Quasiclassical calculation

Quasiclassical calculations are similar to classical trajectory calculations with the addition of terms to account for quantum effects. The inclusion of tunneling and quantized energy levels improves the accuracy of results for light atoms, such as hydrogen transfer, and lower-temperature reactions. 

There has recently been an upsurge of interest in the classical approach as a complement to full quantum dynamics. In many cases, it is found that the agreement between classical and quantum results for the dissociation probability is acceptable if not perfect [55-60], This is illustrated in Fig. 7, which shows the quantum dissociation probability computed for the H2/Cu(l 0 0) system compared to classical and quasiclassical results [57]. In quasiclassical calculations, we use classical methods to... 

B.Friedrich, S.Pick, L.Hladek, Z.Herman, E.E.Nikitin, A.I.Reznikov, and S.YaUmanskii, Dynamics of charge transfer Ar + He -> Ar +He" at low collision energies Comparison of experimental results with quasiclassical calculations of the differential cross sections, J. Chem. Phys. 84, 807 (1986)... 

E.E.Nikitin, C.Noda, and R.N.Zare, On the quasiclassical calculation of fundamental and overtone intensities. J. Chem. Phys. 89,46 (1993)... 

Under the condition when one can use FO perturbation approach in quantum and quasiclassical calculations, the classical mean square eneigy transfer can also be calculated in the FO classical perturbation theory. This again opens a possibility for comparison of FOD and FOA (now classical) approximations. Fig.4 shows the... 

Chen and Schaefer[29] have calculated an accurate ab initio potential energy surface for LiFH, An analytic Bond-order fit to this potential energy surface was performed by Lagana.[30-35] Quasiclassical calculations of the Li + FH — LiF -h H reactive scattering properties were used to further refine the potential energy surface so as to reproduce experimental results. Three dimensional reactive scattering cross sections have also been carried out using reduced dimensionality techniques. 

J.M. Alvarino, E. Garcia and A. Lagana, Quasiclassical Calculations for alkali/alkaline earth F hydrogen halide chemical reactions using supercomputers in this book. 

Quantum and corresponding quasiclassical calculations of Sibert et al.(lO) for HC overtone relaxation in benzene yielded subpicosecond lifetimes consistent with the linewidths observed in the room temperature experiments of Reddy et al.(l). The model Hamiltonian used by these authors incorporates only kinetic coupling between curvilinear HC stretch and HCC bend modes. It is clear, however, that the HCC bend force constant must be attenuated by stretching of the HC bond, and Lu et al.(lO) have shown that the nature and rate of short time IVR are sensitive to the magnitude of this attenuation. In this work we summarize a recent classical trajectory study of a two mode model of stretch-bend interaction in a HC fragment of benzene(13). Our aim is to understand the sensitivity of short time IVR to potential coupling in terms of the classical phase space structure of the stretch-bend Hamiltonian. 

QUASICLASSICAL CALCULATIONS FOR ALKALI AND ALKALINE EARTH + HYDROGEN HALIDE CHEMICAL REACTIONS USING SUPERCOMPUTERS... 

Quasiclassical trajectory calculations have been performed on the ab initio WDRB and DIM surfaces, and thermal rate constants for the collinear reaction have been calculated from the quantal calculations, the quasiclassical calculations, and transition state theory. These will be reported in a future publication. 

Fig. 2. Apparently, the threshold errors of the quasiclassical calculations illustrated in Fig. 1 are more important at 444 K, and they compensate the rigid-rotator errors enough to even change the direction of the difference for some transitions. The trajectory calculations should be most reliable at high temperature. Some additional inelastic cross sections are presented in section VI where they are compared to reactive state-to-state cross sections.

The = 0 quasiclassical calculations for the PK2 surface showed a systematic decrease in the rate constant as ji increased. It is not clear whether this same trend will hold for the nonzero-... 

A quasiclassical calculation was carried out for this system as described in the previous section. In Fig. 4 the probability of transition to the excited potential energy surface as a function of translational energy is plotted for one laser field strength and a series of laser frequencies. Peaks occur at the predicted translational eneriges. 

Fig. 5. Total reaction probability on the upper-state surface for the model H + H2 system as a function of initial relative translational energy as determined by a quasiclassical calculation.

Fig. 7. Total reaction probability on the lower-state surface for the model H 4- H2 system as a function of initial relative translational energy E as determined by a quasiclassical calculation. H2 is initially in its ground vibrational state. The dotted curve is the laser-free result. The curves are for a laser power such that yOl O 0 01 eV and frequency fiw = 0.017 ag (solid curve), 0,0165 sq (dashed curve), and 0.016 ag (dash-dot curve).

This equation assumes that the internal energy states can be treated as being continuous. The one dimensional (collinear) quantum calculations for the H + p2 and H + CI2 potential surfaces have been extended to three dimensions by various assumptions based upon experimental data or upon information theory. The end results are in rather close agreement with the full three-dimensional quasiclassical calculations on the same potentials. The introduction of Franck-Condon-like integrals into onedimensional (collinear) models simulates the one-dimensional quantum results rather well These Franck-Condon-like calculations are... 

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