Also, since the transferring nuclear wavepacket is propagated via the time-dependent Schrodinger equation, using an efficient and accurate “distributed approximating functional” propagator, all quantum effects pertaining to the quantized H/D nucleus as well as those arising from the electronic degrees of freedom within the model are included. The kinetic isotope effect was computed using the transmission amplitude of the wavepacket and the experimental value was reproduced. Some physical insights gleaned from our studies are:

  • Tunneling for both hydrogen and deuterium occurs through the existence of distorted, spherical “s”-type hydrogen nuclear wavefunctions and “p”-type polarized hydrogen nuclear wavefunctions for transfer along the donor-acceptor axis.

  • There is also a significant population transfer through distorted “p”-type hydrogen nuclear wavefunctions directed perpendicular to the donor-acceptor axis [via intervening “$\pi$”-type interactions] which underlines the three-dimensional nature of the tunneling process. The quantum dynamical evolution indicates a significant contribution from tunneling processes both along the donor-acceptor axis and along directions perpendicular to the donor-acceptor axis.

  • The hydrogen nuclear wavefunctions display curve-crossings, in a fashion similar to electronic states. The tunneling process is vibrationally non-adiabatic and is facilitated by these curve-crossings. In our calculations multiple proton and deuteron excited states (greater than five) were shown to contribute to tunneling.

  • The inclusion of nuclear quantization shifted the transition-state towards the reactants. The precise location of the shifted transition state, however, depends on the populations of each hydrogen and deuterium eigenstate during dynamics.

Poster describing some of this work: Poster 1. Poster 2.