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Accurate description of nonadiabatic dynamics of molecules at metal surfaces involving electron transfer has been a long-standing challenge for theory. Here, we tackle this problem by first constructing high-dimensional neural network diabatic potentials including state crossings determined by constrained density functional theory, then applying mixed quantum-classical surface hopping simulations to evolve coupled electron-nuclear motion. Our approach accurately describes the nonadiabatic effects in CO scattering from Au(111) without empirical parameters and yields results agreeing well with experiments under various conditions for this benchmark system. We find that both adiabatic and nonadiabatic energy loss channels have important contributions to the vibrational relaxation of highly vibrationally excited CO(v_{i}=17), whereas relaxation of low vibrationally excited states of CO(v_{i}=2) is weak and dominated by nonadiabatic energy loss. The presented approach paves the way for accurate first-principles simulations of electron transfer mediated nonadiabatic dynamics at metal surfaces.

Modern software engineering of electronic structure codes has seen a paradigm shift from monolithic workflows toward object-based modularity. Software objectivity allows for greater flexibility in the application of electronic structure calculations, with particular benefits when integrated with approaches for data-driven analysis. Here, we discuss different approaches to create deep modular interfaces that connect big-data workflows and electronic structure codes and explore the diversity of use cases that they can enable. We present two such interface approaches for the semi-empirical electronic structure package, DFTB+. In one case, DFTB+ is applied as a library and provides data to an external workflow; in another, DFTB+receives data via external bindings and processes the information subsequently within an internal workflow. We provide a general framework to enable data exchange workflows for embedding new machine-learning-based Hamiltonians within DFTB+ or enabling deep integration of DFTB+ in multiscale embedding workflows. These modular interfaces demonstrate opportunities in emergent software and workflows to accelerate scientific discovery by harnessing existing software capabilities., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

Predicting the degradation processes of molecules over long time scales is a key aspect of industrial materials design. However, it is made computationally challenging by the need to construct large networks of chemical reactions that are relevant to the experimental conditions that kinetic models must mirror, with every reaction requiring accurate kinetic data. Here, we showcase Kinetica.jl , a new software package for constructing large-scale chemical reaction networks in a fully automated fashion by exploring chemical reaction space with a kinetics-driven algorithm; coupled to efficient machine-learning models of activation energies for sampled elementary reactions, we show how this approach readily enables generation and kinetic characterization of networks containing ∼10 3 chemical species and ≃10 4 -10 5 reactions. Symbolic-numeric modeling of the generated reaction networks is used to allow for flexible, efficient computation of kinetic profiles under experimentally realizable conditions such as continuously variable temperature regimes, enabling direct connection between bottom-up reaction networks and experimental observations. Highly efficient propagation of long-time-scale kinetic profiles is required for automated reaction network refinement and is enabled here by a new discrete kinetic approximation. The resulting Kinetica.jl simulation package therefore enables automated generation, characterization, and long-time-scale modeling of complex chemical reaction systems. We demonstrate this for hydrocarbon pyrolysis simulated over time scales of seconds, using transient temperature profiles representing those of tubular flow reactor experiments.

We report the quantitative adsorption structure of pristine graphene on Cu(111) determined using the normal incidence x-ray standing wave technique. The experiments constitute an important benchmark reference for the development of density functional theory approximations able to capture long-range dispersion interactions. Electronic structure calculations based on many-body dispersion-inclusive density functional theory are able to accurately predict the absolute measure and variation of adsorption height when the coexistence of multiple moiré superstructures is considered. This provides a structural model consistent with scanning probe microscopy results.

The role of the inorganic substrate termination, within the organic-inorganic interface, has been well studied for systems that contain strong localised bonding. However, how varying the substrate termination affects coordination to delocalised electronic states, like that found in aromatic molecules, is an open question. Azupyrene, a non-alternant polycyclic aromatic hydrocarbon, is known to bind strongly to metal surfaces through its delocalised π orbitals, thus yielding an ideal probe into delocalised surface-adsorbate interactions. Normal incidence X-ray standing wave (NIXSW) measurements and density functional theory calculations are reported for the adsorption of azupyrene on the (111), (110) and (100) surface facets of copper to investigate the dependence of the adsorption structure on the substrate termination. Structural models based on hybrid density functional theory calculations with non-local many-body dispersion yield excellent agreement with the experimental NIXSW results. No statistically significant difference in the azupyrene adsorption height was observed between the (111) and (100) surfaces. On the Cu(110) surface, the molecule was found to adsorb 0.06 ± 0.04 Å closer to the substrate than on the other surface facets. The most energetically favoured adsorption site on each surface, as determined by DFT, is subtly different, but in each case involved a configuration where the aromatic rings were centred above a hollow site, consistent with previous reports for the adsorption of small aromatic molecules on metal surfaces.

