Kelvin probe force microscopy (KPFM) probes local surface-potential variations through the electrostatic force between a conductive tip and a surface, which depends on the potential difference and the tip-surface capacitance gradient (CG). In heterodyne KPFM, the oscillating tip is usually treated by combining a bias-modulated electric field with a first-order truncated Taylor-series expansion of the CG. Although convenient, this treatment is limited to a poorly defined small-amplitude regime and leaves the convergence of the series unresolved. Here, we establish a rigorous spectral description of the CG dynamics and of the resulting electrostatic force beyond this approximation. We formulate a non-truncated Taylor-series description of the CG and prove its convergence for a realistic Hudlet-based capacitance model in both monomodal and bimodal motion. In the monomodal case, we show the equivalence between Fourier-series and Taylor-series descriptions, derive explicit expressions for the dominant Fourier coefficients, and introduce order-truncation criteria that replace the usual qualitative notion of a small-amplitude regime. We then extend the formalism to bimodal motion and derive the effective CG coefficients governing the static, first-eigenmode, and second-eigenmode components of the electrostatic interaction. Numerical simulations confirm the convergence of the Taylor-based coefficients toward the Fourier coefficients and support the truncation-regime hierarchy in both configurations. This work establishes the formal basis for describing electrostatic force components and AFM observables in open-loop heterodyne experiments and provides a general framework for CG dynamics in multimode force microscopy involving nonlinear electromechanical coupling and frequency conversion.

Supramolecular self-assemblies based on metal-organic coordination provide a tunable platform for constructing functional nanostructures on surfaces, with potential applications in catalysis, magnetism, and optoelectronics. Rational design of assemblies requires understanding how their electronic structures can be tuned by various factors, such as precursor design and substrate choice. While phase transformations can significantly alter both structural and electronic properties, most reported cases involve changes in chemical composition or bonding configurations. In contrast, systematic studies of geometric relaxation, which is modulated without altering chemical identity, remain limited, as such transformations often demand high temperatures that risk side reactions. In this study, we demonstrate a room-temperature phase transformation in a supramolecular self-assembly of Ag-carboxylate complexes derived from 3,5-dinitrobenzoic acid on Ag(111), proceeding without any changes in chemical composition. Combining scanning tunneling microscopy and spectroscopy with density functional theory calculations, we track a stepwise transformation among three distinct hexagonal lattices. The transformation induces subtle geometric relaxation that strengthens metal-molecule interactions, thereby modulating the collective electronic structure. Unlike previous studies on polymorphic organic assemblies, this work reveals a composition-preserving, phase-transformation-driven route to modulate electronic structures in metal-organic coordination assemblies, enabling tuning of physicochemical functionalities in surface-confined molecular architectures.

Heterodyne Kelvin probe force microscopy (He-KPFM) enables high-sensitivity electrostatic measurements by converting a bias-modulated interaction into a resonant response at a higher cantilever eigenmode. While the "direct" heterodyne actuation of the second eigenmode is well established, the dynamical back-action of this heterodyne-driven motion on the fundamental eigenmode has remained largely unexplored, particularly in open-loop operation where the second mode is excited to a finite amplitude. Here, we demonstrate an inverse heterodyne effect: a force component generated by heterodyne frequency conversion acts back on the first eigenmode and produces measurable inter-mode energy exchange. The analysis combines a bimodal virial and power-balance framework with a non-truncated description of the tip-surface capacitance-gradient dynamics developed and validated in a companion manuscript submitted concurrently to the same journal. On this basis, we derive closed-form expressions linking inverse heterodyne coupling to the experimentally accessible observables of non-contact AFM open-loop amplitude-modulated He-KPFM. The theory predicts that inverse heterodyne coupling appears predominantly in the dissipation channel, with a sharply resonant dependence on the demodulation frequency near the second-eigenmode resonance, while its conservative contribution to the frequency shift remains comparatively weaker under typical conditions. Ultrahigh-vacuum experiments validate these predictions and isolate the inverse heterodyne signature through frequency- and voltage-dependent measurements. Beyond KPFM, this work connects heterodyne force microscopy to a broader class of driven multimode systems in which nonlinear coupling and frequency conversion produce inter-mode energy transfer, back-action, and dissipation-based observables.

