Effective tunneling coupling

The classical effect of coupled motion is to reduce the primary KIE by coupling the primary H translation with the a-secondary H bending modes, which has the effect of leaking some of the primary KIE into the a-secondary KIE. This leads to an enhanced a-secondary KIE, as this position acquires some of the characteristics of the primary position. The extent to which coupled motion can inflate the a-secondary KIEs in the absence of tunneling has been discussed, and serves as a tunneling discriminator [25, 50-52]. 

It is the combined effect of coupled motion and turmeling that leads to the largest anomalies [25, 52]. In addition to the classical effects of coupled motion, tunneling further increases the a-secondary KIE while significantly increasing the primary KIE. In ADH, as well as several other enzymatic and chemical examples, both tunneling and coupled motion have been invoked to reproduce the experimentally observed primary and a-secondary KIEs [6, 10, 25, 26, 49, 53-55]. 

Kohen, A. (2003) Kinetic isotope effects as probes for hydrogen tunneling, coupled motion and dynamics contributions to enzyme catalysis, Progr. React. Kinet. Mech. 28, 119-156. 

If all the PES coordinates are split off in this way, the original multidimensional problem reduces to that of one-dimensional tunneling in the effective barrier (1.10) of a particle which is coupled to the heat bath. This problem is known as the dissipative tunneling problem, which has been intensively studied for the past 15 years, primarily in connection with tunneling phenomena in solid state physics [Caldeira and Leggett 1983]. Interaction with the heat bath leads to the friction force that acts on the particle moving in the one-dimensional potential (1.10), and, as a consequence, a> is replaced by the Kramers frequency [Kramers 1940] defined by... 

The solution of the spin-boson problem with arbitrary coupling has been discussed in detail by Leggett et al. [1987]. The displacement of the equilibrium positions of the bath oscillators in the transition results in the effective renormalization of the tunneling matrix element by the bath overlap integral... 

Although the rotation barrier is chiefly created by the high-frequency modes, it is necessary to consider coupling to low-frequency vibrations in order to account for subtler effects such as temperature shift and broadening of tunneling lines. The interaction with the vibrations q (with masses and frequencies m , tu ) has the form... 

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