are not valid, and the magnitude of the isotope effect may depend strongly on some or all of the neglected factors. Thus, kinetic isotope effects for elements other than hydrogen are often much more difficult to rationalize or interpret. In many cases and especially for hydrogen-transfer reactions, contributions to kinetic isotope effects from tunneling are significant (see below). Tunneling In some cases, an additional rate enhancement is seen for the lighter isotope, possibly due to quantum mechanical tunnelling. This is typically only observed for reactions involving bonds to hydrogen atoms. Tunneling occurs when a molecule penetrates through a potential energy barrier rather than over it. Although not allowed by the laws of classical mechanics, particles can pass through classically forbidden regions of space in quantum mechanics based on wave–particle duality. Analysis of tunneling can be made using Bell's modification of the Arrhenius equation, which includes the addition of a tunneling factor, Q: where A is the Arrhenius parameter, E is the barrier height and where and Examination of the β term shows exponential dependency on the mass of the particle. As a result, tunneling is much more likely for a lighter particle such as hydrogen. Simply doubling the mass of a tunneling proton by replacing it with its deuterium isotope drastically reduces the rate of such reactions. As a result, very large kinetic isotope effects are observed that can not be accounted for by differences in zero point energies. In addition, the β term depends linearly with barrier width, 2a. As with mass, tunneling is greatest for small barrier widths. Optimal tunneling distances of protons between donor and acceptor atom is 0.4 Å. Transient kinetic isotope effect Isotopic effect expressed with the equations given above only refer to reactions that can be described with first-order kinetics. In all instances in which this is not possible, transient kinetic isotope effects should be taken into account using the GEBIK and GEBIF equations. Experiments Simmons and Hartwig refer to the following three cases as the main types of kinetic isotope effect experiments involving C-H bond functionalization: A) KIE determined from absolute rates of two parallel reactions In this experiment, the rate constants for the normal substrate and its isotopically labeled analogue are determined independently, and the KIE is obtained as a ratio of the two. The accuracy of the measured KIE is severely limited by the accuracy with which each of these rate