Conformational preferences of endohedral metallofullerenes on Ag, Au, and MgO surfaces: Theoretical studies.

In this report, we study the ordering of C60 , Sc3 N@C80 , and Dy2 ScN@C80 molecules on different metallic and dielectric surfaces such as Ag(100), Au(111), and MgO(100). By using DFT techniques, we can classify different types of cage-to-surface arrangements and their relative energies. Using a proposed homogenous sampling of the conformational space for the M3 N cluster, we determine a potential energy map that is capable of providing a structural distribution for a given energy window. We find that Coulomb interaction is a dominant force that governs the system's stability and order. However, a deep analysis of the charge density rearrangements reveals that even though the integral charges may be considered as a qualitative control parameter, it fails to provide quantitative data due to the importance of spatial characteristics of charge densities.

Imaging the Single-Electron Ln-Ln Bonding Orbital in a Dimetallofullerene Molecular Magnet.

Chemically robust single-molecule magnets (SMMs) with sufficiently high blocking temperatures TB are among the key building blocks for the realization of molecular spintronic or quantum computing devices. Such device applications require access to the magnetic system of a SMM molecule by means of electronic transport, which primarily depends on the interaction of magnetic orbitals with the electronic states of the metallic electrodes. Scanning tunneling microscopy in combination with ab initio calculations allows to directly address the unoccupied component of the single-electron molecular orbital that mediates the ferromagnetic exchange coupling between two 4f ions within a lanthanide endohedral dimetallofullerene deposited on a graphene surface. The single-electron metal-metal bond provides a direct access to the molecule's magnetic system in the transport experiments, paving the way for investigation and controlled manipulation of the spin system of individual dimetallofullerene SMMs, essential for molecular spintronics.

Caught in Phase Transition: Snapshot of the Metallofullerene Sc3N@C70 Rotation in the Crystal.

The molecular structure of Sc3N@C2v(7854)-C70 was determined by single-crystal X-ray diffraction. Variable-temperature X-ray diffraction analysis unraveled the details of the phase transition caused by the temperature-driven jumplike rotation of the fullerene cage between two orientations. Whereas in the lower-temperature P21/c phase the fullerene predominantly occupies one orientation, two orientations become equally occupied in the higher-temperature C2/m phase. This work provides a rare example of the well-defined order-disorder transition in metallofullerene crystals and thus gives important insight into the problem of disorder impeding metallofullerene crystallography.

Single-Electron Lanthanide-Lanthanide Bonds Inside Fullerenes toward Robust Redox-Active Molecular Magnets.

A characteristic phenomenon of lanthanide-fullerene interactions is the transfer of metal valence electrons to the carbon cage. With early lanthanides such as La, a complete transfer of six valence electrons takes place for the metal dimers encapsulated in the fullerene cage. However, the low energy of the σ-type Ln-Ln bonding orbital in the second half of the lanthanide row limits the Ln2 → fullerene transfer to only five electrons. One electron remains in the Ln-Ln bonding orbital, whereas the fullerene cage with a formal charge of -5 is left electron-deficient. Such Ln2@C80 molecules are unstable in the neutral form but can be stabilized by substitution of one carbon atom by nitrogen to give azafullerenes Ln2@C79N or by quenching the unpaired electron on the fullerene cage by reacting it with a chemical such as benzyl bromide, transforming one sp2 carbon into an sp3 carbon and yielding the monoadduct Ln2@C80(CH2Ph). Because of the presence of the Ln-Ln bonding molecular orbital with one electron, the Ln2@C79N and Ln2@C80(R) molecules feature a unique single-electron Ln-Ln bond and an unconventional +2.5 oxidation state of the lanthanides. In this Account, which brings together metallofullerenes, molecular magnets, and lanthanides in unconventional valence states, we review the progress in the studies of dimetallofullerenes with single-electron Ln-Ln bonds and highlight the consequences of the unpaired electron residing in the Ln-Ln bonding orbital for the magnetic interactions between Ln ions. Usually, Ln···Ln exchange coupling in polynuclear lanthanide compounds is weak because of the core nature of 4f electrons. However, when interactions between Ln centers are mediated by a radical bridge, stronger coupling may be achieved because of the diffuse nature of radical-based orbitals. Ultimately, when the role of a radical bridge is played by a single unpaired electron in the Ln-Ln bonding orbital, the strength of the exchange coupling is increased dramatically. Giant exchange coupling in endohedral Ln2 dimers is combined with a rather strong axial ligand field exerted on the lanthanide ions by the fullerene cage and the excess electron density localized between two Ln ions. As a result, Ln2@C79N and Ln2@C80(CH2Ph) compounds exhibit slow relaxation of magnetization and exceptionally high blocking temperatures for Ln = Dy and Tb. At low temperatures, the [Ln3+-e-Ln3+] fragment behaves as a single giant spin. Furthermore, the Ln-Ln bonding orbital in dimetallofullerenes is redox-active, which allows its population to be changed by electrochemical reactions, thus changing the magnetic properties because the change in the number of electrons residing in the Ln-Ln orbital affects the magnetic structure of the molecule.

