Carbon Nanorings: A Challenge to Theoretical Chemistry

Noncovalent interactions and properties of host-guest systems based on C82/C82Gd bucky-balls and symmetry broken nanohoop TP-[11]CPP

The nanoscale host-guest interactions between a symmetry broken carbonaceous nanohoop TP-[11]cycloparaphenylene (TP-[11]CPP) and endohedral metallofullerene (EMF) C82Gd were explored by using density functional theory calculations. The geometry mutual-matching between TP-[11]CPP and C82Gd is perfect, and the two main configurations of TP-[11]CPP@C82Gd host-guest complexes could be formed spontaneously with high binding energies. Interestingly, the position of the Gd atom in the C82 cage can be adjusted by its external host molecule. The binding strength depends on the structure of the host, but the binding thermodynamics is decided by the structure of the fullerene cage. The selective binding of empty cage C82 from its mixture with EMF C82Gd is discussed by using a standard Boltzmann expression of statistical thermodynamics. In addition, the FT-IR and UV-visible spectra are simulated, host-guest noncovalent interaction regions are investigated based on the electron density and reduced density gradient, and magnetic susceptibility is preliminarily investigated, which may be helpful for a deep understanding of the present host-guest systems in the future. It is anticipated that such a theoretical calculation regarding to carbonaceous nanosize host-guest structures would be a driven force for the developments of novel nanohoop@EMF systems in functional materials, nonchromatographic separation and even nano single molecular electret devices.

Theoretical Prediction on a Novel Reduction-Responsive Nanoring Having a Disulfide Group for Facile Encapsulation and Release of Fullerenes C60 and C70

In this work, a novel reduction-responsive disulfide bond-containing cycloparaphenylene nanoring molecule (DSCPP) with a pyriform shape has been designed. In addition, the interactions between the designed nanoring (host) and fullerenes C₆₀ and C₇₀ (guests) were investigated theoretically at the M06-2X/6-31G(d,p) and M06-L/MIDI! levels of theory. By analyzing geometric characteristics and host-guest binding energies, it is revealed that the designed DSCPP is an ideal host molecule of guests C₆₀ and C₇₀. DSCPP presents excellent elastic deformation during the encapsulation of C₆₀ and C₇₀. The high binding energies suggest that both DSCPP⊃C₆₀ and DSCPP⊃C₇₀ (∼92 and 118 kJ·mol^-1 at the M06-2X/6-31G(d,p) level of theory) are stable host-guest complexes, and the guest C₇₀ is more strongly encapsulated than C₆₀ in the gas phase. The thermodynamic information indicates that the formation of the two host-guest complexes is thermodynamically spontaneous. In addition, the frontier molecular orbital (FMO) features and intermolecular weak interaction region between DSCPP and fullerenes gusts are discussed to further understand the structures and properties of the DSCPP⊃fullerene systems. Finally, the ring-opening mechanism of the DSCPP under reduction conditions is investigated.

Corannulene–fullerene C70 noncovalent interactions and their effect on the behavior of charge transport and optical property

Corannulene–fullerene C₇₀ noncovalent interactions and their effect on the behavior of charge transport and optical property are investigated at a molecular level via the dispersion-corrected density functional theory calculations.

A novel photo-responsive azobenzene-containing nanoring host for fullerene-guest facile encapsulation and release

Azobenzenes in particular have been proved to have a robust photo-response, in which their configuration can transform between the trans- and cis-form upon UV-visible irradiation. Accordingly, azobenzene-containing molecules are frequently applied in the design of the guests, involving so-called host-guest chemistry. In this paper, a novel photo-responsive nanoring host molecule ([4]AB) has been designed by introducing four azobenzene groups onto the ring, and interactions between the designed nanoring host and fullerenes C60 and C70 guests were investigated at both the M06-L/MIDI! as well as M06-2X/6-31G(d) level of theory. By analyzing the geometric characteristics and host-guest binding energies, it is revealed that the designed [4]AB with diameter ca. 13.4 Å is an ideal host molecule for the encapsulation of guests C60 and C70 fullerene. Meanwhile, inferred from UV-vis-NIR spectroscopy, the guest C60 and C70 could be facilely released from the cavity of the [4]AB via configuration transformation between trans- and cis-form of the host under 474 and 506 nm photo-irradiation, respectively. Frontier orbital features, weak interaction regions, infrared spectroscopy and (1)H NMR spectra have also been theoretically simulated. The present work would provide a new strategy for facile reversible encapsulation and release of fullerene guest by a novel nanoring host.

Theoretical exploration of the nanoscale host–guest interactions between [n]cycloparaphenylenes (n = 10, 8 and 9) and fullerene C60: from single- to three-potential well

The host–guest interactions between C₆₀ and [n]cycloparaphenylene ([n]CPP; n = 10, 8 and 9) are in the manner of single-, double- and three-potential wells, respectively.

Energy interactions in amyloid-like fibrils from NNQQNY

We use large-scale MP2 calculations to analyze the interactions appearing in amyloid fibers, which are difficult to determine experimentally. To this end, dimers and trimers of the hexapeptide NNQQNY from the yeast prion-like protein Sup35 were considered as model systems. We studied the energy interactions present in the three levels of organization in which the formation of amyloid fibrils is structured. The structural changes in the hydrogen bonds were studied too. It was found that the most energetic process is the formation of the β-sheet, which is equally due to both hydrogen bonds and van der Waals interactions. The aromatic rings help stabilize these aggregates through stacking of the aromatic rings of tyrosine, the stability produced by the aromatics residues increasing with their aromaticity. The formation of the basic unit of the assembled proto-fiber, the steric zipper, is less energetic and is associated to both dispersion forces and hydrogen bonds. The interactions between pair of β-sheets across the peptide-to-peptide contact through the tyrosine rings are cooperative and due to dispersion effects. Moreover, the strength of this interaction can rationalize the variation of mobility of the aromatic ring in the tyrosine units found in solid NMR experiments.

Electron-rich carbon nanorings as macrocyclic hosts for fullerenes

Electron-rich cycloparaphenyleneacetylenes as well as their twin "glasses-like" conjugates form stable complexes with fullerenes.

Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante et al., J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra-mu-acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.

Unbiased auxiliary basis sets for accurate two-electron integral approximations

We propose Cholesky decomposition (CD) of the atomic two-electron integral matrix as a robust and general technique for generating auxiliary basis sets for the density fitting approximation. The atomic CD (aCD) auxiliary basis set is calculated on the fly and is not biased toward a particular quantum chemical method. Moreover, the accuracy of the aCD basis set can be controlled with a single parameter.

Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals

The authors propose a new algorithm, "local K" (LK), for fast evaluation of the exchange Fock matrix in case the Cholesky decomposition of the electron repulsion integrals is used. The novelty lies in the fact that rigorous upper bounds to the contribution from each occupied orbital to the exchange Fock matrix are employed. By formulating these inequalities in terms of localized orbitals, the scaling of computing the exchange Fock matrix is reduced from quartic to quadratic with only negligible prescreening overhead and strict error control. Compared to the unscreened Cholesky algorithm, the computational saving is substantial for systems of medium and large sizes. By virtue of its general formulation, the LK algorithm can be used also within the class of methods that employ auxiliary basis set expansions for representing the electron repulsion integrals.