The discrete and charge-separated nature of matter - electrons and nuclei - results in local electrostatic fields that are ubiquitous in nanoscale structures and relevant in catalysis, nanoelectronics and quantum nanoscience. Surface-averaging techniques provide only limited experimental access to these potentials, which are determined by the shape, material, and environment of the nanostructure. Here, we image the potential over adatoms, chains, and clusters of Ag and Au atoms assembled on Ag(111) and quantify their surface dipole moments. By focusing on the total charge density, these data establish a benchmark for theory. Our density functional theory calculations show a very good agreement with experiment and allow a deeper analysis of the dipole formation mechanisms, their dependence on fundamental atomic properties and on the shape of the nanostructures. We formulate an intuitive picture of the basic mechanisms behind dipole formation, allowing better design choices for future nanoscale systems such as single-atom catalysts., (© 2024. The Author(s).)

The reactive chemistry of molecular hydrogen at surfaces, notably dissociative sticking and hydrogen evolution, plays a crucial role in energy storage and fuel cells. Theoretical studies can help to decipher underlying mechanisms and reaction design, but studying dynamics at surfaces is computationally challenging due to the complex electronic structure at interfaces and the high sensitivity of dynamics to reaction barriers. In addition, ab initio molecular dynamics, based on density functional theory, is too computationally demanding to accurately predict reactive sticking or desorption probabilities, as it requires averaging over tens of thousands of initial conditions. High-dimensional machine learning-based interatomic potentials are starting to be more commonly used in gas-surface dynamics, yet robust approaches to generate reliable training data and assess how model uncertainty affects the prediction of dynamic observables are not well established. Here, we employ ensemble learning to adaptively generate training data while assessing model performance with full uncertainty quantification (UQ) for reaction probabilities of hydrogen scattering on different copper facets. We use this approach to investigate the performance of two message-passing neural networks, SchNet and PaiNN. Ensemble-based UQ and iterative refinement allow us to expose the shortcomings of the invariant pairwise-distance-based feature representation in the SchNet model for gas-surface dynamics., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

Many-body dispersion (MBD) is a powerful framework to treat van der Waals (vdW) dispersion interactions in density-functional theory and related atomistic modeling methods. Several independent implementations of MBD with varying degree of functionality exist across a number of electronic structure codes, which both limits the current users of those codes and complicates dissemination of new variants of MBD. Here, we develop and document libMBD, a library implementation of MBD that is functionally complete, efficient, easy to integrate with any electronic structure code, and already integrated in FHI-aims, DFTB+, VASP, Q-Chem, CASTEP, and Quantum ESPRESSO. libMBD is written in modern Fortran with bindings to C and Python, uses MPI/ScaLAPACK for parallelization, and implements MBD for both finite and periodic systems, with analytical gradients with respect to all input parameters. The computational cost has asymptotic cubic scaling with system size, and evaluation of gradients only changes the prefactor of the scaling law, with libMBD exhibiting strong scaling up to 256 processor cores. Other MBD properties beyond energy and gradients can be calculated with libMBD, such as the charge-density polarization, first-order Coulomb correction, the dielectric function, or the order-by-order expansion of the energy in the dipole interaction. Calculations on supramolecular complexes with MBD-corrected electronic structure methods and a meta-review of previous applications of MBD demonstrate the broad applicability of the libMBD package to treat vdW interactions., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

Polycrystalline boron-doped diamond (BDD) is widely used as a working electrode material in electrochemistry, and its properties, such as its stability, make it an appealing support material for nanostructures in electrocatalytic applications. Recent experiments have shown that electrodeposition can lead to the creation of stable small nanoclusters and even single gold adatoms on the BDD surfaces. We investigate the adsorption energy and kinetic stability of single gold atoms adsorbed onto an atomistic model of BDD surfaces by using density functional theory. The surface model is constructed using hybrid quantum mechanics/molecular mechanics embedding techniques and is based on an oxygen-terminated diamond (110) surface. We use the hybrid quantum mechanics/molecular mechanics method to assess the ability of different density functional approximations to predict the adsorption structure, energy, and barrier for diffusion on pristine and defective surfaces. We find that surface defects (vacancies and surface dopants) strongly anchor adatoms on vacancy sites. We further investigated the thermal stability of gold adatoms, which reveals high barriers associated with lateral diffusion away from the vacancy site. The result provides an explanation for the high stability of experimentally imaged single gold adatoms on BDD and a starting point to investigate the early stages of nucleation during metal surface deposition., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

