The effect of cyclopentafusion on the aromatic properties of pyrene and its cyclopentafused congeners has been studied by calculating resonance energies, using the valence bond (VB) method, and nucleus independent chemical shifts using DIGLO. The VB resonance energy is only slightly affected by cyclopentafusion. The resonance interactions between Kekulé resonance structures that lead to six π electron (benzene-like) conjugated circuits have the largest contributions to the resonance energy, in favor of Clar's model. For all compounds these contributions are of similar magnitude. Hence, according to the resonance criterion, all compounds have the same aromatic character. In contrast, the total NICS values show a decrease of aromatic character of the compounds in the series upon the addition of externally fused five-membered rings. However, in line with the resonance criterion, the diamagnetic part of the shielding tensor perpendicular to the molecular framework is nearly constant for all compounds, provided that comparable gauge origins are chosen. Thus, care should be taken by comparing the aromatic character of rings of different molecules by considering only their total NICS values.

The geometry and energy of 1,3,5-cyclohexatriene, the reference molecule for the determination of the extra stabilization of benzene, have been calculated using an Ab Initio Valence Bond method. The theoretical resonance energy, according to Dewar, calculated as the energy difference between two-structure benzene and single-structure 1,3,5-cyclohexatriene, both with completely optimized geometries and orbitals, is only )12.05 kcal/mol. Resonance energies of )25.37 (local orbitals), )19.82 (delocal orbitals) and )44.13 (breathing orbitals) kcal/mol are found using the Pauling definition. The concept of the vertical resonance energy, however, is proven to be not tenable beyond a minimal basis. Ó

epoc ABSTRACT: C m H m (m ¼ 4, 6, 8) species are analyzed in D mh and D (1/2)mh geometries by means of valence bond (VB) calculations. The fundamental factors that distinguish aromatic and antiaromatic modes of electron delocalization are elucidated by analysis of the mixing between the covalent-state and ionic structures that distribute the electrons in all possible modes available in the cycle. The major difference found is that, by contrast to the aromatic species where all the ionic structures mix into the covalent state, in the antiaromatic species the set of diagonal-ionic structures is excluded from mixing with the covalent-state, owing to its fundamental symmetry features. This exclusion of covalent-ionic mixing is expressed at the most fundamental building blocks of the wavefunction; the spin-alternant state. The spin-alternant state is a resonance hybrid of the two spin-alternant determinants. This resonance hybrid will support a collective motion of the p -electrons around the perimeter of the ring only if ionic structures can mix to mediate the electronic flow. It is shown that in aromatic species all the ionic structures mix and sustain a continuous electronic flow around the ring perimeter. By contrast, owing to the exclusion of the diagonal-ionic structures in antiaromatic compounds, the electronic flow in antiaromatic species is interrupted. Symmetry and angular momentum analyses of the ground state in the presence of an external magnetic field show that the properties of the spin-alternant state can qualitatively describe the magnetic properties of the two classes. The continuous flow of -electrons mediated by the ionic structures of aromatic species is responsible for the enhanced diamagnetism of these species. By contrast, paramagnetic -ring current in antiaromatic species becomes possible only in the presence of the magnetic field that allows the mixing of the otherwise excluded ionic structures. Scheme 1. Vertical resonance energies (VREs) calculated by valence bond (Ref. 10) for benzene, CBD and COT in their uniform D mh geometries (with equal C-C bond lengths) 732 A. SHURKI ET AL.Figure 5. The reduced resonance between the spin-alternant determinants describes a collective circular motion of the -electrons. The propensity of this 'motion' depends on the overlap and matrix element of the determinants 738 A. SHURKI ET AL.

The effect of ring deformation on aromaticity has been studied for bent benzene molecules in which two carbon atoms have been bent out of plane, resulting in a boat conformation. Valence‐bond self‐consistent field (VBSCF) calculations have been performed on these molecules to obtain insight into the aromaticity of bent benzenes. Results for total energy, structure energies, weights, and orbital overlaps show that the molecule keeps its aromatic nature up to 55°. After 55° a transition to Dewar benzene occurs. The valence‐bond model, by showing the weights of both Dewar and Kekulé structures, is an excellent tool to study deformed benzene. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 213–221, 1999

The Ab Initio Valence Bond program TURTLE has been under development for about 12 years and is now becoming useful for the non-specialist computational chemist as is exemplified by its incorporation in the GAMESS-UK program. We describe here the principles of the matrix evaluation and orbital optimisation algorithms and the extensions required to use the Valence Bond wavefunctions in analytical (nuclear) gradient calculations. For the applications, the emphasis is on the selective use of restrictions on the orbitals in the Valence Bond wavefunctions, to investigate chemical concepts, in particular resonance in aromatic systems.

Geometry optimizations have been performed for benzene and cyclobutadiene and for the corresponding moieties with nonresonating double bonds, viz. 1,3,5-cyclohexatriene and 1,3-cyclobutadiene. The calculations were done using the valence bond self-consistent field method including orbital optimization. Both strictly local and delocalized p-like orbitals were used for the system, which influences the strengths of the bonds. The calculations result in geometries and resonance and stabilization energies for benzene and cyclobutadiene, which are compared with theoretical models of aromaticity. The importance of resonance is discussed.

A gradient method for general valence bond wave functions is presented. The electronic energy is used as a Lagrange multiplier. The derivatives of the normalization and of the first-and second-order cofactors present in the energy expression have to be evaluated, giving rise to first-, second-, and third-order cofactors. This evaluation is done using an extension of methods described previously. The use of gradients is illustrated with some calculations on organic molecules, viz. ethene, 1, 4-butadiene, and benzene.

these problems. We give examples of applications running on Astro-WISE and EGEE and review future development of the merged system.