Nonlocal metal response

In the language of reciprocal space, nonlocal metal response refers to the dependence of the metal dielectric constant on the wavevector k of the various plane waves into which any probing electric fields can be decomposed. Such an effect is often mentioned in reports on SERS, but it is usually neglected. One of the oldest papers addressing the importance of nonlocal effects on the polarizability of an adsorbed molecule is the article by Antoniewicz, who studied the static polarizability of a polarizable point dipole close to a linearized Thomas-Fermi metal [63], The static dielectric constant eTF(k) of such a model metal can be written as ... 

Several other studies have appeared that are worthy of note. In a series of works by Keller [89-94] and Apell [95], the nonlocal nonlinear response for free-elec-tron-like metals have been examined using various theoretical approaches which are basically extensions of linear theories on the optical response of metals. The results [92] reduce to those obtained by Rudnick and Stern [26] using a similar approach when the free-electron gas is considered to be homogeneous. 

The use of a bulk-like dielectric constant, such as those in Equations (2.334)-(2.336), neglects the specific contribution given by the surface to the dielectric response of the metal specimen. For metal particles, such a contribution is often introduced in the model by considering the surface as an additional source of scattering for the metal conduction electrons, which consequently affects the relaxation time r [69], Experiments indicate that the precise chemical nature of the surface also plays a role [70], The presence of a surface affects the nonlocal part of the metal response as well, giving rise to surface-assisted excitations of electron-hole pairs. The consequences of these excitations appear to be important for short molecule-metal distances [71], It is worth remarking that, when the size of the metal particle becomes very small (2-3 nm), the electron behaviour is affected by the confinement, and the metal response deviates from that of the bulk (quantum size effects) [70],... 

Figure 3.31 As (due to orientational response of aqueous solvent) versus e, calculated for ET in a large binuclear transition metal complex (D (Ru2+/3+) and A (Co2+/3+) sites bridged by a tetraproline moiety) molecular-level results obtained from a nonlocal polarization response theory (NRFT, solid lines) continuum results are given by dashed lines, referring to numerical solution of the Poisson equation with vdW (cont./vdW) and SAS (cont./SAS) cavities, or as the limit of the NRFT results when the full k-dependent structure factor (5(k)) is replaced by 5(0) 5(k) for bulk water was obtained from a fluid model based on polarizable dipolar spheres (s = 1.8 refers to ambient water (square)). For an alternative model based on TIP3 water (where, nominally, 6 = ), ambient water corresponds to the diamond. (Reprinted from A. A. Milishuk and D. V. Matyushov, Chem Phys., 324, 172. Copyright (2006), with permission from Elsevier).

W. H. Weber and G. W. Ford, Enhanced Raman scattering by adsorbates including the nonlocal response of the metal and excitation of nonradiative modes, Phys. Rev. Lett. 44, 1774-1777 (1980). 

Although quite obvious, it is important to remark that a perfect conductor-like model completely neglects the chemical nature of the metal (i.e., all the metals behave in the same way). This is different to what happens for solvents, where even the simplest models include at least one solvent-specific parameter, the static dielectric constant. However, the chemical nature of the metal is relevant for another aspect of the static dielectric response that is neglected by the conductor model the nonlocal effects. They will be discussed in the following Section, The Response Properties of a Molecule Close to a Metal Specimen Surface Enhanced Phenomena and Related Continuum Models. 

Concerning the use of DFT to treat metal-molecule interactions, we remark that present exchange-correlation functionals give rise to difficulties in properly treating dispersion interactions, and the extension of the works on CMs in this direction (e.g., improving the description of the solid response, by including surface and nonlocal effects) seems a promising field. 

The molecule is often represented as a polarizable point dipole. A few attempts have been performed with finite size models, such as dielectric spheres [64], To the best of our knowledge, the first model that joined a quantum mechanical description of the molecule with a continuum description of the metal was that by Hilton and Oxtoby [72], They considered an hydrogen atom in front of a perfect conductor plate, and they calculated the static polarizability aeff to demonstrate that the effect of the image potential on aeff could not justify SERS enhancement. In recent years, PCM has been extended to systems composed of a molecule, a metal specimen and possibly a solvent or a matrix embedding the metal-molecule system in a molecularly shaped cavity [62,73-78], In particular, the molecule was treated at the Hartree-Fock, DFT or ZINDO level, while for the metal different models have been explored for SERS and luminescence calculations, metal aggregates composed of several spherical particles, characterized by the experimental frequency-dependent dielectric constant. For luminescence, the effects of the surface roughness and the nonlocal response of the metal (at the Lindhard level) for planar metal surfaces have been also explored. The calculation of static and dynamic electrostatic interactions between the molecule, the complex shaped metal body and the solvent or matrix was done by using a BEM coupled, in some versions of the model, with an IEF approach. 

The inclusion of relativistic corrections in the GGA thus does not resolve the problems of the GGA with the 5d transition metals, suggesting that the nonlocal contributions to Exc n beyond the first density gradient are important in these systems. In addition, the spin-orbit coupling of the valence electrons, neglected in this work, could be partially responsible for this discrepancy [25,30]. 

The disadvantage of the pseudo-Hamiltonian is that one does not have very much flexibility in matching the core response to valence electrons with different angular momentum because the restrictions on the mass tensor are too severe, especially for first-row and transition metal atoms (i.e., for the cases with strong nonlocalities). In particular, for transition metals it is not possible to use an Ar core because the first electron must always go into an s state [48]. In fact, this is of secondary importance since for accurate calculations, which are the aim of QMC, one has to include 35 and 3p states in the valence space for the 3d transition elements. 

The dielectric response of the interface can be described in a unified manner in terms of the nonlocal electrostatic theory [88, 89]. Indeed, it vras shown to be possible to express the electric properties of the interface through the dielectric function of the metal/solvent system, not applying a particular form of this function, for any structure of the interface. Such an approach allows revealing general properties of the double layer and expressing the parameters involved via the nonlocal dielectric function. We briefly... 

Another major area of application of TDDFT involves clusters, large and small, covalent and metallic, and everything in between,as, for example, Met-Cars. Several studies include solvent effects, one example being the behavior of metal ions in explicit water. TDDFT in the realm of linear response can also be used to examine chirality,including calculating both electric and magnetic circular dichroism, " and it has been applied to both helical aromatics and to artemisinin complexes in solution. " There exist applications in materials and quantum dots, but, as discussed below, the optical response of bulk solids requires some nonlocal... 

R. Fuchs and F. Claro, Multipolar response of small metallic spheres nonlocal theory, Phys. Rev. B3 (8), in-nn (i987). 

The account of the nonlocal character of the dielectric response modifies the Fresnel equations. In the framework of the jellium model for a metal, the reflection coefficients in s- and p-polarizations can be represented as °... 

For flat metallic surfaces nonlocal response theory has shed some light on the resonance mechanism (Liebsch 1989 Jensen et al. 1997). However, it has been shown that due to a large contribution of bulk... 

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