Collective electronic oscillators method

In Fig. 8 we also provide electronic couplings reported by Tretiak et al. [11] for the LH2 of Rs. moUschianum. These couplings were calculated using the collective electronic oscillators (CEO) method [86, 87]. Note that the B800-carotenoid couplings differ between the two species, owing to the 90° difference in orientation of the B800 Bchls. 

Here p is the frequency of plasmon oscillations in a system of free electrons (3.7). The oscillator strengths ft introduced previously differ from the usual fm (see Section IV) in their normalization (Efl, / = 1). A method for calculating the thus defined oscillator strengths from experimental values of e2 is presented in Ref. 89. Since the energy range essential for collective oscillations is ho> < 30 eV, the electrons of inner atomic shells can be disregarded. Thus, the value of ne is determined by the density of valence electrons only, and only the transitions of these electrons should be taken into account in the sum over i in formula (3.15). A convenient formula for calculating the frequencies molecular liquids is presented in ref. 89 ... 

More quantitatively, the value (0.66) that we obtain for the intensity ratio (0— 1 )/(0—0) of the b lines disagrees with the measured value (0.52). [The calculations by Philpott et al. Provide, on the contrary, too weak a value (0.37)]. In addition to the lack of accuracy inherent in methods of measuring oscillator strengths of strong transitions, it appears probable that inclusion of upper electronic states in (2.87) would, by the induction of a complementary collective coupling, improve the accord with the measured values. 

An optical transduction method that is often used with ultrathin hlms, such as LB hlms, is that of surface plasmon resonance [30, 31]. Surface plasma waves are collective oscillations of the free electrons at the boundary of a metal and a dielectric. These can be excited by means of evanescent electromagnetic waves. This excitation is associated with a minimum in the intensity of the radiation reflected from the thin him system, called surface plasmon resonance (SPR). The sensitivity of SPR is noteworthy, and changes in refractive index of 10 may be monitored thus the technique compares favorably with ellipsometry. The method has been used with LB hlms to provide both gas detectors [29] and sensors for metal ions in solution [32]. 

The photoabsorption spectrum a(co) of a cluster measures the cross-section for electronic excitations induced by an external electromagnetic field oscillating at frequency co. Experimental measurements of a(co) of free clusters in a beam have been reported, most notably for size-selected alkali-metal clusters [4]. Data for size-selected silver aggregates are also available, both for free clusters and for clusters in a frozen argon matrix [94]. The experimental results for the very small species (dimers and trimers) display the variety of excitations that are characteristic of molecular spectra. Beyond these sizes, the spectra are dominated by collective modes, precursors of plasma excitations in the metal. This distinction provides a clear indication of which theoretical method is best suited to analyze the experimental data for the very small systems, standard chemical approaches are required (Cl, coupled clusters), whereas for larger aggregates the many-body perturbation methods developed by the solid-state community provide a computationally more appealing alternative. We briefly sketch two of these approaches, which can be adapted to a DFT framework (1) the random phase approximation (RPA) of Bohm and Pines [95] and the closely related time-dependent density functional theory (TD-DFT) [96], and (2) the GW method of Hedin and Lundqvist [97]. 

Apart from these few examples, most nanostruc-tured materials are synthetic. Empirical methods for the manufacture of stained glasses have been known for centuries. It is now well established that these methods make use of the diffusion-controlled growth of metal nanoparticles. The geometrical constraints on the electron motion and the electromagnetic field distribution in noble-metal nanoparticles lead to the existence of a particular collective oscillation mode, called the plasmon oscillation, which is responsible for the coloration of the material. It has been noticed recently that the beautiful tone of Maya blue, a paint often used in Mesoamer-ica, involves simultaneously metal nanoparticles and a superlattice organization [3.1]. 

Many techniques have been developed to measure the Young s modulus and the stress of the mesoscopic systems [12, 13]. Besides the traditional Vickers microhardness test, techniques mostly used for nanostructures are tensile test using an atomic force microscope (AFM) cantilever, a nanotensile tester, a transmission electron microscopy (TEM)-based tensile tester, an AFM nanoindenter, an AFM three-point bending tester, an AFM wire free-end displacement tester, an AFM elastic-plastic indentation tester, and a nanoindentation tester. Surface acoustic waves (SAWs), ultrasonic waves, atomic force acoustic microscopy (AFAM), and electric field-induced oscillations in AFM and in TEM are also used. Comparatively, the methods of SAWs, ultrasonic waves, field-induced oscillations, and an AFAM could minimize the artifacts because of their nondestructive nature though these techniques collect statistic information from responses of all the chemical bonds involved [14]. 

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