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This chapter has focused on a number of commonly used analytical and numerical electrodynamics methods that can be used to model the optical properties of plasmonic nanostructures, with emphasis on nonconventional applications of these methods to problems that have been recently been of interest in the surface spectroscopy field, especially surface-enhanced Raman scattering (SERS). A dipole reradiation (DR) methodology was added to the analytical approach of Mie theory to DR effects in SERS intensities, which is a more accurate expression for the electromagnetic enhancement theory than the commonly used plane-wave (PW) enhancement expression. We show that DR/PW differences can be significant for certain choices of detector locations due to interference and multipole effects, and generally the DR enhancements are smaller than PW. The numerical 2D finite-difference time-domain (FDTD) method was modified through the incorporation of the hydrodynamic Drude model dielectric constant, enabling the calculation of spatially nonlocal dielectric responses for arbitrarily shaped nanostructures. Nonlocal effects become important when structural features extend below around 10 nm where the dielectric constant becomes a function of both the wavevector and the frequency. The importance of including nonlocal effects was demonstrated by calculating the optical response of cylindrical and triangular nanowires. The discrete dipole approximation (DDA) provides an alternative method for determining nanoparticle optical properties that uses a similar grid to FDTD, but with different convergence characteristics. We show that for cube-shaped particles the two methods have similar convergence behavior, but accuracy is a problem for DDA, while representing the frequency dependence dielectric constant is a problem for FDTD. A general many-body formalism describing plasmon-enhanced linear spectroscopies was developed by linking the numerical DDA method with electronic structure theory based on Q-Chem. This methodology allows the calculation of the linear-response and scattering properties between a molecule, which is described quantum mechanically, interacting with a classically described metal nanostructure. To demonstrate this formalism the linear response and scattering of a pyridine–Ag spheroidal system was calculated as a function of excitation energy and aspect ratio.

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