Exact quantum,quasiclassical forward and reverse reaction probabilities for a colldmear asymmetric model reaction

Detailed quasiclassical and time-independent quantum reaction probabilities are given for a surface on which large discrepancies between quasiclassical and wavepacket results have previously been found. The quasiclassical results are shown to agree relatively reasonably with the oscillation-averaged time-independent quantum ones if the quasiclassical reverse probabilities are chosen in the threshold region.     

Calculation of the rates of atomic reactions at low energies

The theory of binary atomic reactions is discussed. The matrix Schrödinger equation in the space of electron channels is used for the wave functions of the relative motion of the nuclei; this gives the corresponding quasiclassical equation by retention of terms linear in . Criterion (10) applies for quasiclassical nuclear motion. The additional restriction (13) causes the quasiclassical matrix equation (9) to go over to the basic equation (15) in the method of the central parameter, which indicates the region of application of that method. An Algol-60 program has been drawn up for calculating the rates of atomic reactions via the central-parameter or quasiclassical methods.     

On the quasiclassical approach to collision theory

The exact equation for the quasiclassical trajectory for atom-diatomic oscillator collisions with linear force interaction and constant harmonic frequency is presented. The example indicates necessary modifications for conventional quasiclassical collision theory.     

Constraints at the transition state of the D + H2 reaction: quantum bottlenecks vs. stereodynamics

This article presents a quasiclassical trajectory method for the calculation of cumulative reaction probabilities by sampling of the helicity quantum number of the reagents (k). The method is applied to the D + H(2) reaction at various total angular momentum (J) values, and the helicity-resolved quasiclassical cumulative reaction probabilities are compared to their quantum mechanical counterparts. The agreement between the two sets of results is fairly good. In particular, k-dependent, J-independent reaction thresholds found with quantum methods are reproduced by the quasiclassical calculations. The shift of these thresholds with increasing k, which has been previously attributed to the quantum bottleneck states taking part in the reaction, is revisited and discussed also in terms of the reaction stereodynamics.     

Dynamics of the 18O + 16O2(υ=0) exchange reaction on a new potential energy surface for ground-state ozone

A quasiclassical trajectory study of the thermoneutral isotopic oxygen exchange reaction was made using a recently reported potential energy surface for the ground state of ozone. The calculated macroscopic rate constants show an improvement over the previous quasiclassical results when compared with the experimental values.     

A classical mechanical study of the LiFH system

A three dimensional and collinear quasiclassical study of the Li + HF → LiF + H reaction is performed on the Zeiri—Shapiro semi-empirical potential energy surface. The results are compared to a recent experimental study. In agreement with experiment ≈43% of available energy is channeled to the internal (vibrational and rotational) mode of the LiF product, most of which, we show, ends up as rotation (≈33%) and only the remaining 10% as vibration. The differential cross section is shown to peak in the forward—backward directions as also observed experimentally. The calculated cross section is more backward peaked than the experimental one. The accuracy of the quasiclassical method for this system is assessed by comparison of collinear results with available quantal calculations. It is shown that the average product vibrational distributions are adequately given by the quasiclassical method. The results are analyzed using periodic-orbit-dividing surfaces which predict correctly the onset of the various dynamic barriers.     

The semiclassical and the quasiclassical partition function of a quartic anharmonic oscillator

After a substitution a known Laplace-type integral is used to derive quantum corrections to the classical partition function of a quartic anharmonic oscillator in the framework of the Wigner—Kirkwood perturbation expansion. By straightforward calculations results are given in a closed form allowing the analytical formulation of the thermodynamic functions H, E, S, C_υ. The numerical results agree for arbitrary anharmonicity and for high and intermediate temperatures with the numerical partition function calculated from the Hioe—Montroll eigenvalues. Furthermore, the same integral type is used for the analytical calculation of a “quasiclassical” partition function and of “quasiclassical” moments. In the trace formulation of the partition function all commutators are neglected. The harmonic oscillator density matrix is applied to the evaluation of the truncated trace expressions. The “quasiclassical” partition function is an exact upper bound and lies always below the classical partition function.     

Multidimensional tunneling in the [1,5] shift in (Z)-1,3-pentadiene: how useful are Swain-Schaad exponents at detecting tunneling?

