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.

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.

Covalent and non-covalent coupling of a Au102 nanocluster with a fluorophore: energy transfer, quenching and intracellular pH sensing.

Interactions between an atomically precise gold nanocluster Au102(p-MBA)44 (p-MBA = para mercaptobenzoic acid) and a fluorescent organic dye molecule (KU, azadioxatriangulenium) are studied. In solution, the constituents form spontaneously a weakly bound complex leading to quenching of fluorescence of the KU dye via energy transfer. The KU can be separated from the complex by lowering pH, leading to recovery of fluorescence, which forms a basis for an optical reversible pH sensor. However, the sensor is not a stable entity, which could be delivered inside cells. For this purpose, a covalently bound hybrid is synthesized by linking the KU dye to the ligand layer of the cluster via an ester bond. Covalent linking facilitates entry of the cluster-dye hybrids into cells via endocytosis. Inside cells, the hybrids accumulate in endosomes where Au102 releases its cargo via hydrolysis of the ester bond. Changes of the local pH inside endosomes regulate reversible fluorescence due to variations in the interactions between the Au102 cluster and the dye. This work presents a concept for delivering reporter molecules into cells by using atomically precise gold nanoclusters as carriers and paves the way for future developments of cluster-reporter sensors for in vivo measurements of e.g. absolute pH values or ion concentrations.

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.

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.

Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials.

Properties of solid-liquid interfaces are of immense importance for electrocatalytic and electrochemical systems, but modeling such interfaces at the atomic level presents a serious challenge and approaches beyond standard methodologies are needed. An atomistic computational scheme needs to treat at least part of the system quantum mechanically to describe adsorption and reactions, while the entire system is in thermal equilibrium. The experimentally relevant macroscopic control variables are temperature, electrode potential, and the choice of the solvent and ions, and these need to be explicitly included in the computational model as well; this calls for a thermodynamic ensemble with fixed ion and electrode potentials. In this work, a general framework within density functional theory (DFT) with fixed electron and ion chemical potentials in the grand canonical (GC) ensemble is established for modeling electrocatalytic and electrochemical interfaces. Starting from a fully quantum mechanical description of multi-component GC-DFT for nuclei and electrons, a systematic coarse-graining is employed to establish various computational schemes including (i) the combination of classical and electronic DFTs within the GC ensemble and (ii) on the simplest level a chemically and physically sound way to obtain various (modified) Poisson-Boltzmann (mPB) implicit solvent models. The detailed and rigorous derivation clearly establishes which approximations are needed for coarse-graining as well as highlights which details and interactions are omitted in vein of computational feasibility. The transparent approximations also allow removing some of the constraints and coarse-graining if needed. We implement various mPB models within a linear dielectric continuum in the GPAW code and test their capabilities to model capacitance of electrochemical interfaces as well as study different approaches for modeling partly periodic charged systems. Our rigorous and well-defined DFT coarse-graining scheme to continuum electrolytes highlights the inadequacy of current linear dielectric models for treating properties of the electrochemical interface.

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.

Low Molecular Weight Norbornadiene Derivatives for Molecular Solar-Thermal Energy Storage.

Molecular solar-thermal energy storage systems are based on molecular switches that reversibly convert solar energy into chemical energy. Herein, we report the synthesis, characterization, and computational evaluation of a series of low molecular weight (193-260 g mol(-1) ) norbornadiene-quadricyclane systems. The molecules feature cyano acceptor and ethynyl-substituted aromatic donor groups, leading to a good match with solar irradiation, quantitative photo-thermal conversion between the norbornadiene and quadricyclane, as well as high energy storage densities (396-629 kJ kg(-1) ). The spectroscopic properties and energy storage capability have been further evaluated through density functional theory calculations, which indicate that the ethynyl moiety plays a critical role in obtaining the high oscillator strengths seen for these molecules.

Optimization of Norbornadiene Compounds for Solar Thermal Storage by First-Principles Calculations.

Molecular photoswitches capable of storing solar energy are interesting candidates for future renewable energy applications. Here, using quantum mechanical calculations, we carry out a systematic screening of crucial optical (solar spectrum match) and thermal (storage energy density) properties of 64 such compounds based on the norbornadiene-quadricyclane system. Whereas a substantial number of these molecules reach the theoretical maximum solar power conversion efficiency, this requires a strong red-shift of the absorption spectrum, which causes undesirable absorption by the photoisomer as well as reduced thermal stability. These compounds typically also have a large molecular mass, leading to low storage densities. By contrast, single-substituted systems achieve a good compromise between efficiency and storage density, while avoiding competing absorption by the photo-isomer. This establishes guiding principles for the future development of molecular solar thermal storage systems.

