Quantum mechanical exchange in a transition metal hydride complex: NMR data for [cp(PPh3)IrH3]+ fitted by a two-dimensional model

Abstract

A two-dimensional model for hydrogen pair exchange in transition metal trihydrides is used to interpret NMR data observed for [cp(PPh3)IrH3]+. Inspired by quantum chemical results for [cp(PH3)IrH3]+, the model describes a combined process of rotational tunneling and IrH2 bending that merges into an H2 “lift-off’’ motion at a small proton–proton distance. The condensed environment with which the tunneling system interacts is represented by a heat bath. A second-order perturbation treatment yields a master equation for the populations of the vibrational states within each of the rotational symmetry species A and B and for the respective AB coherences. A theoretical basis is provided for the evolution of the tunneling (AB) coherence as a damped oscillation in agreement with an independent treatment very recently published by Szymanski [J. Chem. Phys. 104, 8216 (1996)]. A simplified model assumption, containing one adjustable parameter, is made for the system–bath interaction. The temperature-dependent frequency of the tunneling process is found to be close to the Boltzmann average of the tunnel frequencies in the individual vibrational states. Both the calculated temperature-dependent coherence damping-rate constant and the tunnel frequency fit the experimental data after adjustment of three parameters describing the potential energy surface and of the parameter representing the system–bath interaction strength.