T. G. Schmalz

C60 carbon cages

Abstract Arrangements of carbon atoms in cage-like structures with no dangling bonds are considered as possible novel allotropic forms of carbon. Five different C60 cages, having certain favorable structural characteristics, are identified. Quantitative resonance-theoretic calculations are made and compared to simpe Huckel results. The favored structure is found to be the so-called Buckminsterfullerene structure.

Favorable structures for higher fullerenes

A study is made of elemental carbon cages corresponding to polyhedra with hexagonal and pentagonal faces such that no two pentagons abut. All such preferable cages of up to ν=94 vertices are generated, and simple Huckel MO and resonance-theoretic computations are made. The graphical structures more favored by these computations are reported for the experimentally relevant vertex (or atomic) counts of ν=60, 70, 76, 78, 84, and 90. The NMR line patterns for these favorable structures are also given.

The poly-polyphenanthrene family of multi-phase π-network polymers in a valence-bond picture☆

Abstract A family of long polymer strips are argued to exhibit distinct phases each with a different long-range ordering in electronic structure. Degenerate ground-state phases necessarily occur (due to symmetry) for odd width strips, and may also occur for even width strips. A new type of solitonic excitation is indicated; it may be viewed as consisting of a group of bound solitons that cannot mutually annihilate (i.e. there are no antisolitons in the group). Valence-bond and band-theoretic molecular-orbital views are compared.

Alternant boron nitride cages: A theoretical study

Heteroatomic cages (BN/2NN/2) with borons and nitrogens fully replacing alternant sets of carbons in cages are built graph-theoretically and investigated via the semiempirical MNDO Hamiltonian. The comparison with their parent carbon cages CN is made in terms both of electronic and of geometric changes. Infinite classes first of octahedral symmetry and second of hexagonal-bipyramidal symmetry fullerenoid cages are considered in detail. The difference in the electronegativities for boron and nitrogen implies the opening of HOMO-LUMO gaps for alternant BN clusters. In general, the borons prefer planar geometry (sp2 hybridization) while the nitrogens prefer pyramidalization (sp3 hybridization).

Reply to Comment on “Favourable structures for higher fullerenes”

Abstract We have recomputed the isomer count for 60-atom fullerenes. We find 1812 isomers rather than 1790 as reported earlier.

Preferable Fullerenes and Clar-Sextet Cages

Abstract All 558 fullerenes satisfying the isolated-pentagon rule and having no more than 96 vertices are generated and analyzed. A novel subclass of cages of especially favored π-network “topology” is identified, given several structural characterizations, and all such cages of up to 120 vertices are generated and analyzed.

The magnetic susceptibility of Buckminsterfullerene

Abstract It is argued that the analysis of the magnetic susceptibility of icosahedral C 60 given by Haddon and Elser in a recent Letter underestimates the aromatic character of Buckminsterfullerene. Instead, it is argued that, when compared against the best available local reference structure, the ab initio calculation of Fowler, Lazzeretti, and Zanasi should be interpreted as showing a significant degree of delocalization consistent with an aromatic structure.

All acyclic hydrocarbons: formula periodic table and property overlap plots via chemical combinatorics

It is sought to extend the characterization of isomer classes by using combinatoric techniques long used for isomer enumerations. To this end a general family of isomers (which is challenging to deal with even at the level of conventional enumeration) is considered, namely that of all acyclic hydrocarbons CnH2m with classical valence structures. This set of hydrocarbons is partitioned into structural-isomer classes, and these in turn are presented in the form of a ‘‘ formula periodic table’’ with n and m identifying rows and columns, respectively. Then various isomer-class-averaged characteristics (beyond isomer enumerations) are sought to be entered into the associated positions in this periodic table. Such characteristics include heat of formation, magnetic susceptibility and index of refraction, each of which may be estimated via substructural ‘‘cluster expansion’’. These cluster-expansion-estimated property averages as well as associated standard deviations are developed by way of a generating-function chemical combinatorics for isomers of up to n=25 carbons and 2m=52 hydrogens. These results then are incorporated in property ‘‘ overlap plots’’ to reveal overall isomer-class property trends in the periodic table for this set of ≈1013 structural isomers distributed over ≈360 isomer classes.

Real‐space renormalization for Heisenberg models on two‐dimensional lattices

Real‐space renormalization methods which simply shift and rescale the interaction parameters in the nearest‐neighbor Heisenberg model are investigated for two‐dimensional lattices of equivalent sites. Results are presented for the hexagonal, square‐planar, triangular, and Kagome lattices via three different renormalization techniques. The first, which has been studied for some time, uses perturbation theory to evaluate the renormalized interactions. The second uses the variational method to improve on the perturbative results. The third method is based on a cluster expansion and is found to give much improved agreement with numerical results form Monte Carlo calculations, but it does not provide a variational bound to the exact solution. The dependence of all three methods on the size and shape of the renormalized block of sites is also investigated.

A distance-dependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene

The Hubbard model, which is widely used in physics but is mostly unfamiliar to chemists, provides an attractive yet simple model for chemistry beyond the self consistent field molecular orbital approximation. The Hubbard model adds an effective electron-electron repulsion when two electrons occupy the same atomic orbital to the familiar Hückel Hamiltonian. Thus it breaks the degeneracy between excited singlet and triplet states and allows an explicit treatment of electron correlation. We show how to evaluate the parameters of the model from high-level ab initio calculations on two-atom fragments and then to transfer the parameters to large molecules and polymers where accurate ab initio calculations are difficult or impossible. The recently developed MS-RASPT2 method is used to generate accurate potential energy curves for ethene as a function of carbon-carbon bond length, which are used to parameterize the model for conjugated hydrocarbons. Test applications to several conjugated/aromatic molecules show that even though the model is very simple, it is capable of reasonably accurate predictions for bond lengths, and predicts molecular excitation energies in reasonable agreement with those from the MS-RASPT2 method.