Direct measurement of the electric polarizability of isolated C60 molecules

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.

Introducing a novel C50N10 azafullerene with chained nitrogen atoms on a buckyball pole: structure, stability, vibration, and electronic properties

CONTEXT

Fullerenes are of high significance due to their unique chemical properties and various applications in technology, particularly materials science, drug delivery, electronics, and nanoelectronics. In the recent years, many attempts have been focused to introduce new heteroatom-doped fullerenes having advanced chemical properties and tunable electronic traits, which make them a potential candidate for application in many branches of sciences. In this study, a novel C₅₀N₁₀ azafullerene with a fascinating structure of chained nitrogen atoms on a buckyball pole, with different electronic and optical properties compared to its other analogs, is introduced and trace of N-N substructures on the surface of C₆₀ fullerene cage is investigated. For this molecule, four structural isomers including 3 structures with chain N atoms on a fullerene buckyball pole (NP isomers) and one isomer with separated N atoms (SN isomer) have been studied. All isomers have been studied with and without symmetry constraints, and the symmetry influence on the structure and stability of each isomer has been investigated. Although the studied NP structures have lower stability than the SN isomer, some reasons (such as their more all-carbon hexagonal rings, breaking some of their N-N bonds for partial opening of the cage and creating bigger rings in order to get rid of the unfavorable strain, as well as decreasing the N-N lone pair repulsions) lead to the acceptable stability of these structures with the bonded N atoms. The results of atomization energy and vibrational frequency calculations indicate that isomers with the bonded N atoms have acceptable stabilities and do not decompose into their constituent components. Investigation on the structural parameters demonstrates important roles of the number of all-carbon hexagonal rings, the number of N-N junction, and the molecule symmetry in the stability of the structures with the bonded N atoms. Study on the electronic and optical properties indicates that the target structures exhibit high electronic polarizability, relatively small HOMO/LUMO gap, high first- and second-order hyperpolarizability, and also large third-order nonlinear optical properties.

METHODS

All calculations have been performed using Gaussian G09 software using density functional theory (DFT) approach. Three-parameter Beck hybrid exchange functional (B3) hybridized with nonlocal correlation functional of Lee, Yang, and Parr (LYP) has been employed as the level of DFT calculations. All optimizations have been performed at double-zeta polarized (DZP) split valence 6-31G(d,p) and also at split valence TZP 6-311G(d,p) basis sets. The global minimum structures have been confirmed by frequency calculations at the same level of optimizations. The natural bond orbital (NBO) analyses, frontier orbital surfaces imaging, atomic charges, and charge transfer analyses have been achieved by GenNBO program package.

Geometrical Stability and Nonlinear Optical Properties of Crystallogen and Pnictogen Fullerene Analogues

The linear and nonlinear optical (NLO) properties of fullerene and fullerene-like structures, including crystallogen and pnictogen elements, are computed quantum mechanically. The tensors of optical polarizability, α, and second hyperpolarizability, γ, for a series of buckyball fullerene analogues, namely, Si₆₀, Ge₆₀, Sn₆₀, Pb₆₀, P₆₀, As₆₀, Sb₆₀, and Bi₆₀, are reported and analyzed. The eight considered nanocages are here classified into four categories: nanocages stabilized in the X₆₀ form, including C₆₀, As₆₀, Sb₆₀, and Bi₆₀; nanocages that are not stabilized in the X₆₀ form but are found to be stable in a distorted buckled b-X₆₀ form, with X = Si and Ge; nanocages stabilized only in an exohedral decorated X₆₀-Y₆₀ form, X = Sn, Y = H or F; and finally nanocages that are not stable in either distorted or decorated form; however, their corresponding tabular nanotubes are found to be stable; such group includes P and Pb elements. A suggested nomenclature for the above-mentioned fullerenes is given for the first time, where many geometrical, energetic, and optical parameters are discussed extensively. These systems are energetically stable. The cohesive energies of Bi₆₀ and Sn₆₀-F₆₀ range from -1.2 to -4.8 eV/atom and can be compared to -2.4 and -3.3 eV/atom from the corresponding 2D bismuthene and stanene monolayers, respectively. While bismuthellene, Bi₆₀, shows vigorous optical responses compared to standard fullerene, the (9, 0) phosphorus nanotube gives not only enhanced polarizability and second hyperpolarizability but also an inducing first hyperpolarizability, β, which was null by symmetry in the case of spherical fullerenes. The proposed models are expected to be promising materials for optoelectronic and NLO applications.

