Electronic states metal surfaces

For two and three dimensions, it provides a crude but useful picture for electronic states on surfaces or in crystals, respectively. Free motion within a spherical volume gives rise to eigenfunctions that are used in nuclear physics to describe the motions of neutrons and protons in nuclei. In the so-called shell model of nuclei, the neutrons and protons fill separate s, p, d, etc orbitals with each type of nucleon forced to obey the Pauli principle. These orbitals are not the same in their radial shapes as the s, p, d, etc orbitals of atoms because, in atoms, there is an additional radial potential V(r) = -Ze2/r present. However, their angular shapes are the same as in atomic structure because, in both cases, the potential is independent of 0 and (f>. This same spherical box model has been used to describe the orbitals of valence electrons in clusters of mono-valent metal atoms such as Csn, Cu , Na and their positive and negative ions. Because of the metallic nature of these species, their valence electrons are sufficiently delocalized to render this simple model rather effective (see T. P. Martin, T. Bergmann, H. Gohlich, and T. Lange, J. Phys. Chem. 95, 6421 (1991)). 

The decay of the nanoparticle plasmons can be either radiative, ie by emission of a photon, or non-radiative (Figure 7.5). Within the Drude-Sommerfeld model the plasmon is a superposition of many independent electron oscillations. The non-radiative decay is thus due to a dephasing of the oscillation of individual electrons. In terms of the Drude-Sommerfeld model this is described by scattering events with phonons, lattice ions, other conduction or core electrons, the metal surface, impurities, etc. As a result of the Pauli exclusion principle, the electrons can be excited into empty states only in the CB, which in turn results in electron-hole pair generation. These excitations can be divided into inter- and intraband excitations by the origin of the electron either in the d-band or the CB (Figure 7.5) [15]. 

Second harmonic generation has been recognized as a powerful probe to study the electronic states at surfaces and interfaces [16]. Under the electric dipole approximation, second-order nonlinear processes are forbidden in centrosymmetric systems. This principle makes the phenomena surface-specific in many cases. Indeed, the capability of SHG spectroscopy to explore surface electronic states has been demonstrated on various systems, dye molecules at solid/liquid interfaces [17], organic molecules at liquid/air interfaces [18], semiconductor surface states [19], organic molecules at metal surfaces [20], and so on. 

Ballhausen s latest book [30], Molecular Electronic Structures of Transition Metal Complexes appeared in 1979, 25 years after his first article. It can be seen as his answer to the question What is a molecule - in particular a transition metal complex He starts with his conclusion from a series of articles on the chemical bond [31], Chemistry is one huge manifestation of quantum mechanics . He then introduces the Bom-Oppenheimer approximation as the basis for applying electronic and nuclear coordinates, and lets the picture of a molecule unfold itself with the concepts of electronic states, potential surfaces, transitions, vibronic couplings, etc. The presentation is traditional, but contains many refinings in the discussion of a molecule s ground state as well as its excited states. The world of transition metal complexes is favoured through the choice of examples. 

Chemisorption occurs when the attractive potential well is large so that upon adsorption a strong chemical bond to a surface is fonued. Chemisorption involves changes to both the molecule and surface electronic states. For example, when oxygen adsorbs onto a metal surface, a partially ionic bond is created as charge transfers from the substrate to the oxygen atom. Other chemisorbed species interact in a more covalent maimer by sharing electrons, but this still involves perturbations to the electronic system. 

Many of the fiindamental physical and chemical processes at surfaces and interfaces occur on extremely fast time scales. For example, atomic and molecular motions take place on time scales as short as 100 fs, while surface electronic states may have lifetimes as short as 10 fs. With the dramatic recent advances in laser tecluiology, however, such time scales have become increasingly accessible. Surface nonlinear optics provides an attractive approach to capture such events directly in the time domain. Some examples of application of the method include probing the dynamics of melting on the time scale of phonon vibrations [82], photoisomerization of molecules [88], molecular dynamics of adsorbates [89, 90], interfacial solvent dynamics [91], transient band-flattening in semiconductors [92] and laser-induced desorption [93]. A review article discussing such time-resolved studies in metals can be found in... 

Figure Bl.22.4. Differential IR absorption spectra from a metal-oxide silicon field-effect transistor (MOSFET) as a fiinction of gate voltage (or inversion layer density, n, which is the parameter reported in the figure). Clear peaks are seen in these spectra for the 0-1, 0-2 and 0-3 inter-electric-field subband transitions that develop for charge carriers when confined to a narrow (<100 A) region near the oxide-semiconductor interface. The inset shows a schematic representation of the attenuated total reflection (ATR) arrangement used in these experiments. These data provide an example of the use of ATR IR spectroscopy for the probing of electronic states in semiconductor surfaces [44]-...

