Simulating Surface-Enhanced Hyper-Raman Scattering Using Atomistic Electrodynamics-Quantum Mechanical Models

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.

Molecular Simulation Study of Surface-Enhanced Raman Scattering of Liquid Water

We developed in our previous study [J. Chem. Phys., 2021, 155, 174118, J. Phys. Chem. A, 2022, 126, 4762] a classical electronic and molecular dynamics simulation method to describe the optical response of metal material in solution based on an atomistic model by incorporating the classical equation of motion for free electrons under an applied electric field. To show further usefulness of the method, in the present study, we apply it to surface-enhanced Raman scattering of liquid water to examine the signal enhancement of the solution system caused by plasmon resonance effects of a silver nanoparticle.

A Full Quantum Mechanical Approach Assessing the Chemical and Electromagnetic Effect in TERS

Tip-enhanced Raman spectroscopy (TERS) is a valuable method for surface analysis with nanometer to angstrom-scale resolution; however, the accurate simulation of particular TERS signals remains a computational challenge. We approach this challenge by combining the two main contributors to plasmon-enhanced Raman spectroscopy and to the high resolution in TERS, in particular, the electromagnetic and the chemical effect, into one quantum mechanical simulation. The electromagnetic effect describes the sample's interaction with the strong, highly localized, and inhomogeneous electric fields associated with the plasmonic tip and is typically the thematic focus for most mechanistic studies. On the other hand, the chemical effect covers the different responses to the extremely close-range and highly position-sensitive chemical interaction between the apex tip atom(s) and the sample, and, as we could show in previous works, plays an often underestimated role. Starting from a (time-dependent) density functional theory description of the chemical model system, comprised of a tin(II) phthalocyanine sample molecule and a single silver atom as the tip, we introduce the electromagnetic effect through a series of static point charges that recreate the electric field in the vicinity of the plasmonic Ag nanoparticle. By scanning the tip over the molecule along a 3D grid, we can investigate the system's Raman response on each position for nonresonant and resonant illumination. Simulating both effects on their own already hints at the achievable signal enhancement and resolution, but the combination of both creates even stronger evidence that TERS is capable of resolving submolecular features.

Analytic high-order energy derivatives for metal nanoparticle-mediated infrared and Raman scattering spectra within the framework of quantum mechanics/molecular mechanics model with induced charges and dipoles

This work is devoted to deriving and implementing analytic second- and third-order energy derivatives with respect to the nuclear coordinates and external electric field within the framework of the hybrid quantum mechanics/molecular mechanics method with induced charges and dipoles (QM/DIM). Using these analytic energy derivatives, one can efficiently compute the harmonic vibrational frequencies, infrared (IR) and Raman scattering (RS) spectra of the molecule in the proximity of noble metal clusters/nanoparticles. The validity and accuracy of these analytic implementations are demonstrated by the comparison of results obtained by the finite-difference method and the analytic approaches and by the full QM and QM/DIM calculations. The complexes formed by pyridine and two sizes of gold clusters (Au18 and Au32) at varying intersystem distances of 3, 4, and 5 Å are used as the test systems, and Raman spectra of 4,4'-bipyridine in the proximity of Au2057 and Ag2057 metal nanoparticles (MNP) are calculated by the QM/DIM method and compared with experimental results as well. We find that the QM/DIM model can well reproduce the IR spectra obtained from full QM calculations for all the configurations, while although it properly enhances some of the vibrational modes, it artificially overestimates RS spectral intensities of several modes for the systems with very short intersystem distance. We show that this could be improved, however, by incorporating the hyperpolarizability of the gold metal cluster in the evaluation of RS intensities. Additionally, we address the potential impact of charge migration between the adsorbate and MNPs.

