3Σg−)→O(3P)+NO(X 2Π) reaction. The calculations have been carried out, on these recently published potential energy surfaces, using the real wave packet method together with a new dispersion fitted finite difference technique for evaluating the action of the radial kinetic energy operator. Reaction probabilities, corresponding to the O2 reactant in its ground vibrational-rotational state, have been calculated for both surfaces and for many different values of the total angular momentum quantum number (J), within the helicity decoupling approximation. The reaction probabilities associated with all other relevant J values have been interpolated, and to a smaller extent extrapolated, using a capture model, to yield probabilities as a function of energy. The probabilities have in turn been summed to yield energy dependent cross sections and then used to compute rate constants. These rate constants are compared with ones obtained from quasiclassical trajectory (QCT) and variational transition state theory (VTST) calculations performed on the same surfaces. There is a good agreement between the wave packet and QCT cross sections for reaction on both potential energy surfaces considered, with the exception of the near threshold region, where the reaction probability is dominated by tunnelling. Comparison of the predicted rate constants shows that for the 2 2A′ surface, above 300 K, the wave packet, QCT and VTST results are quite similar. For the 1 2A″ surface, however, significant differences occur between the wave packet and the other methods. These differences become smaller with increasing temperature. It is likely that these differences arise, at least in part, from the fact that, when calculating the rate constants, the reactants are restricted to be in their lowest vibrational-rotational state in the wave packet calculations but are selected from a thermally equilibrated population in the other methods.

Hot atom reaction yields in Mu*+H2 and T*+H2 from quasiclassical trajectory cross sections on the Liu–Siegbahn–Truhlar–Horowitz surface

In order to provide an assessment of the “global” accuracy of the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential surface for H3, hot atom reaction yields, which are determined from collision processes over an energy range much wider than that of single-collision experiments, have been calculated for the Mu*+H2 and T*+H2 systems. The isotopic comparison of muonium (Mu=μ+e−), an ultralight isotope of hydrogen (mMu/mH≈1/9), with the heaviest H-atom isotope, tritium, is a novel approach in testing the global accuracy of the H3 surface. These reaction yields have been calculated using a formalism developed for (μ+) charge exchange, with input cross sections for elastic, inelastic (rovibrational excitation) and reactive collisions determined from quasi classical trajectories on the LSTH surface, in the center-of-mass energy range 0.5–11 eV. The rate of energy loss of the hot atom (Mu* or T*) due to elastic and inelastic collisions with the moderator (H2) drastically affects the hot atom reaction yield. In particular, the forwardness of the angular differential cross section for the elastic process plays a crucial role in determining the stopping power for hot atoms. Good agreement is obtained in the absolute yields for both Mu*+H2 and T*+H2, for the first time from microscopic cross sections, demonstrating that the LSTH surface remains surprisingly accurate over a wide range of energy and isotopic mass.

Accurate 3 dimensional quantum dynamical study of the Ne+H2+→NeH++H reaction

In this work a comprehensive, fully converged coupled states (CS) quantum mechanical (QM) study of the endothermic Ne+H2+ ion-molecule reaction is presented. The computed dynamical properties are compared with quasi-classical trajectory (QCT) and with the available experimental data. To this end, the analytical potential energy surface of Pendergast, Heck, Hayes, and Jacquet was employed. The two main features of the dynamical behavior for this system are: (1) the rich structure present in the state-selected integral cross section energy-dependent curves, which may be attributed to resonances surviving the partial wave summation; and (2) the large differences between the quantum and the QCT cross sections which are caused by the inability of classical mechanics to conserve the zero point energy. Also noteworthy are the strong enhancement of the reactivity due to higher vibrational states and the effect of the activated complex, formed during the reaction process, on the angular and the rotational distributions.

A test of the semiclassical Wigner method for the reaction F + H2 → H + HF

Abstract We compute the vibrationally resolved integral cross sections σ R (ν′), differential cross sections, and opacity functions for the reaction F + H 2 ( ν = 0, j = 0, 1) → H + HF( ν ′, j ′) on the 6SEC potential energy surface by the quasiclassical trajectory technique as well as the Wigner method. In both cases, the Langer correction of the initial H 2 rotational energy is implemented. The results are compared with the recent quasiclassical trajectory calculations on the same surface without the Langer correction and quantum mechanical calculations. It is shown that use of the Wigner phase space functions to describe the H 2 and HF vibrational degrees of freedom reduces the total integral cross sections, smooths the selective HF( ν ′ = 3) forward peak in the HF center-of-mass angular distributions, and dramatically increases the σ R ( ν ′ = 3)/ σ R ( ν ′ = 2) vibrational branching ratio. These results indicate that the disagreements between the quasiclassical trajectory cross sections and the quantum mechanical ones observed in the previous works cannot be minimized by just a proper choice and weighting of the initial conditions in the quasiclassical trajectory calculations.

Comparison of cross sections from the quasi-classical trajectory method and the jz-conserving centrifugal sudden approximation with accurate quantum results for an atom-rigid nonlinear polyatomic collision

We report the results of a series of calculations of state-to-state integral cross sections for collisions between O and nonvibrating H2O in the gas phase on a model nonreactive potential energy surface. The dynamical methods used include converged quantum mechanical scattering calculations, the j(z) conserving centrifugal sudden (j(z)-CCS) approximation, and quasi-classical trajectory (QCT) calculations. We consider three total energies 0.001, 0.002, and 0.005 E(h) and the nine initial states with rotational angular momentum less than or equal to 2 (h/2 pi). The j(z)-CCS approximation gives good results, while the QCT method can be quite unreliable for transitions to specific rotational sublevels. However, the QCT cross sections summed over final sublevels and averaged over initial sublevels are in better agreement with the quantum results.