Single-Molecule Magnets DyM2 N@C80 and Dy2 MN@C80 (M=Sc, Lu): The Impact of Diamagnetic Metals on Dy3+ Magnetic Anisotropy, Dy⋠⋠⋠Dy Coupling, and Mixing of Molecular and Lattice Vibrations.

The substitution of scandium in fullerene single-molecule magnets (SMMs) DySc2 N@C80 and Dy2 ScN@C80 by lutetium has been studied to explore the influence of the diamagnetic metal on the SMM performance of dysprosium nitride clusterfullerenes. The use of lutetium led to an improved SMM performance of DyLu2 N@C80 , which shows a higher blocking temperature of magnetization (TB =9.5 K), longer relaxation times, and broader hysteresis than DySc2 N@C80 (TB =6.9 K). At the same time, Dy2 LuN@C80 was found to have a similar blocking temperature of magnetization to Dy2 ScN@C80 (TB =8 K), but substantially different interactions between the magnetic moments of the dysprosium ions in the Dy2 MN clusters. Surprisingly, although the intramolecular dipolar interactions in Dy2 LuN@C80 and Dy2 ScN@C80 are of similar strength, the exchange interactions in Dy2 LuN@C80 are close to zero. Analysis of the low-frequency molecular and lattice vibrations showed strong mixing of the lattice modes and endohedral cluster librations in k-space. This mixing simplifies the spin-lattice relaxation by conserving the momentum during the spin flip and helping to distribute the moment and energy further into the lattice.

Substrate-Independent Magnetic Bistability in Monolayers of the Single-Molecule Magnet Dy2 ScN@C80 on Metals and Insulators.

Magnetic hysteresis is demonstrated for monolayers of the single-molecule magnet (SMM) Dy2 ScN@C80 deposited on Au(111), Ag(100), and MgO|Ag(100) surfaces by vacuum sublimation. The topography and electronic structure of Dy2 ScN@C80 adsorbed on Au(111) were studied by STM. X-ray magnetic CD studies show that the Dy2 ScN@C80 monolayers exhibit similarly broad magnetic hysteresis independent on the substrate used, but the orientation of the Dy2 ScN cluster depends strongly on the surface. DFT calculations show that the extent of the electronic interaction of the fullerene molecules with the surface is increasing dramatically from MgO to Au(111) and Ag(100). However, the charge redistribution at the fullerene-surface interface is fully absorbed by the carbon cage, leaving the state of the endohedral cluster intact. This Faraday cage effect of the fullerene preserves the magnetic bistability of fullerene-SMMs on conducting substrates and facilitates their application in molecular spintronics.

Endohedral metal-nitride cluster ordering in metallofullerene-NiII(OEP) complexes and crystals: a theoretical study.

The ordering of endohedral clusterfullerenes Sc3N@C80 and YSc2N@C80 co-crystallized with Ni(OEP) and isolated complexes with Ni(OEP) have been investigated theoretically. Having used multiple orientations of M3N clusters inside the cages with Fibonacci sampling, we describe the effect of intermolecular interactions on the orientation of the endohedral cluster.

High Blocking Temperature of Magnetization and Giant Coercivity in the Azafullerene Tb2 @C79 N with a Single-Electron Terbium-Terbium Bond.

The azafullerene Tb2 @C79 N is found to be a single-molecule magnet with a high 100-s blocking temperature of magnetization of 24 K and large coercivity. Tb magnetic moments with an easy-axis single-ion magnetic anisotropy are strongly coupled by the unpaired spin of the single-electron Tb-Tb bond. Relaxation of magnetization in Tb2 @C79 N below 15 K proceeds via quantum tunneling of magnetization with the characteristic time τQTM =16 462±1230 s. At higher temperature, relaxation follows the Orbach mechanism with a barrier of 757±4 K, corresponding to the excited states, in which one of the Tb spins is flipped.