Distributed Polarizability Model for Covalently Bonded Fullerene Nanoaggregates: Origins of Polarizability Exaltation

Polarizability exaltation is typical for (C₆₀)_n nanostructures. It relates to the ratio between the mean polarizabilities of (C₆₀)_n and C₆₀: the first one is higher than the n-fold mean polarizability of the original fullerene. This phenomenon is used in the design of novel fullerene compounds and the understanding of its properties but still has no chemical rationalization. In the present work, we studied the distributed polarizability of (C₆₀)₂ and isomeric (C₆₀)₃ nanoaggregates with the density functional theory method. We found that polarizability exaltation increases with the size of the nanostructure and originates from the response of the sp²-hybridized carbon atoms to the external electric field. The highest contributions to the dipole polarizability of (C₆₀)₂ and (C₆₀)₃ come from the most remote atoms of the marginal fullerene cores. The sp³-hybridized carbon atoms of cyclobutane bridges negligibly contribute to the molecular property. A similar major contribution to the molecular polarizability from the marginal atoms is observed for related carbon nanostructures isomeric to (C₆₀)₂ (tubular fullerene and nanopeanut). Additionally, we discuss the analogy between the polarizability exaltation of covalently bonded (C₆₀)_n and the increase in the polarizability found in experiments on fullerene nanoclusters/films as compared with the isolated molecules.

Fourth generation cryogenic neutral cluster beam apparatus for studying fundamental properties of metallic clusters

A cryogenic beam apparatus for studying neutral clusters has been built and tested. The lowest beam temperature reaches less than 9 K at a repetition rate of 20 Hz. Mechanical decoupling from the refrigerator avoids misalignment during temperature ramping. Adopting a permanent magnet based magnetic deflector eliminates the hysteresis and electric noise of the traditional electromagnet and offers excellent reproducibility of the applied magnetic field. The mass spectrometer can operate in either Mass Spectroscopy Time-Of-Flight mode or Position-Sensitive Time-Of-Flight mode with spatial resolution better than 7 μm. Its performance is demonstrated with niobium and cobalt clusters.

Density Functional Response Calculations of Dispersion Coefficients C6 and C9 of Closed- and Open-Shell Systems

Dipole polarizabilities and C₆ and C₉ dispersion coefficients are computed for closed- and open-shell atoms and molecules, using dynamic (time-dependent) density functional (TD-DFT) linear response theory as implemented in the response module of the NWChem quantum chemistry package. The response module is capable of accurate calculations of these properties, based on spin-restricted and spin-unrestricted formalisms. The calculated static polarizabilities and dispersion coefficients are compared to available experimental and other theoretical data. The behavior of the dynamic polarizability at imaginary frequencies is analyzed for differently sized closed- and open-shell systems. An interpolation method enforcing the monotonic decrease of the polarizability with increasing imaginary frequency is beneficial for the integration used to obtain C₆ and C₉. Scaling of the TD-DFT data by ratios of the static polarizability, which can be calculated with a variety of methods, including highly accurate theories, may be used as a leading-order correction.

Interactions between large molecules pose a puzzle for reference quantum mechanical methods

Quantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol^-1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules.

