Tunneling effect, definition

This review shows how the photochemistry of ketones can be rationalized through a single model, the Tunnel Effect Theory (TET), which treats reactions of ketones as radiationless transitions from reactant to product potential energy curves (PEC). Two critical approximations are involved in the development of this theory (i) the representation of reactants and products as diatomic harmonic oscillators of appropriate reduced masses and force constants (ii) the definition of a unidimensional reaction coordinate (RC) as the sum of the reactant and product bond distensions to the transition state. Within these approximations, TET is used to calculate the reactivity parameters of the most important photoreactions of ketones, using only a partially adjustable parameter, whose physical meaning is well understood and which admits only predictable variations. 

It is very important to remember that this definition of a PES is based on the assumption that the atomic positions can be exactly specified, which is the ultimate condition for the structure or shape of a molecule. This means adoption of the Born-Oppenheimer (B.O.) approximation, in which the nuclei are viewed as stationary point charges, whereas the electrons are described quantum mechanically [5]. This approximation is justified by the fact that the electrons are much lighter than the nuclei and hence are moving faster. The classical nature of the atomic nuclei is usually a valid approximation, but the zero-point vibrational energy of molecules or the tunneling effect, for example, make it evident that it does not always hold. 

The discussion in this paper will omit consideration of the splitting of the various torsional levels through the tunneling effect, since this can rarely be resolved in vibrational spectroscopy. As previously stated, the observation and definite assignment of these modes by infrared spectroscopy is often difficult due to weakly active or inactive modes.16,20 This is particularly true of attempts to study unperturbed molecules in fluid phases. 

The condition (6A) is necessary for the definition of the activated complex in Eyring s theory as far as the translation motion along the classical reaction path is concerned. If this condition is not fulfilled, the quantum-mechanical penetration of the potential barrier, i.e ,the nuclear tunnel effect, has to be taken into account. Then, the formula (5A) has to be corrected by an additional factor... 

Kinetic complexity definition, 43 Klinman s approach, 46 Kinetic isotope effects, 28 for 2,4,6-collidine, 31 a-secondary, 35 and coupled motion, 35, 40 in enzyme-catalyzed reactions, 35 as indicators of quantum tunneling, 70 in multistep enzymatic reactions, 44-45 normal temperature dependence, 37 Northrop notation, 45 Northrop s method of calculation, 55 rule of geometric mean, 36 secondary effects and transition state, 37 semiclassical treatment for hydrogen transfer,... 

OBSERVATIONS THAT DO NOT DEFINITIVELY INDICATE TUNNELING Large isotope effects per se do not indicate tunneling... 

A simpler approach than that of Bosenquet is afforded by an equation empirically derived by Davidson (Dl) from the wind tunnel experiments of Bryant (B6). It does not consider the effect of the vertical gradient of air temperature, but this does not eliminate it in favor of the Bosenquet formula, since the effect of air stability on effective stack height is not definitely known for all conditions. The Bryant-Davidson expression is... 

Let us assume that a variable A(t) is coupled to the reaction coordinate and that (A) is its mean value. If a measurement of some property P depends on (A), but not on the particular details of the time dependence of A(t), then we will call it a statistical dependence. If the property P depends on particular details of the dynamics of A(t) we will call it a dynamical dependence. Note that in this definition it is not the mode A(t) alone that causes dynamical effects, but it also depends on the timescale of the measured property P. Promoting vibrations (to be discussed in Sections 2-4) are a dynamic effect in this sense, since their dynamics is coupled to the reaction coordinate and have similar timescales. Conformation fluctuations that enhance tunneling (to be discussed in Section 5) are a statistical effect the reaction rate is the sum of transition state theory (TST) rates for barriers corresponding to some configuration, weighted by the probability that the system reaches that configuration. This distinction between dynamic and statistical phenomena in proteins was first made in the classic paper of Agmon and Hopfield.4 We will discuss three kinds of motions ... 

Ncff is just the inverse of the rate fluctuation. This is the traditional definition of the number of effective decay, or reaction, channels in the random matrix approach to the statistics of decay rates. This approach has been used both in nuclear (16) and chemical (17) physics. Comparing this result with the RRKM prediction, one can see that Mc(t(E) replaces N (E). One can use either a vibrationally adiabatic tunneling model (17) or a model of hopping between two electronic surfaces in the Condon approximation (40) to show that, when a global random matrix model is used for the Hamiltonian, Neff = N in the classical limit. 

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