Computational electrodynamics

A. Taflove and S.C. Hagness, Computational electrodynamics the finite-difference time-domain method, 2 ed., (ArtechHouse, Norwood, 2000). 

K. L. Shlager, and J. B. Schneider, A survey of the finite-difference time domain literature, in A. Taflove (Ed,), Advances in computational electrodynamics the finite difference time domain method (Artech House, 1998), pp. 1- 62. 

A. Taflove and S. C. Hagness, Computational Electrodynamics The Finite-Difference Time-Domain Method, 3rd ed. Norwood, MA Artech House, 2005. 

E. Turkel, High-order methods, in Advances in Computational Electrodynamics The... 

S. D. Gedney, J. A. Roden, N. K. Madsen. A. H. Mohammadian, W. F. Hall, V. Sankar, and C. Rowell, Explicit time-domain solutions of Maxwell s equations via generalized grids, in Advances in Computational Electrodynamics The Finite-Difference Time-Domain Method, A. Taflove, Ed. Norwood, MA Artech House, 1998, ch. 4, pp. 163—262. 

This review is concerned with the advances in our understanding of chemical problems that have occurred as a result of developments in computational electrodynamics, with an emphasis on problems involving the optical properties of nanoscale metal particles. In addition, in part of the review we describe theoretical methods that mix classical electrodynamics with molecular quantum mechanics, and which thereby enable one to describe the optical properties of molecules that interact with nanoparticles. Our focus will be on linear optical properties, and on the interaction of electromagnetic fields with materials that are large enough in size that the size of the wavelength matters. We will not consider intense laser fields, or the interaction of fields with atoms or small molecules. 

This article is divided into two sections. In the first section, we overview the recent computational electrodynamics studies that have been performed on metallic (silver or gold) particles with an emphasis on problems of more interest to chemistry, such as the detection of molecules through adsorption-induced shifts of the plasmon resonance wavelength. In the second section, we turn our attention to a subject of more direct interest to theoretical chemistry, namely the calculation of SERS intensities using electronic stmcture methods. The challenge to the electronic structure community here is how to treat the interaction of an electronically localized system like a molecule with an electronically delocalized structure like a metal particle that is tens of nanometer in dimension. There have been attempts at dealing with this problem that we will describe, but this is a field that is still in a relatively primitive state, so our review will also consider new developments in the field that are likely to be important in the future. 

In this section we review the many recent studies that have been performed using computational electrodynamics methods with gold and silver nanoparticles, often with molecular adsorbates that one wishes to detect. Until about 10 years ago, almost all studies... 

One limitation of both Mie theory and the computational electrodynamics methods is that the results are only as good as the dielectric constants that are used. Ideally, one would be able to calculate such information directly from electronic structure calculations, but in reality this is not practical for metals like silver and gold so the information is derived from experimental data that is obtained for bulk metal (or more typically for films). Here we use experimental dielectric constants from Hunter and Lynch (HL) [48] (with some smoothing [12] as the HL compilation combines data from different sources that do not overlap perfectly). Other compilations of dielectric constant information are also available, but the HL compilation is relatively recent, and it provides a careful analysis of data from many sources that attempt to reduce problems from void formation in the film structure. 

Computational electrodynamics has made great progress during the past de-... 

The inter-particle distance dependence of the near-field coupling would therefore reflect the distance decay of the near-field itself. In other words, each particle senses the near-field due to the other particle. By varying the distance of the other particle and monitoring the LSPR response, the spatial profile of the near-field can be deduced. The plot of the LSPR red-shift as a function of inter-particle gap (surface-to-surface separation) shows a much more rapid decay of the near-field than predicted by the dipolar model. This is because the dipolar model does not take into account the multipolar interactions between the particles, which become increasingly important at smaller and smaller inter-particle gaps. Plasmon coupling is therefore a multipolar interaction and its true distance-dependence can be quantitatively reproduced only by a complete treatment that includes all modes of interaction (dipolar, quadrupolar, octupolar). Computational electrodynamics methods such as discrete dipole approximation (DDA) (see Chapter 2) and finite-difference-time-domain (FDTD), which include a full multipolar treatment in addition to finite-size retardation effects, fit experimental trends well. 

Taflove, A., Computational Electrodynamics the Finite Difference Time-domain Method, Artech House, Boston, 1995. 

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