Inverse secondary equilibrium isotope effects on silver-ethylene and $-d_1$complexes

Abstract

The origin of the inverse secondary equilibrium isotope effects on silverethylene and -$d_1$ complexes was studied in the condensed phase at 273 K. Comparing the inverse isotope effects of the internal modes with those of the external modes, zero point energy and vibrational excitation terms contribute to the positive effects, whereas classical vibrational partition function or external terms contribute to the negative effects. Assuming the complex forming reaction at 273 K as frozen system, the calculated isotope effect at 273 K, $K_d/K_h=1.056$, found to be in reasonably good agreement with the experimental value, 1.047. The thermodynamic quantities, i.e., $\triangle{G}_d-\triangle{G}_h$, $\triangle{H}_d-\triangle{H}_h$, and $\triangle{S}_d-\triangle{S}_h$, in this study are -29.5 cal/mole, -64.0 cal/mole, and -0.13 cal/mole degree, respectively. Among the vibrational characteristic modes by the isotope substitution, the contributions to the inverse isotope effect are mainly due to $CH_2$ rocking and $CH_2$ twisting modes.