Complexes with Atomic Gold Ions: Efficient Bis-Ligand Formation

Complexes of atomic gold with a variety of ligands have been formed by passing helium nanodroplets (HNDs) through two pickup cells containing gold vapor and the vapor of another dopant, namely a rare gas, a diatomic molecule (H₂, N₂, O₂, I₂, P₂), or various polyatomic molecules (H₂O, CO₂, SF₆, C₆H₆, adamantane, imidazole, dicyclopentadiene, and fullerene). The doped HNDs were irradiated by electrons; ensuing cations were identified in a high-resolution mass spectrometer. Anions were detected for benzene, dicyclopentadiene, and fullerene. For most ligands L, the abundance distribution of AuL_n⁺ versus size n displays a remarkable enhancement at n = 2. The propensity towards bis-ligand formation is attributed to the formation of covalent bonds in Au⁺L₂ which adopt a dumbbell structure, L-Au⁺-L, as previously found for L = Xe and C₆₀. Another interesting observation is the effect of gold on the degree of ionization-induced intramolecular fragmentation. For most systems gold enhances the fragmentation, i.e., intramolecular fragmentation in AuL_n⁺ is larger than in pure L_n⁺. Hydrogen, on the other hand, behaves differently, as intramolecular fragmentation in Au(H₂)_n⁺ is weaker than in pure (H₂)_n⁺ by an order of magnitude.

Metal oxide adsorption on fullerene C60 and its potential for adsorption of pollutant gases; density functional theory studies

Combinations of fullerene and metal oxides (MOx) are interesting, not only because they display the individual properties of fullerene and of MOx nanoparticles, but they may also exhibit synergetic properties that are advantageous for gas sensing applications. In the present work, the adsorption of some different MOxs on fullerene C₆₀, and also the NO₂ and CO sensing properties of these complexes, have been theoretically studied. All quantum mechanical computations have been carried out using Gaussian G09, employing the DFT method at the B97D/6-311G(d,p) level. NBO theory has been used for analysis of the charge transfers during gas adsorption. The chemical nature of the newly formed bonds in the studied complexes and their relative strength have been analysed using AIM2000 software. The results show that MOx/C₆₀ complexes are much stronger adsorbents for NO₂ and CO than C₆₀ is. It is also expected that these complexes have more optical and electrical sensitivity in the selectivity towards gases, including NO₂ and CO.

Combinations of C₆₀ and metal oxides (MOx) are interesting, not only because they display the individual properties of C₆₀ and of MOx nanoparticles, but they may also exhibit synergetic properties that are advantageous for gas sensing applications.

Electron confinement meet electron delocalization: non-additivity and finite-size effects in the polarizabilities and dispersion coefficients of the fullerenes

In this work, we used finite-field derivative techniques and density functional theory (DFT) to compute the static isotropic polarizability series (αl with l = 1, 2, 3) for the C60-C84 fullerenes and quantitatively assess the intrinsic non-additivity in these fundamental response properties. By comparing against classical models of the fullerenes as conducting spherical shells (or solid spheres) of uniform electron density, a detailed critical analysis of the derived effective scaling laws (α1 ∼ N1.2, α2 ∼ N2.0, α3 ∼ N2.7) demonstrates that the electronic structure of finite-sized fullerenes-a unique dichotomy of electron confinement and delocalization effects due to their quasi-spherical cage-like structures and encapsulated void spaces-simultaneously limits and enhances their quantum mechanical response to electric field perturbations. Corresponding frequency-dependent polarizabilities were obtained by inputting the αl series into the hollow sphere model (within the modified single frequency approximation), and used to compute the molecular dispersion coefficients (Cn with n = 6, 8, 9, 10) needed to describe the non-trivial van der Waals (vdW) interactions in fullerene-based systems. Using first-order perturbation theory in conjunction with >140 000 DFT calculations, we also computed the non-negligible zero-point vibrational contributions to α1 in C60 and C70, thereby enabling a more accurate and direct comparison between theory and experiment for these quintessential nanostructures.

