Optical response of silver clusters and their hollow shells from linear-response TDDFT

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.

Orbital-Free Methods for Plasmonics: Linear Response

Plasmonic systems, such as metal nanoparticles, are widely used in different application areas, going from biology to photovoltaics.The modeling of the optical response of such systems is of fundamental importance to analyze their behavior and to design new systems with required properties.When the characteristic sizes/distances reach a few nanometers, non-local and spill-out effects become relevant and conventional classical electrodynamics models are no more appropriate. Methods based on the Time-Dependent Density-Functional Theory (TD-DFT) represent the current reference for the description of quantum effects. However, TD-DFT is based on knowledge of all occupied orbitals whose calculation is computationally prohibitive to model large plasmonic systems of interest for applications.On the other hand, methods based on the Orbital-Free (OF) formulation of TD-DFT, can scale linearly with the system size.In this Review, OF methods ranging from semiclassical models to the quantum hydrodynamic theory, will be derived from the linear response TD-DFT, so that the key approximations and properties of each method can be clearly highlighted. The accuracy of the various approximations will be then validated for the linear optical properties of jellium nanoparticles, the most relevant model system in plasmonics. OF methods can describe the collective excitations in plasmonic systems with great accuracy andwithout system-tuned parameters. The accuracy on these methods depends only on the accuracy on the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will be indicated.

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.

Plasmon Couplings from Subsystem Time-Dependent Density Functional Theory

Many applications in plasmonics are related to the coupling between metallic nanoparticles (MNPs) or between an emitter and a MNP. The theoretical analysis of such a coupling is thus of fundamental importance to analyze the plasmonic behavior and to design new systems. While classical methods neglect quantum and spill-out effects, time-dependent density functional theory (TD-DFT) considers all of them and with Kohn-Sham orbitals delocalized over the whole system. Thus, within TD-DFT, no definite separation of the subsystems (the single MNP or the emitter) and their couplings is directly available. This important feature is obtained here using the subsystem formulation of TD-DFT, which has been originally developed in the context of weakly interacting organic molecules. In subsystem TD-DFT, interacting MNPs are treated independently, thus allowing us to compute the plasmon couplings directly from the subsystem TD-DFT transition densities. We show that subsystem TD-DFT, as well as a simplified version of it in which kinetic contributions are neglected, can reproduce the reference TD-DFT calculations for gap distances greater than about 6 Å or even smaller in the case of hybrid plasmonic systems (i.e., molecules interacting with MNPs). We also show that the subsystem TD-DFT can be also used as a tool to analyze the impact of charge-transfer effects.

Effects of ligands on (de-)enhancement of plasmonic excitations of silver, gold and bimetallic nanoclusters: TD-DFT+TB calculations

Metal nanoclusters can be synthesized in various sizes and shapes and are typically protected with ligands to stabilize them. These ligands can also be used to tune the plasmonic properties of the clusters as the absorption spectrum of a protected cluster can be significantly altered compared to the bare cluster. In this paper, we computationally investigate the influence of thiolate ligands on the plasmonic intensity for silver, gold and alloy clusters. Using time-dependent density functional theory with tight-binding approximations, TD-DFT+TB, we show that this level of theory can reproduce the broad experimental spectra of Au₁₄₄(SR)₆₀ and Ag₅₃Au₉₁(SR)₆₀ (R = CH₃) compounds with satisfactory agreement. As TD-DFT+TB does not depend on atom-type parameters we were able to apply this approach on large ligand-protected clusters with various compositions. With these calculations we predict that the effect of ligands on the absorption can be a quenching as well as an enhancement. We furthermore show that it is possible to unambiguously identify the plasmonic peaks by the scaled Coulomb kernel technique and explain the influence of ligands on the intensity (de-)enhancement by analyzing the plasmonic excitations in terms of the dominant orbital contributions.

