Publisher Correction: The effect of hydration number on the interfacial transport of sodium ions.

In this Letter, the links to Supplementary Videos 5, 7, 9 and 10 were incorrect, and there were some formatting errors in the Supplementary Video legends. These errors have been corrected online.

The effect of hydration number on the interfacial transport of sodium ions.

Ion hydration and transport at interfaces are relevant to a wide range of applied fields and natural processes1-5. Interfacial effects are particularly profound in confined geometries such as nanometre-sized channels6-8, where the mechanisms of ion transport in bulk solutions may not apply9,10. To correlate atomic structure with the transport properties of hydrated ions, both the interfacial inhomogeneity and the complex competing interactions among ions, water and surfaces require detailed molecular-level characterization. Here we constructed individual sodium ion (Na+) hydrates on a NaCl(001) surface by progressively attaching single water molecules (one to five) to the Na+ ion using a combined scanning tunnelling microscopy and noncontact atomic force microscopy system. We found that the Na+ ion hydrated with three water molecules diffuses orders of magnitude more quickly than other ion hydrates. Ab initio calculations revealed that such high ion mobility arises from the existence of a metastable state, in which the three water molecules around the Na+ ion can rotate collectively with a rather small energy barrier. This scenario would apply even at room temperature according to our classical molecular dynamics simulations. Our work suggests that anomalously high diffusion rates for specific hydration numbers of ions are generally determined by the degree of symmetry match between the hydrates and the surface lattice.

Submolecular Resolution by Variation of the Inelastic Electron Tunneling Spectroscopy Amplitude and its Relation to the AFM/STM Signal.

Here we show scanning tunneling microscopy (STM), noncontact atomic force microscopy (AFM), and inelastic electron tunneling spectroscopy (IETS) measurements on an organic molecule with a CO-terminated tip at 5 K. The high-resolution contrast observed simultaneously in all channels unambiguously demonstrates the common imaging mechanism in STM/AFM/IETS, related to the lateral bending of the CO-functionalized tip. The IETS spectroscopy reveals that the submolecular contrast at 5 K consists of both renormalization of vibrational frequency and variation of the amplitude of the IETS signal. This finding is also corroborated by first principles simulations. We extend accordingly the probe-particle AFM/STM/IETS model to include these two main ingredients necessary to reproduce the high-resolution IETS contrast. We also employ the first principles simulations to get more insight into a different response of frustrated translation and rotational modes of the CO tip during imaging.

Submolecular Resolution Imaging of Molecules by Atomic Force Microscopy: The Influence of the Electrostatic Force.

The forces governing the contrast in submolecular resolution imaging of molecules with atomic force microscopy (AFM) have recently become a topic of intense debate. Here, we show that the electrostatic force is essential to understand the contrast in atomically resolved AFM images of polar molecules. Specifically, we image strongly polarized molecules with negatively and positively charged tips. A contrast inversion is observed above the polar groups. By taking into account the electrostatic forces between tip and molecule, the observed contrast differences can be reproduced using a molecular mechanics model. In addition, we analyze the height dependence of the various force components contributing to the high-resolution AFM contrast.

Charge-state dynamics in electrostatic force spectroscopy.

We present a numerical model that allows us to study the response of an oscillating probe in electrostatic force spectroscopy to charge switching in quantum dots at various time scales. The model provides more insight into the behavior of frequency shift and dissipated energy under different scanning conditions when measuring a temporarily charged quantum dot on a surface. Namely, we analyze the dependence of the frequency shift, the dissipated energy, and their fluctuations on the resonance frequency of the tip and on the electron tunneling rates across the tip-quantum dot and quantum dot-sample junctions. We discuss two complementary approaches to simulating the charge dynamics, a stochastic and a deterministic one. In addition, we derive analytic formulas valid for small amplitudes, describing relations between the frequency shift, dissipated energy, and the characteristic rates driving the charging and discharging processes.

Charge Redistribution and Transport in Molecular Contacts.

The forces between two single molecules brought into contact, and their connection with charge transport through the molecular junction, are studied here using non contact AFM, STM, and density functional theory simulations. A carbon monoxide molecule approaching an acetylene molecule (C_{2}H_{2}) initially feels weak attractive electrostatic forces, partly arising from charge reorganization in the presence of molecular . We find that the molecular contact is chemically passive, and protects the electron tunneling barrier from collapsing, even in the limit of repulsive forces. However, we find subtle conductance and force variations at different contacting sites along the C_{2}H_{2} molecule attributed to a weak overlap of their respective frontier orbitals.