Rates, kinetic isotope effects (KIE), and Swain-Schaad exponents (SSE) have been calculated for a variety of isotopologues for the [1,5] shift in (Z)-1,3-pentadiene using mPW1K/6-31+G(d,p). Quantum mechanical effects along the reaction coordinate were incorporated with the zero-curvature tunneling (ZCT) model and with the multidimensional small curvature tunneling (SCT) model, which allows for coupling of modes perpendicular to the reaction coordinate. The latter model gives the best agreement with experimental rates and primary KIEs. The small quasiclassical primary KIE (2.6) is rationalized in terms of a nonlinear transition state. For sp3 to sp2 rehybridization, the quasiclassical alpha-secondary KIE shows an unusual inverse effect due to compression of the nonbonding hydrogens in the suprafacial transition state. SCT transmission coefficients (kappa) increase the rates by as much as one order of magnitude. Tunneling allows the reactant to evade 1-2.5 kcal/mol of the barrier depending on the isotope. Inclusion of tunneling in the secondary KIE increases it beyond the equilibrium isotope effect and converts the inverse effect (0.95) into a normal KIE (1.12). Tunneling was found to deflate the primary y SSE but by an amount too small to distinguish it from the quasiclassical SSE. On the other hand, when a specific labeling pattern is used, the difference between the quasiclassical secondary SSE (4.1) and the tunneling secondary SSE (2.3) may be sufficiently large to detect tunneling. The mixed secondary SSE shows even larger differences.     

A new quasiclassical method for modeling the high-resolution spectra of polyatomic systems

A new quasiclassical method for quantum autocorrelation functions based on the semiclassical limit in Wigner phase space has been derived. Unlike the existing quasiclassical method, the new method enables long-time simulations, thus making it possible to locate quantum spectral lines very precisely. The new method has been tested for a one-dimensional anharmonic oscillator fitted to the H(2) molecule and for a six-dimensional calculation of the Ar(2)I van der Waals cluster in adiabatic approximation. The obtained results compare well with the benchmark quantum-mechanical calculations and are also roughly comparable to the experimental Ar(2)I(-) zero-kinetic-energy photoelectron spectrum, which is available in the literature.     

An adiabatic capture theory and quasiclassical trajectory study of C + NO and O + CN on the 2A', 2A", and 4A" potential energy surfaces

The adiabatic capture centrifugal sudden approximation (ACCSA) has been applied to the C + NO and O + CN reactions, along with quasiclassical trajectory simulations. Existing global analytic fits to the potential energy surfaces of the CNO system in the (2)A', (2)A", and (4)A" electronic states have been used. Thermal rate constants for reaction in each of the electronic states have been calculated. In all cases a strong temperature dependence is evident in the calculated rate constants. The agreement between the calculated adiabatic capture and quasiclassical trajectory rate constants is excellent in some cases, but these rate constants differ considerably in other cases. This behavior is analyzed in terms of the anisotropy of the potential energy surfaces. On the basis of this analysis, we propose a new diagnostic for the reliability of ACCSA capture calculations.     

The direct histogram method for quasiclassical collision dynamics: application to collinear atom-diatom scattering

A method is presented for directly propagating ensembles of collision trajectories, such the histogram-type final state distributions are obtained. A substantial savings over standard quasiclassical methods is possible since only a few trajectory ensembles need to be propagated.     

Quantum and quasiclassical state-to-state dynamics of the NH + H reaction: competition between abstraction and exchange channels

Quantum and quasiclassical state-to-state dynamics for the NH + H' reaction at high collision energies up to 1.6 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction (NH + H' → N + HH') and thermoneutral exchange (NH + H' → H + NH') channels were investigated from the same set of wave packets using an efficient coordinate transformation method. It is found that the abstraction represents a minor reaction channel in the energy range studied, primarily due to endothermicity. The cross section for the abstraction reaction increases monotonically with the collision energy, while that for the exchange reaction is relatively energy insensitive. As a result, the thermal rate constant for the abstraction reaction follows the Arrhenius law, where that for the exchange reaction is nearly temperature independent. Finally, it is shown that the quantum mechanical results can be reasonably reproduced by the Gaussian-binning quasiclassical trajectory method and to a lesser extent by a quantum statistical model.     

