Hybrid theoretical models for molecular nanoplasmonics

Unraveling the mechanism of tip-enhanced molecular energy transfer

Electronic Energy Transfer (EET) between chromophores is fundamental in many natural light-harvesting complexes, serving as a critical step for solar energy funneling in photosynthetic plants and bacteria. The complicated role of the environment in mediating this process in natural architectures has been addressed by recent scanning tunneling microscope experiments involving EET between two molecules supported on a solid substrate. These measurements demonstrated that EET in such conditions has peculiar features, such as a steep dependence on the donor-acceptor distance, reminiscent of a short-range mechanism more than of a Förster-like process. By using state of the art hybrid ab initio/electromagnetic modeling, here we provide a comprehensive theoretical analysis of tip-enhanced EET. In particular, we show that this process can be understood as a complex interplay of electromagnetic-based molecular plasmonic processes, whose result may effectively mimic short range effects. Therefore, the established identification of an exponential decay with Dexter-like effects does not hold for tip-enhanced EET, and accurate electromagnetic modeling is needed to identify the EET mechanism.

Peeking into the Femtosecond Hot-Carrier Dynamics Reveals Unexpected Mechanisms in Plasmonic Photocatalysis

Plasmonic-driven photocatalysis may lead to reaction selectivity that cannot be otherwise achieved. A fundamental role is played by hot carriers, i.e., electrons and holes generated upon plasmonic decay within the metal nanostructure interacting with molecular species. Understanding the elusive microscopic mechanism behind such selectivity is a key step in the rational design of hot-carrier reactions. To accomplish that, we present state-of-the-art multiscale simulations, going beyond density functional theory, of hot-carrier injections for the rate-determining step of a photocatalytic reaction. We focus on carbon dioxide reduction, for which it was experimentally shown that the presence of a rhodium nanocube under illumination leads to the selective production of methane against carbon monoxide. We show that selectivity is due to a (predominantly) direct hole injection from rhodium to the reaction intermediate CHO. Unexpectedly, such an injection does not promote the selective reaction path by favoring proper bond breaking but rather by promoting bonding of the proper molecular fragment to the surface.

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.

The Rise and Current Status of Polaritonic Photochemistry and Photophysics

The interaction between molecular electronic transitions and electromagnetic fields can be enlarged to the point where distinct hybrid light-matter states, polaritons, emerge. The photonic contribution to these states results in increased complexity as well as an opening to modify the photophysics and photochemistry beyond what normally can be seen in organic molecules. It is today evident that polaritons offer opportunities for molecular photochemistry and photophysics, which has caused an ever-rising interest in the field. Focusing on the experimental landmarks, this review takes its reader from the advent of the field of polaritonic chemistry, over the split into polariton chemistry and photochemistry, to present day status within polaritonic photochemistry and photophysics. To introduce the field, the review starts with a general description of light-matter interactions, how to enhance these, and what characterizes the coupling strength. Then the photochemistry and photophysics of strongly coupled systems using Fabry-Perot and plasmonic cavities are described. This is followed by a description of room-temperature Bose-Einstein condensation/polariton lasing in polaritonic systems. The review ends with a discussion on the benefits, limitations, and future developments of strong exciton-photon coupling using organic molecules.

The role of dephasing for dark state coupling in a molecular Tavis-Cummings model

The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis-Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis-Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population.

Time Evolution of Plasmonic Features in Pentagonal Ag Clusters

In the present work, we apply recently developed real-time descriptors to study the time evolution of plasmonic features of pentagonal Ag clusters. The method is based on the propagation of the time-dependent Schrödinger equation within a singly excited TDDFT ansatz. We use transition contribution maps (TCMs) and induced density to characterize the optical longitudinal and transverse response of such clusters, when interacting with pulses resonant with the low-energy (around 2-3 eV, A1) size-dependent or the high-energy (around 4 eV, E1) size-independent peak. TCMs plots on the analyzed clusters, Ag25+ and Ag43+ show off-diagonal peaks consistent with a plasmonic response when a longitudinal pulse resonant at A1 frequency is applied, and dominant diagonal spots, typical of a molecular transition, when a transverse E1 pulse is employed. Induced densities confirm this behavior, with a dipole-like charge distribution in the first case. The optical features show a time delay with respect to the evolution of the external pulse, consistent with those found in the literature for real-time TDDFT calculations on metal clusters.

