Kinetic carbon-13 and deuterium isotope effects are calculated for the SN2 reaction of CH3I with CN-. The normal vibrational frequencies of CH3I, the transition state I · · · CH3 · · · CN, and the corresponding isotope substituted reactants and transition states are evaluated from the force constants by solving the secular equation on an IBM 7094 computer.Values for 7 force constants of the planar CH3 moiety in the transition state (with an sp2 C atom) are obtained by comparison with suitable stable molecules. The stretching force constants related to the bonds being broken or newly formed (fCC, fCC and the interaction between these two stretches, /12) are chosen in such a way that either a zero or imaginary value for νʟ≠ will result. Agreement between calculated and experimental methyl-C13 isotope effects (k12/ k13) can be obtained only in sample calculations with sufficiently large values of f12 which lead to imaginary νʟ≠ values. Furthermore, the difference between fCI and fCC must be small (in the order of 1 mdyn/Å). The bending force constants, fHCI and fHCC, exert relatively little influence on k12/k13. They are important for the D isotope effect, however. As soon as experimental data on kH/kD are available it will be possible to derive a value for fHCC in the transition state if fHCI is kept constant at 0.205 mdynA, and if fCI, fCC and f12 are held in a reasonable order of magnitude. There is no agreement between experimental and calculated cyanide-C13 isotope effects. Possible explanations are discussed. — Since fCI and fCC cannot differ much it must be concluded that the transition state is relatively “symmetric”, with approximately equal amounts of bond making and bond breaking.
Separation Property of Solutions for a Semilinear Elliptic Equation
