Electrostatic potentials of atomic nanostructures at metal surfaces quantified by scanning quantum dot microscopy.

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.

Probing the role of surface termination in the adsorption of azupyrene on copper.

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.

Machine Learning Interatomic Potentials for Reactive Hydrogen Dynamics at Metal Surfaces Based on Iterative Refinement of Reaction Probabilities.

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.

libMBD: A general-purpose package for scalable quantum many-body dispersion calculations.

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.

Stability of Single Gold Atoms on Defective and Doped Diamond Surfaces.

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.

Assessing Mixed Quantum-Classical Molecular Dynamics Methods for Nonadiabatic Dynamics of Molecules on Metal Surfaces.

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.

Characterizing Molecule-Metal Surface Chemistry with Ab Initio Simulation of X-ray Absorption and Photoemission Spectra.

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.

Efficient implementation and performance analysis of the independent electron surface hopping method for dynamics at metal surfaces.

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.

High-throughput property-driven generative design of functional organic molecules.

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.

Long-range dispersion-inclusive machine learning potentials for structure search and optimization of hybrid organic-inorganic interfaces.

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.

Stereodynamics of adiabatic and non-adiabatic energy transfer in a molecule surface encounter.

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.

Topological Stone-Wales Defects Enhance Bonding and Electronic Coupling at the Graphene/Metal Interface.

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.

NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase.

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 H2 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.

Design Principles for Metastable Standing Molecules.

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.

Direct Experimental Evidence for Substrate Adatom Incorporation into a Molecular Overlayer.

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)-F4TCNQ 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.

Thermodynamic Driving Forces for Substrate Atom Extraction by Adsorption of Strong Electron Acceptor Molecules.

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 F4TCNQ 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 F4TCNQ 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.

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.

The stabilization potential of a standing molecule.

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.

Core Electron Binding Energies in Solids from Periodic All-Electron Δ-Self-Consistent-Field Calculations.

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.

Determining the Effect of Hot Electron Dissipation on Molecular Scattering Experiments at Metal Surfaces.

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.