Patrick W. Fowler

A stable non-classical metallofullerene family.

In the evolving field of fullerenes, nanotubes and endohedral metallofullerenes, the isolated-pentagon rule (IPR) is sacrosanct — exceptions have been predicted, but no bare carbon cages with adjacent pentagons have been characterized. Small organic molecules with metal-stabilized fused five-membered rings (pentalenes) have been created, however, and here we describe a family of non-classical endohedral metallofullerenes with the general structure AxSc3−xN@C 68 (where x = 0–2, A is a rare-earth metal, Sc is scandium and N is nitrogen) that has a non-IPR cage of only 68 carbon atoms containing annelated five-membered rings. This internal ring network is metal-stabilized and is accessible for external organic reaction chemistry.

Molecular graphs, point groups, and fullerenes

A general and convenient method is described by which one can obtain the point group, the 13C NMR pattern, and the number of IR‐ and Raman‐active vibrations of any given fullerene structure directly from its molecular graph. The method is based on certain ‘‘topological’’ atomic coordinates, the Cartesian components of which in a topological principal axis system are proportional to the components of three selected eigenvectors of the adjacency matrix of the graph. Its practical utility lies in combination with existing theoretical results, including analytical molecular‐orbital rules which predict two distinct families of closed‐shell fullerenes and a systematic search which generates all known Cn fullerene graphs. The overall strategy is illustrated in an experimentally relevant application to the 24 distinct isolated‐pentagon fullerene isomers of C84.

BORON-NITROGEN ANALOGUES OF THE FULLERENES : ELECTRONIC AND STRUCTURAL PROPERTIES

Abstract On the basis of a systematic density functional tight-binding study of boron-nitrogen polyhedra (BN) x composed entirely of four- and six-membered rings, it is predicted that octahedron-like structures B 12 N 12 , B 16 N 16 and B 28 N 28 are “magic” (i.e. anomalously stable) clusters. The infrared spectrum of B 12 N 12 is predicted. The similarities and differences between these “inorganic fullerenes” and the carbon-based equivalents are outlined. Ahigh stability of the (BN) x clusters is found to correlate with a large HOMO-LUMO gap.

Counter‐Rotating Ring Currents in Coronene and Corannulene

Explicit ab initio current-density maps contradict the annulene-within-an-annulene model of [n]circulenes: in both coronene and corannulene the expected diamagnetic current on the perimeter is opposed by the central, paramagnetic ring current.

π-Systems in three dimensions

Abstract Highly symmetric, three-connected carbon clusters are treated as three-dimensional π-systems, using spherical harmonics to classify the orbitals. Simple Huckel calculations predict stable closed shells for neutral C 60 and C 70 , in agreement with recent experimental observations. A previously proposed C 120 structure is unstable with respect to two C 60 clusters. Neutral C 20 and C 80 are not closed-shell in icosahedral symmetry. Inclusion of interaction between the exo π-systems and skeletal edge bonding does not change the predicted electron count.

Velocity-dependent property surfaces and the theory of vibrational circular dichroism

Abstract The familiar idea of a molecular property surface in which a property (such as the dipole moment) is expressed as a function of nuclear coordinates R I , is extended to cover properties odd under time-reversal by including the nuclear velocities ·R I as variables. One such property is the magnetic dipole moment m . This approach relates magnetic dipole vibrational transition moments to derivatives (∂ m / ∂ ·R I ) which may be calculated within the clamped-nucleus approximation, and used in the theory of vibrational circular dichroism. The same derivatives describe the electric field at a nucleus induced by an external dynamic magnetic field, leading to a physically transparent description of VCD. Sum rules relate these derivatives to the molecular paramagnetizability.

Pentagon adjacency as a determinant of fullerene stability

Optimisation of geometries of all 40 fullerene isomers of C40, using methods from molecular mechanics and tight-binding to full abinitio SCF and DFT approaches, confirms minimisation of pentagon adjacency as a major factor in relative stability. The consensus predictions of 11 out of 12 methods are that the isomer of lowest total energy is the D2 cage with the smallest possible adjacency count, and that energies rise linearly with the number of adjacencies. Quantum mechanical methods predict a slope of 80–100 kJ mol-1 per adjacency. Molecular mechanics methods are outliers, with the Tersoff potential giving a different minimum and its Brenner modification a poor correlation and much smaller penalty.

RING CURRENTS IN AROMATIC HYDROCARBONS

Coupled Hartree-Fock theory is used to compute and map the current density induced in planar hydrocarbons by an external magnetic field. Results of useful accuracy can be obtained with modest (6-31G**) basis sets by employing a continuous gauge transformation. Maps are presented and discussed for benzene, naphthalene, anthracene, tetracene, pentacene, heptacene, and biphenylene.

Increasing cost of pentagon adjacency for larger fullerenes

The cost of a pentagon adjacency in a fullerene cage grows linearly from 72 kJ mol−1 for C30 to 111 kJ mol−1 for C60, according to systematic QCFF/PI model calculations on a set of 2624 structural isomers.

Systematics of bonding in non-icosahedral carbon clusters

General formulas are presented for the vertex numbers, ν, of pentagon+hexagon polyhedra of icosahedral, tetrahedral or dihedral symmetries. Criteria for uniqueness of representation, isomer counts and grouping of pentagons are established. All polyhedra with 256 vertices or less and belonging to T, D5, D6or their supergroups are listed. With the addition of C3ν to the dihedral and higher groups, at least one pentagon+hexagon cluster is found for all even ν≥20 except for ν = 22 which is unrealisable in any symmetry, and ν = 46 (for which a C3 polyhedron exists). Carbon clusters with closed electronic shells are shown to be generated by a geometrical leapfrog procedure: for all ν = 60+6k (where k is zero or greater than one) at least one closed shell structure is predicted. In dihedral symmetry closed shells also exist for some other values of ν. Separation of the 12 pentagonal faces is not sufficient to ensure a closed electronic shell but appears to be a necessary condition in dihedral or tetrahedral symmetry.