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Point-dipole approximation for small systems of strongly coupled radiating nanorods.

ABSTRACT: Systems of closely-spaced resonators can be strongly coupled by interactions mediated by scattered electromagnetic fields. In large systems the resulting response has been shown to be more sensitive to these collective interactions than to the detailed structure of individual resonators. Attempts to describe such systems have resulted in point-dipole approximations to resonators that are computationally efficient for large resonator ensembles. Here we provide a detailed study for the validity of point dipole approximations in small systems of strongly coupled plasmonic nanorods, including the cases of both super-radiant and subradiant excitations, where the characteristics of the excitation depends on the spatial separation between the nanorods. We show that over an appreciable range of rod lengths centered on 210 nm, when the relative separation kl in terms of the resonance wave number of light k satisfies [Formula: see text], the point electric dipole model becomes accurate. However, when the resonators are closer, the finite-size and geometry of the resonators modifies the excitation modes, in particular the cooperative mode line shifts of the point dipole approximation begin to rapidly diverge at small separations. We also construct simplified effective models by describing a pair of nanorods as a single effective metamolecule.

SUBMITTER: Watson DW

PROVIDER: S-EPMC6450961 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:The validity of the popular point-dipole approximation for interpretation of the zero-field splitting (ZFS) parameter (D-value) in EPR spectroscopy is studied. This approximation is of central importance for the determination of distances by analysis of EPR data. In this work, a detailed experimental (EPR spectroscopy and X-ray crystallography) and theoretical study for a model system (2,2',5,5'-tetra(tert-butyl)-4,4'-bis(ethoxy-carbonyl)-3,3'-bipyrrolyl-1,1'-dioxyl) was performed to understand the scope and limitations of the point-dipole model in EPR spectroscopy. For this diradical, the radical-radical distance derived with the point-dipole approximation deviates significantly (by approximately 40%) from the results derived from the X-ray analysis. Explicit quantum chemical calculation of the D-value on the basis of B3LYP density functional calculations leads to excellent quantitative agreement with the measured D-value. The quantitative accuracy of the employed methodology was confirmed for two additional systems that have previously been experimentally characterized. We therefore analyzed the contributions to the D-value of the target system in detail. This analysis leads to insight into the reasons for the failure of the point-dipole approximation. The analysis was then extended to an in silico study of five classes of model systems. Linkers of varying length and bond saturation were introduced between the radical-carrying groups. This allows for the analysis of the distance dependence of the D-parameter as well as the through-bond and through-space spin-spin interaction. From these results we established the limitations of the point-dipole approximation. The results of this analysis demonstrate that even very modest amounts of spin delocalization can cause significant deviations from pure point-dipole behavior and consequently cause the EPR derived distances to deviate from the N-O midpoint distance by up to several angstroms. If unsaturated linkers are used, the distance dependence of D does not follow the inverse cubic behavior predicted by the point-dipole model. However, for commonly used nonaromatic nitroxide rings connected by a saturated linker, the point-dipole approximation works well. Among the various point-dipole variants tested in this work for delocalized spins, the most successful one is based on distributed point-dipoles with spin populations derived from quantum chemical calculations. The distance dependence of the isotropic Heisenberg exchange parameter J has also been studied theoretically. The decay was found to be monoexponential with a decay constant of approximately 1 A(-1). Thus at linker lengths between 6-8 carbon atoms between a nitroxide radical pair, a switch from the strong to the weak exchange limit is predicted.

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Point-dipole approximation for small systems of strongly coupled radiating nanorods.

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