Mixed quantum-classical (MQC) methods for simulating the dynamics of molecules at metal surfaces have the potential to accurately and efficiently provide mechanistic insight into reactive processes. Here, we introduce simple two-dimensional models for the scattering of diatomic molecules at metal surfaces based on recently published electronic structure data. We apply several MQC methods to investigate their ability to capture how nonadiabatic effects influence molecule-metal energy transfer during the scattering process. Specifically, we compare molecular dynamics with electronic friction, Ehrenfest dynamics, independent electron surface hopping, and the broadened classical master equation approach. In the case of independent electron surface hopping, we implement a simple decoherence correction approach and assess its impact on vibrationally inelastic scattering. Our results show that simple, low-dimensional models can be used to qualitatively capture experimentally observed vibrational energy transfer and provide insight into the relative performance of different MQC schemes. We observe that all approaches predict similar kinetic energy dependence but return different vibrational energy distributions. Finally, by varying the molecule-metal coupling, we can assess the coupling regime in which some MQC methods become unsuitable., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

Independent electron surface hopping (IESH) is a computational algorithm for simulating the mixed quantum-classical molecular dynamics of adsorbate atoms and molecules interacting with metal surfaces. It is capable of modeling the nonadiabatic effects of electron-hole pair excitations on molecular dynamics. Here, we present a transparent, reliable, and efficient implementation of IESH, demonstrating its ability to predict scattering and desorption probabilities across a variety of systems, ranging from model Hamiltonians to full dimensional atomistic systems. We further show how the algorithm can be modified to account for the application of an external bias potential, comparing its accuracy to results obtained using the hierarchical quantum master equation. Our results show that IESH is a practical method for modeling coupled electron-nuclear dynamics at metal surfaces, especially for highly energetic scattering events.

The design of molecules and materials with tailored properties is challenging, as candidate molecules must satisfy multiple competing requirements that are often difficult to measure or compute. While molecular structures produced through generative deep learning will satisfy these patterns, they often only possess specific target properties by chance and not by design, which makes molecular discovery via this route inefficient. In this work, we predict molecules with (Pareto-)optimal properties by combining a generative deep learning model that predicts three-dimensional conformations of molecules with a supervised deep learning model that takes these as inputs and predicts their electronic structure. Optimization of (multiple) molecular properties is achieved by screening newly generated molecules for desirable electronic properties and reusing hit molecules to retrain the generative model with a bias. The approach is demonstrated to find optimal molecules for organic electronics applications. Our method is generally applicable and eliminates the need for quantum chemical calculations during predictions, making it suitable for high-throughput screening in materials and catalyst design., (© 2023. The Author(s), under exclusive licence to Springer Nature America, Inc.)

The results are presented of a detailed combined experimental and theoretical investigation of the influence of coadsorbed electron-donating alkali atoms and the prototypical electron acceptor molecule 7,7,8,8-tetracyanoquinodimethane (TCNQ) on the Ag(100) surface. Several coadsorption phases were characterized by scanning tunneling microscopy, low-energy electron diffraction, and soft X-ray photoelectron spectroscopy. Quantitative structural data were obtained using normal-incidence X-ray standing wave (NIXSW) measurements and compared with the results of density functional theory (DFT) calculations using several different methods of dispersion correction. Generally, good agreement between theory and experiment was achieved for the quantitative structures, albeit with the prediction of the alkali atom heights being challenging for some methods. The adsorption structures depend sensitively on the interplay of molecule-metal charge transfer and long-range dispersion forces, which are controlled by the composition ratio between alkali atoms and TCNQ. The large difference in atomic size between K and Cs has negligible effects on stability, whereas increasing the ratio of K/TCNQ from 1:4 to 1:1 leads to a weakening of molecule-metal interaction strength in favor of stronger ionic bonds within the two-dimensional alkali-organic network. A strong dependence of the work function on the alkali donor-TCNQ acceptor coadsorption ratio is predicted., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

X-ray photoemission and X-ray absorption spectroscopy are important techniques to characterize chemical bonding at surfaces and are often used to identify the strength and nature of adsorbate-substrate interactions. In this study, we judge the ability of X-ray spectroscopic techniques to identify different regimes of chemical bonding at metal-organic interfaces. To achieve this, we sample different interaction strength regimes in a comprehensive and systematic way by comparing two topological isomers, azulene and naphthalene, adsorbed on three metal substrates with varying reactivity, namely the (111) facets of Ag, Cu, and Pt. Using density functional theory, we simulate core-level binding energies and X-ray absorption spectra of the molecular carbon species. The simulated spectra reveal three distinct characteristics based on the molecule-specific spectral features which we attribute to types of surface chemical bonding with varying strength. We find that weak physisorption only leads to minor changes compared to the gas-phase spectra, weak chemisorption leads to charge transfer and significant spectral changes, and strong chemisorption leads to a loss of the molecule-specific features in the spectra. The classification we provide is aimed at assisting interpretation of experimental X-ray spectra for complex metal-organic interfaces., Competing Interests: The authors declare no competing financial interest., (© 2023 The Authors. Published by American Chemical Society.)

