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.

Sequential Selective Dissolution of Coinage Metals in Recyclable Ionic Media.

Coinage metals Cu, Ag, and Au are essential for modern electronics and their recycling from waste materials is becoming increasingly important to guarantee the security of their supply. Designing new sustainable and selective procedures that would substitute currently used processes is crucial. Here, we describe an unprecedented approach for the sequential dissolution of single metals from Cu, Ag, and Au mixtures using biomass-derived ionic solvents and green oxidants. First, Cu can be selectively dissolved in the presence of Ag and Au with a choline chloride/urea/H2O2 mixture, followed by the dissolution of Ag in lactic acid/H2O2. Finally, the metallic Au, which is not soluble in either solution above, is dissolved in choline chloride/urea/Oxone. Subsequently, the metals were simply and quantitatively recovered from dissolutions, and the solvents were recycled and reused. The applicability of the developed approach was demonstrated by recovering metals from electronic waste substrates such as printed circuit boards, gold fingers, and solar panels. The dissolution reactions and selectivity were explored with different analytical techniques and DFT calculations. We anticipate our approach will pave a new way for the contemporary and sustainable recycling of multi-metal waste substrates.

Approximating constant potential DFT with canonical DFT and electrostatic corrections.

The complexity of electrochemical interfaces has led to the development of several approximate density functional theory (DFT)-based schemes to study reaction thermodynamics and kinetics as a function of electrode potential. While fixed electrode potential conditions can be simulated with grand canonical ensemble DFT (GCE-DFT), various electrostatic corrections on canonical, constant charge DFT are often applied instead. In this work, we present a systematic derivation and analysis of the different electrostatic corrections on canonical DFT to understand their physical validity, implicit assumptions, and scope of applicability. Our work highlights the need to carefully address the suitability of a given model for the problem under study, especially if physical or chemical insight in addition to reaction energetics is sought. In particular, we analytically show that the different corrections cannot differentiate between electrostatic interactions and covalent or charge-transfer interactions. By numerically testing different models for CO2 adsorption on a single-atom catalyst as a function of the electrode potential, we further show that computed capacitances, dipole moments, and the obtained physical insight depend sensitively on the chosen approximation. These features limit the scope, generality, and physical insight of these corrective schemes despite their proven practicality for specific systems and energetics. Finally, we suggest guidelines for choosing different electrostatic corrections and propose the use of conceptual DFT to develop more general approximations for electrochemical interfaces and reactions using canonical DFT.

Cations Determine the Mechanism and Selectivity of Alkaline Oxygen Reduction Reaction on Pt(111).

The proton-coupled electron transfer (PCET) mechanism of the oxygen reduction reaction (ORR) is a long-standing enigma in electrocatalysis. Despite decades of research, the factors determining the microscopic mechanism of ORR-PCET as a function of pH, electrolyte, and electrode potential remain unresolved, even on the prototypical Pt(111) surface. Herein, we integrate advanced experiments, simulations, and theory to uncover the mechanism of the cation effects on alkaline ORR on well-defined Pt(111). We unveil a dual-cation effect where cations simultaneously determine i) the active electrode surface by controlling the formation of Pt-O and Pt-OH overlayers and ii) the competition between inner- and outer-sphere PCET steps. The cation-dependent transition from Pt-O to Pt-OH determines the ORR mechanism, activity, and selectivity. These findings provide direct evidence that the electrolyte affects the ORR mechanism and performance, with important consequences for the practical design of electrochemical systems and computational catalyst screening studies. Our work highlights the importance of complementary insight from experiments and simulations to understand how different components of the electrochemical interface contribute to electrocatalytic processes.

Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid-liquid interfaces.

Multi-electron, multi-proton transfer is important in a wide spectrum of processes spanning biological, chemical and physical systems. These reactions have attracted significant interest due to both fundamental curiosity and potential applications in energy technology. In this Perspective Review, we shed light on modern aspects of electrode processes in the 21st century, in particular on the recent advances and challenges in multistep electron/proton transfers at solid-liquid interfaces. Ongoing developments of analytical techniques and operando spectrometry at electrode/electrolyte interfaces and reliable computational approaches to simulate complicated interfacial electrochemical reactions enable us to obtain microscopic insights about these complex processes, such as the role of quantum effects in electrochemical reactions. Our motivation in this Perspective Review is to provide a comprehensive survey and discussion of state-of-the-art developments in experiments, materials, and theories for modern electrode process science, as well as to present an outlook for the future directions in this field.

