Vibrational energy transfer at the gas–solid interface: The role of collective and of localized vibrational modes

Abstract

We present a study of energy transfer (kinetic to vibrational) in collisions of atoms with diatomic molecules adsorbed on the surface of a metal substrate, for hyperthermal collision energies (0.1 to 1.0 eV). In order to make the many-body problem computationally tractable, atomic motions are restricted to one spatial dimension and the combined diatomic-metal target is modeled by a linear chain of coupled harmonic oscillators, so that vibrations of the target can be solved analytically for any arbitrary number of atoms. The collision is described in the semiclassical limit appropriate for hyperthermal velocities: translation of the projectile is obtained from a classical trajectory, while vibration of the target is treated quantum mechanically. The intensity of scattered atoms is obtained from the time-correlation function of the semiclassical transition operator. As a result, the intensity is evaluated analytically without need of internal-state expansions, and it includes the quantum-statistical average over the distribution of initial phonon states at nonzero temperature. The theory is applied to He projectiles scattered from OCPtx, OCNix, N2Wx, and from the pure metals. The results are presented in the form of energy-loss spectral simulated for a typical experimental detector of finite resolution. The calculations are done with realistic values of force constants and He-target potentials. Hence the one-dimensional model contains the basic vibrational features of the gas–solid interface, namely: a very large number of low-frequency modes involving collective vibrations of the target atoms and a few high-frequency modes whose atomic displacements are localized near the surface (the latter roughly correspond to the vibration of the free diatomic and to stretching of the diatom-substrate bond). The simulated spectra show rich structure due to many-quantum excitations of collective and localized modes. We show how the structure is related to the eigenfrequencies and eigenvectors of the target, and we examine how the contributions of each mode vary with collision energy and target temperature. We find that excitation of localized modes follow a Poisson distribution and only the first few transitions are significantly excited. In contrast, collective modes undergo many-quantum transitions characterized by a quasicontinuous and Gaussian distribution of energy transfer. We derive simple expressions that explain the amounts of energy transferred to each mode in terms of the physical parameters (force constants, atomic masses, temperature, thickness of the target, and strength of the potential). The simulations indicate that vibrational transitions of the adsorbed molecule can be resolved from the backgrond of substrate phonons using present technology. They also suggest that lattice phonon structure could be observed using a thin substrate film weakly coupled to an underlying support. We also find that the spectrum is quite sensitive to small variations of the projectile-adsorbate potential, so that scattering experiments can yield information about how intermolecular forces are changed by chemisorption.