Performance of semiempirical methods in fullerene chemistry: relative energies and nucleus-independent chemical shifts

Systematic Construction and Calculation of Electronic Properties of Fullerene Series Related by Rotational Symmetry: From Fullerenes to Bicapped Nanotubes

The results herein demonstrate that the methods of circumscribing and the facile calculation of Hückel molecular orbital (HMO) eigenvalues by mirror-plane fragmentation have a broad application in the construction of carbon cluster series and the systematic study of trends in their electronic properties. In comparing open-ended nanotubes and their isomeric elongated fullerenes (bicapped nanotubes), we show that the former are more aromatic but the latter are more conjugated and that progressive elongation increases aromaticity and conjugation in both. Recursion equations that will allow one to obtain the eigenvalues to all 5-endcapped nanotubes are given.

The Electronic Structure of Amorphous Carbon Nanodots

We have studied hydrogen-passivated amorphous carbon nanostructures with semiempirical molecular orbital theory in order to provide an understanding of the factors that affect their electronic properties. Amorphous structures were first constructed using periodic calculations in a melt/quench protocol. Pure periodic amorphous carbon structures and their counterparts doped with nitrogen and/or oxygen feature large electronic band gaps. Surprisingly, descriptors such as the elemental composition and the number of sp(3)-atoms only influence the electronic structure weakly. Instead, the exact topology of the sp(2)-network in terms of effective conjugation defines the band gap. Amorphous carbon nanodots of different structures and sizes were cut out of the periodic structures. Our calculations predict the occurrence of localized electronic surface states, which give rise to interesting effects such as amphoteric reactivity and predicted optical band gaps in the near-UV/visible range. Optical and electronic gaps display a dependence on particle size similar to that of inorganic colloidal quantum dots.

The topology of fullerenes

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96-145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

The first structural confirmation of a C102 fullerene as C102Cl20 containing a non-IPR carbon cage

The chlorination of a pristine C102 fullerene separated by HPLC from fullerene soot afforded crystals of C102Cl20 with a non-IPR (IPR = isolated pentagon rule) cage containing two pairs of fused pentagons; structural reconstruction of a two-step Stone-Wales rearrangement revealed the starting IPR isomer (no. 19) of C102.

COMPUTATIONAL NICS AND 13C NMR ChARACTERIZATION OF SUBSTITUTION PATTERNS OF C60-nNn FULLERENES (n = 1–12)

DFT calculations are applied to evaluate the effects of atomic arrangements of dopant atoms on electronic features of the most stable structures of C 60−n N n(n = 1–12) fullerenes. Our study reveals that 13 C isotropic chemical shifts (δiso) of the nuclei at C–N pentagon–hexagon (ph) junctions appear at downfield values while there are no tangible values of δiso for the nuclei at C–N hexagon–hexagon (hh) junctions; the carbon sites attached to the first neighbors of nitrogen at hh junctions (the second neighboring effect) yield upfield values of δiso. Moreover, compensation between diatropic and paratropic ring currents leads to slightly less negative NICS value in C59N heterofullerene (-3.6) compared to the parent fullerene C60 (-4.25). However, with incorporating more nitrogen atoms into the cage the aromaticity first increases, up to the 66π-system C54N6 and C53N7 , yielding the most negative NICS values of -26.3 and -26.8, respectively, and then decreases so that NICS finally reaches the value of -6.6 ppm for C48N12 heterofullerene. On the basis of distinct value predicted for each heterofullerene, one expects that NICS values may also be useful for identification of the molecules through their endohedral 3 He NMR chemical shifts.

Aromaticity and kinetic stability of fullerene C₃₆ isomers and their molecular ions

The aromatic character of fullerene C(36) isomers was examined by the Hess-Schaad resonance energy (HSRE), topological resonance energy (TRE) and the percentage topological resonance energy (%TRE) models. According to the nucleus-independent chemical shift (NICS) at the cage center, C(36) fullerene isomers must be highly aromatic with negative values. However, they are predicted to be antiaromatic with negative HSREs and negative TREs. The TRE method revealed that they all are aromatized by acquiring two or more electrons. NICSs at the cage center and the 2(N + 1)(2) rule cannot be used as an indicator of the aromatic stabilization for C(36) isomers and their molecular ions. We utilized the bond resonance energy (BRE) model to estimate the kinetic stability of C(36) isomers and their molecular ions. C(36) isomers are only stabilized kinetically in penta- and hexavalent molecular anions. All the results indicate that aromaticity and kinetic stability are closely related to the cyclic motion of π electrons.

