Tunneling multidimensional models

In realistic systems, the separation of the modes according to their frequencies and subsequent reduction to one dimension is often impossible with the above-described methods. In this case an accurate multidimensional analysis is needed. Another case in which a multidimensional study is required and which obviously cannot be accounted for within the dissipative tunneling model is that of complex PES with several saddle points and therefore with several MEPs and tunneling paths. 

While the goal of the previous models is to carry out analytical calculations and gain insight into the physical picture, the multidimensional calculations are expected to give a quantitative description of concrete chemical systems. However at present we are just at the beginning of this process, and only a few examples of numerical multidimensional computations, mostly on rather idealized PES, have been performed so far. Nonetheless these pioneering studies have established a number of novel features of tunneling reactions, which do not show up in the effectively one-dimensional models. 

In essence, the goal of this review is to describe the evolution of notions about tunneling, from the Gamov one-dimension model potential barrier penetration to multidimensional quantum motion with account for an active role of the medium. Such evolution goes on in various branches of modern chemical physics and the physics of solids. Therefore, the analysis of the common features of developing theories seems timely and important. 

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