Origin of High-Resolution IETS-STM Images of Organic Molecules with Functionalized Tips.

Recently, the family of high-resolution scanning probe imaging techniques using decorated tips has been complemented by a method based on inelastic electron tunneling spectroscopy (IETS). The new technique resolves the inner structure of organic molecules by mapping the vibrational energy of a single carbon monoxide (CO) molecule positioned at the apex of a scanning tunneling microscope (STM) tip. Here, we explain high-resolution IETS imaging by extending a model developed earlier for STM and atomic force microscopy (AFM) imaging with decorated tips. In particular, we show that the tip decorated with CO acts as a nanoscale sensor that changes the energy of its frustrated translation mode in response to changes of the local curvature of the surface potential. In addition, we show that high resolution AFM, STM, and IETS-STM images can deliver information about the charge distribution within molecules deposited on a surface. To demonstrate this, we extend our mechanical model by taking into account electrostatic forces acting on the decorated tip in the surface Hartree potential.

Computational Design of Photosensitive Polymer Templates To Drive Molecular Nanofabrication.

Molecular electronics promises the ultimate level of miniaturization of computers and other machines as organic molecules are the smallest known physical objects with nontrivial structure and function. But despite the plethora of molecular switches, memories, and motors developed during the almost 50-years long history of molecular electronics, mass production of molecular computers is still an elusive goal. This is mostly due to the lack of scalable nanofabrication methods capable of rapidly producing complex structures (similar to silicon chips or living cells) with atomic precision and a small number of defects. Living nature solves this problem by using linear polymer templates encoding large volumes of structural information into sequence of hydrogen bonded end groups which can be efficiently replicated and which can drive assembly of other molecular components into complex supramolecular structures. In this paper, we propose a nanofabrication method based on a class of photosensitive polymers inspired by these natural principles, which can operate in concert with UV photolithography used for fabrication of current microelectronic processors. We believe that such a method will enable a smooth transition from silicon toward molecular nanoelectronics and photonics. To demonstrate its feasibility, we performed a computational screening of candidate molecules that can selectively bind and therefore allow the deterministic assembly of molecular components. In the process, we unearthed trends and design principles applicable beyond the immediate scope of our proposed nanofabrication method, e.g., to biologically relevant DNA analogues and molecular recognition within hydrogen-bonded systems.

Calculation of non-adiabatic coupling vectors in a local-orbital basis set.

Most of today's molecular-dynamics simulations of materials are based on the Born-Oppenheimer approximation. There are many cases, however, in which the coupling of the electrons and nuclei is important and it is necessary to go beyond the Born-Oppenheimer approximation. In these methods, the non-adiabatic coupling vectors are fundamental since they represent the link between the classical atomic motion of the nuclei and the time evolution of the quantum electronic state. In this paper we analyze the calculation of non-adiabatic coupling vectors in a basis set of local orbitals and derive an expression to calculate them in a practical and computationally efficient way. Some examples of the application of this expression using a local-orbital density functional theory approach are presented for a few simple molecules: H3, formaldimine, and azobenzene. These results show that the approach presented here, using the Slater transition-state density, is a very promising way for the practical calculation of non-adiabatic coupling vectors for large systems.

Real Space Visualization of Entangled Excitonic States in Charged Molecular Assemblies.

Entanglement of excitons holds great promise for the future of quantum computing, which would use individual molecular dyes as building blocks of their circuitry. Studying entangled excitonic eigenstates emerging in coupled molecular assemblies in the near-field with submolecular resolution has the potential to bring insight into the photophysics of these fascinating quantum phenomena. In contrast to far-field spectroscopies, near-field spectroscopic mapping permits direct identification of the individual eigenmodes, type of exciton coupling, including excited states otherwise inaccessible in the far field (dark states). Here we combine tip-enhanced spectromicroscopy with atomic force microscopy to inspect delocalized single-exciton states of charged molecular assemblies engineered from individual perylenetetracarboxylic dianhydride (PTCDA) molecules. Hyperspectral mapping of the eigenstates and comparison with calculated many-body optical transitions reveals a second low-lying excited state of the anion monomers and its role in the exciton entanglement within the assemblies. We demonstrate control over the exciton coupling by switching the assembly charge states. Our results reveal the possibility of tailoring excitonic properties of organic dye aggregates for advanced functionalities and establish the methodology to address them individually at the nanoscale.