Search for lowest-energy nonclassical fullerenes III: C22

Density functional and second-order Møller-Plesset perturbation (MP2) methods were employed in the investigation of low-lying C22 isomers. All cage structures with four-, five-, six-, and seven-membered rings were examined with the monocyclic ring, bowl, and other noncage structures. Cage isomers were first identified via graph theoretical methods, and noncages were identified by basin-hopping methods. Initial isomer screenings were carried out at the PBE/DND level of theory. Low-lying isomers, within 0.6 eV of the predicted lowest-energy isomer, were further evaluated at the PBE1PBE/cc-pVTZ and MP2/cc-pVTZ levels. Our results confirm that the cage structures are more stable than the ring structure and the bowl structure. The lowest-energy structure for C22 is predicted to be the C22-1 cage containing one four-membered ring. Anion photoelectron and optical spectra of the six lowest-lying isomers are also computed.

Self-consistent polarization neglect of diatomic differential overlap: application to water clusters

Semiempirical self-consistent field (SCF) methods based on the neglect of diatomic differential overlap (NDDO) formalism have the ability to treat the formation and breaking of chemical bonds but have been found to poorly describe hydrogen bonding and weak electrostatic complexes. In contrast, most empirical potentials are not able to describe bond breaking and formation but have the ability to add missing elements of hydrogen bonding by using classical electrostatic interactions. We present a new method which combines aspects of both NDDO-based SCF techniques and classical descriptions of polarization to describe the diffuse nature of the electronic wavefunction in a self-consistent manner. We develop the "self-consistent polarization neglect of diatomic differential overlap" (SCP-NDDO) theory with the additional description of molecular dispersion developed as a second-order perturbation theory expression. The current study seeks to model water-water interactions as a test case. To this end, we have parametrized the method to accurate ab initio complete basis set limit estimates of small water cluster binding energies of Xantheas and co-workers [J. Chem. Phys. 116, 1493 (2002); 120, 823 (2004)]. Overall agreement with the ab initio binding energies (n=2-6, and 8) is achieved with a rms error of 0.19 kcal/mol. We achieve noticeable improvements in the structure, vibrational frequencies, and energetic predictions of water clusters (n< or =21) relative to standard NDDO-based methods.

High-resolution kinetic energy release distributions and dissociation energies for fullerene ions Cn+, 42 < or = n < or = 90

We have measured the kinetic energy released in the unimolecular dissociation of fullerene ions, Cn+ --> C(n-2)+ + C2, for sizes 42 < or = n < or = 90. A three-sector-field mass spectrometer equipped with two electric sectors has been used in order to ensure that contributions from isotopomers of different masses do not distort the experimental kinetic energy release distributions. We apply the concept of microcanonical temperature to derive from these data the dissociation energies of fullerene cations. They are converted to dissociation energies of neutral fullerenes with help of published adiabatic ionization energies. The results are compared with literature values.

Search for suitable approximation methods for fullerene structure and relative stability studies: Case study with C50

Local density approximation (LDA), several popular general gradient approximation (GGA), hybrid module based density functional theoretical methods: SVWN, BLYP, PBE, HCTH, B3LYP, PBE1PBE, B1LYP, and BHandHLYP, and some nonstandard hybrid methods are applied in geometry prediction for C60 and C70. HCTH with 3-21G basis set is found to be one of the best methods for fullerene structural prediction. In the predictions of relative stability of C50 isomers, PM3 is an efficient method in the first step for sorting out the most stable isomers. HCTH with 3-21G predicts very good geometries for C50, similar to the performance of B3LYP6-31G(d). The gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital from the predictions of all the density functional theory methods has the following descending order: E(gap)(half-and-half hybrid)>E(gap)(B3LYP)>E(gap)(HCTH)(GGA)>E(gap)(SVWN)(LDA).

Circuit Resonance Energy: A Key Quantity That Links Energetic and Magnetic Criteria of Aromaticity

Energetic and magnetic criteria of aromaticity are different in nature and sometimes make different predictions as to the aromaticity of a polycyclic pi-system. Thus, some charged polycyclic pi-systems are aromatic but paratropic. We derived the individual circuit contributions to aromaticity from the magnetic response of a polycyclic pi-system and named them circuit resonance energies (CREs). Each CRE has the same sign and essentially the same magnitude as the corresponding cyclic conjugation energy (CCE) defined by Bosanac and Gutman. Such CREs were found to play a crucial role in associating the energetic criteria for determining the degree of aromaticity with the magnetic ones. We can now interpret both energetic and magnetic criteria of aromaticity consistently in terms of CREs. Ring-current diamagnetism proved to be the tendency of a cyclic pi-system to retain aromatic stabilization energy (ASE) at the level of individual circuits.

