Professor Greg Benesh and collaborators’ research deals primarily with the study of surfaces with and without adsorbed layers of atoms. The analysis of a surface system can be formulated more generally as an embedding problem: how to find the properties of an interacting system of particles that is subject to boundary conditions imposed by an underlying medium. Examples of embedding problems include local magnetic moments arising from transition metal impurities in paramagnetic crystals, vacancies, chemisorbed molecules on surfaces, and surfaces themselves—which are merely two-dimensional inpurities in a three-dimensional crystal.
My collaborators and I have developed a self-consistent method in which the exact influence of an infinite substrate is communicated to the impurity region by means of an embedding potential. For quantum mechanical problems, the embedding potential is an additional term in the impurity region’s hamiltonian, which causes the wave function solutions to match in amplitude and derivative to solutions in the underlying medium across an embedding surface.
For surfaces, our approach embeds the surface region onto a semi-infinite bulk crystal. The resulting semi-infinite geometry has been found to be much more accurate than the slab and slab-superlattice geometries which are often employed. The influence of the underlying medium is important for experiments such as angle-resolved photoemission and inverse photoemission spectroscopies, which probe the spectrum of electronic states; these states can be very different in a slab from those of a semi-infinite system. By including, through the embedding potential, the propagation of the wavefunctions into the substrate, the embedding method accurately describes both discrete surface states and the bulk continuum of states. On surfaces of aluminum, nickel, and platinum the method has been shown to yield better work functions and more exact surface state energies than slabs of much greater thickness.
These ideas can be employed in a variety of new systems. The main idea is to make the impurity region large enough so that it does not have a significant effect on the underlying medium. For example, electronic screening causes the influence of an impurity atom to be negligible beyond a few neighboring shells of atoms. However, the influence of the much larger substrate is still significant in the impurity region. The exact influence of the perfect substrate medium can be communicated via an embedding potential. We have employed embedding potentials that have been derived variationally. They are related to the Green’s function of the underlying medium.