We investigated the reactivity of a gem-dichlorovinyl-carbazole precursor in the on-surface synthesis approach. Our findings reveal that, on the Au(111) surface, the thermally-induced dehalogenation reaction led to the formation of cumulene dimers. Contrastingly, the more reactive Cu(111) surface promoted the formation of a polyheterocyclic compound exhibiting extended aromaticity. The latter was found to be related to the dehydrogenation of the amine groups, which did not occur on Au(111), thus promoting the different reactivity observed. At higher annealing temperature, selective C-H activation led to the formation of well-defined organometallic chains. In addition, we found that the amine complexation with metal adatom on Cu(111) was an inhibiting factor for the dimerization reaction, a challenge that could be overcome through proper control of the deposition conditions.

On-surface chemistry aims to overcome the limitations of conventional in-solution synthesis by taking advantage of the confinement in two dimensions to master highly ordered covalent structures with tailored properties. So far, most of the reported work is conducted on metal substrates and relies on unconventional mechanisms, thereby precluding a direct transposition of well-established organic reactions from solutions to surfaces. In addition, the intrinsic properties and reactivity of metal substrates often limit the activation methods available to trigger on-surface reactions, and photoinduced processes are especially difficult to handle due to quenching of the adsorbed precursor molecules. Herein, the photoinduced deoxygenation of dibenzothiophene S -oxide (DBTO) derivatives is transposed from solutions to insulating alkali halide surfaces in ultra-high vacuum. By combining in-solution and on-surface investigations by means of scanning tunneling microscopy, non-contact atomic force microscopy, as well as bias spectroscopy measurements, we provide evidence of the successful on-surface deoxygenation of individual DBTO derivatives under UV irradiation. The photoinduced deoxygenation is conducted at low temperature (<25 K) on a NaCl thin film formed on a Au(111) substrate to yield the reduced dibenzothiophene (DBT) product with excellent chemoselectivity. This work thus opens the way to in-situ photocontrolled charge state manipulation in purely organic compounds.

Atomically precise on-surface synthesis of graphene nanoribbons (GNRs) with well-defined width and edge configuration has been widely advanced during the past decade. The main bottom-up growth strategy relies on the thermally activated Ullmann-like coupling reaction followed by the cyclodehydrogenation of tailor-made precursors to achieve the desired precision. We present a systematic investigation of the growth mechanism of chevron GNR on the Ag(111), Au(111), and Cu(111) surfaces in ultrahigh vacuum. We found that the multistep reaction follows different pathways with different activation temperatures depending on the supporting surface. The importance of the as-released Br and their potential influence on the growth process are discussed. The different intermediate states were investigated by low-temperature scanning tunneling microscopy in combination with thermal desorption spectroscopy and kinetic Monte Carlo simulations.

Non-contact atomic force microscopy (nc-AFM) offers a unique experimental framework for topographical imaging of surfaces with atomic and/or sub-molecular resolution. The technique also permits to perform frequency shift spectroscopy to quantitatively evaluate the tip–sample interaction forces and potentials above individual atoms or molecules. The stiffness of the probe, k, is then required to perform the frequency shift-to-force conversion. However, this quantity is generally known with little precision. An accurate stiffness calibration is therefore mandatory if accurate force measurements are targeted. In nc-AFM, the probe may either be a silicon cantilever, a quartz tuning fork (QTF), or a length extensional resonator (LER). When used in ultrahigh vacuum (UHV) and at low temperature, the technique mostly employs QTFs, based on the so-called qPlus design, which actually covers different types of sensors in terms of size and design of the electrodes. They all have in common a QTF featuring a metallic tip glued at the free end of one of its prongs. In this study, we report the stiffness calibration of a particular type of qPlus sensor in UHV and at 9.8 K by means of thermal noise measurements. The stiffness calibration of such high-k sensors, featuring high quality factors (Q) as well, requires to master both the acquisition parameters and the data post-processing. Our approach relies both on numerical simulations and experimental results. A thorough analysis of the thermal noise power spectral density of the qPlus fluctuations leads to an estimated stiffness of the first flexural eigenmode of ≃2000 N/m, with a maximum uncertainty of 10%, whereas the static stiffness of the sensor without tip is expected to be ≃3300 N/m. The former value must not be considered as being representative of a generic value for any qPlus, as our study stresses the influence of the tip on the estimated stiffness and points towards the need for the individual calibration of these probes. Although the framework focuses on a particular kind of sensor, it may be adapted to any high-k, high-Q nc-AFM probe used under similar conditions, such as silicon cantilevers and LERs.

