P.W. Fowler

How unusual is C60? Magic numbers for carbon clusters

Abstract Icosahedral carbon clusters with pentagonal and hexagonal faces are Goldberg polyhedra. They have 20(b2 +bc + c2) atoms, where b and c are non-negative integers, and obey an electron-counting rule similar to the famous Huckel (4n + 2) prescription. When b − c is divisible by 3 the cluster has a multiple of 60 atoms and is closed-shell; otherwise it has 60n + 20 atoms and is open-shell. A geometrical interpretation of this rule is: open-shell Goldberg clusters have atoms on the C3 axes, closed-shell clusters do not. Closed shells are predicted for C60, C180, C240, C420, C540,.... Irrespective of pointgroup symmetry, structures of large clusters may be generated by a leapfrog method from smaller ones. A tetrahedral structure generated in this way is the best candidate for C120

Electric and magnetic properties of the aromatic sixty-carbon cage

Abstract We report the use of large supercomputer resources to perform the first ab initio calculations on the polarisability and magnetisability of C 60 and its smaller analogue C 20 2+ . It is found that both molecules have the high polarisability characteristic of π systems and the diamagnetic magnetisability typical of aromatic molecules. Insofar as it is possible to extrapolate to the basis-set limit, the calculations predict net diamagnetism for the clusters, and a diamagnetic effect on the NMR chemical shift of an encapsulated atom.

Unconventional ring currents in an 'all-metal aromatic', Al42-

Abstract The square planar anion Al 4 2− supports an unconventional diamagnetic ring current which originates in the σ system, has negligible contribution from the two-electron π system, and survives in pyramidal bimetallic clusters MAl 4 − (M=Li, Na, Cu).

Pseudo-π currents: rapid and accurate visualisation of ring currents in conjugated hydrocarbons

Abstract An inexpensive method for accurate simulation of π contributions to ring currents is proposed. A conjugated carbon framework is formally replaced by a set of hydrogen atoms bearing single 1s (STO-3G) orbitals. Calculation, with the ipsocentric CTOCD-DZ method, of the in-plane σ current density induced by a perpendicular magnetic field then gives a close numerical match to the out-of-plane π current density of the original carbon system at a height of 1 bohr. This ‘pseudo-π’ method depends on the one-to-one correspondence in symmetry between σ and π orbitals and is capable of reproducing the general pattern of π current, its specific features and its orbital decomposition for polycyclic hydrocarbon systems.

C36, A HEXAVALENT BUILDING BLOCK FOR FULLERENE COMPOUNDS AND SOLIDS

Abstract Structures and energies are calculated at the DFTB level for C 36 -based fullerenes, hydrides, oligomers and solids. The two fullerenes with minimal pentagon adjacencies are isoenergetic. The isomer implicated in recent experiments has C 6 v broken symmetry, a small HOMO–LUMO gap and can gain or lose up to six electrons. C 36 forms stronger inter-cage bonds than larger fullerenes. A favoured σ -bonding pattern rationalises a dimer with ten times the stabilisation of (C 60 ) 2 , a linear polymer, a ‘superbenzene’ oligomer, a ‘supergraphite’ layer and a hexagonal close-packed solid with a monomer stabilisation of 522 kJ mol −1 and a d -spacing (6.82 A) compatible with the experiments.

Ring current and electron delocalisation in an all-metal cluster, Al42−

Abstract Localised-orbital analysis of the current density induced by a perpendicular magnetic field in square-planar Al 4 2− demonstrates the intrinsic non-localisability of the σ electrons of this metallic cluster and confirms their dominant role in its diamagnetic ring current. Though delocalised, the π electrons do not give rise to a significant ring current.

Calculations of two- and three-body dispersion coefficients for ions in crystals

Coupled Hartree-Fock theory is used to calculate two and three body dispersion coefficients for in-crystal ions (Li+, Na+, K+, Rb+, Mg2+, Ca2+, F-, Cl-, O2-) subject to both electrostatic and overlap interactions. For anions the reduction of the dispersion coefficients in the crystalline environment parallels the decrease of the static polarizability. From comparison of ab initio results with those of the Slater-Kirkwood formula we propose an empirical scheme for calculating in-crystal dispersion coefficients from accurate static polarizabilities. We find that two-body dispersion forces are not responsible for the greater stability of the 8 : 8 compared to the 6 : 6 polymorph of CsCl. A correlated Moller-Plesset calculation of the static polarizability of Rb+ confirms our previous scheme for deriving polarizabilities from experiment.

The Jahn–Teller instability of fivefold degenerate states in icosahedral molecules

The linear H⊗(g⊕2h) Jahn–Teller problem, relevant to the instability of icosahedral molecules in fivefold degenerate states, is analyzed in detail for the first time. The method of the isostationary function is used to identify all the extrema of the corresponding potential energy surface. Depending on one single mode‐splitting parameter, two different coupling regimes are possible, favoring either pentagonal or trigonal minima. The saddle points on interconversion paths between equivalent minima are identified and the topology of the low‐energy regions of the surface is determined. The results are found to be in agreement with the epikernel principle. In addition the symmetry characteristics of the principal warping term under the SO(5) symmetry group of electronic space are assigned.

Rotational spectra and structures of van der Waals dimers of Ar with a series of fluorocarbons: Ar⋅⋅⋅CH2CHF, Ar⋅⋅⋅CH2CF2, and Ar⋅⋅⋅CHFCF2

Rotational spectra of van der Waals dimers between an argon atom and CH2CHF, CH2CF2, and CHFCF2 have been obtained by pulsed‐supersonic nozzle Fourier transform microwave spectroscopy. Analysis of the derived spectroscopic constants shows that the dimers have structures such that for CH2CHF, CH2CF2, and CHFCF2 the Ar atom is positioned over the FCCH, FCF, and FCCF atomic chains with Ar‐molecular center‐of‐mass distances of 3.62 A, 3.51 A, and 3.56 A, and angles between the Ar–cm axis and molecular planes of 48.2°, 72.9°, and 60.5°, respectively. Structures for the three dimers are also predicted with a simple multisite model which describes the anisotropy of the dispersive interaction; both the Ar acceptor site and the atom–atom distances are satisfactorily reproduced.

Polarisabilities of triply bonded molecules: The 14- and 26-electron systems CN−, N2, HCN, C2H2, C2N2, HC3N and C4H2

Abstract Dipole moments and polarisabilities are calculated by correlated methods for a series of linear molecules containing NN, CN and CC triple bonds. A compact polarised basis gives near-Hartree-Fock anisotropic polarisabilities with largest component along the molecular axis and roughly additive behaviour with increasing chain length. Correlation corrections to the polarisability are insignificant for these systems.