Comparative Ab-Initio Study of Substituted Norbornadiene-Quadricyclane Compounds for Solar Thermal Storage.

Molecular photoswitches that are capable of storing solar energy, so-called molecular solar thermal storage systems, are interesting candidates for future renewable energy applications. In this context, substituted norbornadiene-quadricyclane systems have received renewed interest due to recent advances in their synthesis. The optical, thermodynamic, and kinetic properties of these systems can vary dramatically depending on the chosen substituents. The molecular design of optimal compounds therefore requires a detailed understanding of the effect of individual substituents as well as their interplay. Here, we model absorption spectra, potential energy storage, and thermal barriers for back-conversion of several substituted systems using both single-reference (density functional theory using PBE, B3LYP, CAM-B3LYP, M06, M06-2x, and M06-L functionals as well as MP2 calculations) and multireference methods (complete active space techniques). Already the diaryl substituted compound displays a strong red-shift compared to the unsubstituted system, which is shown to result from the extension of the conjugated π-system upon substitution. Using specific donor/acceptor groups gives rise to a further albeit relatively smaller red-shift. The calculated storage energy is found to be rather insensitive to the specific substituents, although solvent effects are likely to be important and require further study. The barrier for thermal back-conversion exhibits strong multireference character and as a result is noticeably correlated with the red-shift. Two possible reaction paths for the thermal back-conversion of diaryl substituted quadricyclane are identified and it is shown that among the compounds considered the path via the acceptor side is systematically favored. Finally, the present study establishes the basis for high-throughput screening of norbornadiene-quadricyclane compounds as it provides guidelines for the level of accuracy that can be expected for key properties from several different techniques.

van der Waals interactions are critical in Car-Parrinello molecular dynamics simulations of porphyrin-fullerene dyads.

The interplay between electrostatic and van der Waals (vdW) interactions in porphyrin-C60 dyads is still under debate despite its importance in influencing the structural characteristics of such complexes considered for various applications in molecular photovoltaics. In this article, we sample the conformational space of a porphyrin-C60 dyad using Car-Parrinello molecular dynamics simulations with and without empirical vdW corrections. Long-range vdW interactions, which are poorly described by the commonly used density functional theory functionals, prove to be essential for a proper dynamics of the dyad moieties. Inclusion of vdW corrections brings porphyrin and C60 close together in an orientation that is in agreement with experimental observations. The structural differences arising from the vdW corrections are shown to be significant for several properties and potentially less important for others. Additionally, our Mulliken population analysis reveals that contrary to the common belief, porphyrin is not the primary electron donating moiety for C60 . In the considered dyad, fullerene's affinity for electrons is primarily satisfied by charge transfer from the amide group of the linker. However, we show that in the absence of another suitable bound donor, C60 can withdraw electrons from porphyrin if it is sufficiently close.

Porphyrin adsorbed on the (101[combining macron]0) surface of the wurtzite structure of ZnO--conformation induced effects on the electron transfer characteristics.

Electron transfer at the adsorbate-surface interface is crucial in many applications but the steps taking place prior to and during the electron transfer are not always thoroughly understood. In this work a model system of 4-(porphyrin-5-yl)benzoic acid adsorbed as a corresponding benzoate on the ZnO wurtzite (101[combining macron]0) surface is studied using density functional theory (DFT) and time-dependent DFT. Emphasis is on the initial photoexcitation of porphyrin and on the strength of coupling between the porphyrin LUMO or LUMO + 1 and the ZnO conduction band that plays a role in the electron transfer. Firstly, ZnO wurtzite bulk is optimized to minimum energy geometry and the properties of the isolated ZnO (101[combining macron]0) surface model and the porphyrin model are discussed to gain insight into the combined system. Secondly, various orientations of the model porphyrin on the ZnO surface are studied: the porphyrin model standing perpendicularly to the surface and gradually brought close to the surface by tilting the linker in a few steps. The porphyrin model approaches the surface either sideways with hydrogen atoms of the porphyrin ring coming down first or twisted in a ca. 45° angle, giving rise to π-interactions of the porphyrin ring with ZnO. Because porphyrins are closely packed and near the surface, emerging van der Waals (vdW) interactions are examined using Grimme's D2 method. While the orientation affects the initial excitation of porphyrin only slightly, the coupling between the LUMO and LUMO + 1 of porphyrin and the conduction band of ZnO increases considerably if porphyrin is close to the surface, especially if the π-electrons are interacting with the surface. Based on the results of coupling studies, not only the distance between porphyrin and the ZnO surface but also the orientation of porphyrin can greatly affect the electron transfer.