U. Lorenz, Peter Saalfrank

• We present a rigorous method to set up a system-bath Hamiltonian for the coupling of adsorbate vibrations (the system) to surface phonons (the bath). The Hamiltonian is straightforward to derive and exact up to second order in the environment coordinates, thus capable of treating one- and two-phonon contributions to vibration-phonon coupling. The construction of the Hamiltonian uses orthogonal coordinates for system and bath modes, is based on an embedded cluster approach, and generalizes previous Hamiltonians of a similar type, but avoids several (additional) approximations. While the parametrization of the full Hamiltonian is in principle feasible by a first principles quantum mechanical treatment, here we adopt in the spirit of a QM/MM model a combination of density functional theory (“QM”, for the system) and a semiempirical forcefield (“MM”, for the bath). We apply the Hamiltonian to a fully H-covered Si(100)-(2 × 1) surface, using Fermi’s Golden Rule to obtain vibrational relaxation rates of various H–Si bending modes of thisWe present a rigorous method to set up a system-bath Hamiltonian for the coupling of adsorbate vibrations (the system) to surface phonons (the bath). The Hamiltonian is straightforward to derive and exact up to second order in the environment coordinates, thus capable of treating one- and two-phonon contributions to vibration-phonon coupling. The construction of the Hamiltonian uses orthogonal coordinates for system and bath modes, is based on an embedded cluster approach, and generalizes previous Hamiltonians of a similar type, but avoids several (additional) approximations. While the parametrization of the full Hamiltonian is in principle feasible by a first principles quantum mechanical treatment, here we adopt in the spirit of a QM/MM model a combination of density functional theory (“QM”, for the system) and a semiempirical forcefield (“MM”, for the bath). We apply the Hamiltonian to a fully H-covered Si(100)-(2 × 1) surface, using Fermi’s Golden Rule to obtain vibrational relaxation rates of various H–Si bending modes of this system. As in earlier work it is found that the relaxation is dominated by two-phonon contributions because of an energy gap between the Si–H bending modes and the Si phonon bands. We obtain vibrational lifetimes (of the first excited state) on the order of 2 ps at K. The lifetimes depend only little on the type of bending mode (symmetric vs. antisymmetric, parallel vs. perpendicular to the Si2H2 dimers). They decrease by a factor of about two when heating the surface to 300 K. We also study isotope effects by replacing adsorbed H atoms by deuterium, D. The Si–D bending modes are shifted into the Si phonon band of the solid, opening up one-phonon decay channels and reducing the lifetimes to few hundred fs.…