Electronic circular dichroism from real-time propagation in state space

In this paper, we propose to compute the electronic circular dichroism (ECD) spectra of chiral molecules using a real-time propagation of the time-dependent Schrödinger equation (TDSE) in the space of electronic field-free eigenstates, by coupling TDSE with a given treatment of the electronic structure of the target. The time-dependent induced magnetic moment is used to compute the ECD spectrum from an explicit electric perturbation. The full matrix representing the transition magnetic moment in the space of electronic states is generated from that among pairs of molecular orbitals. In the present work, we show the ECD spectra of methyloxirane, of several conformers of L-alanine, and of the Λ-Co(acac)₃ complex, computed from a singly excited ansatz of time-dependent density functional theory eigenstates. The time-domain ECD spectra properly reproduce the frequency-domain ones obtained in the linear-response regime and quantitatively agree with the available experimental data. Moreover, the time-domain approach to ECD allows us to naturally go beyond the ground-state rotationally averaged ECD spectrum, which is the standard outcome of the linear-response theory, e.g., by computing the ECD spectra from electronic excited states.

Recent Developments in Plasmonic Alloy Nanoparticles: Synthesis, Modelling, Properties and Applications

Despite the traditional plasmonic materials are counted on one hand, there are a lot of possible combinations leading to alloys with other elements of the periodic table, in particular those renowned for magnetic or catalytic properties. It is not a surprise, therefore, that nanoalloys are considered for their ability to open new perspectives in the panorama of plasmonics, representing a leading research sector nowadays. This is demonstrated by a long list of studies describing multiple applications of nanoalloys in photonics, photocatalysis, sensing and magneto-optics, where plasmons are combined with other physical and chemical phenomena. In some remarkable cases, the amplification of the conventional properties and even new effects emerged. However, this field is still in its infancy and several challenges must be overcome, starting with the synthesis (control of composition, crystalline order, size, processability, achievement of metastable phases and disordered compounds) as well as the modelling of the structure and properties (accuracy of results, reliability of structural predictions, description of disordered phases, evolution over time) of nanoalloys. To foster the research on plasmonic nanoalloys, here we provide an overview of the most recent results and developments in the field, organized according to synthetic strategies, modelling approaches, dominant properties and reported applications. Considering the several plasmonic nanoalloys under development as well as the large number of those still awaiting synthesis, modelling, properties assessment and technological exploitation, we expect a great impact on the forthcoming solutions for sustainability, ultrasensitive and accurate detection, information processing and many other fields.

Inverse design of molecule-metal nanoparticle systems interacting with light for desired photophysical properties

Molecules close to a metal nanoparticle (NP) have significantly different photophysical properties from those of the isolated one. In order to harness the potential of the molecule-NP system, appropriate design guidelines are required. Here, we propose an inverse design method of the optimal molecule-NP systems and incident electric field for desired photophysical properties. It is based on a gradient-based optimization search within the time-dependent quantum chemical description for the molecule and the continuum model for the metal NP. We designed the optimal molecule, relative molecule-NP spatial conformation, and incident electric field of a molecule-NP system to maximize the population transfer to the target electronic state of the molecule. The design results were presented and discussed. The present method is promising as the basis for designing molecule-NP systems and incident fields and accelerates discoveries of efficient molecular plasmonics systems.

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

Optical properties of metal nanostructures are the basis of several scientific and technological applications. When the nanostructure characteristic size is of the order of few nm or less, it is generally accepted that only a description that explicitly describes electrons by quantum mechanics can reproduce faithfully its optical response. For example, the plasmon resonance shift upon shrinking the nanostructure size (red-shift for simple metals, blue-shift for d-metals such as gold and silver) is universally accepted to originate from the quantum nature of the system. Here we show instead that an atomistic approach based on classical physics, ωFQFμ (frequency dependent fluctuating charges and fluctuating dipoles), is able to reproduce all the typical "quantum" size effects, such as the sign and the magnitude of the plasmon shift, the progressive loss of the plasmon resonance for gold, the atomistically detailed features in the induced electron density, and the non local effects in the nanoparticle response. To support our findings, we compare the ωFQFμ results for Ag and Au with literature time-dependent DFT simulations, showing the capability of fully classical physics to reproduce these TDDFT results. Only electron tunneling between nanostructures emerges as a genuine quantum mechanical effect, that we had to include in the model by an ad hoc term.

