GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Tailoring Hot-Carrier Distributions of Plasmonic Nanostructures through Surface Alloying.

Alloyed metal nanoparticles are a promising platform for plasmonically enabled hot-carrier generation, which can be used to drive photochemical reactions. Although the non-plasmonic component in these systems has been investigated for its potential to enhance catalytic activity, its capacity to affect the photochemical process favorably has been underexplored by comparison. Here, we study the impact of surface alloy species and concentration on hot-carrier generation in Ag nanoparticles. By first-principles simulations, we photoexcite the localized surface plasmon, allow it to dephase, and calculate spatially and energetically resolved hot-carrier distributions. We show that the presence of non-noble species in the topmost surface layer drastically enhances hot-hole generation at the surface at the expense of hot-hole generation in the bulk, due to the additional d-type states that are introduced to the surface. The energy of the generated holes can be tuned by choice of the alloyant, with systematic trends across the d-band block. Already low surface alloy concentrations have a large impact, with a saturation of the enhancement effect typically close to 75% of a monolayer. Hot-electron generation at the surface is hindered slightly by alloying, but here a judicious choice of the alloy composition allows one to strike a balance between hot electrons and holes. Our work underscores the promise of utilizing multicomponent nanoparticles to achieve enhanced control over plasmonic catalysis and provides guidelines for how hot-carrier distributions can be tailored by designing the electronic structure of the surface through alloying.

Hot-Carrier Transfer across a Nanoparticle-Molecule Junction: The Importance of Orbital Hybridization and Level Alignment.

While direct hot-carrier transfer can increase photocatalytic activity, it is difficult to discern experimentally and competes with several other mechanisms. To shed light on these aspects, here, we model from first-principles hot-carrier generation across the interface between plasmonic nanoparticles and a CO molecule. The hot-electron transfer probability depends nonmonotonically on the nanoparticle-molecule distance and can be effective at long distances, even before a strong chemical bond can form; hot-hole transfer on the other hand is limited to shorter distances. These observations can be explained by the energetic alignment between molecular and nanoparticle states as well as the excitation frequency. The hybridization of the molecular orbitals is the key predictor for hot-carrier transfer in these systems, emphasizing the necessity of ground state hybridization for accurate predictions. Finally, we show a nontrivial dependence of the hot-carrier distribution on the excitation energy, which could be exploited when optimizing photocatalytic systems.

Ultrastrong Coupling of a Single Molecule to a Plasmonic Nanocavity: A First-Principles Study.

Ultrastrong coupling (USC) is a distinct regime of light-matter interaction in which the coupling strength is comparable to the resonance energy of the cavity or emitter. In the USC regime, common approximations to quantum optical Hamiltonians, such as the rotating wave approximation, break down as the ground state of the coupled system gains photonic character due to admixing of vacuum states with higher excited states, leading to ground-state energy changes. USC is usually achieved by collective coherent coupling of many quantum emitters to a single mode cavity, whereas USC with a single molecule remains challenging. Here, we show by time-dependent density functional theory (TDDFT) calculations that a single organic molecule can reach USC with a plasmonic dimer, consisting of a few hundred atoms. In this context, we discuss the capacity of TDDFT to represent strong coupling and its connection to the quantum optical Hamiltonian. We find that USC leads to appreciable ground-state energy modifications accounting for a non-negligible part of the total interaction energy, comparable to k B T at room temperature.

Real-time time-dependent density functional theory implementation of electronic circular dichroism applied to nanoscale metal-organic clusters.

Electronic circular dichroism (ECD) is a powerful spectroscopy method for investigating chiral properties at the molecular level. ECD calculations with the commonly used linear-response time-dependent density functional theory (LR-TDDFT) framework can be prohibitively costly for large systems. To alleviate this problem, we present here an ECD implementation within the projector augmented-wave method in a real-time-propagation TDDFT framework in the open-source GPAW code. Our implementation supports both local atomic basis sets and real-space finite-difference representations of wave functions. We benchmark our implementation against an existing LR-TDDFT implementation in GPAW for small chiral molecules. We then demonstrate the efficiency of our local atomic basis set implementation for a large hybrid nanocluster and discuss the chiroptical properties of the cluster.

Dipolar coupling of nanoparticle-molecule assemblies: An efficient approach for studying strong coupling.

