numerical value of a deuterium kinetic isotope effect using density functional theory calculations is now relatively routine. Moreover, several qualitative and semi-quantitative models allow rough estimates of deuterium isotope effects to be made without calculations, often providing enough information to rationalize experimental data or even support or refute different mechanistic possibilities. Starting materials containing deuterium are often commercially available, making the synthesis of isotopically enriched starting materials relatively straightforward. Also, due to the large relative difference in the mass of deuterium and protium and the attendant differences in vibrational frequencies, the magnitude of the isotope effect is larger than any other pair of isotopes except protium and tritium, allowing both primary and secondary isotope effects to be easily measured and interpreted. In contrast, secondary effects are generally very small for heavier elements and close in magnitude to the experimental uncertainty, which complicates their interpretation and limits their utility. In the context of isotope effects, hydrogen is frequently used to refer to the light isotope, protium (1H), specifically. In the rest of this article, reference to hydrogen and deuterium in parallel grammatical constructions or direct comparisons between them should be interpreted as referring to protium and deuterium. The theory of kinetic isotope effects was first formulated by Jacob Bigeleisen in 1949. Bigeleisen's general formula for deuterium kinetic isotope effects (which is also applicable to heavier elements) is given below. It employs transition state theory and a statistical mechanical treatment of translational, rotational, and vibrational levels for the calculation of rate constants kH and kD. However, this formula is "semi-classical" in that it neglects the contribution from quantum tunneling, which is often introduced as a separate correction factor. Bigeleisen's formula also does not deal with differences in non-bonded repulsive interactions caused by the slightly shorter C–D bond compared to a C–H bond. In the equation, quantities with the subscripts H or D refer to the hydrogen- or deuterium-substituted species, respectively, while quantities with or without the double-dagger, ‡, refer to the transition state or reactant ground state, respectively. (Strictly speaking, a term resulting from an isotopic difference in transmission coefficients should also be included.) , where we define and . Here, h is the Planck constant, kB is the Boltzmann constant, is the frequency of the vibration, expressed in wavenumbers, c is the speed of light, NA is the Avogadro constant, and R is the universal gas constant. The σX (X =