Toward Efficient GW Calculations Using Numerical Atomic Orbitals: Benchmarking and Application to Molecular Dynamics Simulations

The use of atomic orbitals in Hedin's GW approximation provides, in principle, an inexpensive alternative to plane-wave basis sets, especially when modeling large molecules. However, benchmarking of the algorithms and basis sets is essential for a careful balance between cost and accuracy. In this paper, we present an implementation of the GW approximation using numerical atomic orbitals and a pseudopotential treatment of core electrons. The combination of a contour deformation technique with a one-shot extraction of quasiparticle energies provides an efficient scheme for many applications. The performance of the implementation with respect to the basis set convergence and the effect of the use of pseudopotentials has been tested for the 117 closed-shell molecules from the G2/97 test set and 24 larger acceptor molecules from another recently proposed test set. Moreover, to demonstrate the potential of our method, we compute the thermally averaged GW density of states of a large photochromic compound by sampling ab initio molecular dynamics trajectories at different temperatures. The computed thermal line widths indicate approximately twice as large electron-phonon couplings with GW than with standard DFT-GGA calculations. This is further confirmed using frozen-phonon calculations.

Density-functional tight-binding approach for metal clusters, nanoparticles, surfaces and bulk: application to silver and gold

Density-functional based tight-binding (DFTB) is an efficient quantum mechanical method that can describe a variety of systems, going from organic and inorganic compounds to metallic and hybrid materials. The present topical review addresses the ability and performance of DFTB to investigate energetic, structural, spectroscopic and dynamical properties of gold and silver materials. After a brief overview of the theoretical basis of DFTB, its parametrization and its transferability, we report its past and recent applications to gold and silver systems, including small clusters, nanoparticles, bulk and surfaces, bare and interacting with various organic and inorganic compounds. The range of applications covered by those studies goes from plasmonics and molecular electronics, to energy conversion and surface chemistry. Finally, perspectives of DFTB in the field of gold and silver surfaces and NPs are outlined.

Insight on agglomerates of gold nanoparticles in glass based on surface plasmon resonance spectrum: study by multi-spheres T-matrix method

The formation of a localized surface plasmon resonance (SPR) spectrum of randomly distributed gold nanoparticles in the surface layer of silicate float glass, generated and implanted by UV ArF-excimer laser irradiation of a thin gold layer sputter-coated on the glass surface, was studied by the T-matrix method, which enables particle agglomeration to be taken into account. The experimental technique used is promising for the production of submicron patterns of plasmonic nanoparticles (given by laser masks or gratings) without damage to the glass surface. Analysis of the applicability of the multi-spheres T-matrix (MSTM) method to the studied material was performed through calculations of SPR characteristics for differently arranged and structured gold nanoparticles (gold nanoparticles in solution, particles pairs, and core-shell silver-gold nanoparticles) for which either experimental data or results of the modeling by other methods are available. For the studied gold nanoparticles in glass, it was revealed that the theoretical description of their SPR spectrum requires consideration of the plasmon coupling between particles, which can be done effectively by MSTM calculations. The obtained statistical distributions over particle sizes and over interparticle distances demonstrated the saturation behavior with respect to the number of particles under consideration, which enabled us to determine the effective aggregate of particles, sufficient to form the SPR spectrum. The suggested technique for the fitting of an experimental SPR spectrum of gold nanoparticles in glass by varying the geometrical parameters of the particles aggregate in the recurring calculations of spectrum by MSTM method enabled us to determine statistical characteristics of the aggregate: the average distance between particles, average size, and size distribution of the particles. The fitting strategy of the SPR spectrum presented here can be applied to nanoparticles of any nature and in various substances, and, in principle, can be extended for particles with non-spherical shapes, like ellipsoids, rod-like and other T-matrix-solvable shapes.

Atomic-Scale Lightning Rod Effect in Plasmonic Picocavities: A Classical View to a Quantum Effect

Plasmonic gaps are known to produce nanoscale localization and enhancement of optical fields, providing small effective mode volumes of about a few hundred nm³. Atomistic quantum calculations based on time-dependent density functional theory reveal the effect of subnanometric localization of electromagnetic fields due to the presence of atomic-scale features at the interfaces of plasmonic gaps. Using a classical model, we explain this as a nonresonant lightning rod effect at the atomic scale that produces an extra enhancement over that of the plasmonic background. The near-field distribution of atomic-scale hot spots around atomic features is robust against dynamical screening and spill-out effects and follows the potential landscape determined by the electron density around the atomic sites. A detailed comparison of the field distribution around atomic hot spots from full quantum atomistic calculations and from the local classical approach considering the geometrical profile of the atoms' electronic density validates the use of a classical framework to determine the effective mode volume in these extreme subnanometric optical cavities. This finding is of practical importance for the community of surface-enhanced molecular spectroscopy and quantum nanophotonics, as it provides an adequate description of the local electromagnetic fields around atomic-scale features with use of simplified classical methods.