Richness and complexity of Raman spectra related to graphene materials is established from years to decades, with, among others: the well-known G, D, 2D, ... bands plus a plethora of weaker bands related to disorder behavior, doping, stress, crystal orientation or stacking information. Herein, we report on how to detect crumpling effects in Raman spectra, using a large variety of few and multilayer graphene. The main finding is that these crumples enhance the G band intensity like it does with twisted bi layer graphene. We updated the D over G band intensity ratio versus G bandwidth plot, which is generally used to disentangle point and linear defects origin, by reporting surface defects created by crumples. Moreover, we report for the first time on the existence 23 resonant additional bands at 633 nm. We attribute them to edge modes formed by high density of crumples. We use Raman plots (2D bands versus G band positions and widths) to gain qualitative information about the way layers are stacked.

By moving individual Fe-porphyrin-based molecules with the tip of a scanning tunneling microscope in the vicinity of the elbow of the herringbone-reconstructed Au(111) containing a Br atom, we reversibly and continuously control their magnetic state. Several regimes are obtained experimentally and explored theoretically: from the integer spin limit, through intermediate magnetic states with renormalized magnetic anisotropy, until the Kondo-screened regime, corresponding to a progressive increase of charge fluctuations and mixed valency due to an increase in the interaction of the molecular Fe states with the substrate Fermi sea. Our study demonstrates the potential of utilizing charge fluctuations to generate and tune quantum magnetic states in molecule-surface hybrids.

The supramolecular self-assembly of s-indacene-1,3,5,7(2H,6H)-tetrone on the Cu(111) surface was investigated under ultrahigh vacuum by room-temperature scanning tunneling microscopy supported by theoretical modelling based on density functional theory. In total, six different phases were found, driven by hydrogen bonding, metal ligand coordination or covalent coupling. Host-guest interactions allowed for the accommodation of molecular or metal clusters inside the open nanoporous patterns. In one phase, molecular trapping was stochastically observed inside the large periodic nanopores created inside the supramolecular network. The three metal-organic networks observed resulted in the creation of different kinds of regular arrays of isolated metal adatoms or adatom clusters with a lattice period larger than 1 nm.

We use an on-surface synthesis approach to drive the homocoupling reaction of a simple dithiophenyl-functionalized precursor on Cu(111). The C-S activation reaction is initiated at low annealing temperature and yields unsaturated hydrocarbon chains interconnected in a fully conjugated reticulated network. High-resolution atomic force microscopy imaging reveals the opening of the thiophenyl rings and the presence of trans- and cis-oligoacetylene chains as well as pentalene units. The chemical transformations were studied by C 1s and S 2p core level photoemission spectroscopy and supported by theoretical calculations. At higher annealing temperature, additional cyclization reactions take place, leading to the formation of small graphene flakes.

We describe the self-assembly of s-indacene-tetrone on Ag(111), Ag(100), and Ag(110) surfaces and the formation of three hydrogen-bonded supramolecular phases representing a complex self-accommodating honeycomb network. The differences in terms of relative host-guest stability and molecular density are analyzed and discussed. Different epitaxial behaviors of the two-dimensional self-assembly are found as a response to the variations in the crystallographic orientation of the surface.

Sequential reactivity is creating various kinds of macromolecular compounds with distinct prochirality using an on-surface synthesis approach.

We have investigated the role played by the atomic structure and reactivity of the supporting Ag(111) and Cu(111) surfaces on the formation of 2D metal-organic networks (2D-MONs) involving metal adatom clusters spawned by these two surfaces. While the hexahydroxytriphenylene (HHTP) molecule forms complexes with Ag-3 and Cu-3 adatom clusters on, respectively, the Ag(111) and Cu(111) surfaces, an extended order is only observed in the 2D-MON on Ag(111). By combining scanning tunneling microscopy measurements, density functional theory calculations, and microscopy image simulations, we show that the formation of Ag-HHTP metal-organic complexes is structurally compatible with a periodic arrangement of HHTP on the Ag(111) surface. In contrast, on Cu(111), tightly bonded and localized Cu-HHTP motifs are stabilized by the interaction of Cu adclusters with HHTP. However, they cannot match the surface structure of Cu(111) to form an extended 2D-MON. We observed that the formation of large 2D-MON domains on a metallic surface is only possible when the periodicity of the adsorbed surface assembly is weakly perturbed by the addition of metal adclusters that reinforced the bonding.

