effect approaches this maximum varies. A model developed by Westheimer predicted that symmetrical (thermoneutral, by the Hammond Postulate), linear transition states have the largest isotope effects, while transition states that are "early" or "late" (for exothermic or endothermic reactions, respectively), or nonlinear (e.g. cyclic) exhibit smaller effects. These predictions have since received extensive experimental support. For secondary deuterium isotope effects, Streitwieser proposed that weakening (or strengthening, in the case of an inverse isotope effect) of bending modes from the reactant ground state to the transition state are largely responsible for observed isotope effects. These changes are attributed to a change in steric environment when the carbon bound to the H/D undergoes rehybridization from sp3 to sp2 or vice versa (an α secondary kinetic isotope effect), or bond weakening due to hyperconjugation in cases where a carbocation is being generated one carbon atom away (a β secondary kinetic isotope effect). These isotope effects have a theoretical maximum of kH/kD = 20.5 ≈ 1.4. For a secondary kinetic isotope effect at the α position, rehybridization from sp3 to sp2 produces a normal isotope effect, while rehybridization from sp2 to sp3 results in an inverse isotope effect with a theoretical minimum of kH/kD = 2-0.5 ≈ 0.7. In practice, kH/kD ~ 1.1-1.2 and kH/kD ~ 0.8-0.9 are typical for α secondary kinetic isotope effects, while kH/kD ~ 1.15-1.3 are typical for β secondary kinetic isotope effect. For reactants containing several isotopically substituted β-hydrogen atoms, the observed isotope effect is often the result of several H/D's at the β position acting in concert. In these cases, the effect of each isotopically labeled atom is multiplicative, and cases where kH/kD > 2 are not uncommon. The following simple expressions relating deuterium and tritium kinetic isotope effects, which are also known as the Swain equation (or the Swain-Schaad-Stivers equations), can be derived from the general expression given above using some simplifications: ; i.e., . In deriving these expressions, the reasonable approximation that reduced masses are approximately equal to the masses of the hydrogen, deuterium, or tritium was used. In addition, the vibrational motion was assumed to be approximated by a harmonic oscillator, so that (X = H, D, or T). The subscript "s" refers to these "semi-classical" kinetic isotope effects, which disregard quantum tunneling. Tunneling contributions must be treated separately as a correction factor. For isotope effects involving elements other than hydrogen, many of these simplifications