Molecular energy transfer and reactions at solid surfaces depend on the molecular orientation relative to the surface. While such steric effects have been largely understood in electronically adiabatic processes, the orientation-dependent energy transfer in NO scattering from Au(111) was complicated by electron-mediated nonadiabatic effects, thus lacking a clear interpretation and posing a great challenge for theories. Herein, we investigate the stereodynamics of adiabatic and nonadiabatic energy transfer via molecular dynamics simulations of NO( v = 3) scattering from Au(111) using realistic initial orientation distributions based on accurate neural network fitted adiabatic potential energy surface and electronic friction tensor. Our results reproduce the observed stronger vibrational relaxation for N-first orientation and enhanced rotational rainbow for O-first orientation, and demonstrate how adiabatic anisotropic interactions steer molecules into the more attractive N-first orientation to experience more significant energy transfer. Remaining disagreements with experiment suggest the direction for further developments of nonadiabatic theories for gas-surface scattering.

Defects play a critical role for the functionality and performance of materials, but the understanding of the related effects is often lacking, because the typically low concentrations of defects make them difficult to study. A prominent case is the topological defects in two-dimensional materials such as graphene. The performance of graphene-based (opto-)electronic devices depends critically on the properties of the graphene/metal interfaces at the contacting electrodes. The question of how these interface properties depend on the ubiquitous topological defects in graphene is of high practical relevance, but could not be answered so far. Here, we focus on the prototypical Stone-Wales (S-W) topological defect and combine theoretical analysis with experimental investigations of molecular model systems. We show that the embedded defects undergo enhanced bonding and electron transfer with a copper surface, compared to regular graphene. These findings are experimentally corroborated using molecular models, where azupyrene mimics the S-W defect, while its isomer pyrene represents the ideal graphene structure. Experimental interaction energies, electronic-structure analysis, and adsorption distance differences confirm the defect-controlled bonding quantitatively. Our study reveals the important role of defects for the electronic coupling at graphene/metal interfaces and suggests that topological defect engineering can be used for performance control.

The computational prediction of the structure and stability of hybrid organic-inorganic interfaces provides important insights into the measurable properties of electronic thin film devices, coatings, and catalyst surfaces and plays an important role in their rational design. However, the rich diversity of molecular configurations and the important role of long-range interactions in such systems make it difficult to use machine learning (ML) potentials to facilitate structure exploration that otherwise requires computationally expensive electronic structure calculations. We present an ML approach that enables fast, yet accurate, structure optimizations by combining two different types of deep neural networks trained on high-level electronic structure data. The first model is a short-ranged interatomic ML potential trained on local energies and forces, while the second is an ML model of effective atomic volumes derived from atoms-in-molecules partitioning. The latter can be used to connect short-range potentials to well-established density-dependent long-range dispersion correction methods. For two systems, specifically gold nanoclusters on diamond (110) surfaces and organic π-conjugated molecules on silver (111) surfaces, we train models on sparse structure relaxation data from density functional theory and show the ability of the models to deliver highly efficient structure optimizations and semi-quantitative energy predictions of adsorption structures., Competing Interests: There is no conflict of interest to declare., (This journal is © The Royal Society of Chemistry.)

Reactions involving adsorbates on metallic surfaces and impurities in bulk metals are ubiquitous in a wide range of technological applications. The theoretical modeling of such reactions presents a formidable challenge for theory because nuclear quantum effects (NQEs) can play a prominent role and the coupling of the atomic motion with the electrons in the metal gives rise to important non-adiabatic effects (NAEs) that alter atomic dynamics. In this work, we derive a theoretical framework that captures both NQEs and NAEs and, due to its high efficiency, can be applied to first-principles calculations of reaction rates in high-dimensional realistic systems. More specifically, we develop a method that we coin ring polymer instanton with explicit friction (RPI-EF), starting from the ring polymer instanton formalism applied to a system-bath model. We derive general equations that incorporate the spatial and frequency dependence of the friction tensor and then combine this method with the ab initio electronic friction formalism for the calculation of thermal reaction rates. We show that the connection between RPI-EF and the form of the electronic friction tensor presented in this work does not require any further approximations, and it is expected to be valid as long as the approximations of both underlying theories remain valid.

In Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], we presented the ring-polymer instanton with explicit friction (RPI-EF) method and showed how it can be connected to the ab initio electronic friction formalism. This framework allows for the calculation of tunneling reaction rates that incorporate the quantum nature of the nuclei and certain types of non-adiabatic effects (NAEs) present in metals. In this paper, we analyze the performance of RPI-EF on model potentials and apply it to realistic systems. For a 1D double-well model, we benchmark the method against numerically exact results obtained from multi-layer multi-configuration time-dependent Hartree calculations. We demonstrate that RPI-EF is accurate for medium and high friction strengths and less accurate for extremely low friction values. We also show quantitatively how the inclusion of NAEs lowers the crossover temperature into the deep tunneling regime, reduces the tunneling rates, and, in certain regimes, steers the quantum dynamics by modifying the tunneling pathways. As a showcase of the efficiency of this method, we present a study of hydrogen and deuterium hopping between neighboring interstitial sites in selected bulk metals. The results show that multidimensional vibrational coupling and nuclear quantum effects have a larger impact than NAEs on the tunneling rates of diffusion in metals. Together with Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], these results advance the calculations of dissipative tunneling rates from first principles.

Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in the condensed phase. To facilitate effective development, code sharing, and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon. Using the Julia programming language, we have developed the NQCDynamics.jl package, which provides a framework for established and emerging methods for performing semiclassical and mixed quantum-classical dynamics in the condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods, which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit. We further demonstrate the capabilities of the package on two examples of chemical dynamics in the condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semiclassical and mixed quantum-classical nonadiabatic methods and the reactive scattering of H 2 on Ag(111) using the molecular dynamics with electronic friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems.

While the phenomenon of metal substrate adatom incorporation into molecular overlayers is generally believed to occur in several systems, the experimental evidence for this relies on the interpretation of scanning tunneling microscopy (STM) images, which can be ambiguous and provides no quantitative structural information. We show that surface X-ray diffraction (SXRD) uniquely provides unambiguous identification of these metal adatoms. We present the results of a detailed structural study of the Au(111)-F 4 TCNQ system, combining surface characterization by STM, low-energy electron diffraction, and soft X-ray photoelectron spectroscopy with quantitative experimental structural information from normal incidence X-ray standing wave (NIXSW) and SXRD, together with dispersion-corrected density functional theory (DFT) calculations. Excellent agreement is found between the NIXSW data and the DFT calculations regarding the height and conformation of the adsorbed molecule, which has a twisted geometry rather than the previously supposed inverted bowl shape. SXRD measurements provide unequivocal evidence for the presence and location of Au adatoms, while the DFT calculations show this reconstruction to be strongly energetically favored., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

Molecular nanofabrication with a scanning probe microscope (SPM) is a promising route toward the prototyping of metastable functional molecular structures and devices which do not form spontaneously. The aspect of mechanical stability is crucial for such structures, especially if they extend into the third dimension vertical to the surface. A prominent example is freestanding molecules fabricated on a metal which can function as field emitters or electric field sensors. Improving the stability of such molecular configurations is an optimization task involving many degrees of freedom and therefore best tackled by computational nanostructure design. Here, we use density functional theory to study 3,4,9,10-perylene-tetracarboxylic dianhydride (PTCDA) standing on the Ag(111) surface as well as on the tip of a scanning probe microscope. We cast our results into a simple set of design principles for such metastable structures, the validity of which we subsequently demonstrate in two computational case studies. Our work proves the capabilities of computational nanostructure design in the field of metastable molecular structures and offers the intuition needed to fabricate new devices without tedious trial and error., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)

A quantitative structural investigation is reported, aimed at resolving the issue of whether substrate adatoms are incorporated into the monolayers formed by strong molecular electron acceptors deposited onto metallic electrodes. A combination of normal-incidence X-ray standing waves, low-energy electron diffraction, scanning tunnelling microscopy, and X-ray photoelectron spectroscopy measurements demonstrate that the systems TCNQ and F 4 TCNQ on Ag(100) lie at the boundary between these two possibilities and thus represent ideal model systems with which to study this effect. A room-temperature commensurate phase of adsorbed TCNQ is found not to involve Ag adatoms, but to adopt an inverted bowl configuration, long predicted but not previously identified experimentally. By contrast, a similar phase of adsorbed F 4 TCNQ does lead to Ag adatom incorporation in the overlayer, the cyano end groups of the molecule being twisted relative to the planar quinoid ring. Density functional theory (DFT) calculations show that this behavior is consistent with the adsorption energetics. Annealing of the commensurate TCNQ overlayer phase leads to an incommensurate phase that does appear to incorporate Ag adatoms. Our results indicate that the inclusion (or exclusion) of metal atoms into the organic monolayers is the result of both thermodynamic and kinetic factors., Competing Interests: The authors declare no competing financial interest., (© 2022 American Chemical Society.)

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., (© 2021. The Author(s).)

The part-by-part assembly of functional nanoscale machinery is a central goal of nanotechnology. With the recent fabrication of an isolated standing molecule with a scanning probe microscope, the third dimension perpendicular to the surface will soon become accessible to molecule-based construction. Beyond the flatlands of the surface, a wealth of structures and functionalities is waiting for exploration, but issues of stability are becoming more critical. Here, we combine scanning probe experiments with ab initio potential energy calculations to investigate the thermal stability of a prototypical standing molecule. We reveal its generic stabilization mechanism, a fine balance between covalent and van der Waals interactions including the latter’s long-range screening by many-body effects, and find a remarkable agreement between measured and calculated stabilizing potentials. Beyond their relevance for the design and construction of three-dimensional molecular devices at surfaces, our results also indicate that standing molecules may serve as tunable mechanical gigahertz oscillators.