We present a combined scanning tunneling microscopy (STM), noncontact atomic force microscopy (ncAFM), and differential reflectance spectroscopy (DRS) study aiming at the characterization of the relationship between structural and optical properties of a supramolecular assembly of a curcuminoid derivative adsorbed on two kinds of substrates: bilayers of KCl on Au(111) [2 ML KCl/Au(111)] and KCl(001) bulk. The molecule features a difluoroboron (BF2) complex as well as cyano (CN) end groups, which induces an internal dipole moment of a few Debyes. The comparative study of the structural properties of the molecules adsorbed on 2 ML KCl/Au(111), which allows for STM characterization, and KCl bulk, which allows for nc-AFM and DRS characterization, shows that the molecular adsorption is similar on both substrates. STM and nc-AFM give evidence that the on-surface condensation of the molecules into supramolecular assemblies is steered by two main interactions: the molecule-substrate interaction between the CN end groups of the molecule and the cationic K+ species, as well as an in-plane intermolecular interaction involving BF2 and phenyl groups. Based on density functional theory calculations, we propose an epitaxial molecular structure described by a two-molecule unit cell forming an 8 x 2 supercell on the KCl surface that grows in form of ribbons along the (100) or (010) directions of the substrate, which are polar. Among several possible stereoisomers for the molecule, it is found that the balance between vertical and in-plane interactions selects the one whose size matches the distance between K+ species to condense on the substrate and not the most stable one stemming from the gas phase. Finally, optical spectroscopy in solvent and DRS measurements performed on the supramolecular assembly exhibit similar features identified as three absorption peaks tracing a pi pi* electronic transition followed by a vibronic progression, plus a broader band featuring a set of higher-energy transitions. Due to both the weak electrostatic interactions and a lack of pi-pi interactions in the condensed molecular phase, DR spectra exhibit no major excitonic effect, but a nonrigid redshift of the molecular absorption band compared to the situation in solvent. This observation is found to be consistent with the isomer selection due to the transition from the gas phase to the on-surface condensed phase.

Molecular self-assembly on surfaces is driven by the range of interactions between the molecules themselves and the substrate. Generally, a face-on structure is favored for aromatic molecules lying flat on the surface. Here, we report on the supramolecular self-assembly of 5,10,15,20-tetrakis(10-bromoanthracen-9-yl)porphyrin on the Ag(111) and Ag(110) surfaces. Well-ordered molecular chains were observed by room-temperature scanning tunneling microscopy on both surfaces. The relatively small size of the unit cell revealed an edge-on configuration of the porphyrin macrocycles, that is, perpendicular to the surface plane, as confirmed by molecular mechanics calculations. Distinct intermolecular interactions were found on the two surfaces, providing different molecular chain orientations on Ag(111) and Ag(110).

Nowadays, graphene occupies a special place among two-dimensional materials due to its unique properties [1]. Nevertheless, graphene has several important drawbacks such as chemical inertness, zero band gap, and its 2D structure which makes it a material that is difficult to manipulate. These limitations can be overcome by tuning graphene’s properties at microand nanoscales by chemical functionalization, which introduces defects in graphene’s electronic structure [2-4], and by mechanical modifications [5], the so-called graphene “origami”, which consists in the control of the 3D structure to tune electronic and mechanical properties of graphene and provides better characterization of 3D graphene. In the present work, we used the atomic force microscope (AFM) tip to form 3D graphene structures. The technique consists in nanomechanical folding of single-layer graphene deposed on Si substrate by means of cut and push zigzag movements of an AFM tip [6]. Graphene was detached at 4x4 μm square zones and compacted at the top of the 4x4 μm squares. Thus, we created a series of folded multilayer graphene (MLG) structures, which were characterized by Raman spectroscopy, AFM, SEM and TEM. Interestingly, the Raman analysis revealed a 100-time increase of the G-band intensity, compared to the pristine single-layer graphene, and a 10-20 cm-1 blue-shift of the 2D-band which kept nearly unimodal Lorentzian shape. TEM study of the cross-section of folded structures showed several dozens of well-organized stacked graphene layers with interlayer distance of 0,360,40 nm which exceeds one of graphite (0,323 nm). These data evidence the weak interaction of the layers in the folded structures. In order to control the shape and organization of folded graphene, we are exploring the influence of the various cut and push process parameters, such as the tip force, the zigzag motion speed etc.