A recursive cell multipole method for atomistic electrodynamics models.

For large plasmonic nanoparticles, retardation effects become important once their length becomes comparable to the wavelength of light. However, most models do not incorporate retardation effects due to the high computational cost of solving for the optical properties of large atomistic electrodynamics systems. In this work, we derive and implement a recursive fast multipole method (FMM) in Cartesian coordinates that includes retardation effects. In this method, higher-order electrodynamic interaction tensors used for the FMM are calculated recursively, thus greatly reducing the implementation complexity of the model. This method allows for solving of the optical properties of large atomistic nanoparticles with controlled accuracy; in practice, taking the expansion to the fifth order provides a good balance of accuracy and computational time. Finally, we study the effects retardation has on the near- and far-field properties of large plasmonic nanoparticles with over a million atoms using this method. We specifically focus on nanorods and their dimers, which are known to generate highly confined fields in their junctions. In the future, this method can be applied to simulations in which accurate near-field properties are required, such as surface-enhanced Raman scattering.

Local-Field Effects in Linear Response Properties within a Polarizable Frozen Density Embedding Method.

In this work, we present a polarizable frozen density embedding (FDE) method for calculating polarizabilities of coupled subsystems. The method (FDE-pol) combines a FDE method with an explicit polarization model such that the expensive freeze/thaw cycles can be bypassed, and approximate nonadditive kinetic potentials are avoided by enforcing external orthogonality between the subsystems. To describe the polarization of the frozen environment, we introduce a Hirshfeld partition-based density-dependent method for calculating the atomic polarizabilities of atoms in molecules, which alleviates the need to fit the atomic parameters to a specific system of interest or to a larger general set of molecules. We show that the Hirshfeld partition-based method predicts molecular polarizabilities close to the basis set limit, and thus, a single basis set-dependent scaling parameter can be introduced to improve the agreement against the reference polarizability data. To test the model, we characterized the uncoupled and coupled response of small interacting molecular complexes. Here, the coupled response properties include the perturbation of the frozen system due to the external perturbation which is ignored in the uncoupled response. We show that FDE-pol can accurately reproduce both the exact uncoupled polarizability and the coupled polarizabilities of the supermolecular systems. Using damped response theory, we also demonstrate that the coupled frequency-dependent polarizability can be described by including local field effects. The results emphasize the necessity of including local-field effects for describing the response properties of coupled subsystems, as well as the importance of accurate atomic polarizability models.

Measuring Local Electric Fields and Local Charge Densities at Electrode Surfaces Using Graphene-Enhanced Raman Spectroscopy (GERS)-Based Stark-Shifts.

We report spectroscopic measurements of the local electric fields and local charge densities at electrode surfaces using graphene-enhanced Raman spectroscopy (GERS) based on the Stark-shifts of surface-bound molecules and the G band frequency shift in graphene. Here, monolayer graphene is used as the working electrode in a three-terminal potentiostat while Raman spectra are collected in situ under applied electrochemical potentials using a water immersion lens. First, a thin layer (1 Å) of copper(II) phthalocyanine (CuPc) molecules are deposited on monolayer graphene by thermal evaporation. GERS spectra are then taken in an aqueous solution as a function of the applied electrochemical potential. The shifts in vibrational frequencies of the graphene G band and CuPc are obtained simultaneously and correlated. The upshifts in the G band Raman mode are used to determine the free carrier density in the graphene sheet under these applied potentials. Of the three dominant peaks in the Raman spectra of CuPc (i.e., 1531, 1450, and 1340 cm-1), only the 1531 cm-1 peak exhibits Stark-shifts and can, thus, be used to report the local electric field strength at the electrode surface under electrochemical working conditions. Between applied electrochemical potentials from -0.8 V to 0.8 V vs NHE, the free carrier density in the graphene electrode spans a range from -4 × 1012 cm-2 to 2 × 1012 cm-2. Corresponding Stark-shifts in the CuPc peak around 1531 cm-1 are observed up to 1.0 cm-1 over a range of electric field strengths between -3.78 × 106 and 1.85 × 106 V/cm. Slightly larger Stark-shifts are observed in a 1 M KCl solution, compared to those observed in DI water, as expected based on the higher ion concentration of the electrolyte. Based on our data, we determine the Stark shift tuning rate to be 0.178 cm-1/ (106 V/cm), which is relatively small due to the planar nature of the CuPc molecule, which largely lies perpendicular to the electric field at this electrode surface. Computational simulations using density functional theory (DFT) predict similar Stark shifts and provide a detailed atomistic picture of the electric field-induced perturbations to the surface-bound CuPc molecules.