Hyper-Raman Spectroscopy of Benzene and Pyridine Revisited

Hyper-Raman (HR) spectra of benzene- h6, - d6, and pyridine in the liquid phase excited at 1064 nm were measured by a picosecond laser with a high repetition rate. Although benzene and pyridine are important aromatic molecules, the qualities of the HR spectra previously reported were not high enough to be compared with those of IR and Raman spectroscopy. Our HR spectroscopic system significantly improves sensitivity that enables the detection of HR bands of benzene and pyridine not observed before. In addition to band assignments, we interpret HR bands of benzene based on the vibronic coupling theory of (pre-) resonance hyper-Raman scattering. Depolarization ratios of HR bands of benzene and pyridine, estimated from polarized-HR measurements, are first examined from a theoretical point of view of HR spectroscopy. Moreover, we evaluate quantum chemical calculations for HR spectra by comparing experimental and computational spectra. We show that the frequency dependent polarizability and hyperpolarizability calculations using time-dependent density functional theory (TD-DFT) well reproduce the HR experiment for bulk aromatic compounds.

A discrete interaction model/quantum mechanical method for simulating surface-enhanced Raman spectroscopy in solution

Since surface-enhanced Raman scattering (SERS) is of considerable interest for sensing applications in aqueous solution, the role that solvent plays in the spectroscopy must be understood. However, these efforts are hindered due to a lack of simulation approaches for modeling solvent effects in SERS. In this work, we present an atomistic electrodynamics-quantum mechanical method to simulate SERS in aqueous solution based on the discrete interaction model/quantum mechanical method. This method combines an atomistic electrodynamics model of the nanoparticle with a time-dependent density functional theory description of the molecule and a polarizable embedding method for the solvent. The explicit treatment of solvent molecules and nanoparticles results in a large number of polarizable dipoles that need to be considered. To reduce the computational cost, a simple cut-off based approach has been implemented to limit the number of dipoles that need to be treated without sacrificing accuracy. As a test of this method, we have studied how solvent affects the SERS of pyridine in the junction between two nanoparticles in aqueous solution. We find that the solvent leads to an enhanced SERS due to an increased local field at the position of the pyridine. We further demonstrate the importance of both image field and local field effects in determining the enhancements and the spectral signatures. Our results show the importance of describing the local environment due to the solvent molecules when modeling SERS.

Surface-enhanced hyper-Raman scattering of Rhodamine 6G isotopologues: Assignment of lower vibrational frequencies

We report a comprehensive experimental and theoretical study of the lower-wavenumber vibrational modes in the surface-enhanced hyper-Raman scattering (SEHRS) of Rhodamine 6G (R6G) and its isotopologue R6G-d4. Measurements acquired on-resonance with two different electronic states, S₁ and S₂, are compared to the time-dependent density functional theory computations of the resonance hyper-Raman spectra and electrodynamics-quantum mechanical computations of the SEHRS spectra on-resonance with S₁ and S₂. After accounting for surface orientation, we find excellent agreement between experiment and theory for both R6G and its isotopologue. We then present a detailed analysis of the complex vibronic coupling effects in R6G and the importance of surface orientation for characterizing the system. This combination of theory and experiment allows, for the first time, an unambiguous assignment of lower-wavenumber vibrational modes of R6G and its isotopologue R6G-d4.

Hybrid theoretical models for molecular nanoplasmonics

The multidisciplinary nature of the research in molecular nanoplasmonics, i.e., the use of plasmonic nanostructures to enhance, control, or suppress properties of molecules interacting with light, led to contributions from different theory communities over the years, with the aim of understanding, interpreting, and predicting the physical and chemical phenomena occurring at molecular- and nano-scale in the presence of light. Multiscale hybrid techniques, using a different level of description for the molecule and the plasmonic nanosystems, permit a reliable representation of the atomistic details and of collective features, such as plasmons, in such complex systems. Here, we focus on a selected set of topics of current interest in molecular plasmonics (control of electronic excitations in light-harvesting systems, polaritonic chemistry, hot-carrier generation, and plasmon-enhanced catalysis). We discuss how their description may benefit from a hybrid modeling approach and what are the main challenges for the application of such models. In doing so, we also provide an introduction to such models and to the selected topics, as well as general discussions on their theoretical descriptions.