Our intention is to give a brief survey of advanced theoretical methods used to detennine the electronic and geometric stmcture of solids and surfaces. The electronic stmcture encompasses the energies and wavefunctions (and other properties derived from them) of the electronic states in solids, while the geometric stmcture refers to the equilibrium atomic positions. Quantities that can be derived from the electronic stmcture calculations include the electronic (electron energies, charge densities), vibrational (phonon spectra), stmctiiral (lattice constants, equilibrium stmctiires), mechanical (bulk moduli, elastic constants) and optical (absorption, transmission) properties of crystals. We will also report on teclmiques used to study solid surfaces, with particular examples drawn from chemisorption on transition metal surfaces. 

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

In this section, we extend the above discussion to the isotopomers of X3 systems, where X stands for an alkali metal atom. For the lowest two electronic states, the permutational properties of the electronic wave functions are similar to those of Lij. Their potential energy surfaces show that the baniers for pseudorotation are very low [80], and we must regard the concerned particles as identical. The Na atom has a nuclear spin " K, and K have nuclear... 

A value close to 4.8 V has been obtained in four different laboratories using quite different approaches (solid metal/solution Ay, 44 emersed electrodes,40,47 work function changes48), and is apparently supported by indirect estimates of electronic energy levels. The consistency of results around 4.8 V suggests that the value of 4.44 V is probably due to the value of 0 not reflecting the actual state of an Hg jet or pool. According to some authors,44 the actual value of 0 for Hg in the stream should be 4.8 V in that the metal surface would be oxidized. 

Kolb and Franke have demonstrated how surface reconstruction phenomena can be studied in situ with the help of potential-induced surface states using electroreflectance (ER) spectroscopy.449,488,543,544 The optical properties of reconstructed and unreconstructed Au(100) have been found to be remarkably different. In recent model calculations it was shown that the accumulation of negative charges at a metal surface favors surface reconstruction because the increased sp-electron density at the surface gives rise to an increased compressive stress between surface atoms, forcing them into a densely packed structure.532... 

This backdonation of electron density from the metal surface also results in an unusually low N-N streching frequency in the a-N2 state compared to the one in the y-N2 state, i.e. 1415 cm 1 and 2100 cm"1, respectively, for Fe(l 11)68. Thus the propensity for dissociation of the a-N2 state is comparatively higher and this state is considered as a precursor for dissociation. Because of the weak adsorption of the y-state both the corresponding adsorption rate and saturation coverage for molecular nitrogen are strongly dependent on the adsorption temperature. At room temperature on most transition metals the initial sticking coefficient does not exceed 10 3. 

The coadsorption of oxygen as well as of other electronegative additives on metal surfaces favors in general the 7t-bonded molecular state of ethylene, as the latter exhibits, compared to the di-o bonded state, a more pronounced electron donor character and a negligible backdonation of electron density from the metal surface. 

Figure 7.9. Schematic representation of the density of states N(E) in the conduction band of two transition metal electrodes (W and R) and of the definitions of work function O, chemical potential of electrons p, electrochemical potential of electrons or Fermi level p, surface potential x, Galvani (or inner) potential (p and Volta (or outer) potential for the catalyst (W) and for the reference electrode (R). The measured potential difference UWr is by definition the difference in p q>, p and p are spatially uniform O and can vary locally on the metal surfaces 21 the T terms are equal, see Fig. 5.18, for the case of fast spillover, in which case they also vanish for an overall neutral cell Reprinted with permission from The Electrochemical Society.

C07-0131. A hydrogen atom undergoes an electronic transition from the = 4 to the = 2 state. In the process the H atom emits a photon, which then strikes a cesium metal surface and ejects an electron. It takes 3.23 X 10 J to remove an electron from Cs metal. Calculate (a) the energy of the — 4 state of the H atom (b) the wavelength of the emitted photon (c) the energy of the ejected electron and (d) the wavelength of the ejected electron. 

Consider an atom approaching the surface in Fig. 6.23. If the upper level of the atom originally contained an electron, then upon adsorption it will transfer part of this electron density to the metal and become positively charged. This is the case with alkali atoms. The atom forms a dipole with the positive end towards the outside, which counteracts the double layer that constitutes the surface contribution to the work function of the metal (Fig. 6.13). Thus alkali atoms reduce the work function of a metal surface simply because they all have a high-lying s electron state that tends to donate charge to the metal surface. 

The STEM Is Ideally suited for the characterization of these materials, because one Is normally measuring high atomic number elements In low atomic number metal oxide matrices, thus facilitating favorable contrast effects for observation of dispersed metal crystallites due to diffraction and elastic scattering of electrons as a function of Z number. The ability to observe and measure areas 2 nm In size In real time makes analysis of many metal particles relatively rapid and convenient. As with all techniques, limitations are encountered. Information such as metal surface areas, oxidation states of elements, chemical reactivity, etc., are often desired. Consequently, additional Input from other characterization techniques should be sought to complement the STEM data. 

---