Evidence of exciton-libron coupling in chirally adsorbed single molecules.

Interplay between motion of nuclei and excitations has an important role in molecular photophysics of natural and artificial structures. Here we provide a detailed analysis of coupling between quantized librational modes (librons) and charged excited states (trions) on single phthalocyanine dyes adsorbed on a surface. By means of tip-induced electroluminescence performed with a scanning probe microscope, we identify libronic signatures in spectra of chirally adsorbed phthalocyanines and find that these signatures are absent from spectra of symmetrically adsorbed species. We create a model of the libronic coupling based on the Franck-Condon principle to simulate the spectral features. Experimentally measured librational spectra match very well the theoretically calculated librational eigenenergies and peak intensities (Franck-Condon factors). Moreover, the comparison reveals an unexpected depopulation channel for the zero libron of the excited state that can be effectively controlled by tuning the size of the nanocavity. Our results showcase the possibility of characterizing the dynamics of molecules by their low-energy molecular modes using µeV-resolved tip-enhanced spectroscopy.

Interplay of conductance, force, and structural change in metallic point contacts.

The coupling between two atomically sharp nanocontacts provides tunable access to a fundamental underlying interaction: the formation of the bond between two atoms as they are brought into contact. Here we report a detailed experimental and theoretical analysis of the relation between the chemical force and the tunneling current during bond formation in atom-scale metallic junctions and their dependence on distance, junction structure, and material. We found that the short-range force as well as the conductance in two prototypical metal junctions depend exponentially on the distance and that they have essentially the same exponents. In the transition regime between tunneling and point contact, large short-range forces generate structural relaxations which are concomitant with modifications of the surface electronic structure and the collapse of the tunneling barrier.

Recognition tunneling.

Single molecules in a tunnel junction can now be interrogated reliably using chemically functionalized electrodes. Monitoring stochastic bonding fluctuations between a ligand bound to one electrode and its target bound to a second electrode ('tethered molecule-pair' configuration) gives insight into the nature of the intermolecular bonding at a single molecule-pair level, and defines the requirements for reproducible tunneling data. Simulations show that there is an instability in the tunnel gap at large currents, and this results in a multiplicity of contacts with a corresponding spread in the measured currents. At small currents (i.e. large gaps) the gap is stable, and functionalizing a pair of electrodes with recognition reagents (the 'free-analyte' configuration) can generate a distinct tunneling signal when an analyte molecule is trapped in the gap. This opens up a new interface between chemistry and electronics with immediate implications for rapid sequencing of single DNA molecules.

Quantifying the evolution of atomic interaction of a complex surface with a functionalized atomic force microscopy tip.

Terminating the tip of an atomic force microscope with a CO molecule allows data to be acquired with a well-known and inert apex. Previous studies have shown conflicting results regarding the electrostatic interaction, indicating in some cases that the negative charge at the apex of the CO dominates, whereas in other cases the positive charge at the end of the metal tip dominates. To clarify this, we investigated [Formula: see text](111). [Formula: see text] is an ionic crystal and the (111) surface does not possess charge inversion symmetry. Far from the surface, the interaction is dominated by electrostatics via the negative charge at the apex. Closer to the surface, Pauli repulsion and CO bending dominate, which leads to an unexpected appearance of the complex 3-atom unit cell. We compare simulated data in which the electrostatics are modeled by point particles versus a charge density calculated by DFT. We also compare modeling Pauli repulsion via individual Lennard-Jones potentials versus a total charge density overlap. In doing so, we determine forcefield parameters useful for future investigations of biochemical processes.

Automated structure discovery in atomic force microscopy.

Atomic force microscopy (AFM) with molecule-functionalized tips has emerged as the primary experimental technique for probing the atomic structure of organic molecules on surfaces. Most experiments have been limited to nearly planar aromatic molecules due to difficulties with interpretation of highly distorted AFM images originating from nonplanar molecules. Here, we develop a deep learning infrastructure that matches a set of AFM images with a unique descriptor characterizing the molecular configuration, allowing us to predict the molecular structure directly. We apply this methodology to resolve several distinct adsorption configurations of 1S-camphor on Cu(111) based on low-temperature AFM measurements. This approach will open the door to applying high-resolution AFM to a large variety of systems, for which routine atomic and chemical structural resolution on the level of individual objects/molecules would be a major breakthrough.

