Discrete dipole approximation electronics

In this chapter, absorption and scattering efficiencies spectra will be presented for silver nanoparticles (NPs) with different shapes and dimensions. All the spectra are calculated in the discrete dipole approximation framework (see Chapter 2), with the Palik complex dielectric function e(lattice dispersion relation (LDR) prescription for the polarizability (see Sec. 2.4.3.2). For dimensions of the NPs smaller than the mean free path of the conduction electrons, the surface damping correction A sd is added to the Palik dielectric function (see Sec. 2.3), as several works have shown that the dielectric constant is strongly dependent on the size and the shape of the nanoparticle [21-23]. 

In the present work, we have calculated the K/3 /Koc x-ray intensity ratios for 3d transition elements excited by PI and EC, taking into account both effects described above. The calculations were made using the discrete-variational (DV) X(X molecular orbital (MO) method (19). The electronic states and wave functions in molecules were obtained for tetrahedral (Td) and octahedral (Oh) clusters. The x-ray emission rates were estimated by the DV integration method (20) with the MO wave functions in the dipole approximation. The calculated results are compared with the experimental data. 

The UV-VIS spectrum, usually an A or log A vs. plot, in a first approximation reflects the discrete electronic states as absorption maxima at different v ,ax positions which are correlated with the molecular structure and geometry. The extinction coefficient e or more likely the integral absorption / e(v) dv, which is approximately the product of times the halfwidth AVi/2> gives information on the transition dipole moment or the Einstein coefficient of absorption or induced emission B n, which are interrelated by... 

Let us look first at the transition of the original definitions as integrals over the charge density, Eqs. (4.5), (4.6) and (4.8), to quantum mechanics that we will illustrate for the example of the electric dipole moment. In the Born-Oppenheimer approximation, Section 2.2, the electrons in a molecule form a continuous charge distribution whereas the discrete nuclear charges are located at fixed points Rk- The expression, Eq. (4.5) for the a-component of the electric dipole moment can therefore be rewritten as... 

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