Semiclassical adiabatic ground-state

The ESA-CSA calculations on the LEPS surface for D+C H were also extended [33] to the H+CilH, H+CilD and D+CilD exchange reactions. Here it was found that the room temperature rate constants agreed to within a factor of two with those obtained using the classical trajectory method and a variational state theory with semiclassical adiabatic ground-state transmission coefficients [38]. 

MINI, MIDI and MAXI basis sets, 161 Minimum basis set, 152 Minimum Energy Path (MEP), 344, 390 Minimum Energy Path Semiclassical Adiabatic Ground-state (MEiPSAC) model, 392... 

Small Cmvature Semiclassical Adiabatic Ground-state (SCSAC) model, 392 Small rings, 27 Sn2 reaction, 305, 367 Softness, defined from the electron density, 353... 

The relative rates of the reactions leading to formation of either ground-state or excited-state products can be evaluated in terms of formalisms developed by Marcus [26], Hopfield [27], Jortner [28], and others [29]. The development of the semiclassical and quantum-mechanical expressions for electron transfer are discussed in Chapters. 3-5 (Volume I, Part 1). A general expression for the rate constant of a non-adiabatic electron-transfer process is given below. 

We first consider the case where the reaction probabilities are computed for the adiabatic model with the reaction-path curvature neglected, the so-called vibrationally adiabatic zero-curvature approximation [36]. We approximate the quantum mechanical ground-state probabilities P (E) for the one-dimensional scattering problem by a uniform semiclassical expression [48], which for E < is given by... 

Figure 9 This figure depicts two kinds of semiclassical paths which contribute to the exchange scattering amplitude for a triatomic system ABC. An equipotential energy surface for the ground adiabatic electronic state of H3 is represented. The OXYZ frame is the same as the OXKYZK frame of Fig. 5 with the subscript suppressed. The conical intersection configurations for H, (equilateral triangles) are represented by points on the OY axis. The dashed path partially encircles the conical intersection line, whereas the solid one does not. (From Ref. 36.)...

Pig. 6.6 (Left) Bunch of branching paths given by the PSANB method (solid cnrves) and those of the semiclassical Ehrenfest dynamics (dotted curves) for initial momentums k = 16.06, 19.3, 22.5, 25.7, 28.9 and 32.1, starting from the initial position R = 2.0 on the ground state potential. (Right) The branching of the quantum wavepackets by the non-adiabatic transition with the initial central momentum of 1 = 32.1. A simple super position of xi (R, t) (denoted as Low) and x2 (R,t) (denoted as High) are drawn. (Reprinted with permission from T. Yonehara et al., J. Chem. Phys. 129, 134109 (2008)). 

Ohrn and co-workers have developed a direct dynamics approach which incorporates both the electrons and nuclei dynamics (END).""" The complete electron-nuclear coupling terms are retained in the calculation and, as a result, the dynamics is not constrained to a single Born-Oppenheimer potential energy surface i.e., electronic non-adiabaticity is explicitly included. A complication in this approach is the computational demand in propagating an electronic wavefunction which is an accurate representation of the ground electronic state as well as multiple excited electronic states. This approach will become more widely used as computation becomes more powerful. In its initial development,""" Deumens et al. used END and treated the dynamics of the nuclei purely classical as in the above classical direct dynamics. More recently, a semiclassical description of the nuclear motion has been implemented by incorporating Heller s""" "" Gaussian wave packet dynamics."" ... 

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