Quantum Instanton Theory And Its Applications To Chemical Reaction Rates In Complex Systems

The quantum instanton approximation(QI), developed from the semiclassical transition state theory, is extended to evaluate the gas phase SiHA+H→SiH3+H2 reaction and condensed phase H/Ni reactions with potential energy surfaces proposed by Espinosa-Garcia et al. and Wonchoba et al., respectively. The path integral Monte Carlo and the adaptive umbrella sampling techniques are employed to manipulate the quantum instanton formula.For the gas phase SiH4+H→SiH3+H2 reaction, the calculated rate constants and isotope effects show good agreements with available experimental data. Meanwhile, we demonstrate that the QI theory is essentially the same as the variational transition state theory in the classical limit, and the instanton stationary condition to decide the dividing surfaces has the activity of minimizing the recrossing. Furthermore, the QI formula can be recast into the Arrhenius form. Detailed comparisons of quantum and classical quantities show that quantum correction for the prefactor is more important than that for the free energy.For the processes of H/Ni, we have investigated the free energy profiles along the reaction paths and their temperature dependences, as well as the rates and the diffusion coefficients. The predicted rates are consistent with experimental ones at high temperatures. For the process of H diffusion on Ni(100), the hydrogen tunneling begins to dominate the diffusion process as temperature decreases to 80K, and the transition temperature is found to be 70K under which the turning points of the instanton orbit are nearly located at the two hollow sites. For the process of H diffusion on Ni(111), it is found that the fcc and hcp binding sites have the same free energy, manifesting that the nickel atoms beneath the surface have little effect on the surface diffusion process. For the other processes, such as H transports between surface and subsurface, and H diffusion in interior of bulk nickel, we have drawn several conclusions:(1) The hydrogen at the subsurface octahedral site is much more stable than the one at the subsurface tetrahedral site; (2) The hydrogen at the fee binding site is much easier to get into bulk nickel than the one at the hcp site; (3) The temperature dependence of free energy profile reveals that the hydrogen in the interior tetrahedral vacancy becomes unstable at low temperatures, so the process of H diffusion in interior of bulk Ni should be a single kinetic step reaction at low temperature, while it should be two individual kinetic steps reaction at high temperature; (4) The classical relaxations of the lattices reduce the prefactors and dramatically lower the free energy barriers, compared with the rigid lattices; (5) The quantum motions of the lattice atoms affect the free energies little at 300K, but they reduce the rates by 20-40% through hindering the prefactors, compared with the classical relaxations of lattice atoms.