T.B. Grimley

Interactions between adatoms on metals and their effects on the heat of adsorption at low surface coverage

Abstract The indirect interaction between adatoms on a metal surface which arises because the adatoms share the itinerant electrons of the system will lead to a dependence of the heat of adsorption on the surface coverage. This dependence is investigated by treating a simple model Hamiltonian in the ordinary Hartree-Fock approximation. The indirect interaction has many-body character, but this does not affect the initial slope of the curve of heat versus coverage. Estimates of this slope for both thermally equilibriated, and randomly distributed adatoms on tungsten indicate that for the former, but not for the latter, an initial rise in the heat with coverage is possible on the (110) plane if the dipole moment of the surface bond is not too large.

Non-adiabatic processes in adsorption/desorption phenomena

Abstract The coupling between electronic and nuclear motions, which is neglected in the adiabatic approximation, allows energy flow between the two sorts of motion. In chemisorption systems, such energy flow is a non-adiabatic effect which has several consequences; among them are the broadening of the IR vibration line of a chemisorbed atom, and the possibility of a gas-phase atom losing enough energy to stick on to the substrate. In this paper model calculations are reported which indicate that IR linewidths and sticking coefficients due to non-adiabatic effects can be important.

Electron transfer in the reflection of atoms from metal surfaces

Abstract The resonance mechanism for positive and negative ionization of an atom reflected from a metal surface is treated in the time-dependent Hartree-Fock approximation assuming that the atom moves on its classical trajectory. A simple model is parameterized to describe 30–500 eV Na atoms reflected from tungsten, and the ionization probabilities are calculated by numerical integration of the equation of motion of the time evolution operator. Significant ionization can only occur if either the ionization level, or the affinity level of the atom crosses the Fermi level beyond the range of the atom-metal hopping interaction. On clean tungsten, the former situation applies, and the probability of positive ionization is nearly unity, and of negative ionization nearly zero.

Chemisorption theory in the Hartree-Fock approximation

To overcome the limitation of conventional quantum chemistry computer programs using the Hartree-Fock approximation which can only handle small clusters of atoms, Dysons equation is used to embed an adsorbate/absorbent cluster in the surface of the semi-infinite adsorbent. The embedding problem is formulated correctly, but to have a practical scheme, an approximate version is needed. This version uses a tight-binding electron Green function in the adsorbent beyond the cluster, but the correct self-consistent Green function in the adsorbate/adsorbent cluster. Calculations have been made for hydrogen on the (100) surfaces of two simple, and two face-centred cubic s band solids.

The interaction between two hydrogen atoms adsorbed on (100) tungsten

The through-bond interaction of two H atoms on (100) tungsten has been calculated in a surface molecule approximation using both Andersons and Hubbards hamiltonians, and assuming a linear WzH local geometry for chemisorbed hydrogen. There is a short range repulsion preventing two such adsorbed H atoms from occupying adjacent sites amounting to 0.020 Ryd for Andersons model, and 0.010 Ryd for that of Hubbard.

Surface science lettersTheory of ion neutralisation scattering from surfaces

A method for the calculation of the probability of neutralisation of an ion, which is scattered from the surface of a solid is presented. It assumes the ion to move along a classical trajectory and solves for the time evolution operator for the electronic system. For one electron Hamiltonians the solution can be carried out exactly. Results are presented for scattering from a semi-infinite linear chain.

Overlap effects in the theory of adsorption using Anderson's Hamiltonian

When Andersons model Hamiltonian is applied to the adsorption of atoms by metals, the basis orbitals cannot be regarded as orthogonal, and overlap effects must therefore be included in the theory. This is easily accomplished, not only in the Hartree-Fock approximation, but also in the exact many-body theory. Only the former is discussed in detail. Numerical calculations with parameters chosen to represent some features of the adsorption of hydrogen, and sodium atoms by tungsten are reported, and it is shown that, whereas overlap is essential in a quantitative treatment of the binding energies, the work of elucidating the electronic structures of adsorbed atoms can be started without including it explicitly in the theory.

Lifetimes of electronically adiabatic vibrational states of a chemisorbed atom

A Green function formalism is introduced to deal with the non-adiabatic coupling of a chemisorbed atom with a metal. Starting from the Born-Oppenheimer system of coupled equations, general formulae for the phonon relaxation rate, and the energy renormalization on an electronically adiabatic potential energy curve have been obtained. This theory is applied to the Grimley-Pisani model of chemisorption. Numerical results for a linear atomic chain with one adatom, and for a cluster model, by treating the motion of the adatom in the harmonic approximation, are presented.

A model for non-adiabatic coupling on metals: The sticking problem

Abstract A simple quantum model is introduced to deal with the continuum of electron-hole pair excitations produced by a reactive gas atom moving near a metal surface. The sticking coefficient due to the electron-hole pair mechanism is defined for both box- and o-function-normalization of the gas atoms nuclear wavefunctions, and the equivalence of the two definitions is proved for a large box. The sticking coefficient is calculated in the distorted wave Bom approximation for hydrogen atoms with kinetic energies in the range 0–80 meV. It shows a maximum at about 21 meV due to a quantum mechanical resonance in the transmission of the hydrogen atom into the chemisorption potential well. The maximum value of the sticking coefficient is 0.4. The role in electron-hole pair sticking of the spectral density at the Fermi level of the surface bond order is emphasized, and discussed.

A model Hamiltonian for phonon energy transfer in gas—solid collisions

Abstract Using the formalism of second quantization in the occupation number representation, a model Hamiltonian of the form H = H loc + H nonloc + H loc − nonloc is developed. H loc describes the gas atom-phonon system when the gas atom is near the surface, and the phonon operators are only in this term. H nonmloc describes the gas atom moving in a static potential with no bound states, and H loc-nonloc couples these two parts of H . The method of solution is to diagonalize H loc and then to embed it in the continuum of scattering states of H nonloc . The model is designed so that this diagonalization can be performed essentially exactly for a large class of gas-metal systems. The procedure is illustrated with a simple example which nevertheless shows how multi-phonon processes can dominate in desorption.