Speaker
Description
We are interested in the adhesion rate that occurs through the collision process between an atom or molecule and a surface. This adsorption mechanism is of great importance in the fields of Physics and Chemistry, explaining phenomena such as catalysis and corrosion. Qualitatively, the problem can be described as an initially neutral atom approaching a metallic surface. The overlap between the orbitals of this atom and those of the surface grows, allowing for charge transfer. When an electron is transferred, the atom becomes electrically charged, and consequently, an image charge potential appears, accelerating the particle towards the surface. In the subsequent collision, the generation of phonons and electron-hole pairs in the metal steals energy from the incident atom, which can become trapped in the attractive potential. Therefore, there is a probability that this particle will be adsorbed by the surface. The theoretical challenge is to calculate this probability, which is known as the Sticking coefficient 𝑆.
The Born-Oppenheimer approximation, traditionally used to separate the nuclear part of the wave function from the electronic part, is not capable of explaining the phenomenon. Additionally, we cannot use adiabatic approximations since it is precisely the non-adiabatic effects that enable energy loss from the atom. Therefore, a complete calculation employing a precise numerical treatment of the time-dependent wave function Ψ(𝑧,𝑡) is necessary. The modeling of this problem is simplified by the normal incidence of a neutral hydrogen atom onto the surface of a metal, which will be described by a featureless conduction band. To describe the electronic part, we will employ Anderson's model of an impurity with an additional term that represents the image charge potential.
Simplistically, the procedure to find 𝑆 is based on calculating the spectrum of electronic energies using the Numerical Renormalization Group (NRG) method for each value of the distance 𝑧. In the initial state, the particle is far from the surface, and its wave function is the product of the initial electronic state and a Gaussian centered at an initial position, which describes the nuclear part. The Crank-Nicolson procedure allows for the calculation of the temporal evolution of the wave function until, after the collision, the function splits into one part localized near the surface and another that moves away from it. The spatial integral of the squared modulus of the first part determines the Sticking coefficient 𝑆.