A statistical quasiclassical trajectory model for atom-diatom insertion reactions

A statistical model based on the quasiclassical trajectory method is presented in this work for atom-diatom insertion reactions. The basic difference between this and the corresponding statistical quantum model (SQM) lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar. In particular, it is shown that conservation of parity can be taken into account in a natural and precise way in the statistical quasiclassical trajectory (SQCT) model. Additionally, the SQCT model complies with the principle of detailed balance and overcomes the problem of the zero point energy in the products. As a test, the model is applied to the H3+ and H+D2 exchange reactions. The excellent agreement between the SQCT and SQM results, especially in the case of the differential cross sections, indicates that the effect of tunneling through the centrifugal barrier is negligible. The effect of ignoring quantum mechanical parity conservation is also investigated.     

An approximate estimate of the Li+HF reactivity

An estimate of the energy dependence of the quantum reactive cross section of the Li+HF reaction obtained using an infinite order sudden technique is compared with quasiclassical results. Approximations introduced in order to adapt a computational scheme developed for systems having a very heavy central atom are also examined.     

Direct dynamics trajectory study of the reaction of formaldehyde cation with D2: vibrational and zero-point energy effects on quasiclassical trajectories

Quasiclassical, direct dynamics trajectories have been used to study the reaction of formaldehyde cation with molecular hydrogen, simulating the conditions in an experimental study of H2CO+ vibrational effects on this reaction. Effects of five different H2CO+ modes were probed, and we also examined different approaches to treating zero-point energy in quasiclassical trajectories. The calculated absolute cross-sections are in excellent agreement with experiments, and the results provide insight into the reaction mechanism, product scattering behavior, and energy disposal, and how they vary with impact parameter and reactant state. The reaction is sharply orientation-dependent, even at high collision energies, and both trajectories and experiment find that H2CO+ vibration inhibits reaction. On the other hand, the trajectories do not reproduce the anomalously strong effect of nu2(+) (the CO stretch). The origin of the discrepancy and approaches for minimizing such problems in quasiclassical trajectories are discussed.     

Scattering in the quasiperiodic and chaotic regimes

The results of a quasiclassical investigation of the scattering process for a collinear collision between a particle and two coupled anharmonic oscillators is reported. The energy transfer was found to fall at the critical energy where the oscillators made the transition from quasiperiodic to chaotic motion.     

On the rate and activation energy of the Br + Br2 ataom-exchange reaction

The Br + Br₂ atom-exchange reaction has been studied using quasiclassical trajectories and a semi-empirical potential-energy surface with shallow, long-range wells. The computed reaction rate coefficient is in good agreement with experiment. The computed reaction activation energy is ? 1 kcal/mole.     

Rate coefficient calculations on the three-dimensional D + HCl → DCl + H reaction using a new quantum-dynamical approximation

Rate coefficient calculations for the three-dimensional D + HCl→DC1 + H reaction are reported. A new quantum method is used, which involves applying the energy sudden approximation to the entrance channel and the centrifugal sudden approximation to the exit channel. Good agreement with quasiclassical results is obtained.     

A reduced dimensionality quasiclassical and quantum study of the proton transfer reaction H3O(+)+H2O-->H2O+H3O(+)

We report quantum and quasiclassical calculations of proton transfer in the reaction H(3)O(+)+H(2)O in three degrees of freedom, the two OH(+) bond lengths and the OH(+)O angle. The reduced dimensional potential energy surface is obtained from the full dimensional OSS3(p) energy function of H(5)O(2) (+) [L. Ojamae, I. Shavitt, and S. J. Singer, J. Chem. Phys. 109, 5547 (1998)], with an additional long-range correction to reproduce the correct ion-molecule interaction. This surface is used to perform both quasiclassical trajectory and quantum reactive scattering calculations of the zero total angular momentum cumulative reaction probability and cross sections for initial rotational states 0, 1, and 2. Comparison of these quantities are made to assess the importance of quantum effects in this reduced dimensional reaction. Additional quasiclassical cross sections are calculated to obtain the thermal rate constant for the reaction.     

On the semiclassical initial value calculation of thermal rate coefficients for the N+N2 reaction

In this paper we compare semiclassical initial value representation, conventional transition state theory with Wigner and Eckart tunneling correction, quantum reduced dimensionality, and quasiclassical thermal rate coefficients for N+N(2) exchange reaction.