Size-dependent polarizabilities and van der Waals dispersion coefficients of fullerenes from large-scale complex polarization propagator calculations

While the anomalous non-additive size-dependencies of static dipole polarizabilities and van der Waals C₆ dispersion coefficients of carbon fullerenes are well established, the widespread reported scalings for the latter (ranging from N^2.2 to N^2.8) call for a comprehensive first-principles investigation. With a highly efficient implementation of the linear complex polarization propagator, we have performed Hartree-Fock and Kohn-Sham density functional theory calculations of the frequency-dependent polarizabilities for fullerenes consisting of up to 540 carbon atoms. Our results for the static polarizabilities and C₆ coefficients show scalings of N^1.2 and N^2.2, respectively, thereby deviating significantly from the previously reported values obtained with the use of semi-classical/empirical methods. Arguably, our reported values are the most accurate to date as they represent the first ab initio or first-principles treatment of fullerenes up to a convincing system size.

Electronic Polarizability as the Fundamental Variable in the Dielectric Properties of Two-Dimensional Materials

The dielectric constant, which defines the polarization of the media, is a key quantity in condensed matter. It determines several electronic and optoelectronic properties important for a plethora of modern technologies from computer memory to field effect transistors and communication circuits. Moreover, the importance of the dielectric constant in describing electromagnetic interactions through screening plays a critical role in understanding fundamental molecular interactions. Here, we show that despite its fundamental transcendence, the dielectric constant does not define unequivocally the dielectric properties of two-dimensional (2D) materials due to the locality of their electrostatic screening. Instead, the electronic polarizability correctly captures the dielectric nature of a 2D material which is united to other physical quantities in an atomically thin layer. We reveal a long-sought universal formalism where electronic, geometrical, and dielectric properties are intrinsically correlated through the polarizability, opening the door to probe quantities yet not directly measurable including the real covalent thickness of a layer. We unify the concept of dielectric properties in any material dimension finding a global dielectric anisotropy index defining their controllability through dimensionality.

Are Buckminsterfullerenes Molecular Ball Bearings?

Buckminsterfullerenes (C₆₀) are near-spherical molecules, which freely rotate at room temperature in the solid state and when dissolved in solution. An intriguing question arises as to whether C₆₀ molecules can act as "molecular ball bearings," that is, preventing direct contact between two solid surfaces while simultaneously dissipating shear stress through fast rotation. To explore this, we performed measurements of friction across a solution of C₆₀ in the boundary lubrication regime. High-resolution shear and normal force measurements between mica sheets separated by C₆₀ solution were made using a surface force balance to provide single-asperity contact and sub-nanometer resolution in film thickness. We find that, even at a small volume fraction, C₆₀ forms a solidlike amorphous boundary film sustaining a high normal load, suggesting that this system undergoes a glass transition under confinement. The C₆₀ film gives rise to a low friction coefficient up to moderate applied loads, and we discuss the possible relevance of the ball-bearing effect at the molecular scale.

Model potential study of non-valence correlation-bound anions of (C60)n clusters: the role of electric field-induced charge transfer

Orbitals associated with the non-valence correlation-bound anions of the C₆₀ dimer and linear trimer from calculations allowing charge transfer.

A Quantum Ruler for Magnetic Deflectometry

Matter-wave near-field interference can imprint a nano-scale fringe pattern onto a molecular beam, which allows observing its shifts in the presence of even very small external forces. Here we demonstrate quantum interference of the pre-vitamin 7-dehydrocholesterol and discuss the conceptual challenges of magnetic deflectometry in a near-field interferometer as a tool to explore photochemical processes within molecules whose center of mass is quantum delocalized.

C60 as Electron Acceptor and Donor: A Comparative DFT Study of Li@C60 and F@C60

Fullerene (C60) is a stable prototype system for a special class of nanomaterials. In this work, the smallest alkali metal (Li) and halogen (F) atoms were encapsulated in the C60 cage, and comparative quantum chemical calculations (QCCs) were performed on their various properties using a density functional theory approach. It was noted that the off-centre distance of Li is higher than that of F. The QCCs of the charge transfer to and from C60 were also analysed. Although charge transfer to and from the C60 cage takes place in both cases, Li@C60 becomes more polar than F@C60, suggesting a better electron-accepting nature of C60 than electron-donating behaviour. This fact is consistent with the natural bond orbital (NBO) charge on the trapped atoms and the dipole moment as well as the binding energy values of the encapsulated C60. Although the encapsulation of both atoms reduces the frontier orbital energy gap, the frontier orbital gap of Li@C60 is smaller than that of F@C60. More interestingly, the depression in the polarizability of Li@C60 is significantly large relative to that of F@C60. These findings also support the tendency of C60 to act as electron acceptor. This study provides some insights into the fundamental properties of C60 and should be helpful in designing new endofullerene complexes for a variety of applications.