Collective response in light-matter interactions: The interplay between strong coupling and local dynamics

Strong molecule-radiation field coupling is often reached when a large number N of molecules respond collectively to the radiation field. In electronic strong coupling, molecular nuclear dynamics following polariton excitation reflects (a) the timescale separation between the fast electronic and photonic dynamics and the slow nuclear motion on one hand, and (b) the interplay between the collective nature of the molecule-field coupling and the local nature of the molecules nuclear response on the other. The first implies that the electronic excitation takes place, in the spirit of the Born approximation, at an approximately fixed nuclear configuration. The second can be rephrased as the intriguing question, can the collective nature of the optical excitation lead to collective nuclear motion following polariton formation, resulting in so-called polaron decoupled dynamics. We address this issue by studying the dynamical properties of a simplified Holstein-Tavis-Cummings type model, in which boson modes representing molecular vibrations are replaced by two-level systems while the boson frequency and the vibronic coupling are represented by the coupling between these levels (that induces Rabi oscillations between them) and electronic state dependence of this coupling. We investigate the short-time behavior of this model following polariton excitation as well as its response to CW driving and its density of states spectrum. We find that, while some aspects of the dynamical behavior appear to adhere to the polaron decoupling picture, the observed dynamics mostly reflect the local nature of the nuclear configuration of the electronic polariton rather than this picture.

Computational Analyses of Plasmonics of a Silver Nanoparticle in a Vacuum and in a Water Solution by Classical Electronic and Molecular Dynamics Simulations

We present basic optical responses of a silver nanoparticle (Ag309) in a vacuum and a water solution obtained by classical electronic and molecular dynamics (CEMD) calculations, where the CEMD is our previously developed force-field based molecular dynamics simulation method that incorporates the classical equation of motion for free electrons in metal and an interaction with the applied oscillating electric field (Yamada, A. J. Chem. Phys. 2021, 155, 174118)). The present work is the follow-up of the previous study. Calculated absorption spectra in the visible region with various conditions are reported together with parameter determination for realistic analyses as well as the verification of the method. Time-domain optical responses of Ag309 in water solvent are as well analyzed in terms of the plasmon resonance excitation under a subpicosecond light pulse and its thermal relaxation.

Theoretical Challenges in Polaritonic Chemistry

Polaritonic chemistry exploits strong light-matter coupling between molecules and confined electromagnetic field modes to enable new chemical reactivities. In systems displaying this functionality, the choice of the cavity determines both the confinement of the electromagnetic field and the number of molecules that are involved in the process. While in wavelength-scale optical cavities the light-matter interaction is ruled by collective effects, plasmonic subwavelength nanocavities allow even single molecules to reach strong coupling. Due to these very distinct situations, a multiscale theoretical toolbox is then required to explore the rich phenomenology of polaritonic chemistry. Within this framework, each component of the system (molecules and electromagnetic modes) needs to be treated in sufficient detail to obtain reliable results. Starting from the very general aspects of light-molecule interactions in typical experimental setups, we underline the basic concepts that should be taken into account when operating in this new area of research. Building on these considerations, we then provide a map of the theoretical tools already available to tackle chemical applications of molecular polaritons at different scales. Throughout the discussion, we draw attention to both the successes and the challenges still ahead in the theoretical description of polaritonic chemistry.

Experimental characterization techniques for plasmon-assisted chemistry

Plasmon-assisted chemistry is the result of a complex interplay between electromagnetic near fields, heat and charge transfer on the nanoscale. The disentanglement of their roles is non-trivial. Therefore, a thorough knowledge of the chemical, structural and spectral properties of the plasmonic/molecular system being used is required. Specific techniques are needed to fully characterize optical near fields, temperature and hot carriers with spatial, energetic and/or temporal resolution. The timescales for all relevant physical and chemical processes can range from a few femtoseconds to milliseconds, which necessitates the use of time-resolved techniques for monitoring the underlying dynamics. In this Review, we focus on experimental techniques to tackle these challenges. We further outline the difficulties when going from the ensemble level to single-particle measurements. Finally, a thorough understanding of plasmon-assisted chemistry also requires a substantial joint experimental and theoretical effort.