Escaping scaling relationships for water dissociation at interfacial sites of zirconia-supported Rh and Pt clusters.

Water dissociation is an important reaction involved in many industrial processes. In this computational study, the dissociation of water is used as a model reaction for probing the activity of interfacial sites of globally optimized ZrO2 supported Pt and Rh clusters under the framework of density functional theory. Our findings demonstrate that the perimeter sites of these small clusters can activate water, but the dissociation behavior varies considerably between sites. It is shown that the studied clusters break scaling relationships for water dissociation, suggesting that these catalysts may achieve activities beyond the maximum imposed by such relations. Furthermore, we observed large differences in the thermodynamics of the water dissociation reaction between global minimum and near-global minimum isomers of the clusters. Overall, our results highlight the uniqueness of interfacial sites in catalytic reactions and the need for developing new concepts and tools to deal with the associated complexity.

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.

Cation-induced changes in the inner- and outer-sphere mechanisms of electrocatalytic CO2 reduction.

The underlying mechanism of cation effects on CO2RR remains debated. Herein, we study cation effects by simulating both outer-sphere electron transfer (OS-ET) and inner-sphere electron transfer (IS-ET) pathways during CO2RR via constrained density functional theory molecular dynamics (cDFT-MD) and slow-growth DFT-MD (SG-DFT-MD), respectively. Our results show without any cations, only OS-ET is feasible with a barrier of 1.21 eV. In the presence of K+ (Li+), OS-ET shows a very high barrier of 2.93 eV (4.15 eV) thus being prohibited. However, cations promote CO2 activation through IS-ET with the barrier of only 0.61 eV (K+) and 0.91 eV (Li+), generating the key intermediate (adsorbed CO[Formula: see text]). Without cations, CO2-to-CO[Formula: see text](ads) conversion cannot proceed. Our findings reveal cation effects arise from short-range Coulomb interactions with reaction intermediates. These results disclose that cations modulate the inner- and outer-sphere pathways of CO2RR, offering substantial insights on the cation specificity in the initial CO2RR steps.

Addressing Dynamics at Catalytic Heterogeneous Interfaces with DFT-MD: Anomalous Temperature Distributions from Commonly Used Thermostats.

Density functional theory-based molecular dynamics (DFT-MD) has been widely used for studying the chemistry of heterogeneous interfacial systems under operational conditions. We report frequently overlooked errors in thermostated or constant-temperature DFT-MD simulations applied to study (electro)catalytic chemistry. Our results demonstrate that commonly used thermostats such as Nosé-Hoover, Berendsen, and simple velocity-rescaling methods fail to provide a reliable temperature description for systems considered. Instead, nonconstant temperatures and large temperature gradients within the different parts of the system are observed. The errors are not a "feature" of any particular code but are present in several ab initio molecular dynamics implementations. This uneven temperature distribution, due to inadequate thermostatting, is well-known in the classical MD community, where it is ascribed to the failure in kinetic energy equipartition among different degrees of freedom in heterogeneous systems (Harvey et al. J. Comput. Chem. 1998, 726-740) and termed the flying ice cube effect. We provide tantamount evidence that interfacial systems are susceptible to substantial flying ice cube effects and demonstrate that the traditional Nosé-Hoover and Berendsen thermostats should be applied with care when simulating, for example, catalytic properties or structures of solvated interfaces and supported clusters. We conclude that the flying ice cube effect in these systems can be conveniently avoided using Langevin dynamics.

Adiabatic versus non-adiabatic electron transfer at 2D electrode materials.

2D electrode materials are often deployed on conductive supports for electrochemistry and there is a great need to understand fundamental electrochemical processes in this electrode configuration. Here, an integrated experimental-theoretical approach is used to resolve the key electronic interactions in outer-sphere electron transfer (OS-ET), a cornerstone elementary electrochemical reaction, at graphene as-grown on a copper electrode. Using scanning electrochemical cell microscopy, and co-located structural microscopy, the classical hexaamineruthenium (III/II) couple shows the ET kinetics trend: monolayer > bilayer > multilayer graphene. This trend is rationalized quantitatively through the development of rate theory, using the Schmickler-Newns-Anderson model Hamiltonian for ET, with the explicit incorporation of electrostatic interactions in the double layer, and parameterized using constant potential density functional theory calculations. The ET mechanism is predominantly adiabatic; the addition of subsequent graphene layers increases the contact potential, producing an increase in the effective barrier to ET at the electrode/electrolyte interface.