Tunneling multi-dimensional

It should be noted, however, tliat even tlie best one-dimensional tunneling estimate is still likely to underestimate the full tunneling contribution, since tunneling may occur through dimensions of the PES other than die reaction coordinate. Multi-dimensional tunneling approximations are sufficiently complex, however, tliat tliey will not be further discussed here. 

Sometimes we just say VTST/MT. The MT acronym ( multi-dimensional tunneling ) can denote ZCT, SCT, LCT, or OMT, all of which are multidimensional, but we usually use SCT or OMT when we carry out MT calculations. 

Tunneling is a ubiquitous phenomenon. It is observed in biological systems (1), and in electrochemical cells (2). Alpha particle disintegration (3), the Stark effect (4), superconductivity in thin films (5), field-electron emission (6), and field-ionization (7) are tunneling phenomena. Even the disappearance of a black hole (or the fate of a multi-dimensional universe) may depend on tunneling, but on a cosmological scale (S-9). 

To deal with the ET rate in such a case, our strategy is to combine the generalized nonadiabatic transition state theory (NA-TST) and the Zhu-Nakamura (ZN) nonadiabatic transition probability.The generalized NA-TST is formulated based on Miller s reactive flux-flux correlation function approach. The ZN theory, on the other hand, is practically free from the drawbacks of the LZ theory mentioned above. Numerical tests have also confirmed that it is essential for accurate evaluation of the thermal rate constant to take into account the multi-dimensional topography of the seam surface and to treat the nonadiabatic electronic transition and nuclear tunneling effects properly. 

In eqn (12.19), the effects of nonadiabatic transition including the nuclear tunneling are properly taken into account by rj and naturally the main task is to evaluate the thermally averaged transition probability P fl, < ), which has to be evaluated using the Monte Carlo technique for multi-dimensional systems. It is easily shown that the Marcus-Hush formula in adiabatic and nonadiabatic limits can be recovered from eqn (12.19) and eqn (12.20) within the high-temperature approximation. 

Brun, M., R. Demadrille, P. Rannou, A. Pron, J.P. Travers, and B. Grevin. 2004. Multi-scale scanning tunneling microscopy study of self-assembly phenomena in two-dimensional polycrystals of tr-conjugated polymers The case of regioregular poly(dioctylbithiophenealt-fluore-none). Adv Mat 16 2087. 

M. Sala, F. Gatti and S. Guerin, Coherent destruction of tunneling in a six-dimensional model of NHD2 a computational study using the multi-configuration time-dependent Hartree method , J. Chem. Phys. 141, 164326 (2014)... 

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