Quasi-classical studies

D. C. Clary, J. N. L. Connor, and C. J. Edge, Quantum and quasi-classical study of the collinear reaction 0( P) 4 H2 OH 4- H using a LEPS and fitted ab initio potential energy surface,... 

The solvation thermodynamics have been interpreted in a classical study by Frank and Evans in terms of the iceberg model . This model states that the water molecules around an nonpolar solute show an increased quasi-solid structuring. This pattern would account for the strongly negative... 

Classical dynamics is studied as a special case by analyzing the Ehrenfest theorem, coherent states (16) and systems with quasi classical dynamics like the rigid rotor for molecules (17) and the oscillator (18) for various particle systems and for EM field in a laser. 

To study to what extent the mapping approach is able to reproduce the quantum results of Model 111, Eigs. 34 and 35 show the quasi-classical probability densities P (cp,f) for the two cases. The classical calculation for E = 0 is seen to accurately match the initial decay of the quantum-mechanical... 

There has been a long history in theoretical efforts to understand H + H/Cu(lll) and its isotopic analogs because it represents the best studied prototype of an ER/HA reaction. These have evolved from simple 2D collinear quantum dynamics on model PES [386] to 6D quasi-classical dynamics on PES fit to DFT calculations [380,387,388], and even attempts to include lattice motion on ER/HA reactions [389]. These studies show that there is little reflection of incident H because of the deep well and energy scrambling upon impact, i.e., a % 1. Although some of the... 

Thermolysis of l,l-difluoro-2,3-diphenylcyclopropane in supercritical CO2 has allowed the rate of geometrical isomerization [i.e. cis-( 109) to /ra/M-(109)] and racemization [i.e. (/< )-( 109) to (S)-( 109)] to be determined from O2 dependence of the trapping rate of the postulated intermediate 1,3-biradical.246 Above 150 °C, the formation of 2,2-difluoroindane and its decomposition products is reported. A similar thermally induced equilibrating series of stereomutations has been observed with the analogous non-fluorinated cyclopropane in which rate constants and deuterium exchange isotope effects are reported.247 Theoretical studies of this isomerization have focused on classical248 and quasi-classical trajectories.249... 

When we study the effect of charged particles on a substance, we often need to estimate the probabilities of excitation or ionization as functions of the distance from the axis of the track (i.e., of the impact parameter b). This is done using the quasi-classical approach, within which we assume that the charged particle moves along a definite trajectory. In the... 

Skouteris, D., Werner, H.-J., Aoiz, F. J., Banares, L., Castillo, J. F., Menendez, M., Balucani, N., Cartechini, L. and Casavecchia, P. (2001) Experimental and theoretical differential cross sections for the reactions Cl + H2/D2, J. Chem. Phys. 114, 10662-72 Aoiz, F. J., Banares, L., Castillo, J., Menendez, M., Skouteris, D. and Werner, H.-J. (2001) A quantum mechanical and quasi-classical trajectory study of the Cl + H2 reaction and its isotopic variants Dependence of the integral cross section on the collision energy and reagent rotation, J. Chem. Phys. 115, 2074-81. 

The large well depth in the ground electronic state ( 7.2 e ) and the high exoergicity (1.9 e ) makes particularly difficult an exact QM study of the dynamics of this reaction. Theoretical studies often used the quasi-classical trajectory (QCT) method [12. 16. 18, 21]. Only a few quantum-mechanical (QM) studies have been reported. They are exact for the total angular momentum J = 0 but approximate for higher J. Total reaction probability has been calculated with a... 

Quantum mechanical and quasi-classical trajectory study of the C( D) + H2 reaction dynamics, J. Chern. Phy.s. 118, 565-568. 

We recall that our key interest is the study of the tunneling dynamics of the chain polarization or, equivalently, the total pseudo-spin S of the chain. Following Ref. 332, we can estimate, using the quasi-classical approximation, the tunneling rate Hi, or the splitting energy between the states ) and, ) ... 

In the early 1930 s, Eyring and his co-workers made some preliminary studies of the trajectories of systems on potential-energy surfaces, but not much progress could be made until the development of high-speed computers. There has recently been a revival of interest in this field, now known as molecular dynamics. In particular, Karplus, Porter, and Sharma have carried out calculations on the H -b Hg system, using what appears to be a very reliable potential-energy surface. The calculations are quasi-classical in nature the vibrational and rotational states in the Hg molecule are quantized, but the course of the collision is treated classically. 

In principle, any electronic structure method that can produce a gradient and Hessian can be used in quasi-classical dynamics. However, density functional theory (DFT)-based methods are, in general (at the time of writing), limited to ground-state surfaces. CASSCF-based dynamics calculations can be used for excited-state computations, and we will focus our discussion on this method. In this case, the size of the molecule that can be studied is limited by the size of the active space (Section 2.2.1) at present, no more than 10 active elec-... 

In the previous sections random sampling procedures were described for preparing a classical microcanonical ensemble of states. However, for comparison with experiment and to study the rate of intramolecular vibrational energy redistribution (IVR) [12,27] within a molecule, it is important to sample the states (i.e., phase space) of the molecule nonrandomly. Here, both normal and local mode [28] quasi-classical [2-4] sampling schemes are described for nonrandom excitation. 

Theoretically, Nitzamov et al. [6] studied the rate constants and energy partitioning for the OH -I- HBr reaction via quasi-classical trajectories. Liu and coworkers [9] predicted that the OH -I- HBr reaction has a small barrier (<1.0 kcal/mol, from CCSD(T)/6-31 H-G(2df,2p) singlepoint energies), and their theoretical rate constants are comparable with the experimental results [4, 11-14]. 

K for the vibrational frequencies v<, of light gases at the sites minimum potential eneigy in dense polymers. Hence, the quasi-classical aj roximation [SS] is appropriate for studying the behavior and properties of small molecules in dense polymers and we shall use this aj roximation below. 

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