Tailoring the volatility and stability of oligopeptides

Amino acids are essential building blocks of life, and fluorinated derivatives have gained interest in chemistry and medicine. Modern mass spectrometry has enabled the study of oligo- and polypeptides as isolated entities in the gas phase, but predominantly as singly or even multiply charged species. While laser desorption of neutral peptides into adiabatically expanding supersonic noble gas jets is possible, UV-VIS spectroscopy, electric or magnetic deflectometry as well as quantum interferometry would profit from the possibility to prepare thermally slow molecular beams. This has typically been precluded by the fragility of the peptide bond and the fact that a peptide would rather 'fry', i.e. denature and fragment than 'fly'. Here, we explore how tailored perfluoroalkyl functionalization can reduce the intermolecular binding and thus increase the volatility of peptides and compare it to previously explored methylation, acylation and amidation of peptides. We show that this strategy is essential and enables the formation of thermal beams of intact neutral tripeptides, whereas only fragments were observed for an extensively fluoroalkyl-decorated nonapeptide. © 2017 The Authors. Journal of Mass Spectrometry Published by John Wiley & Sons Ltd.

Influence of long-range Coulomb interaction in velocity map imaging

The standard velocity-map imaging (VMI) analysis relies on the simple approximation that the residual Coulomb field experienced by the photoelectron ejected from a neutral or ion system may be neglected. Under this almost universal approximation, the photoelectrons follow ballistic (parabolic) trajectories in the externally applied electric field, and the recorded image may be considered as a 2D projection of the initial photoelectron velocity distribution. There are, however, several circumstances where this approximation is not justified and the influence of long-range forces must absolutely be taken into account for the interpretation and analysis of the recorded images. The aim of this paper is to illustrate this influence by discussing two different situations involving isolated atoms or molecules where the analysis of experimental images cannot be performed without considering long-range Coulomb interactions. The first situation occurs when slow (meV) photoelectrons are photoionized from a neutral system and strongly interact with the attractive Coulomb potential of the residual ion. The result of this interaction is the formation of a more complex structure in the image, as well as the appearance of an intense glory at the center of the image. The second situation, observed also at low energy, occurs in the photodetachment from a multiply charged anion and it is characterized by the presence of a long-range repulsive potential. Then, while the standard VMI approximation is still valid, the very specific features exhibited by the recorded images can be explained only by taking into consideration tunnel detachment through the repulsive Coulomb barrier.

A detailed-balance model for thermionic emission from polyanions: The case of fullerene dianions

A detailed-balance model for thermionic emission from polyanions has been developed and applied to fullerene dianions. The specificity of this delayed decay process is electron tunneling through the repulsive Coulomb barrier (RCB). An analytical expression of the RCB is derived from electrostatic modeling of the fullerene cage. The reverse process, namely, electron attachment to the singly charged anion, is described by a hard sphere cross section weighted by the Wentzel-Kramers-Brillouin tunneling probability. This simple expression leads to a very good agreement with a measured time-resolved kinetic energy distribution of C₈₄^2-. Electron binding energy is reduced when the fullerene cage size decreases, leading to an almost zero one for C₇₀^2- and a negative one for C₆₀^2-. Extension of the model to these systems of interest is discussed, and model outputs are compared with the experimental data from the literature.

Polarizability as a tool to determine the electrostatic shielding effect of nanocarbon cages: a polarizability distribution study on noble gas endohedral fullerenes

A noble gas atom can be treated as a sensor to determine the dielectric properties of nanocages including fullerenes.