Catalysis by Dark States in Vibropolaritonic Chemistry

Collective strong coupling between a disordered ensemble of N localized molecular vibrations and a resonant optical cavity mode gives rise to two polariton and N-1≫2 dark modes. Thus, experimental changes in thermally activated reaction kinetics due to polariton formation appear entropically unlikely and remain a puzzle. Here we show that the overlooked dark modes, while parked at the same energy as bare molecular vibrations, are robustly delocalized across ∼2-3 molecules, yielding enhanced channels of vibrational cooling, concomitantly catalyzing a chemical reaction. As an illustration, we theoretically show an ≈50% increase in an electron transfer rate due to enhanced product stabilization. The reported effects can arise when the homogeneous linewidths of the dark modes are smaller than their energy spacings.

Molecular Polaritonics: Chemical Dynamics Under Strong Light-Matter Coupling

Chemical manifestations of strong light-matter coupling have recently been a subject of intense experimental and theoretical studies. Here we review the present status of this field. Section 1 is an introduction to molecular polaritonics and to collective response aspects of light-matter interactions. Section 2 provides an overview of the key experimental observations of these effects, while Section 3 describes our current theoretical understanding of the effect of strong light-matter coupling on chemical dynamics. A brief outline of applications to energy conversion processes is given in Section 4. Pending technical issues in the construction of theoretical approaches are briefly described in Section 5. Finally, the summary in Section 6 outlines the paths ahead in this exciting endeavor. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Classical electronic and molecular dynamics simulation for optical response of metal system

An extended molecular dynamics simulation that incorporates classical free electron dynamics in the framework of the force-field model has been developed to enable us to describe the optical response of metal materials under the visible light electric field. In the simulation, dynamical atomic point charges follow equations of motion of classical free electrons that include Coulomb interactions with the oscillating field and surrounding atomic sites and collision effects from nearby electrons and ions. This scheme allows us to simulate an interacting system of metals with molecules using an ordinary polarizable force-field and preserves energy conservation in the case without applying an external electric field. As the first applications, we show that the presented simulation accurately reproduces (i) the classical image potential in a metal-charge interaction system and (ii) the dielectric function of bulk metal. We also demonstrate (iii) calculations of absorption spectra of metal nano-particles with and without a water solvent at room temperature, showing reasonable red-shift by the solvent effect, and (iv) plasmon resonant excitation of the metal nano-particle in solution under the visible light pulse and succeeding energy relaxation of the absorbed light energy from electrons to atoms on the metal and to the water solvent. Our attempt thus opens the possibility to expand the force-field based molecular dynamics simulation to an alternative tool for optical-related fields.

Time-Resolved Excited-State Analysis of Molecular Electron Dynamics by TDDFT and Bethe-Salpeter Equation Formalisms

In this work, a theoretical and computational set of tools to study and analyze time-resolved electron dynamics in molecules, under the influence of one or more external pulses, is presented. By coupling electronic-structure methods with the resolution of the time-dependent Schrödinger equation, we developed and implemented the time-resolved induced density of the electronic wavepacket, the time-resolved formulation of the differential projection density of states (ΔPDOS), and of transition contribution map (TCM) to look at the single-electron orbital occupation and localization change in time. Moreover, to further quantify the possible charge transfer, we also defined the energy-integrated ΔPDOS and the fragment-projected TCM. We have used time-dependent density-functional theory (TDDFT), as implemented in ADF software, and the Bethe-Salpeter equation, as provided by MolGW package, for the description of the electronic excited states. This suite of postprocessing tools also provides the time evolution of the electronic states of the system of interest. To illustrate the usefulness of these postprocessing tools, excited-state populations have been computed for HBDI (the chromophore of GFP) and DNQDI molecules interacting with a sequence of two pulses. Time-resolved descriptors have been applied to study the time-resolved electron dynamics of HBDI, DNQDI, LiCN (being a model system for dipole switching upon highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) electronic excitation), and Ag22. The computational analysis tools presented in this article can be employed to help the interpretation of fast and ultrafast spectroscopies on molecular, supramolecular, and composite systems.