Strong light-matter interactions facilitate not only emerging applications in quantum and non-linear optics but also modifications of properties of materials. In particular, the latter possibility has spurred the development of advanced theoretical techniques that can accurately capture both quantum optical and quantum chemical degrees of freedom. These methods are, however, computationally very demanding, which limits their application range. Here, we demonstrate that the optical spectra of nanoparticle-molecule assemblies, including strong coupling effects, can be predicted with good accuracy using a subsystem approach, in which the response functions of different units are coupled only at the dipolar level. We demonstrate this approach by comparison with previous time-dependent density functional theory calculations for fully coupled systems of Al nanoparticles and benzene molecules. While the present study only considers few-particle systems, the approach can be readily extended to much larger systems and to include explicit optical-cavity modes.

Hot-Carrier Generation in Plasmonic Nanoparticles: The Importance of Atomic Structure.

Metal nanoparticles are attractive for plasmon-enhanced generation of hot carriers, which may be harnessed in photochemical reactions. In this work, we analyze the coherent femtosecond dynamics of photon absorption, plasmon formation, and subsequent hot-carrier generation through plasmon dephasing using first-principles simulations. We predict the energetic and spatial hot-carrier distributions in small metal nanoparticles and show that the distribution of hot electrons is very sensitive to the local structure. Our results show that surface sites exhibit enhanced hot-electron generation in comparison to the bulk of the nanoparticle. Although the details of the distribution depend on particle size and shape, as a general trend, lower-coordinated surface sites such as corners, edges, and {100} facets exhibit a higher proportion of hot electrons than higher-coordinated surface sites such as {111} facets or the core sites. The present results thereby demonstrate how hot carriers could be tailored by careful design of atomic-scale structures in nanoscale systems.

Strong plasmon-molecule coupling at the nanoscale revealed by first-principles modeling.

Strong light-matter interactions in both the single-emitter and collective strong coupling regimes attract significant attention due to emerging applications in quantum and nonlinear optics as well as opportunities for modifying material-related properties. Exploration of these phenomena is theoretically demanding, as polaritons exist at the intersection between quantum optics, solid state physics, and quantum chemistry. Fortunately, nanoscale polaritons can be realized in small plasmon-molecule systems, enabling treatment with ab initio methods. Here, we show that time-dependent density-functional theory calculations access the physics of nanoscale plasmon-molecule hybrids and predict vacuum Rabi splitting. By considering a system comprising a few-hundred-atom aluminum nanoparticle interacting with benzene molecules, we show that cavity quantum electrodynamics holds down to resonators of a few cubic nanometers in size, yielding a single-molecule coupling strength exceeding 200 meV due to a massive vacuum field of 4.5 V · nm-1. In a broader perspective, ab initio methods enable parameter-free in-depth studies of polaritonic systems for emerging applications.

Plasmon Excitations in Mixed Metallic Nanoarrays.

Features of the surface plasmon from macroscopic materials emerge in molecular systems, but differentiating collective excitations from single-particle excitations in molecular systems remains elusive. The rich interactions between single-particle electron-hole and collective electron excitations produce phenomena related to the chemical physics aspects within the atomic array. We study the plasmonic properties of atomic arrays of noble (Au, Ag, and Cu) and transition-metal (Pd, Pt) homonuclear chains using time-dependent density functional theory and their Kohn-Sham transition contributions. The response to the electromagnetic radiation is related to both the geometry-dependent confinement of sp-valence electrons and the energy position of d-electrons in the different atomic species and the hybridization between d and sp electrons. It is possible to tune the position of the plasmon resonance, split it into several peaks, and eventually achieve broadband absorption of radiation. Arrays of mixed noble and transition-metal chains may have strongly attenuated plasmonic behavior. The collective nature of the excitations is ascertained using their Kohn-Sham transition contributions. To manipulate the plasmonic response and achieve the desired properties for broad applications, it is vital to understand the origins of these phenomena in atomic chains and their arrays.

Direct hot-carrier transfer in plasmonic catalysis.

Plasmonic metal nanoparticles can concentrate optical energy and enhance chemical reactions on their surfaces. Plasmons can interact with adsorbate orbitals and decay by directly exciting a carrier from the metal to the adsorbate in a process termed the direct-transfer process. Although this process could be useful for enhancing the efficiency of a chemical reaction, it remains poorly understood. Here, we report a preliminary investigation employing time-dependent density-functional theory (TDDFT) calculations to capture this process at a model metal-adsorbate interface formed by a silver nanoparticle (Ag147) and a carbon monoxide molecule (CO). Direct hot-electron transfer is observed to occur from the occupied states of Ag to the unoccupied molecular orbitals of CO. We determine the probability of this process and show that it depends on the adsorption site of CO. Our results are expected to aid the design of more efficient metal-molecule interfaces for plasmonic catalysis.

Plasmon-Induced Direct Hot-Carrier Transfer at Metal-Acceptor Interfaces.