The chemical effect goes resonant - a full quantum mechanical approach on TERS

Lately, experimental evidence of unexpectedly extremely high spatial resolution of tip-enhanced Raman scattering (TERS) has been demonstrated. Theoretically, two different contributions are discussed: an electromagnetic effect, leading to a spatially confined near field due to plasmonic excitations; and the so-called chemical effect originating from the locally modified electronic structure of the molecule due to the close proximity of the plasmonic system. Most of the theoretical efforts have concentrated on the electromagnetic contribution or the chemical effect in case of non-resonant excitation. In this work, we present a fully quantum mechanical description including non-resonant and resonant chemical contributions as well as charge-transfer phenomena of these molecular-plasmonic hybrid systems at the density functional and the time-dependent density functional level of theory. We consider a surface-immobilized tin(ii) phthalocyanine molecule as the molecular system, which is minutely scanned by a plasmonic tip, modeled by a single silver atom. These different relative positions of the Ag atom to the molecule lead to pronounced alterations of the Raman spectra. These Raman spectra vary substantially, both in peak positions and several orders of magnitude in the intensity patterns under non-resonant and resonant conditions, and also, depending on, which electronic states are addressed. Our computational approach reveals that unique - non-resonant and resonant - chemical interactions among the tip and the molecule significantly alter the TERS spectra and are mainly responsible for the high, possibly sub-Angstrom spatial resolution.

A Discrete Interaction Model/Quantum Mechanical Method for Simulating Plasmon-Enhanced Two-Photon Absorption

In this work, we extend the discrete interaction model/quantum mechanical (DIM/QM) method to simulate plasmon-enhanced two-photon absorption (PETPA). The metal nanoparticle is treated atomistically by means of electrodynamics, while the molecule is described using damped cubic response theory within a time-dependent density functional theory framework. Using DIM/QM, we study the PETPA of para-nitroaniline ( p-NA) with a focus on the local and image field effects, the molecular orientation effects, and the molecule-nanoparticle distance effects. Our findings show that the enhancement is more complex than the simple | E|⁴ enhancement mechanism, where | E| is the local field at the position of the molecule. Because of specific interactions with the nanoparticle, we find that a TPA dark state of p-NA can be significantly enhanced through a coupling with the plasmon excitation. The results presented in this work illustrate that the coupling between molecular excitations and plasmons can give rise to unusual and complex behavior in nonlinear spectroscopy that cannot simply be understood by considering the optical properties of the individual molecules and nanoparticles separately. The method presented here provides detailed insights into the enhancement of nonlinear optical properties of molecules coupled to plasmonic nanoparticles.

Surface enhanced hyper Raman scattering (SEHRS) and its applications

Surface enhanced hyper Raman scattering (SEHRS) is the spontaneous, two-photon excited Raman scattering that occurs for molecules residing in high local optical fields of plasmonic nanostructures. Being regarded as a non-linear analogue of surface enhanced Raman scattering (SERS), SEHRS shares most of its properties, but also has additional characteristics. They include complementary spectroscopic information resulting from different selection rules and a stronger enhancement due to the non-linearity in excitation. In practical spectroscopy, this can translate to advantages, which include a high selectivity when probing molecule-surface interactions, the possibility of probing molecules at low concentrations due to the strong enhancement, and the advantages that come with excitation in the near-infrared. In this review, we give examples of the wealth of vibrational spectroscopic information that can be obtained by SEHRS and discuss work that has contributed to understanding the effect and that therefore provides directions for SEHRS spectroscopy. Future applications could range from biophotonics to materials research.

Surface-Enhanced Resonance Hyper-Raman Scattering Elucidates the Molecular Orientation of Rhodamine 6G on Silver Colloids

Herein, we utilize surface-enhanced hyper-Raman scattering (SEHRS) under resonance conditions to probe the adsorbate geometry of rhodamine 6G (R6G) on silver colloids. Our results show resonance SEHRS is highly sensitive to molecular orientation due to non-Condon effects, which do not appear in its linear counterpart surface-enhanced Raman scattering. Comparisons between simulated and measured SEHRS spectra reveal R6G adsorbs mostly perpendicular to the nanoparticle surface along the ethylamine groups with the xanthene ring oriented edgewise. Our results expand upon previous studies that rely on indirect, qualitative probes of R6G's orientation on plasmonic substrates. More importantly, this work represents the first determination of adsorbate geometry by SEHRS and opens up the possibility to study the orientation of single molecules in complex, plasmonic environments.