G. Doyen

Theory of carbon monoxide chemisorption on transition metals

Abstract An Anderson formalism including overlap is used to treat the chemisorption of carbon monoxide on the transition metals Cu, Ni and Pd. According to the generally accepted scheme only coupling of the 2π ∗ - and 5σ-orbitals of CO to the metallic d-states is regarded. The wave functions of the metal surface are approximated by a linear combination of atomic d-orbitals, which are oriented in such a manner that maximum overlap with the 2π ∗ -orbital of CO is achieved. The error involved in this procedure is absorbed into the only adjustable parameter B . Predictions are made for the electronic structure, i.e. the chemisorption levels and occupation numbers. Comparison with results of photoelectron spectroscopy, energy loss spectroscopy and infrared experiments is encouraging. The variation of adsorption energy with geometric location, crystallographic orientation and nature of the substrate metal is extensively treated and compared with experiment. It was possible for example to predict correctly the structure models derived from LEED data and the changes in adsorption energy associated with structural modifications due to varying coverage.

Catalytic oxidation of CO on Pt(111): the influence of surface defects and composition on the reaction dynamics

Abstract Angular distributions of CO 2 , I (γ r ), formed by catalytic reaction between CO and O 2 on a stepped Pt(111) surface, have been measured by means of molecular beam techniques as a function of CO and O coverages, in the presence of “subsurface oxide”, and at varying temperatures. The resulting data can well be fitted by I ( γ r ) = a cos γ r + (1− a ) cos 7 γ r with a being an adjustable parameter which varies with the surface conditions. The cos γ r part is ascribed to particles which were completely accommodated with their translational energy to the surface temperature before leaving the surface, while the cos 7 γ r channel corresponds to molecules carrying excess translational energy from crossing the activation barrier of the surface reaction. The fraction of thermally accommodated particles increases by the presence of steps or “subsurface oxide”, and decreases with O and CO coverage as well as with increasing temperature. The effect of coverage can qualitatively be attributed to the varying participation of defect sites in product formation, while the influence of surface temperature is well reproduced in the framework of a general theoretical model. Scattering experiments with CO 2 revealed that the trapping probability for this molecule (in the temperature range interesting here) is of the order of 0.5, thus confirming the conclusion of incomplete thermal accommodation of a CO 2 molecule interacting with a Pt(111) surface.

Semiempirical model calculations for chemisorption on transition metals: III. CO, N2 and NO on Ni, Cu, Pd and Ag

Abstract An effective one electron Hamiltonian is used to calculate the qualitative behaviour of various physical quantities (adsorption energy, shifts of ionization energies, energy profiles, etc.) over a series of different adsorption systems. The numerical calculations allow for several orbitals on the adsorbed particle as well as for the s- and the d-and in the metal. The experimentally found trends concerning the general features of photoelectron spectra and the variation of the adsorption energy with adsorbate and substrate as well as with the surface orientation and the location of the adsorbed species are reproduced reasonably well. A simple theory of photoemission (the final state is a plane wave) has been combined with the semiempirical calculations. The generally observed decrease of emission from the d-band region can be understood as an interference effect in the initial state.

Semiempirical theory of chemisorption on narrow d‐band metals

A previous developed model is applied to chemisorption of various adsorbates on Ni, Cu, Pd, and Ag surfaces. The aim of the calculations was mainly to predict the trends of various physical properties over a series of different adsorption systems. Adsorption energies, ionization energies, and energy profiles are evaluated and compared with experiment. The difference photoelectron spectra are derived to a first approximation by including the optical matrix elements for excitation into plane wave final states. Chemisorption of atomic hydrogen and oxygen is treated in detail. In the case of hydrogen chemisorption the results agree qualitatively well with conclusions drawn from more elaborate numerical calculations published recently. For oxygen chemisorption the importance of the multiplet structure of the O atom is stressed. In this model the large exchange splitting of the O 2p level is preserved in the adsorbed state; the main effect caused by coupling to the metal is a screening shift by about 8 eV towar...

Semiempirical model calculations for chemisorption on transition metals: I. Exact solution and discussion of a simple model

Abstract A specially parameterized model Hamiltonian for chemisorption is proposed, which treats the interaction between adsorbate and metal electrons in some detail. The exact solution is obtained for the case of an electron band with zero width. It is identical with the Hartree-Fock solution. There are no relaxation effects on the ionization energies within this model. A formalism for performing semiempirical calculations is shown to yield a good approximate solution to the model Hamiltonian for the simple case treated in this paper. Qualitative features of wavefunctions, charge transfer, adsorption energy and ionization energies are discussed.

Semiempirical model calculations for chemisorption on transition metals: II. Description of the theoretical formalism of an extended basis set

Abstract A one electron Hamiltonian for chemisorption on transition metals is developed, which allows for several orbitals on the adparticle as well as for the s- and d-bands of the metal. The broad s-band is simulated by splitting it into several degenerate bands. The validity of this approximation is investigated. An adorbital resonance in this band has a much smaller width than predicted by the orthogonal Anderson model. An exact transformation to a surface molecule is performed, which gives the notion of a d-group orbital a precise meaning. Two different ways of estimating the overlap between adorbitals and metal wave functions are presented. They are suited for s- and d-bands respectively.

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.

A model for sticking at metal surfaces

Abstract A recently developed formalism, which uses a basis set representation with localized wave functions to describe the short range gas atom-photon interaction, is applied to examine the sticking problem. A numerical self-consistent calculation of the local gas atom-photon coupling is presented for a one-dimensional model with a parameterization roughly adequate for He scattering from a transition metal surface. Based on these results a very simple Hamiltonian is constructed, which permits a solution of the transmission problem and yields sticking coefficient one for zero substrate temperature and kinetic energy of the gas atom equal to zero. The influence of the quadratic phonon coupling terms is studied for a special example.

Model Hamiltonian approach to chemisorption: Treatment of diffuse virtual adorbitals

A model Hamiltonian approach to chemisorption is described which is a development of the model described previously for the cases of larger overlaps SA between metal wave functions and adorbitals. Inconsistencies due to basis set overcompleteness are cured. Nonorthogonality between adsorbate projected metal wave functions on different adorbitals is accounted for by explicitly evaluating the overlap integrals between them as well as the hopping terms in the metal part of the Hamiltonian due to coupling of metal wave functions through the adorbitals. Physically adequate hopping between adatom and metal through the core potentials is introduced for high overlap situations. The core hopping terms merge smoothly into the Wolfsberg–Helmholz approximation to core hopping, established earlier to lead to a reasonable description of chemisorption interactions at small overlaps. For the limiting case SA =1, due to completeness of the metal basis set, the adorbitals will be represented by the metal wave functions. k–...

Surface molecule approach to the adsorbate derived ionization energies for PF3 and CO adsorbed on transition metal surfaces

Abstract A surface molecule approach is used to establish a theoretical relationship between the adsorbate induced change of the work function and the screening and stabilization shifts of the adsorbate derived ionization energies. The parameters entering the calculation are deduced from other experimental data. The calculated quantities agree well with the measured values. For the first time an explanation for the opposite sign of the CO induced work function change on Pd and Pt is offered.