Electric and magnetic properties of fullerenes

Field emission microscope for a single fullerene molecule

Applying strong direct current (DC) electric fields on the apex of a sharp metallic tip, electrons can be radially emitted from the apex to vacuum. Subsequently, they magnify the nanoscopic information on the apex, which serves as a field emission microscope (FEM). When depositing molecules on such a tip, peculiar electron emission patterns such as clover leaves appear. These phenomena were first observed seventy years ago. However, the source of these emission patterns has not yet been identified owing to the limited experimental information about molecular configurations on a tip. Here, we used fullerene molecules and characterized the molecule-covered tip by an FEM. In addition to the experiments, simulations were performed to obtain optimized molecular configurations on a tip. Both results indicate that the molecules, the source of the peculiar emission patterns, appear on a molecule layer formed on the tip under strong DC electric fields. Furthermore, the simulations revealed that these molecules are mostly isolated single molecules forming single-molecule-terminated protrusions. Upon the excellent agreements in both results, we concluded that each emission pattern originates from a single molecule. Our work should pave the way to revive old-fashioned electron microscopy as a powerful tool for investigating a single molecule.

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.

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.

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).

Time resolved spectroscopy and gain studies of Fullerenes C60 and C70

The fluorescence decay time of Fullerenes C60 and C70 in pure form as well as in mixture with Coumarin C440 and Quinizarine dyes are studied. Results indicate that the decay of pure fullerenes is constant throughout the solute concentration and it is also independent of excitation wavelength, whereas in the case of mixture with dyes different behavior is noticed. We have also calculated the Stern-Volmer quenching constant and optical gain of both the fullerenes from which it is found that the optical gain is positive for Fullerene C70 only in a very narrow range of concentration.

Cob(I)alamin: insight into the nature of electronically excited states elucidated via quantum chemical computations and analysis of absorption, CD and MCD data

The nature of electronically excited states of the super-reduced form of vitamin B(12) (i.e., cob(I)alamin or B(12s)), a ubiquitous B(12) intermediate, was investigated by performing quantum-chemical calculations within the time-dependent density functional theory (TD-DFT) framework and by establishing their correspondence to experimental data. Using response theory, the electronic absorption (Abs), circular dichroism (CD) and magnetic CD (MCD) spectra of cob(I)alamin were simulated and directly compared with experiment. Several issues have been taken into considerations while performing the TD-DFT calculations, such as strong dependence on the applied exchange-correlation (XC) functional or structural simplification imposed on the cob(I)alamin. In addition, the low-lying transitions were also validated by performing CASSCF/MC-XQDPT2 calculations. By comparing computational results with existing experimental data a new level of understanding of electronic excitations has been established at the molecular level. The present study extends and confirms conclusions reached for other cobalamins. In particular, the better performance of the BP86 functional, rather than hybrid-type, was observed in terms of the excitations associated with both Co d and corrin π localized transitions. In addition, the lowest energy band was associated with multiple metal-to-ligand charge transfer excitations as opposed to the commonly assumed view of a single π → π* transition followed by vibrational progression. Finally, the use of the full cob(I)alamin structure, instead of simplified molecular models, shed new light on the spectral analyses of cobalamin systems and revealed new challenges of this approach related to long-range charge transfer excitations involving side chains.

An electrostatic interaction model for frequency-dependent polarizability: methodology and applications to hydrocarbons and fullerenes

We present an electrostatic interaction model for the calculation of frequency-dependent electronic polarizability. The model is based on the representation of atoms by an induced electric charge and a dipole moment. The extension of the charge-dipole model to the interaction with oscillating electric fields requires us to account for the kinetics of the free moving charges and of the atomic dipoles. This step is achieved by first relating the oscillations of the atomic charges to the currents that flow through the atomic bonds. Adopting a classical description of this system of charges and dipoles, the time evolution of these quantities is determined from the principle that the action be minimized. As an application of this model, we compute the frequency-dependent molecular polarizability of hydrocarbons with different hybridization. We propose parameters for each chemical group, which provide an excellent agreement with reference data provided by current-density-functional theory. We finally study the frequency-dependent molecular polarizability of fullerenes ranging from C(60) to C(1500).

Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level

An implementation of the gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational g tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing CC analytic second-derivative code is described, focusing on the required modifications concerning integral evaluation and treatment of the unperturbed and perturbed two-particle density matrices. An extensive set of test calculations for LiH and BH (up to the full configuration-interaction limit), for a series of simple hydrides (HF, H(2)O, NH(3), and CH(4)) as well as the more challenging molecules CO, N(2), and O(3) [employing the CC singles and doubles (CCSD) and the CCSD approximation augmented by a perturbative treatment of triple excitations] demonstrates the importance of electron correlation for high-accuracy predictions of magnetizabilities and rotational g tensors.

Complex polarization propagator method for calculation of dispersion coefficients of extended pi-conjugated systems: the C6 coefficients of polyacenes and C60

The frequency-dependent polarizabilities and the C6 dipole-dipole dispersion coefficients for the first members of the polyacenes namely benzene, naphthalene, anthracene, and naphthacene as well as the fullerene C60 have been calculated at the time-dependent Hartree-Fock level and the time-dependent density-functional theory level with the hybrid B3LYP exchange-correlation functional. The dynamic polarizabilities at imaginary frequencies are obtained with use of the complex linear polarization propagator method and the C6 coefficients are subsequently determined from the Casimir-Polder relation. We report the first ab initio calculations of the C6 coefficients for the molecules under consideration, and our recommended value for the dispersion coefficient of the fullerene is 101.0 a.u.

Bond order bond polarizability model for fullerene cages and nanotubes

It is still a challenge to accurately calculate the polarizabilities of large fullerene cages and nanotubes. In this paper, a simple bond order bond polarizability relationship for carbon was found, which allowed us to apply the bond polarizability model to any pentagon isolation rule (PIR) fullerene (cage or nanotube). Following this approach, the following simple equation, alpha=1.262n, was obtained relating the static dipole polarizability (alpha) of PIR fullerenes (cages or closed nanotubes) to their number (n) of carbon atoms. Furthermore, it was shown that the polarizabilities of C60 and C70, calculated on the basis of this model, are in excellent agreement with those obtained experimentally and by density-functional theory calculations.