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We aim to elucidate experiment in nanoscale optics and plasmon-enhanced molecular spectroscopy using first-principles theory and computation.  Well-defined descriptions of such phenomena, which involve the simultaneous interaction of molecules, nanoscale plasmon-supporting metals, and the electromagnetic field, are difficult to formulate because of the widely varying length scales over which the relevant chemical and physical processes occur.  The cartoon below shows some typical molecular (a few Ås), plasmonic (tens to a few hundreds of nms), and optical/near-IR field (hundreds to thousands of nms) sizes.

Understanding the big picture - how each interact as a coherent whole - with predictive and rigorous theory will help guide experimentalists who are designing high-efficiency solar cell technology, study molecular sensors capable of detecting the presence of a just a few target molecules, and who measure a variety of plasmon-enhanced linear and nonlinear molecular spectroscopies either in the frequency or time domain.

We accomplish this task by carefully blending together molecular-electron propagator methods as well as explicitly time-dependent descriptions of quantum molecular dynamics coupled to the continuum-electrodynamics of the field and metal.  We also employ purely classical electromagnetic theory to describe nanoscale metal structures and their interaction with light.  Development of the software necessary to explore each of these theoretical concepts is an essential aspect of our research as we work in areas where no black-box applications exist.  Specific projects include:

Nanoscale optics:

We are interested in the electromagnetic scattering properties of small metal particles, either individually, in clusters, or organized into periodic arrays.  By small, we mean on the order of a few 10s to a few 100s of nanometers in size.  Such structures display unique behavior particularly in the visible to near IR, where metallic conduction electrons can be set into coherent oscillatory motion by perturbing radiation. 
This coupling of radiation to matter results in the formation of localized surface-plasmon polaritons - “plasmons” for short - which can act as nanoscopic antennas that relay both exciting and (in)elastically scattered radiation fields to/from nearby molecules.  So strong is this effect that the surface-enhanced Raman scattering of light from a single molecule can be detected in the laboratory.  Nanoparticles also have interesting behavior in and of themselves, which can be addressed with purely continuum electromagnetic theory.  Below is an example of a high-resolution TEM image (right) and computational model (left) of the electromagnetic-field intensity scattered from a nanoscale metal dimer.

In addition to extinction, the shape/volume and magnitude of regions of high field strength can be studied as a function of excitation energy, as exemplified by the region located within the dimer junction (computed at an excitation wavelength of 532 nm).  In order to describe how these systems interact with radiation we employ a number of theoretical and computational techniques to solve the electromagnetic-scattering problem, i.e., to solve Maxwell’s equations.  Examples include finite-difference time-domain (FDTD) and finite-element methods (FEM), as well as the discrete-dipole approximation (DDA) and multipole methods like vector-spherical harmonics.

Quantum many-body theory in molecular plasmonics:

But how do we account for the structure and dynamics of nearby molecules that feel the polarization effects of the exciting field as well as the metal?  Certainly Maxwell’s equations are of no help here.  Rather, we must solve the many-body Schrödinger equation for the molecular electronic and nuclear degrees of freedom coupled to the metal and perturbed by the external field.  Many-body perturbation theoretic and Green’s function methods greatly facilitate our understanding of these complex interactions.  They allows us to compute, among other things, the response and scattering properties of the combined and coupled molecule-metal-field system.  Some dominant contributions to the linear response of the interacting molecular-electronic density are displayed in the diagrams below:

We have numerically implemented the equations that underlie each diagram within local versions of Q-Chem and the DDA.  Much work is now in progress to apply these methods to current experiment as well as to motivate new directions for future experimental inquiry.  There is also great interest in extending and generalizing these methods to explore uncharted paths leading towards enhanced-exciton formation and -charge separation in dye-sensitized solar cells as well as high precision molecular sensing based on the detailed interaction between electronically resonant molecules and the localized surface-plasmon resonances of nanoscale metal particles and surfaces.