can readily interpret the factor of ½ and the sums of terms over ground state and transition state vibrational modes in the exponent of the simplified formula above. For a harmonic oscillator, the vibrational frequency is inversely proportional to the square root of the reduced mass of the vibrating system: , where kf is the force constant. Moreover, the reduced mass is approximated by the mass of the light atom of the system, X = H or D. Because mD is approximately 2mH, . In the case of a homolytic C–H/D bond dissociation, the transition state term disappears, and neglecting other vibrational modes, kH/kD = exp(½Δui). Thus, a larger isotope effect is observed for a stiffer ("stronger") C–H/D bond. For most reactions of interest, a hydrogen atom is transferred between two atoms, with a transition-state [A···H···B]‡ and vibrational modes at the transition state need to be accounted for. Nevertheless, it is still generally true that cleavage of a bond with a higher vibrational frequency will give a larger isotope effect. To calculate the maximum possible value for a non-tunneling deuterium KIE, we consider the case in which the zero-point energy difference between the stretching vibrations of a typical carbon-hydrogen bond (3000 cm−1) and carbon-deuterium bond (2200 cm−1) disappears in the transition state (an energy difference of (1/2)(3000 – 2200 cm−1) = 400 cm−1, or about 1.15 kcal/mol), without any compensation from a zero-point energy difference at the transition state (e.g., from the symmetric A···H···B stretch, which is unique to the transition state). The simplified formula given above predicts a maximum for kH/kD as 6.9. If the complete disappearance of two bending vibrations is also included, kH/kD values as large as 15-20 can be predicted. Bending frequencies are very unlikely to vanish in the transition state, however, and there are only a few cases in which kH/kD values exceed 7-8 near room temperature. Furthermore, it is often found that tunneling is a major factor when they do exceed such values. A value of kH/kD ~ 10 is thought to be maximal for a semi-classical primary kinetic isotope effect (no tunneling) for reactions taking place around 298 K. (The formula for kH/kD has a temperature dependence, so larger isotope effects are possible at lower temperatures). Depending on the nature of the transition state of H-transfer (symmetrical vs. "early" or "late" and linear vs. bent), the extent to which a primary deuterium isotope