Do We Really Need Quantum Mechanics to Describe Plasmonic Properties of Metal Nanostructures?

Atomistic Multiscale Modeling of Colloidal Plasmonic Nanoparticles

A novel fully atomistic multiscale classical approach to model the optical response of solvated real-size plasmonic nanoparticles (NPs) is presented. The model is based on the coupling of the Frequency Dependent Fluctuating Charges and Fluctuating Dipoles (ωFQFμ), specifically designed to describe plasmonic substrates, and the polarizable Fluctuating Charges (FQ) classical force field to model the solvating environment. The resulting ωFQFμ/FQ approach accounts for the interactions between the radiation and the NP, as well as with the surrounding solvent molecules, by incorporating mutual interactions between the plasmonic substrate and solvent. ωFQFμ/FQ is validated against reference TD-DFTB/FQ calculations, demonstrating remarkable accuracy, particularly in reproducing plasmon resonance frequency shifts for structures below the quantum-size limit. The flexibility and reliability of the approach are also demonstrated by simulating the optical response of homogeneous and bimetallic NPs dissolved in pure solvents and solvent mixtures.

Development of discrete interaction models for ultra-fine nanoparticle plasmonics

Plasmonics serves as a most outstanding feature of nanoparticle technology and is nowadays used in numerous applications within imaging, sensing and energy harvesting, like plasmonically enhanced solar cells, nanoparticle bioimaging, plasmon-controlled fluorescence for molecular tracking in living cells, plasmon-controlled electronic molecular devices and surface enhanced Raman spectroscopy for single molecular detection. Although plasmonics has been utilized since ancient times, the understanding of its basic interactions has not been fully achieved even under the emergence of modern nanoscience. In particular, it has been difficult to address the "ultra-fine" 1-10 nm regime, important for applications especially in bioimaging and biomedical areas, where neither classical nor quantum based theoretical methods apply. Recently, new approaches have been put forward to bridge this size gap based on semi-empirical discrete interaction models where each atom makes a difference. A primary aim of this perspective article is to review some of the most salient features of these models, and in particular focus on a recent extension - the extended discrete interaction model (Ex-DIM), where the geometric and environmental features are extended - and highlight a set of benchmark studies using this model concerning size, shape, material, temperature dependence and other characteristics of ultra-fine plasmonic nanoparticles. We also analyze new possibilities offered by the model for designing ultra-fine plasmonic particles for applications in the areas of bioimaging, biosensing, photothermal therapy, infrared light harvesting and photodetection. We foresee that future modelling activities will be closely connected to collaborative experimental work including synthesis, device fabrication and measurements with feedback and validation in a systematic fashion. With this strategy we can expect that modelling of ultra-fine plasmonics particles can be integrated in the development of novel plasmonic systems with unprecedented performance and applicability.

Toward Modeling the Complexity of the Chemical Mechanism in SERS

Surface-enhanced Raman scattering (SERS) provides detailed information about the binding of molecules at interfaces and their interactions with the local environment due to the large enhancement of Raman scattering. This enhancement arises from a combination of the electromagnetic mechanism (EM) and chemical mechanism (CM). While it is commonly accepted that EM gives rise to most of the enhancement, large spectral changes originate from CM. To elucidate the rich information contained in SERS spectra about molecules at interfaces, a comprehensive understanding of the enhancement mechanisms is necessary. In this Perspective, we discuss the current understanding of the enhancement mechanisms and highlight their interplay in complex local environments. We will also discuss emerging areas where the development of computational and theoretical models is needed with specific attention given to how the CM contributes to the spectral changes. Future efforts in modeling should focus on overcoming the challenges presented in this review in order to capture the complexity of CM in SERS.

