On the importance of incorporating dipole reradiation in the modeling of surface enhanced Raman scattering from spheres.

Surface enhanced Raman scattering (SERS) enhancement factors G for nanoparticles consisting of a single Ag sphere or a dimer of Ag nanospheres are calculated using a T-matrix method that rigorously incorporates dipole reradiation (DR) effects. A comparison with the commonly used plane wave (PW) approximation, /E(loc)(omega)/2 /E(loc)(omega(')/2, which for zero Stokes shift is /E(loc)(omega)/4, is made so as to determine the error associated with using the PW enhancement factor instead of DR in modeling SERS intensities. Calculations for the single sphere are performed for various molecule locations, detector locations, and sphere sizes, while the dimer calculations consider the effects of molecule and detector locations for 50 nm diameter spheres with a 2 nm gap. In both the single sphere and dimer calculations, excellent agreement (<0.3%) is found between the PW approximation and DR calculations when the molecule is located along the incident field polarization direction and with the detector along an axis that is orthogonal both to the polarization and wave vector directions. The errors for other molecule locations, different detector locations, and larger sphere sizes can be considerably larger. A qualitative description of the nature of the errors is developed based on interferences between radiation emitted by the sphere and by the molecule and on quadrupole excitation in the metal spheres. An average over molecule and detector locations for both the single sphere and dimer results leads to DR enhancement factors that differ by factors of 2-3 (sometimes higher, sometimes lower) from the PW results. This indicates that for quantitative field enhancement factor calculations, the more rigorous DR result is important.

Whispering-gallery mode resonators: Surface enhanced Raman scattering without plasmons.

Calculations based on the Mie theory are performed to determine the locally enhanced electric fields due to whispering-gallery mode resonances for dielectric microspheres, with emphasis on electromagnetic "hot spots" that are located along the wavevector direction on the surface of the sphere. The local electric field enhancement associated with these hot spots is used to determine the surface enhanced Raman scattering enhancement factors for a molecule, here treated as a classical dipole, located near the surface of the sphere. Both incident and Raman emission enhancements are calculated accurately using an extension of the Mie theory that includes interaction of the Raman dipole field with the sphere. The enhancement factors are calculated for dielectric spheres in vacuum with a refractive index of 1.9 and radii of 5, 10, and 20 microm and for wavelengths that span the visible spectrum. Maximum Raman scattering enhancement factors on the order of 10(3)-10(4) are found at locations slightly off the propagation axis when the incident excitation but not the Stokes-shifted radiation is coincident with a whispering-gallery mode resonance. The enhancement factors are found to vary inversely with the resonance width, and this determines the influence of the mode number and order on the results. Additional calculations are performed for the case where the Stokes-shifted radiation is also on-resonance and Raman enhancement factors as large as 10(8) are found. These enhancement factors are typically a factor of 10(2) smaller than would be obtained from /E/4 enhancement estimates, as enhancement of the Raman dipole emission is significantly reduced compared to the local field enhancement for micron size particles or larger. Conditions under which single-molecule or few-molecule measurements are feasible are identified.

Methods for describing the electromagnetic properties of silver and gold nanoparticles.

This Account provides an overview of the methods that are currently being used to study the electromagnetics of silver and gold nanoparticles, with an emphasis on the determination of extinction and surface-enhanced Raman scattering (SERS) spectra. These methods have proven to be immensely useful in recent years for interpreting a wide range of nanoscience experiments and providing the capability to describe optical properties of particles up to several hundred nanometers in dimension, including arbitrary particle structures and complex dielectric environments (adsorbed layers of molecules, nearby metal films, and other particles). While some of the methods date back to Mie's celebrated work a century ago, others are still at the forefront of algorithm development in computational electromagnetics. This Account gives a qualitative description of the physical and mathematical basis behind the most commonly used methods, including both analytical and numerical methods, as well as representative results of applications that are relevant to current experiments. The analytical methods that we discuss are either derived from Mie theory for spheres or from the quasistatic (Gans) model as applied to spheres and spheroids. In this discussion, we describe the use of Mie theory to determine electromagnetic contributions to SERS enhancements that include for retarded dipole emission effects, and the use of the quasistatic approximation for spheroidal particles interacting with dye adsorbate layers. The numerical methods include the discrete dipole approximation (DDA), the finite difference time domain (FDTD) method, and the finite element method (FEM) based on Whitney forms. We discuss applications such as using DDA to describe the interaction of two gold disks to define electromagnetic hot spots, FDTD for light interacting with metal wires that go from particle-like plasmonic response to the film-like transmission as wire dimension is varied, and FEM studies of electromagnetic fields near cubic particles.

Ultraviolet cavity ringdown spectra and the S1(n,pi) ring-inversion potential energy function for 2-cyclohexen-1-one-d0 and Its 2,6,6-d3 isotopomer.

The cavity ringdown spectra of 2-cyclohexen-1-one (2CHO) and its 2,6,6-d3 isotopomer (2CHO-d3) have been recorded in the spectral region near their S1(n,pi)<--S0 band origins which are at 26,081.3 and 26,075.3 cm-1, respectively. The data allow several of the quantum states of nu39, the ring inversion, to be determined for both the ground and excited electronic states. These were utilized to calculate the one-dimensional potential energy functions which best fit the data. The barriers to inversion for the S0 and S1(n,pi) states were found to be 1,900 +/- 300 and 3,550 +/- 500 cm-1, respectively. Density functional theory calculations predict values of 2,090 and 2,265 cm-1, respectively.

Estimation of electronic coupling for intermolecular electron transfer from cross-reaction data.

Sixty-five electron-transfer reactions including 27 new 0, +1 couples have been added to our data set of cross-reactions between 0 and +1 couples, bringing it to 206 reactions involving 72 couples that have been studied by stopped-flow kinetics in acetonitrile containing supporting electrolyte at 25 degrees C, formal potentials determined by cyclic voltammetry, and analyzed using Marcus cross-rate theory. Perhaps surprisingly, a least-squares analysis demonstrates that intrinsic rate constants exist that predict the cross-rate constants to within a factor of 2 of the observed ones for 93% of the reactions studied, and only three of the reactions have a cross-rate constant that lies outside of the factor of 3, that corresponds to a factor of 10 uncertainty in the rate constant for an unknown couple. Many triarylamines, which have very high intrinsic reactivity, are included among the newly studied couples. The enthalpy contribution to the Marcus reorganization energy, lambda'v, has been calculated for 46 of the couples studied, at the (U)B3LYP/6-31+G (or for the larger and lower barrier compounds, at the less time-consuming (U)B3LYP/6-31G) level. In combination with a modified Levich and Dogodnadze treatment that assumes that the rate constant is proportional to (KeHab2/lambda1/2) exp[-DeltaG/RT], this allows estimation of the electronic coupling (Hab) at the transition state for intermolecular electron transfer, (more properly H'ab, the product of the square root of the encounter complex formation constant times Hab) for these couples. Although the principal factor affecting intermolecular electron-transfer rate constants is clearly lambda, H'ab effects are easily detectable, and the dynamic range in our estimates of them is over a factor of 600.