Fullerene faraday cage keeps magnetic properties of inner cluster pristine.

Any single molecular magnets (SMMs) perspective for application is as good as its magnetization stability in ambient conditions. Endohedral metallofullerenes (EMFs) provide a solid basis for promising SMMs. In this study, we investigated the behavior of functionalized EMFs on a gold surface (EMF-L-Au). Having followed the systems molecular dynamics paths, we observed that the chemically locked inner cluster inside fullerene cage will remain locked even at room temperature due to the ligand-effect. We have located multiple possible minima with different charge arrangements between EMF-L-Au fragments. Remarkably, the charge state of the EMF inner cluster remained virtually constant and so magnetic properties are expected to be untouched. © 2018 Wiley Periodicals, Inc.

Nanoscale x-ray investigation of magnetic metallofullerene peapods.

Endohedral lanthanide ions packed inside carbon nanotubes (CNTs) in a one-dimensional assembly have been studied with a combination of high resolution transmission electron microscopy (HRTEM), scanning transmission x-ray microscopy (STXM), and x-ray magnetic circular dichroism (XMCD). By correlating HRTEM and STXM images we show that structures down to 30 nm are resolved with chemical contrast and record x-ray absorption spectra from endohedral lanthanide ions embedded in individual nanoscale CNT bundles. XMCD measurements of an Er3N@C80 bulk sample and a macroscopic assembly of filled CNTs indicate that the magnetic properties of the endohedral Er3+ ions are unchanged when encapsulated in CNTs. This study demonstrates the feasibility of local magnetic x-ray characterisation of low concentrations of lanthanide ions embedded in molecular nanostructures.

Direct in situ observations of single Fe atom catalytic processes and anomalous diffusion at graphene edges.

Single-atom catalysts are of great interest because of their high efficiency. In the case of chemically deposited sp(2) carbon, the implementation of a single transition metal atom for growth can provide crucial insight into the formation mechanisms of graphene and carbon nanotubes. This knowledge is particularly important if we are to overcome fabrication difficulties in these materials and fully take advantage of their distinct band structures and physical properties. In this work, we present atomically resolved transmission EM in situ investigations of single Fe atoms at graphene edges. Our in situ observations show individual iron atoms diffusing along an edge either removing or adding carbon atoms (viz., catalytic action). The experimental observations of the catalytic behavior of a single Fe atom are in excellent agreement with supporting theoretical studies. In addition, the kinetics of Fe atoms at graphene edges are shown to exhibit anomalous diffusion, which again, is in agreement with our theoretical investigations.

Hierarchical Corannulene-Based Materials: Energy Transfer and Solid-State Photophysics.

We report the first example of a donor-acceptor corannulene-containing hybrid material with rapid ligand-to-ligand energy transfer (ET). Additionally, we provide the first time-resolved photoluminescence (PL) data for any corannulene-based compounds in the solid state. Comprehensive analysis of PL data in combination with theoretical calculations of donor-acceptor exciton coupling was employed to estimate ET rate and efficiency in the prepared material. The ligand-to-ligand ET rate calculated using two models is comparable with that observed in fullerene-containing materials, which are generally considered for molecular electronics development. Thus, the presented studies not only demonstrate the possibility of merging the intrinsic properties of π-bowls, specifically corannulene derivatives, with the versatility of crystalline hybrid scaffolds, but could also foreshadow the engineering of a novel class of hierarchical corannulene-based hybrid materials for optoelectronic devices.

Fulleretic Well-Defined Scaffolds: Donor-Fullerene Alignment Through Metal Coordination and Its Effect on Photophysics.

Herein, we report the first example of a crystalline metal-donor-fullerene framework, in which control of the donor-fullerene mutual orientation was achieved through chemical bond formation, in particular, by metal coordination. The (13) C cross-polarization magic-angle spinning NMR spectroscopy, X-ray diffraction, and time-resolved fluorescence spectroscopy were performed for comprehensive structural analysis and energy-transfer (ET) studies of the fulleretic donor-acceptor scaffold. Furthermore, in combination with photoluminescence measurements, the theoretical calculations of the spectral overlap function, Förster radius, excitation energies, and band structure were employed to elucidate the photophysical and ET processes in the prepared fulleretic material. We envision that the well-defined fulleretic donor-acceptor materials could contribute not only to the basic science of fullerene chemistry but would also be used towards effective development of organic photovoltaics and molecular electronics.