Real-Time Simulation of Ultrafast Electronic Dynamics of Nanoscale Systems Involving an Organic Molecule and a Nanoparticle Dimer

Understanding and predicting the behavior of nanomaterials composed of plasmons interacting with quantum emitters at ultrafast timescales is crucial for the better manipulation of light at the nanoscale and advancing technologies like ultrafast communication and computing. Here we perform a simulation of the "real-time" electronic dynamics of a coupled molecule-metal nanoparticle dimer interacting with an ultrashort resonant laser pulse by combining the real-time time-dependent density functional theory (RT-TDDFT) approach with the time-domain frequency-dependent fluctuating charge (TD-ωFQ) model, an atomistic electromagnetic (AEM) model for the dynamic plasmonic response of nanoparticles. It is shown that the induced dipoles evolve from an exponential decay pattern to a beat pattern with an increase in coupling strength, which is altered by changing the molecular orientation relative to the dimer axis. It is further shown that in the strong coupling regime, both the excited molecule and the plasmon relax rapidly due to the molecule-plasmon interaction, and the efficient coherent energy exchange between the interacting molecule and plasmon modes occurs on a femtosecond (fs) timescale. This work provides guidance on manipulating light-matter interaction and studying molecular plasmonics at extremely fast timescales.

Multiscale modeling of surface enhanced fluorescence

The fluorescence response of a chromophore in the proximity of a plasmonic nanostructure can be enhanced by several orders of magnitude, yielding the so-called surface-enhanced fluorescence (SEF). An in-depth understanding of SEF mechanisms benefits from fully atomistic theoretical models because SEF signals can be non-trivially affected by the atomistic profile of the nanostructure's surface. This work presents the first fully atomistic multiscale approach to SEF, capable of describing realistic structures. The method is based on coupling density functional theory (DFT) with state-of-the-art atomistic electromagnetic approaches, allowing for reliable physically-based modeling of molecule-nanostructure interactions. Computed results remarkably demonstrate the key role of the NP morphology and atomistic features in quenching/enhancing the fluorescence signal.

Time-dependent Kohn-Sham electron dynamics coupled with nonequilibrium plasmonic response via atomistic electromagnetic model

Computational modeling of plasmon-mediated molecular photophysical and photochemical behaviors can help us better understand and tune the bound molecular properties and reactivity and make better decisions to design and control nanostructures. However, computational investigations of coupled plasmon-molecule systems are challenging due to the lack of accurate and efficient protocols to simulate these systems. Here, we present a hybrid scheme by combining the real-time time-dependent density functional theory (RT-TDDFT) approach with the time-domain frequency dependent fluctuating charge (TD-ωFQ) model. At first, we transform ωFQ in the frequency-domain, an atomistic electromagnetic model for the plasmonic response of plasmonic metal nanoparticles (PMNPs), into the time-domain and derive its equation-of-motion formulation. The TD-ωFQ introduces the nonequilibrium plasmonic response of PMNPs and atomistic interactions to the electronic excitation of the quantum mechanical (QM) region. Then, we combine TD-ωFQ with RT-TDDFT. The derived RT-TDDFT/TD-ωFQ scheme allows us to effectively simulate the plasmon-mediated "real-time" electronic dynamics and even the coupled electron-nuclear dynamics by combining them with the nuclear dynamics approaches. As a first application of the RT-TDDFT/TD-ωFQ method, we study the nonradiative decay rate and plasmon-enhanced absorption spectra of two small molecules in the proximity of sodium MNPs. Thanks to the atomistic nature of the ωFQ model, the edge effect of MNP on absorption enhancement has also been investigated and unveiled.

