Beschreibung:
<jats:p>To describe tunneling of light atoms, a method is developed that takes account of the multidimensional nature of the process but remains tractable without becoming inaccurate. It combines the instanton formalism with ab initio potentials and force fields and makes effective use of a number of practical approximations suggested by the nature of the calculations. The tunneling potential is constructed from ab initio calculations that are fully optimized at stationary points. All other vibrations are represented by their harmonic force fields. Changes in the harmonic force fields between stationary points are expressed as couplings with the tunneling mode. The transfer rate is calculated for the instanton path, i.e., the path of least resistance, modulated by adjacent paths which define the damping required for nonoscillatory transfer. The multidimensional transfer integrals, involving all modes that change between the initial state and the transition state, are reduced to quasi-one-dimensional integrals by a number of approximation schemes. Modes with frequencies much higher than the tunneling mode are included in the adiabatic potential. Modes with frequencies much lower than the tunneling mode are treated classically. Modes that are linearly coupled to the tunneling mode are handled by separation of the variables followed by analytical integration. These approaches permit the calculation of most transfer rates without the explicit evaluation of the multidimensional instanton path.</jats:p>
<jats:p>They also specify the parts played by the various modes coupled to the tunneling mode. Totally symmetric modes generally promote tunneling by allowing a more favorable trajectory. Hence low-frequency symmetric modes tend to govern the temperature dependence of the transfer. Modes of the same symmetry as the transfer mode will generally contribute to the barrier and thus cause friction, represented by a Franck–Condon factor in the transfer integral. The method is applied to three molecular inversions whose rate constants have been deduced from magnetic resonance measurements. Inversion rate constants for aziridine and the oxiranyl radical together with their relevant deuterium analogs are calculated as a function of temperature and are found to be in a good agreement with the observed rates. For the dioxolanyl radical such agreement is obtained only after the introduction of an anharmonic correction. While inversions are generally low-frequency modes, the method is equally applicable to transfer governed by high-frequency XH stretch vibrations.</jats:p>