Finding mechanochemical pathways and barriers without transition state search.

In covalent mechanochemistry, precise application of mechanical stress to molecules of interest ("mechanophores") is used to induce to promote desired reaction pathways. Computational prediction of such phenomena and rational mechanophore design involves the computationally costly task of finding relevant transition-state saddles on force-deformed molecular potential energy surfaces (PESs). Finding a transition state often requires an initial guess about the pathway by which the reaction will proceed. Unfortunately, chemical intuition often fails when predicting likely consequences of mechanical stress applied to molecular systems. Here, we describe a fully deterministic method for finding mechanochemically relevant transition states and reaction pathways. The method is based on the observation that application of a sufficiently high mechanical force will eventually destabilize any molecular structure. Mathematically, such destabilization proceeds via a "catastrophe" occurring at a critical force where the energy minimum corresponding to the stable molecular structure coalesces with a transition state. Catastrophe theory predicts the force-deformed PES to have universal behavior in the vicinity of the critical force, allowing us to deduce the molecular structure of the transition state just below the critical force analytically. We then use the previously developed method of tracking transition-state evolution with the force to map out the entire reaction path and to predict the complete force dependence of the reaction barrier. Beyond its applications in mechanochemistry, this approach may be useful as a general method of finding transition states using fictitious forces to target specific reaction mechanisms.

On the calculation of internal forces in mechanically stressed polyatomic molecules.

We discuss how to define and to compute internal forces in a molecule subjected to mechanical stress. Because of the inherently many-body character of intramolecular interactions, internal forces cannot be uniquely defined without specifying a set of internal coordinates used to describe the molecular structure. When such a set is comprised of 3N - 6 interactomic distances (N being the number of atoms) and includes the bond lengths of interest, we show that the associated forces, while satisfying the equation F = ∂V/∂R (where R is the bond length, F is the internal force in this bond, and V is the potential energy of the molecule), can be determined from the molecular geometry alone. We illustrate these ideas using several toy models ranging from small molecules to a graphene sheet and show that the magnitude of the internal force in a bond is not necessarily a good predictor of its strength in response to mechanical loading. At the same time, analysis of internal forces reveals interesting phenomena such as the force multiplication effect, where weak external forces may, e.g., be used to break strong bonds, and offers insight into the catch-bond phenomenon where chemical reactivity is suppressed through application of a force.

Exploring the topography of the stress-modified energy landscapes of mechanosensitive molecules.

We propose a method for computing the activation barrier for chemical reactions involving molecules subjected to mechanical stress. The method avoids reactant and transition-state saddle optimizations at every force by, instead, solving the differential equations governing the force dependence of the critical points (i.e., minima and saddles) on the system's potential energy surface (PES). As a result, only zero-force geometry optimization (or, more generally, optimization performed at a single force value) is required by the method. In many cases, minima and transition-state saddles only exist within a range of forces and disappear beyond a certain critical point. Our method identifies such force-induced instabilities as points at which one of the Hessian eigenvalues vanishes. We elucidate the nature of those instabilities as fold and cusp catastrophes, where two or three critical points on the force-modified PES coalesce, and provide a classification of various physically distinct instability scenarios, each illustrated with a concrete chemical example.

Dynamic and electronic transport properties of DNA translocation through graphene nanopores.

Graphene layers have been targeted in the last years as excellent host materials for sensing a remarkable variety of gases and molecules. Such sensing abilities can also benefit other important scientific fields such as medicine and biology. This has automatically led scientists to probe graphene as a potential platform for sequencing DNA strands. In this work, we use robust numerical tools to model the dynamic and electronic properties of molecular sensor devices composed of a graphene nanopore through which DNA molecules are driven by external electric fields. We performed molecular dynamic simulations to determine the relation between the intensity of the electric field and the translocation time spent by the DNA to pass through the pore. Our results reveal that one can have extra control on the DNA passage when four additional graphene layers are deposited on the top of the main graphene platform containing the pore in a 2 × 2 grid arrangement. In addition to the dynamic analysis, we carried electronic transport calculations on realistic pore structures with diameters reaching nanometer scales. The transmission obtained along the graphene sensor at the Fermi level is affected by the presence of the DNA. However, it is rather hard to distinguish the respective nucleobases. This scenario can be significantly altered when the transport is conducted away from the Fermi level of the graphene platform. Under an energy shift, we observed that the graphene pore manifests selectiveness toward DNA nucleobases.