Plasmon-induced hot-carrier transfer from a metal nanostructure to an acceptor is known to occur via two key mechanisms: (i) indirect transfer, where the hot carriers are produced in the metal nanostructure and subsequently transferred to the acceptor, and (ii) direct transfer, where the plasmons decay by directly exciting carriers from the metal to the acceptor. Unfortunately, an atomic-level understanding of the direct-transfer process, especially with regard to its quantification, remains elusive even though it is estimated to be more efficient compared to the indirect-transfer process. This is due to experimental challenges in separating direct from indirect transfer as both processes occur simultaneously at femtosecond time scales. Here, we employ time-dependent density-functional theory simulations to isolate and study the direct-transfer process at a model metal-acceptor (Ag147-Cd33Se33) interface. Our simulations show that, for a 10 fs Gaussian laser pulse tuned to the plasmon frequency, the plasmon formed in the Ag147-Cd33Se33 system decays within 10 fs and induces the direct transfer with a probability of about 40%. We decompose the direct-transfer process further and demonstrate that the direct injection of both electrons and holes into the acceptor, termed direct hot-electron transfer (DHET) and direct hot-hole transfer (DHHT), takes place with similar probabilities of about 20% each. Finally, effective strategies to control and tune the probabilities of DHET and DHHT processes are proposed. We envision our work to provide guidelines toward the design of metal-acceptor interfaces that enable more efficient plasmonic hot-carrier devices.

Kohn-Sham Decomposition in Real-Time Time-Dependent Density-Functional Theory: An Efficient Tool for Analyzing Plasmonic Excitations.

Electronic excitations can be efficiently analyzed in terms of the underlying Kohn-Sham (KS) electron-hole transitions. While such a decomposition is readily available in the linear-response time-dependent density-functional theory (TDDFT) approaches based on the Casida equations, a comparable analysis is less commonly conducted within the real-time-propagation TDDFT (RT-TDDFT). To improve this situation, we present here an implementation of a KS decomposition tool within the local-basis-set RT-TDDFT code in the free GPAW package. Our implementation is based on postprocessing of data that is readily available during time propagation, which is important for retaining the efficiency of the underlying RT-TDDFT to large systems. After benchmarking our implementation on small benzene derivatives by explicitly reconstructing the Casida eigenvectors from RT-TDDFT, we demonstrate the performance of the method by analyzing the plasmon resonances of icosahedral silver nanoparticles up to Ag561. The method provides a clear description of the splitting of the plasmon in small nanoparticles due to individual single-electron transitions as well as the formation of a distinct d-electron-screened plasmon resonance in larger nanoparticles.

Quantized Evolution of the Plasmonic Response in a Stretched Nanorod.

Quantum aspects, such as electron tunneling between closely separated metallic nanoparticles, are crucial for understanding the plasmonic response of nanoscale systems. We explore quantum effects on the response of the conductively coupled metallic nanoparticle dimer. This is realized by stretching a nanorod, which leads to the formation of a narrowing atomic contact between the two nanorod ends. Based on first-principles time-dependent density-functional-theory calculations, we find a discontinuous evolution of the plasmonic response as the nanorod is stretched. This is especially pronounced for the intensity of the main charge-transfer plasmon mode. We show the correlation between the observed discontinuities and the discrete nature of the conduction channels supported by the formed atomic-sized junction.

Nanoplasmonics simulations at the basis set limit through completeness-optimized, local numerical basis sets.

We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond.

Dynamical coupling of plasmons and molecular excitations by hybrid quantum/classical calculations: time-domain approach.

The presence of plasmonic material influences the optical properties of nearby molecules in untrivial ways due to the dynamical plasmon-molecule coupling. We combine quantum and classical calculation schemes to study this phenomenon in a hybrid system that consists of a Na(2) molecule located in the gap between two Au/Ag nanoparticles. The molecule is treated quantum-mechanically with time-dependent density-functional theory, and the nanoparticles with quasistatic classical electrodynamics. The nanoparticle dimer has a plasmon resonance in the visible part of the electromagnetic spectrum, and the Na(2) molecule has an electron-hole excitation in the same energy range. Due to the dynamical interaction of the two subsystems the plasmon and the molecular excitations couple, creating a hybridized molecular-plasmon excited state. This state has unique properties that yield e.g. enhanced photoabsorption compared to the freestanding Na(2) molecule. The computational approach used enables decoupling of the mutual plasmon-molecule interaction, and our analysis verifies that it is not legitimate to neglect the back coupling effect when describing the dynamical interaction between plasmonic material and nearby molecules. Time-resolved analysis shows nearly instantaneous formation of the coupled state, and provides an intuitive picture of the underlying physics.