Quasiclassical model

E.E. Nikitin and D.V.Shalashilin, Quasiclassical model of vibrational-rotational energy exehange, Khim. Fiz. 11, 1471 (1992)... 

Y.Kami and E.E.Nikitin, Adiabatically corrected quasiclassical model for the vibrational predissociation of van der Waals complexes, Chem.Phys. 191, 235... 

This quasiclassical model summarized correctly describes the observed fact that most transition metals adsorb H2 dissociatively whereas most simple and noble metals do not. It does not, of course, account for detailed variations of the H adsorption properties, for example within transition metals series, but has eliminated earlier controversy about the role of s- and d-electrons in the H-M bonding. 

As explained in the Introduction, one needs to distinguish the following kinds of surface hopping (SH) methods (i) Semiclassical theories based on a connection ansatz of the WKB wave function, " (ii) stochastic implementations of a given deterministic multistate differential equation, e.g. the quantum-classical Liouville equation, and (iii) quasiclassical models such as the well-known SH schemes of Tully and others. " In this chapter, we focus on the latter type of SH method, which has turned out to be the most popular approach to describe nonadiabatic dynamics at conical intersections. 

The above presentation describes how the collision impact parameter is sampled to calculate reaction cros.s-sections. In the following, Monte Carlo sampling of the reactant s Cartesian coordinates and momenta is de.scribed for atom -I- polyatomic collisions. Initial energies are chosen for the reactants, which correspond to quantum mechanical vibrational-rotational energy levels. This is the quasiclassical model. " Extensive reviews have been given of the procedure for selecting initial conditions for atom + diatom collisions. 

Most of our present understanding of the dynamics and of the collisional mechanisms of elementary chemical reactions comes from classical approaches, from simple classical models, and from quasiclassical trajectory studies. More recently, quantum mechanical results on the dynamics of directmode reactions have become available. 

Wadsworth and Wysong made a detailed assessment of the threshold line model (and other dissociation models) for hydrogen dissociation by making comparison with quasiclassical trajectory computations. They found that the original forms of the threshold line models proposed by Macheret and Rich have to be extended to more complete forms in order to avoid singularities at specific values of the collision energies. Some of their findings are shown in the results section. 

It is not possible to consider all of the available DSMC chemistry models in detail. Due to its importance in air chemistry, dissociation has received the most attention, and interesting models have been proposed by Koura, Bird, and Lord. Wadsworth and Wysong compared the threshold line model to those of Refs. 38 and 53. It was concluded that the threshold line model and that of Koura gave results consistent with quasiclassical trajectory calculations for hydrogen dissociation. Some of these data will be shown later in the article. 

E.E.Nikitin, A.I.Reznikov, and S.YaUmanskii, Two-level model of charge exchange with Coulomb interaction in one of the channels Quantum and quasiclassical cross sections in the weak-coupling limit, Zh.Eksp.Teor.Fiz. 91, 1590 (1986)... 

Figure 7. Reaction cross sections for O + H2(v = 0, j) as function of j. (o, ), ( , ), and (A, A) correspond to collision energies Etrjns = 20. 15 and 12 kcal/mol respectively. Open symbols quasiclassical trajectory results [64], full symbols results of the kinematic mass model calculations. Effect of reagent rotation on the distribution of collisions at the barrier is neglected in (a) it is taken into account in (b)[61j.

It should be noted that in the present case the trajectoiy calculations were carried out for coplanar collisions with the vibration of HCl (DCl) fiozen [47], A trajectory was assumed to be reactive if it reached a point on the top of the electronic barrier. There are no corrections of the barrier height due to the vibrational zero-point energy effect in this case. These trajectory results are therefore more directly comparable with the results of the kinematic mass model than the 3-dimensional quasiclassical trajectroiy calculations discussed in the previous case. 

With the above comments in mind, we first briefly discuss a hierarchy of models for VP (Section 2), then dwell on the quantum (Section 3), quasiclassical (Section 4) and classical (Section 5) theories of VP. After that, we compare different approaches (Section 6) and summarize our results on the quantum-classical correspondence for isolated resonances, which is the case for vibrational predissociation. 

Abstract A generalization of the Landau-Teller model for vibrational relaxation of diatoms in collisions with atoms at very low energies is presented. The extrapolation of the semiclassical Landau-Teller approach to the zero-energy Bethe-Wigner limit is based on the quasiclassical Landau method for calculation of transition probabilities, and the recovery of the Landau exponent from the classical collision time. The quantum suppression-enhancement probabilities are calculated for a general potential well, which supports several bound states, and for a Morse potential with arbitrary number of states. The model is applied to interpretation of quantum scattering calculations for the vibrational relaxation of H2 in collisions with He. 

Boron-nitrogen and boron-phosphorous compounds are classical textbook examples of donor-acceptor complexes. The chemical bonds of the Lewis-acid Lewis-base complexes are usually explained in terms of frontier orbital interactions and/or quasiclassical electrostatic attraction in the framework of the Hard and Soft Acid and Base (HSAB) model [73]. We were interested in seeing if the differences between the bond strengths of boron-nitrogen and boron-phosphorous complexes for different boranes, amines and phosphanes can be explained with the EDA method. 

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