Semiclassical approaches path integrals

Considering the semiclassical description of nonadiabatic dynamics, only the mapping approach [99, 100] and the equivalent formulation that is obtained by requantizing the classical electron analog model of Meyer and Miller [112] appear to be amenable to a numerical treatment via an initial-value representation [114, 116, 117, 121, 122]. Other semiclassical formulations such as Pechukas path-integral formulation [45] and the various connection... 

There is a very powerful semiclassical path integral approach due to Wang and Wolynes [305] developed for the cases of moderate dependence of the reaction rate on the environmental coordinates, such as geometrical bottlenecks . Unfortunately, this semiclassical scheme does not work for a (5-functional sink (and it was not intended to). 

From the chemically point of view, the valence states are those situated in the chemical zone -and they are the main concern forthe chemical reactivity by employing the frontier or the outer electrons consequently, the semiclas-sical approximation that models the excited states was expressly presented either as an extension of the quantum Feynman path integral or as a specialization of the Feynman-Kleinert formalism for higher temperature treatment of quantum systems (see Section 2.5). However, due to the correspondences of Table 2.1 one may systematically characterize the semiclassical (or quantum chemical) approaches as one of the limiting situations (Putz, 2009) ... 

Another approach (Newns 1985 Nourtier 1985) is based on the double path integral representation of the scattering probability. The surface dynamics is described in terms of an influence functional that can be found in explicit form in the linear coupling approximation. However, semiclassical evaluation of the path integrals leads to a complex classical trajectory problem that is non-local in time and too difficult for applications. 

---