Quasiclassical trajectory simulations

When potential surfaces are available, quasiclassical trajectory calculations (first introduced by Karplus, et al.496) become possible. Such calculations are the theorist s analogue of experiments and have been quite successful in simulating molecular reactive collisions.497 Opacity functions, excitation functions, and thermally averaged rate coefficients may be computed using such treatments. Since initial conditions may be varied in these calculations, state-to-state cross sections can be obtained, and problems such as vibrational specificity in the energy release of an exoergic reaction and vibrational selectivity in the energy requirement of an endo-... 

In addition, the dynamics of the reverse reactions (-2) and (-3) were investigated using a similar method. In this case translationally excited OH radicals were generated by laser photolysis of H2O2 and the H atoms produced in the reactions were detected by means of VUV-LIF at the Lyman-a-transition. We will compare the experimental results with results from dynamical simulations e.g. quasiclassical trajectory (QCT) calculations and - if possible - with the results obtained by applying quantum scattering (QMS) methods. 

Another valuable use of accurate quantum dynamics calculations is testing the validity of classical simulations for predicting product-state distributions, and reduced-dimensionality studies of this issue are available for both Cl + H2 [67] and H + CI2 [104], In the present case extensive quasiclassical trajectory (( CT) calculations have been carried out for the full-dimensional Cl + D2 reaction by Aoiz and Bahares [105]. An example of how the QCT results compare to the accurate quantum ones is given in Fig. 4, which shows differential cross sections for Cl + D2(v=0J=1) —> DCl(v ) + D, where v and v are initial and final vibrational quantum number, respectively, j is initial rotational quantum number, and the results are summed over final rotational quantum number j. The comparison in Fig. 4 is for an initial relative translational energy of 10.1 kcal. The agreement is quite good. Notice, however, that the QCT method overestimates the amount of vibrationally excited product. 

Sun L, Base WL (2010) Comparisons of classical and Wigner sampling of transition state energy levels for quasiclassical trajectory chemical dynamics simulations. J Chem Phys 133 044313... 

It is quite straightforward to perform quasiclassical trajectory computations (QCT) on the reactions of polyatomic molecules providing a smooth global potential energy surface is available from which derivatives can be obtained with respect to the atomic coordinates. This method is described in detail in Classical Trajectory Simulations Final Conditions. Hamilton s equations are solved to follow the motion of the individual atoms as a function of time and the reactant and product vibrational and rotational states can be set or boxed to quantum mechanical energies. The method does not treat purely quantum mechanical effects such as tunneling, resonances. or interference but it can treat the full state-to-state, eneigy-resolved dynamics of a reaction and also produces rate constants. Numerous applications to polyatomic reactions have been reported. ... 

This account highlights some of the recent developments in methods and current applications of classical trajectory simulations of molecular collisions. It has been more than 60 years since the first classical trajectory calculation was attempted on a mechanical calculator and almost 40 years since the first ensembles of trajectories were calculated on a digital computer and, even though the real world is quantum mechanical, classical trajectory simulations continue to play a crucial role in studies of chemical dynamics. The classical approximation, fortunately, is valid for many processes and conditions of interest to chemists, and the Monte Carlo quasiclassical trajectory approach is relatively simple and straightforward to apply. The work reviewed here clearly illustrates that it continues to be used productively, creatively, and widely, to study the details of chemical processes. 

Dynamics Simulation of the Stereomutation of Cyclopropane C. Doubleday, Jr., K. Bolton, and W. L. Hase, J. Phys. Chem. A, 102, 3648 (1998). Direct Dynamics Quasiclassical Trajectory Study of the Thermal Stereomutations of Cyclopropane. 

An assumed model potential surface and the energy disposal observations can be related via comparison of classical (or quasiclassical) trajectory results to the experimentally measured product state distributions. In the latter part of this review the energy disposal calculated from model potential surfaces designed to simulate a given, well-studied reaction is discussed and compared to the experimental distributions. The classical or quasiclassical trajectory calculations become much more difficult for cases having more than three or four atoms, and the use of approximate models, empirical analogies, and chemical intuition becomes necessary. For such situations the information theoretic analysis developed by Levine and Bernstein is particularly valuable and will be used in this review. 

In a mixed quantum-classical simulation such as a mean-field-trajectory or a surface-hopping calculation, the population probability of the diabatic state v[/ t) is given as the quasiclassical average over the squared modulus of the diabatic electronic coefficients dk t) defined in Eq. (27). This yields... 

Direct dynamics calculations were carried out with quasiclassical normalmode sampling from a canonical ensemble at 923 K (the experimental reaction temperature). Simulations initiated at the vicinity of TS for rearrangement of carbene 13 to 14 via oxirene 12, and 300 trajectories were obtained at DFT methods. The preliminary results reported in the manuscript showed that preferred formation of 15a over 15b by the ratio of 1.8 7.6 depends on the method used. The results were qualitatively consistent with the value of 2.5 deduced from the experiment. The non-unity ratio likely arises from the situation that two methyl groups in 14 are dynamically unequal on the carbene formation process. 

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