Linear Vibronic Coupling Approach for Surface-Enhanced Raman Scattering: Quantifying the Charge-Transfer Enhancement Mechanism

The outstanding amplification observed in surface-enhanced Raman scattering (SERS) is due to several enhancement mechanisms, and standing out among them are the plasmonic (PL) and charge-transfer (CT) mechanisms. The theoretical estimation of the enhancement factors of the CT mechanism is challenging because the excited-state coupling between bright plasmons and dark CT states must be properly introduced into the model to obtain reliable intensities. In this work, we aim at simulating electrochemical SERS spectra, considering models of pyridine on silver clusters subjected to an external electric field E⃗ that represents the effect of an electrode potential Vel. The method adopts quantum dynamical propagations of nuclear wavepackets on the coupled PL and CT states described with linear vibronic coupling models parametrized for each E⃗ through a fragment-based maximum-overlap diabatization. By presenting results at different values of E⃗, we show that indeed there is a relation between the population transferred to the CT states and the total scattered intensity. The tuning and detuning processes of the CT states with the bright PLs as a function of the electric field are in good agreement with those observed in experiments. Finally, our estimations for the CT enhancement factors predict values in the order of 105 to 106, meaning that when the CT and PL states are both in resonance with the excitation wavelength, the CT and PL enhancements are comparable, and vibrational bands whose intensity is amplified by different mechanisms can be observed together, in agreement with what was measured by typical experiments on silver electrodes.

Modeling the near-field effect on molecular excited states using the discrete interaction model/quantum mechanical method

Strong light-matter interactions significantly modify the optical properties of molecules in the vicinity of plasmonic metal nanoparticles. Since the dimension of the plasmonic cavity approaches that of the molecules, it is critical to explicitly describe the nanoparticle junctions. In this work, we use the discrete interaction model/quantum mechanical (DIM/QM) method to model the coupling between the plasmonic near-field and molecular excited states. DIM/QM is a combined electrodynamics/quantum mechanical model that uses an atomistic description of the nanoparticle. We extend the DIM/QM method to include the local field effects in the sum-over-state formalism of time-dependent density functional theory. As a test of the method, we study the interactions between small organic chromophores and metal nanoparticles. In particular, we examine how the inclusion of multiple electronic transitions and intermolecular interactions modify the coupling between molecules and nanoparticles. Using the sum-over-state formalism of DIM/QM, we show that two-state models break down when the plasmon excitation is detuned from the molecular excitations. To gain further insight, we compare the simple coupled-dipole model (CDM) with the DIM/QM model. We find that CDM works well for simple systems but fails when going beyond the single molecule or single nanoparticle cases. We also find that the coupling depends strongly on the site of the nanoparticle in which the chromophore couples to. Our work suggests the importance of explicitly describing the cavity to capture the atomistic level local field environment in which the molecule strongly couples to.

Minimal Auxiliary Basis Set Approach for the Electronic Excitation Spectra of Organic Molecules

We report a minimal auxiliary basis model for time-dependent density functional theory (TDDFT) with hybrid density functionals that can accurately reproduce excitation energies and absorption spectra from TDDFT while reducing cost by about 2 orders of magnitude. Our method, dubbed TDDFT-ris, employs the resolution-of-the-identity technique with just one s-type auxiliary basis function per atom for the linear response operator, where the Gaussian exponents are parametrized across the periodic table using tabulated atomic radii with a single global scaling factor. By tuning on a small test set, we determine a single functional-independent scale factor that balances errors in excitation energies and absorption spectra. Benchmarked on organic molecules and compared to standard TDDFT, TDDFT-ris has an average energy error of only 0.06 eV and yields absorption spectra in close agreement with TDDFT. Thus, TDDFT-ris enables simulation of realistic absorption spectra in large molecules that would be inaccessible from standard TDDFT.

Strain-Induced Plasmon Confinement in Polycrystalline Graphene

Terahertz spectroscopy is a perfect tool to investigate the electronic intraband conductivity of graphene, but a phenomenological model (Drude-Smith) is often needed to describe disorder. By studying the THz response of isotropically strained polycrystalline graphene and using a fully atomistic computational approach to fit the results, we demonstrate here the connection between the Drude-Smith parameters and the microscopic behavior. Importantly, we clearly show that the strain-induced changes in the conductivity originate mainly from the increased separation between the single-crystal grains, leading to enchanced localization of the plasmon excitations. Only at the lowest strain values explored, a behavior consistent with the deformation of the individual grains can instead be observed.