Covalency versus magnetic axiality in Nd molecular magnets: Nd-photoluminescence, strong ligand-field, and unprecedented nephelauxetic effect in fullerenes NdM2N@C80 (M = Sc, Lu, Y).

Nd-based nitride clusterfullerenes NdM2N@C80 with rare-earth metals of different sizes (M = Sc, Y, Lu) were synthesized to elucidate the influence of the cluster composition, shape and internal strain on the structural and magnetic properties. Single crystal X-ray diffraction revealed a very short Nd-N bond length in NdSc2N@C80. For Lu and Y analogs, the further shortening of the Nd-N bond and pyramidalization of the NdM2N cluster are predicted by DFT calculations as a result of the increased cluster size and a strain caused by the limited size of the fullerene cage. The short distance between Nd and nitride ions leads to a very large ligand-field splitting of Nd3+ of 1100-1200 cm-1, while the variation of the NdM2N cluster composition and concomitant internal strain results in the noticeable modulation of the splitting, which could be directly assessed from the well-resolved fine structure in the Nd-based photoluminescence spectra of NdM2N@C80 clusterfullerenes. Photoluminescence measurements also revealed an unprecedentedly strong nephelauxetic effect, pointing to a high degree of covalency. The latter appears detrimental to the magnetic axiality despite the strong ligand field. As a result, the ground magnetic state has considerable transversal components of the pseudospin g-tensor, and the slow magnetic relaxation of NdSc2N@C80 could be observed by AC magnetometry only in the presence of a magnetic field. A combination of the well-resolved magneto-optical states and slow relaxation of magnetization suggests that Nd clusterfullerenes can be useful building blocks for magneto-photonic quantum technologies.

A parabolic model to control quantum interference in T-shaped molecular junctions.

Quantum interference (QI) effects in molecular devices have drawn increasing attention over the past years due to their unique features observed in the conductance spectrum. For the further development of single molecular devices exploiting QI effects, it is of great theoretical and practical interest to develop simple methods controlling the emergence and the positions of QI effects like anti-resonances or Fano line shapes in conductance spectra. In this work, starting from a well-known generic molecular junction with a side group (T-shaped molecule), we propose a simple graphical method to visualize the conditions for the appearance of quantum interference, Fano resonances or anti-resonances, in the conductance spectrum. By introducing a simple graphical representation (parabolic diagram), we can easily visualize the relation between the electronic parameters and the positions of normal resonant peaks and anti-resonant peaks induced by quantum interference in the conductance spectrum. This parabolic model not only can predict the emergence and energetic position of quantum interference from a few electronic parameters but also can enable one to know the coupling between the side group and the main conduction channel from measurements in the case of orthogonal basis. The results obtained within the parabolic model are validated using density-functional based quantum transport calculations in realistic T-shaped molecular junctions.

Improving the molecular spin qubit performance in zirconium MOF composites by mechanochemical dilution and fullerene encapsulation.

Enlarging the quantum coherence times and gaining control over quantum effects in real systems are fundamental for developing quantum technologies. Molecular electron spin qubits are particularly promising candidates for realizing quantum information processing due to their modularity and tunability. Still, there is a constant search for tools to increase their quantum coherence times. Here we present how the mechanochemical introduction of active spin qubits in the form of 10% diluted copper(ii)-porphyrins in the diamagnetic PCN-223 and MOF-525 zirconium-MOF polymorph pair can be achieved. Furthermore, the encapsulation of fullerene during the MOF synthesis directs the process exclusively toward the rare PCN-223 framework with a controllable amount of fullerene in the framework channels. In addition to the templating role, the incorporation of fullerene increases the electron spin-lattice and phase-memory relaxation times, T1 and Tm. Besides decreasing the amount of nuclear spin-bearing solvent guests in the non-activated qubit frameworks, the observed improved relaxation times can be rationalized by modulating the phonon density of states upon fullerene encapsulation.