Open versus Closed 1,3-Dipolar Additions of C60: A Theoretical Investigation on Their Mechanism and Regioselectivity

[reactions: see text] 1,3-Dipolar additions of C60 with dipoles, diazomethane, nitrile oxide, and nitrone have been modeled at the B3LYP/6-31G(d,p)//AM1 level, and their mechanism, regiochemistry, and nature of addition are investigated. All of these reactions lead to the formation of fullerene fused heterocycles; theoretically, these reactions can take up four types of additions, viz., closed [6,6], open [5,6], closed [5,6], and open [6,6] additions, and all of them have been examined. Energetics and thermodynamic analysis of these reactions show that closed [5,6] and open [6,6] additions are not probable and that closed [6,6] additions are the most favored ones and follow a concerted mechanism. Experimental evidence that C60-diazomethane reactions yielded closed [6,6] fullerenopyrazoline provides good support to the theoretical predictions. The observed order of reactivity has been explained based on the double bond character, forcing double bonds in the pentagons of C60, and strain. During the addition, dipoles distort more than C60 and concerted closed [6,6] TSs are found to be more reactant-like or early TS. Inclusion of toluene as solvent through the PCM model increases the reaction rate and exothermicity. NICS values computed at the centers of the reacting benzenoid ring of fullerene clearly reveal, in both open and closed additions, the loss in them of aromaticity during the reaction.

A path from Ih to C1 symmetry for C20 cage molecule

The symmetry of the C20 cage is studied based on the intrinsical relationship among point groups (Bradley, C. J.; Cracknell, A. P. The Mathematical Theory of Symmetry in Solids; Claredon Press: Oxford, 1972). The structure of the C20 cage with I(h) symmetry is constructed, as are eight other structures with subgroup symmetry. A path from I(h) symmetry to C1 symmetry is obtained for the closed-shell electronic state, and the structure with D2h symmetry is the most stable on this path. Using the D2h structure the correlation energy correction is studied on the condition of restricted excitation space at the CCSD(T) level. We obtain curves on the relation between the orbital numbers and the total energy at the CCSD(T), CCSD, and MP2 level, respectively. The results of these curves obtained from MP2 and CCSD(T) methods have the same tendency, while the results of CCSD gradually diverge with an increase in orbital numbers. When the orbitals used in the calculation reach 460, the total energy is -759.644 hartree at MP2 level and is -759.721 hartree by the CCSD(T) method. From the calculation results, we find that a large basis set can improve the reliability of the MP2 method, and to restrict excitation space is necessary when using the CCSD(T) method.

Properties of Fullerene[50] andD5hDecachlorofullerene[50]: A Computational Study

Stimulated by the recent preparation and characterization of the first [50]fullerene derivative, decachlorofullerene[50] (Science 2004, 304, 699), we have performed a systematic density functional study on the electronic and spectroscopic properties of C(50), its anions and derivatives such as C(50)Cl(10) and C(50)Cl(12). The ground state of C(50) has D(3) symmetry with a spheroid shape, and is highly aromatic; the best D(5h)C(50) singlet is nonaromatic. Both D(3)() and D(5h)() isomers of C(50) have high electron affinities and can be reduced easily. Due to the unstable fused pentagon structural features, C(50) is chemically labile and subject to addition reactions such as chlorination, dimerization and polymerization. The equatorial pentagon-pentagon fusions of D(5h)C(50) are active sites for chemical reactions; hence, D(5h)C(50) may behave as a multivalent group. The computed IR, Raman, (13)C NMR and UV-vis spectra of the D(5h)C(50)Cl(10) molecule agree well with the experimental data. Finally, D(5h)C(50)Cl(10) is predicted to have a high electron affinity and, hence, might serve as an electron-acceptor in photonic/photovoltaic applications. The geometry and (13)C NMR chemical shifts of C(50)Cl(12) were computed to assist further isolation experiments.

Isomers of C20: an energy profile III

Semiempirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C(20) isomers that are predicted to exist in and around the ring and cage isomers. Using the optimized Cartesian coordinates for the ring and the cage isomers, a saddle-point calculation was performed. The resulting energy profile, consisting of a series of peaks and valleys, is used as a starting point for the identification and location of fifteen additional isomers of C(20) that are predicted to be energetically stable, both via geometry optimizations and force constant analysis. These additional isomers were subsequently determined to lie adjacent to one another on the potential surface and establish a step-wise transformation between the ring and the cage. Transition-state optimization of the Cartesian coordinates at the saddle point between adjacent isomers was performed to quantify the energy of the transition state. The step-wise process from one isomer to another, which extends out over the three-dimensional surface, is predicted to require approximately 15% less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. However, the net atomic rearrangement for the step-wise process is about four times greater than that of the direct process. Although less in energy, the amount of atomic rearrangement in the step-wise process would make the occurrence of such a route prohibitive. Utilizing the direct distance separating the three primary isomers (ring, bowl, cage), the method of triangulation is performed to quantitatively position other C(20) structures on the potential surface, relative to the ring, bowl, and cage isomers.