Comparison of quasiclassical and quantum dynamics for resonance scattering in the Cl+HCl→ClH+Cl reaction

We present the results of quasiclassical trajectory (QCT) and quantum centrifugal sudden hyperspherical (CSH) scattering calculations for the Cl+HCl→ClH+Cl reaction using a semiempirical potential energy surface. In particular, we report state-to-state integral and differential cross sections in the vicinity of a transition state resonance that occurs at a total energy E of 0.642 eV. This resonance, which is labeled by the transition state quantum numbers (0,0,2), strongly perturbs the cross sections for the initial rovibrational state HCl(v=1, j=5), which was therefore considered in all our calculations. For E≥0.680 eV, which is well removed from the resonance energy, the QCT and CSH results are in good agreement, but for E near the resonance energy, important quantum effects are found in the integral cross sections, product state distributions, and differential cross sections. The CSH integral cross sections show smooth steplike increases for E≊0.642 eV, which are not seen in the QCT results. Associated with these steps are increased branching to the v′=0 product HCl vibrational state, and a strong propensity for the production of rotational states with j′=15 and 16 for v′=0. These features of the product energy partitioning are not present in the QCT results, although the correct rotational distributions are approximately recovered if the final vibrational action is constrained to match its quantum value. The CSH differential cross sections show a sudden shift from backward to sideward scattering between 0.642 and 0.660 eV, while the QCT cross sections remain backward peaked. An analysis of the ‘‘number of atom–diatom encounters,’’ during the course of a reactive collision, shows that there are chattering trajectories. These are associated with sideward scattering, but their probability is low and as a result they do not produce distinct features in the angular distributions. However, if the classical deflection function is weighted by the quantum reaction probability, angular distributions are obtained that are in reasonable agreement with the CSH angular distributions (including resonance features).

Dynamics of heavy + light–heavy atom transfer reactions. The reaction Cl + HCl → ClH + Cl

The effect of reactant rotational energy on the dynamics of the light-atom-transfer reaction Cl + HCl(v= 0, j)→ ClH + Cl has been investigated on an extended London–Eyring–Polanyi–Sato (LEPS) potential-energy surface using the centrifugal-sudden distorted-wave (CSDW) method, together with quasiclassical trajectory (QCT) computations. CSDW cross-sections have been calculated at total energies of Etotal= 0.40 and 0.50 eV, whilst QCT cross-sections were computed at Etotal= 0.50, 0.60, 0.70 and 1.183 eV. In all cases we find that reactant rotational energy is very effective in promoting the reaction, and that the products are formed in highly excited rotational states. The properties of individual trajectories during the course of the reaction have been studied, in order to gain insight into the dynamics of the reaction. For rotationally excited reactants at Etotal= 0.70 and 1.183 eV, trajectories undergoing a ‘figure-of-eight’ motion from an important part of the reaction mechanism.

Quantum mechanical study of the D+H2→HD+H reaction

A quantum mechanical study is made of the D+H2(vi=0,1)→ HD(vf=0,1,2)+H reactions within the infinite order sudden approximation (IOSA) for the total energy interval 0.28≤Et≤1.28 eV. Results at various stages of the calculation are given ranging from most detailed reactive transition probabilities through opacity functions and γ-dependent cross sections to total and state-to-state integral and differential cross sections, as well as rate constants. The cross sections and rate constants are compared with other available theoretical results and experiments. It is found that the IOSA total cross sections for vi=0,1 overlap very nicely with the corresponding quasiclassical trajectory cross sections, except for the tunneling region. A less satisfactory fit is obtained with the distorted wave born approximation results. The calculated rate constants are compared with experiment and a rather good fit is obtained, in particular for rate constants from the ground state.

The origin of cross section thresholds in H+H2: Why quantum dynamics appears to be more vibrationally adiabatic than classical dynamics

In this paper, cross sections and J=0 reaction probabilities from the results of quasiclassical trajectory (QCT) and accurate quantum reactive scattering calculations are presented and compared for H+H2 (v=0) and H+H2 (v=1). For both v=0 and v=1, the energies associated with the effective thresholds for reaction in the quantum results are consistent with the adiabatic treatment of bending motions along the reaction coordinate. This is best illustrated by comparing the 3D J=0 reaction probabilities with those from analogous collinear calculations, and with collinear calculations in which the bending zero point energy is added in adiabatically at every point in collinear configuration space. The quasiclassical trajectory cross sections and probabilities, on the other hand, have thresholds which are well below the quantum thresholds, primarily because of reactive trajectories which have little or no energy in bending near the effective reaction bottleneck. This effect is especially important for H+H2 (v=1) and leads to QCT rate constants which are much higher than the quantum ones at 300 K. Classical methods designed to reduce this threshold error are studied, and the most successful of these is one in which the local bending zero point energy is added adiabatically in the full dimensional configuration space. The origin of the threshold error is examined, and it is found that the constraints associated with the uncertainty principle rather than with vibrational adiabaticity are the most important in determining the threshold behavior associated with bending. These constraints lead to the prediction that the vibrationally adiabatic (ground bending state) threshold is the correct one, which means that the quantum threshold appears to be governed by adiabatic theory even when motional time scales are such that the adiabatic approximation is invalid. The classical threshold, on the other hand, is close to the adiabatic threshold only when motional time scales are appropriate.