Electron distributions surface states calculation

J G 1994. Extended Electron Distributions Applied to the Molecular Mechanics of Some termolecular Interactions. Journal of Computer-Aided Molecular Design 8 653-668. el A and M Karplus 1972. Calculation of Ground and Excited State Potential Surfaces of anjugated Molecules. 1. Formulation and Parameterisation. Journal of the American Chemical Society 1 5612-5622. 

Kliiner et al. [19] has analyzed the bimodal velocity distributions observed in NO desorption from NiO(0 01) shown in Fig. 24 by calculating a full ab initio potential energy surface (PES) for an excited state in addition to the PES for the ground state. Calculation of the electronically excited state uses a NiOj cluster embedded in a semi-infinite Madelung potential of point charges 2. The excited state relevant for laser-induced desorption is an NO -like intermediate, where one electron is transferred from the cluster to the NO molecule. 

Of great importance is the nature of surface bonding of intermediates to the metal this depends very much on the geometry and orientation of the crystal plane on which the chemisorption takes place, and on the orientation and symmetry of emergent orbitals (especially dsp hybrid orbitals at transition metal surfaces) at the metal surface as emphasized and illustrated by Bond (24, 7) (Fig. 5 A). These factors determine the geometry of coordination of the adspecies at the catalyst or electrocatalyst surface. Since that work (41), a great many papers have appeared on molecular-orbital calculations for bonding at surfaces and on surface states and electron-density distributions. 

Figure 34. A comparison of STS spectra and calculated densities of states for pyrite (100), fi om Rosso et al. (1999a). The area-averaged surface electronic structure is seen in the normalized (dI/dV)/(IA ) tunneling spectrum collected over a random distribution of points over the surface (a). Individual, atomically resolved tunneling spectra show site specific features in the LDOS at the surface (b). Calculated local densities of states (LDOS) for tip positions over surface sites (c) show striking similarities to the characteristic features shown in (b). Contributions to the LDOS over siuface Fe and S2 sites originate primarily from Fe 3dz2-like dangling bond states and S 3p states, respectively.

The calculation of /rec requires a stipulation of the surface states that are occupied. Since surface states exchange electrons both with the conduction band and the electrolyte, the statistics are more complex than in a bulk trap. The occupation of the surface states is determined by a demarcation level and in general it is not possible to define a Fermi level [180, 215]. For simplicity we assume here that the trapping-release rate is sufficiently fast, so that the surface state is in equilibrium with the transport states, and the occupancy of both is described by Fermi-Dirac distribution, with a single Fermi level. 

More detailed ARPES studies of nonpolar surfaces for some stoichiometric and nonstoichiometric 3d- and 4d-metal carbides and nitrides reveal a series of finer effects, which could be connected with the specific features of electron distributions near the crystal surface or could be induced by structural vacancies. For example, some states determined experimentally for the (100) surface of NbCo.sa by Lindberg (1987) do not seem to have counterparts in the calculated results for NbCi.o. but... 

We emphasize that 7(a>) and 7 (w) in Eq. (33) contain information about the ground and 1 potential surfaces sketched in Fig. 6.10. The force constants in Eq. (10) require all electrons and are formidable calculations for polyenes [21]. The F-dependent coefficients in Eq. (33), on the other hand, are due to virtual tt-tt excitations. Similarly, the vibronics of two-photon excitations appear in Eq. (34), and the induced intensity depends on the TT-TT spectrum. These EA expressions hold for an isolated molecule or polymer. An isotropic distribution of conjugated backbones in films also gives r(cu) terms due to internal fields [106] or site disorder, and such profiles have been reported in PA [107] and PDA [108] films. Since EA of extended states in semiconductors [109,110] also goes as T (o) and disorder is poorly understood, films are more difficult to model. In crystals. Stark shifts scale as 7 (a>) and induced moments as 7(a>) or TPA. 

When considering surface states in the band gap one should distinguish occupied (donorlike) and unoccupied (acceptorlike) states. Those of the latter type were not directly accessible experimentally so far, but in fact found in band structure calculations of all the surfaces discussed above. Quahtative confirmation of their existence within the band gap was for the (100) and the (111) surfaces obtained from NEXAFS in form of clear surface core exciton resonances. The unoccupied surface states are not electronically active for p-type material, but are expected to become important for n-type diamond. Occupied surface states in the band gap are found only for the clean diamond (111) surface, but can be removed by hydrogen or oxygen termination. All diamond surfaces are semiconducting. In the case of the clean C(lll)2xl and C(110)lxl surfaces, which show symmetric and unbuckled 7T-bonded rows of surface atoms, many-body effects are responsible for the opening of a surface band gap, which caimot be modeled theoretically on the DFT level. Table 10.2 summarizes the reconstructions and surface state distributions of the diamond surfaces discussed above. 

From the point of view of associative desorption, this reaction is an early barrier reaction. That is, the transition state resembles the reactants.46 Early barrier reactions are well known to channel large amounts of the reaction exoergicity into product vibration. For example, the famous chemical-laser reaction, F + H2 — HF(u) + H, is such a reaction producing a highly inverted HF vibrational distribution.47-50 Luntz and co-workers carried out classical trajectory calculation on the Born-Oppenheimer potential energy surface of Fig. 3(c) and found indeed that the properties of this early barrier reaction do include an inverted N2 vibrational distribution that peaks near v = 6 and extends to v = 11 (see Fig. 3(a)). In marked contrast to these theoretical predictions, the experimentally observed N2 vibrational distribution shown in Fig. 3(d) is skewed towards low values of v. The authors of Ref. 44 also employed the electronic friction theory of Tully and Head-Gordon35 in an attempt to model electronically nonadiabatic influences to the reaction. The results of these calculations are shown in... 

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