Theoretical calculations of core electron binding energies are required for the interpretation of experimental X-ray photoelectron spectra, but achieving accurate results for solids has proven difficult. In this work, we demonstrate that accurate absolute core electron binding energies in both metallic and insulating solids can be obtained from periodic all-electron Δ-self-consistent-field (ΔSCF) calculations. In particular, we show that core electron binding energies referenced to the valence band maximum can be obtained as total energy differences between two ( N - 1)-electron systems: one with a core hole and one with an electron removed from the highest occupied valence state. To achieve convergence with respect to the supercell size, the analogy between localized core holes and charged defects is exploited. Excellent agreement between calculated and experimental core electron binding energies is found for both metals and insulators, with a mean absolute error of 0.24 eV for the systems considered.

Light-driven plasmonic enhancement of chemical reactions on metal catalysts is a promising strategy to achieve highly selective and efficient chemical transformations. The study of plasmonic catalyst materials has traditionally focused on late transition metals such as Au, Ag, and Cu. In recent years, there has been increasing interest in the plasmonic properties of a set of earth-abundant elements such as Mg, which exhibit interesting hydrogenation chemistry with potential applications in hydrogen storage. This work explores the optical, electronic, and catalytic properties of a set of metallic Mg nanoclusters with up to 2057 atoms using time-dependent density functional tight-binding and density functional theory calculations. Our results show that Mg nanoclusters are able to produce highly energetic hot electrons with energies of up to 4 eV. By electronic structure analysis, we find that these hot electrons energetically align with electronic states of physisorbed molecular hydrogen, occupation of which by hot electrons can promote the hydrogen dissociation reaction. We also find that the reverse reaction, hydrogen evolution on metallic Mg, can potentially be promoted by hot electrons, but following a different mechanism. Thus, from a theoretical perspective, Mg nanoclusters display very promising behaviour for their use in light promoted storage and release of hydrogen.

Modern functional materials consist of large molecular building blocks with significant chemical complexity which limits spectroscopic property prediction with accurate first-principles methods. Consequently, a targeted design of materials with tailored optoelectronic properties by high-throughput screening is bound to fail without efficient methods to predict molecular excited-state properties across chemical space. In this work, we present a deep neural network that predicts charged quasiparticle excitations for large and complex organic molecules with a rich elemental diversity and a size well out of reach of accurate many body perturbation theory calculations. The model exploits the fundamental underlying physics of molecular resonances as eigenvalues of a latent Hamiltonian matrix and is thus able to accurately describe multiple resonances simultaneously. The performance of this model is demonstrated for a range of organic molecules across chemical composition space and configuration space. We further showcase the model capabilities by predicting photoemission spectra at the level of the GW approximation for previously unseen conjugated molecules., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

Pyrene derivatives play a prominent role in organic electronic devices, including field effect transistors, light emitting diodes, and solar cells. The flexibility in the desired properties has previously been achieved by variation of substituents at the periphery of the pyrene backbone. In contrast, the influence of the topology of the central π-electron system on the relevant properties such as the band gap or the fluorescence behavior has not yet been addressed. In this work, pyrene is compared with its structural isomer azupyrene, which has a π-electron system with non-alternant topology. Using photoelectron spectroscopy, near edge X-ray absorption fine structure spectroscopy, and other methods, it is shown that the electronic band gap of azupyrene is by 0.72 eV smaller than that of pyrene. The difference of the optical band gaps is even larger with 1.09 eV, as determined by ultraviolet-visible absorption spectroscopy. The non-alternant nature of azupyrene is also associated with a more localized charge distribution. Further insight is provided by density functional theory (DFT) calculations of the molecular properties and ab initio coupled cluster calculations of the optical transitions. The concept of aromaticity is used to interpret the major topology-related differences., (© 2021 The Authors. ChemPhysChem published by Wiley-VCH GmbH.)

The computational characterization of inorganic-organic hybrid interfaces is arguably one of the technically most challenging applications of density functional theory. Due to the fundamentally different electronic properties of the inorganic and the organic components of a hybrid interface, the proper choice of the electronic structure method, of the algorithms to solve these methods, and of the parameters that enter these algorithms is highly non-trivial. In fact, computational choices that work well for one of the components often perform poorly for the other. As a consequence, default settings for one materials class are typically inadequate for the hybrid system, which makes calculations employing such settings inefficient and sometimes even prone to erroneous results. To address this issue, we discuss how to choose appropriate atomistic representations for the system under investigation, we highlight the role of the exchange-correlation functional and the van der Waals correction employed in the calculation and we provide tips and tricks how to efficiently converge the self-consistent field cycle and to obtain accurate geometries. We particularly focus on potentially unexpected pitfalls and the errors they incur. As a summary, we provide a list of best practice rules for interface simulations that should especially serve as a useful starting point for less experienced users and newcomers to the field.