Nanopatterning of a covalent organic framework host-guest system

We have used a boroxine-based COF as a template for C60-fullerene self-assembly on graphite. Local removal of the COF by STM based nanomanipulation creates nanocorrals that may host other species.

A Computational Study of the Interaction and Polarization Effects of Complexes Involving Molecular Graphene and C60 or a Nucleobases

A systematic analysis of the molecular structure, energetics, electronic (hyper)polarizabilities and their interaction-induced counterparts of C60 with a series of molecular graphene (MG) models, CmHn, where m = 24, 84, 114, 222, 366, 546 and n = 12, 24, 30, 42, 54, 66, was performed. All the reported data were computed by employing density functional theory and a series of basis sets. The main goal of the study is to investigate how alteration of the size of the MG model affects the strength of the interaction, charge rearrangement, and polarization and interaction-induced polarization of the complex, C60-MG. A Hirshfeld-based scheme has been employed in order to provide information on the intrinsic polarizability density representations of the reported complexes. It was found that the interaction energy increases approaching a limit of -26.98 kcal/mol for m = 366 and 546; the polarizability and second hyperpolarizability increase with increasing the size of MG. An opposite trend was observed for the dipole moment. Interestingly, the variation of the first hyperpolarizability is relatively small with m. Since polarizability is a key factor for the stability of molecular graphene with nucleobases (NB), a study of the magnitude of the interaction-induced polarizability of C84H24-NB complexes is also reported, aiming to reveal changes of its magnitude with the type of NB. The binding strength of C84H24-NB complexes is also computed and found to be in agreement with available theoretical and experimental data. The interaction involved in C60 B12N12H24-NB complexes has also been considered, featuring the effect of contamination on the binding strength between MG and NBs.

Charging C60 islands with the AFM tip

We show that electrons can be transferred on demand from an AFM tip into single bulk-like C60 islands, which are supported on the insulating NaCl(001) surface. We exemplify this by controlled charge-manipulation experiments conducted in ultrahigh vacuum by noncontact AFM (nc-AFM), electrostatic force microscopy (EFM) and Kelvin probe force microscopy (KPFM). KPFM shows a homogeneous contrast at the islands, which is a signature for an equal distribution of the electrons in the T1u band. The charge dissipates during half a day due to an interaction of the charged C60 islands with defects in the near surface region of NaCl. Our results open the perspective in photo-voltaics to study charge attachment, stability and charge exchange with the environment of any C60 bulk-like system.

Static polarization of the supramolecular dyads of fullerene C60 with porphyrin derivatives

The nonlinear optical properties of four supramolecular dyads consisting of fullerene C 60 non-covalently bonded to porphyrin, porphyrazine, tetrabenzoporphyrin and phthalocyanine were investigated by calculating their electronic polarizability and first- and second-order hyperpolarizabilities using the finite field method and the density functional theory with the Grimme dispersion correction. Large first- and second-order hyperpolarizabilities result in nonlinear dependence of the polarization of dyads on the strength of external electric field. The increase in the size of the π-conjugated electron system of the porphyrin analogs leads to the increase of the polarizability and first- and second-order hyperpolarizabilities of the dyads. The absence of the covalent bonds between the components of the dyads prevents the field-induced electron transfer from porphyrin analogs to fullerene. The main reason for the nonlinear behavior of the polarization of dyads is the mutual polarization of fullerene and porphyrin analogs amplified by the external electric field.

Robust and Efficient Auxiliary Density Perturbation Theory Calculations

A new iterative solver for the recently developed time-dependent auxiliary density perturbation theory is presented. It is based on the Eirola-Nevanlinna algorithm for large nonsymmetric linear equation systems. The new methodology is validated by static and dynamic polarizability calculations of small molecules. Comparison between the analytic and iterative solutions of the response equation system shows excellent agreement for the calculated static and dynamic polarizabilities. The new iterative solver reduces the formal scaling from [Symbol: see text](N(4)) to [Symbol: see text](N(3)). Furthermore, the observed computational scaling for linear alkane chains is N(1.6). This subquadratic behavior is possible in systems with a few hundred atoms because of the very small prefactors of the [Symbol: see text](N(3)) and [Symbol: see text](N(2)) steps remaining in the iterative solver. To demonstrate the potential of this new methodology, static polarizabilities of giant fullerenes up to C960, with more than 14,000 basis functions, are calculated.

