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Quasiclassical trajectory method

The mapping approach outlined above has been designed to furnish a well-defined classical limit of nonadiabatic quantum dynamics. The formalism applies in the same way at the quantum-mechanical, semiclassical (see Section VIII), and quasiclassical level, respectively. Most important, no additional assumptions but the standard semiclassical and quasi-classical approximations are needed to get from one level to another. Most of the established mixed quantum-classical methods such as the mean-field-trajectory method or the surface-hopping approach do invoke additional assumptions. The comparison of the mapping approach to these formulations may therefore (i) provide insight into the nature of these additional approximation and (ii) indicate whether the conceptual virtues of the mapping approach may be expected to result in practical advantages. [Pg.308]

The ion-neutral reaction that has received the greatest attention from a theoretical viewpoint is the H2+ -He process. This is because of the relative simplicity of this reaction (a three-electron system), which facilitates accurate theoretical calculations and also to the fact that a wealth of accurate experimental data has been obtained for this interaction. Several different theoretical approaches have been applied to the H2+He reaction, as indicated by the summary presented in Table VI. Most of these have treated the particle-transfer channel only, and few have considered the CID channel. Various theoretical methods applicable to ion-neutral interactions are discussed in the following sections. For the HeH2+ system, calculations using quasiclassical trajectory methods, employing an ab initio potential surface, have been shown to yield results that are in good agreement with the experimental results. [Pg.196]

The quasiclassical trajectory method disregards completely the quantum phenomenon of superposition (13,18,19) consequently, the method fails in treating the reaction features connected with the interference effects such as rainbow or Stueckelberg-type oscillations in the state-to-state differential cross sections (13,17,28). When, however, more averaged characteristics are dealt with (then the interference is quenched), the quasiclassical trajectory method turns out to be a relatively universal and powerful theoretical tool. Total cross-sections (detailed rate constants) of a large variety of microscopic systems can be obtained in a semiquantitative agreement with experiment (6). [Pg.258]

Thus, as long as the interference phenomena are suppressed, the quasiclassical method yields a reasonable qualitative view of the dynamics of elementary processes. We will adopt this view in the forthcoming discussions in the next section it will be shown that the quasiclassical trajectory method can be generalized to treat a large class of electronically nonadiabatic processes. [Pg.258]

The different potential energy surfaces have been used in several calculations of the dynamics of the title reaction using quasiclassical trajectory methods and quantum calculations, see references [71,72] for a general description of these methods. Some capture and statistical calculations have also been reported for this... [Pg.28]

Key words Quasiclassical trajectory method -Reactive cross section - Thermal rate coefficient -Potential-energy surface - Quantum scattering... [Pg.112]

Theory. Usually we do not solve the fundamental equations directly. We use a theory, for example, Har-tree-Fock theory [3], Moller-Plesset perturbation theory [4], coupled-cluster theory [5], Kohn s [6, 7], Newton s [8], or Schlessinger s [9] variational principle for scattering amplitudes, the quasiclassical trajectory method [10], the trajectory surface hopping method [11], classical S-matrix theory [12], the close-coupling approximation... [Pg.191]

The problem of an unphysical flow of ZPE is not a specific feature of the mapping approach, but represents a general flaw of quasiclassical trajectory methods. Numerous approaches have been proposed to fix the ZPE problem.They include a variety of active methods (i.e. the flow of ZPE is controlled and (if necessary) manipulated during the course of individual trajectories) and several passive methods which, for example, discard trajectories not satisfying predefined criteria. However, most of these techniques share the problem that they manipulate individual trajectories, whereas the conservation of ZPE should correspond to a virtue of the ensemble average of trajectories. [Pg.665]

Pig. 8. Time-dependent (a) diabatic and (b) adiabatic electronic excited-state populations and (c) vibrational mean positions as obtained for Model I. Shown are results of the mean-field trajectory method (dotted lines), the quasiclassical mapping approach (thin full lines), and exact quantum calculations (thick full lines). [Pg.666]

The quasiclassical trajectory method was used to study this system, and the variable step size modified Bulirsch-Stoer algorithm was specially developed for recombination problems such as this one. Comparisons were made with the fourth order Adams-Bashforth-Moulton predictor-corrector algorithm, and the modified Bulirsch-Stoer method was always more efficient, with the relative efficiency of the Bulirsch-Stoer method increasing as the desired accuracy increased. We measure the accuracy by computing the rms relative difference between the initial coordinates and momenta and their back-integrated values. For example, for a rms relative difference of 0.01, the ratio of the CPU times for the two methods was 1.6, for a rms relative difference of 0.001 it was 2.0, and for a rms relative difference of 10 it was 3.3. Another advantage of the variable step size method is that the errors in individual trajectories are more similar, e.g. a test run of ten trajectories yielded rms errors which differed by a factor of 53 when using the modified Bulirsch-Stoer... [Pg.374]

Zanchet A, Halvick P, Rayez JC, Bussery-Honvault B, Honvault P. (2007) Cross sections and rate constants for the C( P) -l-OH(X n) CO(X E+)- -H( S) reaction using a quasiclassical trajectory method. J. Chem. Phys. 126 184308 1-6. [Pg.229]

The basic technology of classical trajectory applications to atom-diatom and similar systems has been described and reviewed numerous times. As long as classical microcanonical or canonical ensembles are used to generate and analyze initial and final conditions, it is not difficult to apply classical trajectory methods to polyatomic collision systems as well. The implementation of quasiclassical methods to determine state-resolved cross sections and rate constants in polyatomic systems is, however, much more complicated, and attention has been given to this only recently. The... [Pg.291]

Components of the activation energy (in eV) computed by the quasiclassical trajectory method. [Pg.444]

If the initial diatomic is heteronuclear, the collision complex can separate into two possible product channels. The branching ratio for the two channels reflects the properties of the complex. We have investigated a series of reactions involving the state of oxygen and carbon using the quasiclassical trajectory method to elucidate these mechanistic and dynamical features. [Pg.552]

V. SOME ASPECTS OF THE QUASICLASSICAL TRAJECTORY METHOD AS APPLIED TO COLLISIONAL EXCITATION OF H2O... [Pg.793]


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See also in sourсe #XX -- [ Pg.258 ]




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