X-ray photoemission (XPS) and near edge x-ray absorption fine structure (NEXAFS) spectroscopy play an important role in investigating the structure and electronic structure of materials and surfaces. Ab initio simulations provide crucial support for the interpretation of complex spectra containing overlapping signatures. Approximate core-hole simulation methods based on density functional theory (DFT) such as the delta-self-consistent-field (ΔSCF) method or the transition potential (TP) method are widely used to predict K -shell XPS and NEXAFS signatures of organic molecules, inorganic materials and metal-organic interfaces at reliable accuracy and affordable computational cost. We present the numerical and technical details of our variants of the ΔSCF and TP method (coined ΔIP-TP) to simulate XPS and NEXAFS transitions. Using exemplary molecules in gas-phase, in bulk crystals, and at metal-organic interfaces, we systematically assess how practical simulation choices affect the stability and accuracy of simulations. These include the choice of exchange-correlation functional, basis set, the method of core-hole localization, and the use of periodic boundary conditions (PBC). We particularly focus on the choice of aperiodic or periodic description of systems and how spurious charge effects in periodic calculations affect the simulation outcomes. For the benefit of practitioners in the field, we discuss sensible default choices, limitations of the methods, and future prospects., (Creative Commons Attribution license.)

Nonadiabatic effects that arise from the concerted motion of electrons and atoms at comparable energy and time scales are omnipresent in thermal and light-driven chemistry at metal surfaces. Excited (hot) electrons can measurably affect molecule-metal reactions by contributing to state-dependent reaction probabilities. Vibrational state-to-state scattering of NO on Au(111) has been one of the most studied examples in this regard, providing a testing ground for developing various nonadiabatic theories. This system is often cited as the prime example for the failure of electronic friction theory, a very efficient model accounting for dissipative forces on metal-adsorbed molecules due to the creation of hot electrons in the metal. However, the exact failings compared to experiment and their origin from theory are not established for any system because dynamic properties are affected by many compounding simulation errors of which the quality of nonadiabatic treatment is just one. We use a high-dimensional machine learning representation of electronic structure theory to minimize errors that arise from quantum chemistry. This allows us to perform a comprehensive quantitative analysis of the performance of nonadiabatic molecular dynamics in describing vibrational state-to-state scattering of NO on Au(111) and compare directly to adiabatic results. We find that electronic friction theory accurately predicts elastic and single-quantum energy loss but underestimates multiquantum energy loss and overestimates molecular trapping at high vibrational excitation. Our analysis reveals that multiquantum energy loss can potentially be remedied within friction theory whereas the overestimation of trapping constitutes a genuine breakdown of electronic friction theory. Addressing this overestimation for dynamic processes in catalysis and surface chemistry will likely require more sophisticated theories., Competing Interests: The authors declare no competing financial interest., (© 2020 The Authors. Published by American Chemical Society.)

The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts to answer this question have, among other methods, given rise to semi-empirical quantum chemistry in minimal basis representation. We present an adaptation of the recently proposed SchNet for Orbitals (SchNOrb) deep convolutional neural network model [K. T. Schütt et al., Nat. Commun. 10, 5024 (2019)] for electronic wave functions in an optimized quasi-atomic minimal basis representation. For five organic molecules ranging from 5 to 13 heavy atoms, the model accurately predicts molecular orbital energies and wave functions and provides access to derived properties for chemical bonding analysis. Particularly for larger molecules, the model outperforms the original atomic-orbital-based SchNOrb method in terms of accuracy and scaling. We conclude by discussing the future potential of this approach in quantum chemical workflows.

Efficient charge transfer across metal-organic interfaces is a key physical process in modern organic electronics devices, and characterization of the energy level alignment at the interface is crucial to enable a rational device design. We show that the insertion of alkali atoms can significantly change the structure and electronic properties of a metal-organic interface. Coadsorption of tetracyanoquinodimethane (TCNQ) and potassium on a Ag(111) surface leads to the formation of a two-dimensional charge transfer salt, with properties quite different from those of the two-dimensional Ag adatom TCNQ metal-organic framework formed in the absence of K doping. We establish a highly accurate structural model by combination of quantitative X-ray standing wave measurements, scanning tunnelling microscopy, and density-functional theory (DFT) calculations. Full agreement between the experimental data and the computational prediction of the structure is only achieved by inclusion of a charge-transfer-scaled dispersion correction in the DFT, which correctly accounts for the effects of strong charge transfer on the atomic polarizability of potassium. The commensurate surface layer formed by TCNQ and K is dominated by strong charge transfer and ionic bonding and is accompanied by a structural and electronic decoupling from the underlying metal substrate. The consequence is a significant change in energy level alignment and work function compared to TCNQ on Ag(111). Possible implications of charge-transfer salt formation at metal-organic interfaces for organic thin-film devices are discussed.