Iron-based trinuclear metal-organic nanostructures on a surface with local charge accumulation.

Coordination chemistry relies on harnessing active metal sites within organic matrices. Polynuclear complexes-where organic ligands bind to several metal atoms-are relevant due to their electronic/magnetic properties and potential for functional reactivity pathways. However, their synthesis remains challenging; few geometries and configurations have been achieved. Here, we synthesise-via supramolecular chemistry on a noble metal surface-one-dimensional metal-organic nanostructures composed of terpyridine (tpy)-based molecules coordinated with well-defined polynuclear iron clusters. Combining low-temperature scanning probe microscopy and density functional theory, we demonstrate that the coordination motif consists of coplanar tpy's linked via a quasi-linear tri-iron node in a mixed (positive-)valence metal-metal bond configuration. This unusual linkage is stabilised by local accumulation of electrons between cations, ligand and surface. The latter, enabled by bottom-up on-surface synthesis, yields an electronic structure that hints at a chemically active polynuclear metal centre, paving the way for nanomaterials with novel catalytic/magnetic functionalities.

Weakly perturbative imaging of interfacial water with submolecular resolution by atomic force microscopy.

Scanning probe microscopy has been extensively applied to probe interfacial water in many interdisciplinary fields but the disturbance of the probes on the hydrogen-bonding structure of water has remained an intractable problem. Here, we report submolecular-resolution imaging of the water clusters on a NaCl(001) surface within the nearly noninvasive region by a qPlus-based noncontact atomic force microscopy. Comparison with theoretical simulations reveals that the key lies in probing the weak high-order electrostatic force between the quadrupole-like CO-terminated tip and the polar water molecules at large tip-water distances. This interaction allows the imaging and structural determination of the weakly bonded water clusters and even of their metastable states with negligible disturbance. This work may open an avenue for studying the intrinsic structure and dynamics of ice or water on surfaces, ion hydration, and biological water with atomic precision.

Non-covalent control of spin-state in metal-organic complex by positioning on N-doped graphene.

Nitrogen doping of graphene significantly affects its chemical properties, which is particularly important in molecular sensing and electrocatalysis applications. However, detailed insight into interaction between N-dopant and molecules at the atomic scale is currently lacking. Here we demonstrate control over the spin state of a single iron(II) phthalocyanine molecule by its positioning on N-doped graphene. The spin transition was driven by weak intermixing between orbitals with z-component of N-dopant (pz of N-dopant) and molecule (dxz, dyz, dz2) with subsequent reordering of the Fe d-orbitals. The transition was accompanied by an electron density redistribution within the molecule, sensed by atomic force microscopy with CO-functionalized tip. This demonstrates the unique capability of the high-resolution imaging technique to discriminate between different spin states of single molecules. Moreover, we present a method for triggering spin state transitions and tuning the electronic properties of molecules through weak non-covalent interaction with suitably functionalized graphene.

Donor-Acceptor Properties of a Single-Molecule Altered by On-Surface Complex Formation.

Electron donor-acceptor molecules are of outstanding interest in molecular electronics and organic solar cells for their intramolecular charge transfer controlled via electrical or optical excitation. The preservation of their electronic character in the ground state upon adsorption on a surface is cardinal for their implementation in such single-molecule devices. Here, we investigate by atomic force microscopy and scanning tunneling microscopy a prototypical system consisting of a π-conjugated tetrathiafulvalene-fused dipyridophenazine molecule adsorbed on thin NaCl films on Cu(111). Depending on the adsorption site, the molecule is found either in a nearly undisturbed free state or in a bound state. In the latter case, the molecule adopts a specific adsorption site, leading to the formation of a chelate complex with a single Na+ alkali cation pulled out from the insulating film. Although expected to be electronically decoupled, the charge distribution of the complex is drastically modified, leading to the loss of the intrinsic donor-acceptor character. The chelate complex formation is reversible with respect to lateral manipulations, enabling tunable donor-acceptor molecular switches activated by on-surface coordination.