The influence of distribution of hydroxyl groups on vibrational spectra of fullerenol C60(OH)24 isomers: DFT study

The infrared and Raman spectra of C60(OH)24 molecule with uniform and non-uniform distribution of hydroxyl groups have been investigated using first principle DFT calculations at the B3LYP/6-31G(d,p) level of theory. The important features of the obtained geometries have been measured and compared to experimental results. The reference calculations of C60 molecule geometry and vibrational spectra have been made and compared to available experimental data. The striking differences of infrared spectra between C60(OH)24 molecule with uniform and non-uniform distribution of hydroxyl groups have been shown and discussed. The OH modes have been identified as the most sensitive to C60(OH)24 isomer configuration. The C-C stretching modes in the Raman spectra of the C60(OH)24 molecule have been found as a potential sensor of OH groups distribution over fullerene C60 surface.

Dynamically fluctuating electric dipole moments in fullerene-based magnets

We report here the direct evidence of the existence of a permanent electric dipole moment in both crystal phases of a fullerene-based magnet—the ferromagnetic α-phase and the antiferromagnetic α′-phase of tetra-kis-(dimethylamino)-ethylene-C₆₀ (TDAE-C₆₀)—as determined by dielectric measurements. We propose that the permanent electric dipole originates from the pairing of a TDAE molecule with surrounding C₆₀ molecules. The two polymorphs exhibit clear differences in their dielectric responses at room temperature and during the freezing process with dynamically fluctuating electric dipole moments, although no difference in their room-temperature structures has been previously observed. This result implies that two polymorphs have different local environment around the molecules. In particular, the ferromagnetism of the α-phase is founded on the homogeneous molecule displacement and orientational ordering. The formation of the different phases with respect to the different rotational states in the Jahn–Teller distorted C₆₀s is also discussed.

Scaling laws for van der Waals interactions in nanostructured materials

Van der Waals interactions have a fundamental role in biology, physics and chemistry, in particular in the self-assembly and the ensuing function of nanostructured materials. Here we utilize an efficient microscopic method to demonstrate that van der Waals interactions in nanomaterials act at distances greater than typically assumed, and can be characterized by different scaling laws depending on the dimensionality and size of the system. Specifically, we study the behaviour of van der Waals interactions in single-layer and multilayer graphene, fullerenes of varying size, single-wall carbon nanotubes and graphene nanoribbons. As a function of nanostructure size, the van der Waals coefficients follow unusual trends for all of the considered systems, and deviate significantly from the conventionally employed pairwise-additive picture. We propose that the peculiar van der Waals interactions in nanostructured materials could be exploited to control their self-assembly.

Van der Waals interactions have a large influence on phenomena that occur at short-length scales. Gobre et al. demonstrate that van der Waals interactions in low-dimensional materials act at very large distances, and can significantly influence the self-assembly of nanostructured systems.

Polarizability as a landmark property for fullerene chemistry and materials science

The review summarizes data on dipole polarizability of fullerenes and their derivatives, covering the most widespread classes of fullerene-containing molecules (fullerenes, fullerene exohedral derivatives, fullerene dimers, endofullerenes, fullerene ions, and derivatives with ionic bonds).

Existence of a Correlation Bound s-Type Anion State of C60

It is established using high-level electronic structure calculations that C60 has an s-type correlation-bound anion state with an electron binding energy of about 120 meV. Examination of the "singly occupied" natural orbital of the anion reveals that about 9% of the charge density of the excess electron is localized inside, and about 91% is localized outside the C60 cage. Calculations were also carried out for the He@C60, Ne@C60, and H2O@C60 endohedral complexes. For each of these species, the s-type anion is predicted to be less strongly bound than for C60 itself.