Concept of surface states

The existence of surface states is a consequence of the atomic structure of solids. In an infinite and uniform periodic potential, Bloch functions exist, which explains the band structures of different solids (Kittel, 1986). On solid surfaces, surface states exist at energy levels in the gap of the energy band (Tamm, 1932 Shockley, 1939 Heine, 1963). 

The concept of surface states was proposed by Tamm (1932) using a one-dimensional analytic model. We start with reviewing the proof of the Bloch theorem for a one-dimensional periodic potential U x) with periodicity a (Kittel, 1986)  

The translational symmetry of the potential suggests the wavefunction to have the following property  

In the original paper of Tamm (1932), the concept of surface state is demonstrated with a Kronig-Penney potential (Kittel, 1986) with a boundary, as shown in Fig. 4.5. By solving the Schrodinger equation, exphcit expressions for the surface states and their energy levels can be obtained. In 

The surface states have another boundary condition to be fulfilled. In the vacuum region, x 0, the wavefunction is 

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The vacuum tails of Bloch waves are relatively straightforward to understand. Comparing with other experimental methods, STM is more sensitive to the surface states, both the sample and the tip. Therefore, we will spend more time to explain the concept of surface states, from a theoretical point of view and an experimental point of view. 

Similar to the failures of the free-electron model of metals (Ashcroft and Mermin, 1985, Chapter 3), the fundamental deficiency of the jellium model consists in its total neglect of the atomic structure of the solids. Furthermore, because the jellium model does not have band structure, it does not support the concept of surface states. Regarding STM, the jellium model predicts the correct surface potential (the image force), and is useful for interpreting the distance dependence of tunneling current. However, it is inapplicable for describing STM images with atomic resolution. 

The theoretical chemical application of surface chemical bonding theory, highlighted next, is related to formal chemisorption theory as developed in surface physics, but concentrates on quantum chemical concepts as the electron distribution over bonding and antibonding orbital fragments [5, 6]. It will be seen that both approaches complement each other. The notion of a surface molecule relates to the surface physicists concept of surface state. 

Physical Chemistry of Solid-Gas Interfaces 4.3.1. Concept of surface states ... 

To address these challenges, chemical engineers will need state-of-the-art analytical instruments, particularly those that can provide information about microstmctures for sizes down to atomic dimensions, surface properties in the presence of bulk fluids, and dynamic processes with time constants of less than a nanosecond. It will also be essential that chemical engineers become familiar with modem theoretical concepts of surface physics and chemistry, colloid physical chemistry, and rheology, particrrlarly as it apphes to free surface flow and flow near solid bormdaries. The application of theoretical concepts to rmderstanding the factors controlling surface properties and the evaluation of complex process models will require access to supercomputers. 

Here we use the convenient notation for the transition state A 2d- As we have already have seen, it is customary to introduce the concept of surface coverage when dealing with reactions on surfaces. The coverage of A is given by... 

Lochmuller and coworkers used the formation of excimer species to answer a distance between site question related to the organization and distribution of molecules bound to the surface of silica xerogels such as those used for chromatography bound phases. Pyrene is a flat, poly aromatic molecule whose excited state is more pi-acidic than the ground state. An excited state of pyrene that can approach a ground state pyrene within 7A will form an excimer Pyr +Pyr (Pyr)2. Monomer pyrene emits at a wavelength shorter than the excimer and so isolated versus near-neighbor estimates can be made. In order to do this quantitatively, these researchers turned to measure lifetime because the monomer and excimer are known to have different lifetimes in solution. This is also a way to introduce the concept of excited state lifetime. 

Moreover, as neither the concept of surface initiated homogeneous-heterogeneous reaction (11) can be invoked to explain our results, it can be stated that the methane partial oxidation reaction proceeds via a surface catalysed process which likely involves specific catalyst requirements. However, by comparing the HCHO productivity of the different catalytic systems previously proposed (9) with that of our 5% V205/Si02 catalyst, it emerges that our findings constitute a relevant advancement in this area (23),... 

That surface interactions play such a role clearly demands that some sort of surface state concept be invoked. However, no simple techniques have yielded direct information about the nature of such states. To explain charge transfer, isoenergetic electron or hole processes are normally invoked with a subsequent thermalization of the electron or hole in the semiconductor. This unfortunately necessitates the existence of a surface state at the level of the redox potential. This may of necessity occur when strong chemisorption is present. However, in those cases,... 

In statistical reaction rate theory, the concept of transition state plays a key role. Transition states are supposed to be the boundaries between reactants and products. However, the precise formulation of the transition state as a dividing surface is only possible when we consider transition states in phase space. This is the place where the concepts of normally hyperbolic invariant manifolds (NHIMs) and their stable and unstable manifolds come into play. 

The concept of equilibration of surface states at an interface may be illustrated by the case in which the two contacting phases are solids. In such a case, the energy levels of the surface state electron can be used to explain the surface state equilibration that occurs on contact. When two dissimilar surfaces contact each other, the transfer of surface state electrons occurs to equilibrate the energy levels of surface state electrons at the newly created interface. When two surfaces are separated, each surface retains the equilibrium electron level, which has been just attained on the contact, leading to the creation of the static charge, if a material is, or both materials are, nonconducting. In such a case, the two surfaces stick together by the coulombic attraction and it is necessary to apply force to separate them. 

The concept of surface plasmon coupled cheluminescence has recently been reported by Geddes and co-workers [18]. The observation of surface plasmon-coupled chemiluminescence (SPCC)[18], where the luminescence from chemically induced electronic excited states couples to sur ce plasmons in a thin continuous metal film has been demonstrated for numerous metals [18]. This technology results in highly directional and polarized emission of the chemiluminescence from the prism side of the thin film in the SPCC geometry, as compared to traditional chemiluminescence isotropic slow-glow. 

These kinds of surface states are expected to vary with potential, solvent, electrode, electrolyte and current density. Adsorption of the tetraalkylammonium ion in acetonitrile on p-silicon has been studied by FTIR relection-absorption spectroscopy (30). The adsorption isotherm resulting from such measurements is similar in nature to the surface state density data for this ion on CdTe. The fact that the measured surface state density on CdTe varies with the nature of the cation (Table 2) is consistent with the concept that the states arise from ionic adsorption. 

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. 

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