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule, which limits their applicability for reactive chemistry and chemical analysis. Here we present a deep learning framework for the prediction of the quantum mechanical wavefunction in a local basis of atomic orbitals from which all other ground-state properties can be derived. This approach retains full access to the electronic structure via the wavefunction at force-field-like efficiency and captures quantum mechanics in an analytically differentiable representation. On several examples, we demonstrate that this opens promising avenues to perform inverse design of molecular structures for targeting electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry.

Low-lying electronic excitations in metals, so-called hot electrons, efficiently mediate molecule-metal energy transfer and contribute to energy loss during molecular reactions at surfaces. They furthermore play an important role in plasmon-driven chemistry. Electronic friction represents a simple and effective concept to model hot electron-induced energy loss under ambient conditions. Different methods exist that vary in their description of magnitude, coordinate and directional dependence of friction during reactive molecular scattering at metal surfaces. Using molecular dynamics simulations with electronic friction, we systematically study the effect of hot electrons on measurable state-to-state scattering probabilities of molecular hydrogen from a (111) surface of silver. We assess the ability of ab initio electronic friction methods to accurately describe hot electron-mediated energy loss as a function of initial reaction conditions and electronic temperature. We furthermore find that dynamic scattering results and the ensuing energy loss are highly sensitive to the magnitude of electronic friction. Therefore, existing approximate models of electronic friction, which exhibit inherent uncertainties with respect to the magnitude of electronic friction, may not be applicable for a quantitative prediction of plasmon driven hot electron effects in their current state. We outline a development direction to potentially overcome these limitations.

The local structure of the nonplanar phthalocyanine, vanadyl phthalocyanine (VOPc), adsorbed on Cu(111) at a coverage of approximately one-half of a saturated molecular layer, has been investigated by a combination of normal-incidence X-ray standing waves (NIXSW), scanned-energy mode photoelectron diffraction (PhD), and density-functional theory (DFT), complemented by scanning tunnelling microscopy (STM). Qualitative assessment of the NIXSW data clearly shows that both "up" and "down" orientations of the molecule (with V=O pointing out of, and into, the surface) must coexist on the surface. O 1s PhD proves to be inconclusive regarding the molecular orientation. DFT calculations, using two different dispersion correction schemes, show good quantitative agreement with the NIXSW structural results for equal co-occupation of the two different molecular orientations and clearly favor the many body dispersion (MBD) method to deal with long-range dispersion forces. The calculated relative adsorption energies of the differently oriented molecules at the lowest coverage show a strong preference for the "up" orientation, but at higher local coverages, this energetic difference decreases, and mixed orientation phases are almost energetically equivalent to pure "up"-oriented phases. DFT-based Tersoff-Hamann simulations of STM topographs for the two orientations cast some light on the extent to which such images provide a reliable guide to molecular orientation., Competing Interests: The authors declare no competing financial interest.

The ability of the different approaches proposed to date to include the effects of van der Waals (vdW) dispersion forces in density functional theory (DFT) is currently under debate. Here, we used the diffraction of He on a Ru(0 0 0 1) surface as a challenging benchmark system to analyze the suitability of several representative approaches, from the ones correcting the exchange-correlation generalized gradient approximation (GGA) functional, to the ones correcting the DFT energies through pairwise-based methods. To perform our analysis, we have built seven continuous potential energy surfaces (PESs) and carried out quantum dynamics simulations using a multi-configuration time-dependent Hartree method. Our analysis reveals that standard DFT within the PBE-GGA framework, although it overestimates diffraction probabilities, yields the best results in comparison with available experimental measurements. On the other hand, although several of the existing vdW DFT approaches yield physisorption wells in very good agreement with experiment, they all seem to overestimate the long-distance corrugation of the PES, the region probed by He scattering, resulting in a large overestimation of diffraction probabilities.

In molecular nanotechnology, a single molecule is envisioned to act as the basic building block of electronic devices. Such devices may be of special interest for organic photovoltaics, data storage, and smart materials. However, more often than not the molecular function is quenched upon contact with a conducting support. Trial-and-error-based decoupling strategies via molecular functionalisation and change of substrate have in many instances proven to yield unpredictable results. The adsorbate-substrate interactions that govern the function can be understood with the help of first-principles simulation. Employing dispersion-corrected density-functional theory (DFT) and linear expansion delta-self-consistent-field DFT, the electronic structure of a prototypical surface-adsorbed functional molecule, namely azobenzene adsorbed to (1 1 1) single crystal facets of copper, silver and gold, is investigated and the main reasons for the loss or survival of the switching function upon adsorption are identified. The light-induced switching ability of a functionalised derivative of azobenzene on Au(1 1 1) and azobenzene on Ag(1 1 1) and Au(1 1 1) is assessed based on the excited-state potential energy landscapes of their transient molecular ions, which are believed to be the main intermediates of the experimentally observed isomerisation reaction. We provide a rationalisation of the experimentally observed function or lack thereof that connects to the underlying chemistry of the metal-surface interaction and provides insights into general design strategies for complex light-driven reactions at metal surfaces.