Michał K. Cyrański

Separation of the energetic and geometric contributions to the aromaticity of π-electron carbocyclics.

Separation of the aromaticity index HOMA, based on experimental geometry, into energetic and geometric contributions is proposed for carbocyclic π-electron systems. The decrease of the aromatic character may be due either to an increase of bond length alternation (geometric term) or to the lengthening of the mean bond lengths of the ring (energetic term). On the basis of 169 sets of data for benzene rings in benzenoid hydrocarbons, 116 in para-disubstituted benzene derivatives and 90 in TCNQ molecules in EDA complexes and salts, as well as 48 for five-membered rings in cyclopentadienyl complexes with Rh it is shown that these two terms are uncorrelated, supporting the view of Katritzky et al.1–4 and Jug et al.5 that aromaticity is a multidimensional phenomenon. The separation is applied to five-, six- and seven- membered rings in typical π-electron systems (benzenoid hydrocarbons, fullerenes, fulvene and heptafulvene derivatives). Aromaticity index (HOMA) = 1 - [dearomatization term due to bond length alternations (GEO) + energetic term (EN)]. All terms are accessible from experimental bond lengths.

Separation of the energetic and geometric contributions to the aromaticity. Part IV. A general model for the π-electron systems

Application of the Pauling bond number1 to the aromaticity index HOMA2–3 allowed us to extend its separation into the geometric and energetic contributions for the hetero π-electron systems. The energetic term (EN) represents the part related to resonance energy of a given system. The geometric term represents dearomatization due to an increase of bond length alternation (localisation of double bonds). The Bird indices I5 and I64 well represent aromatic character due to its geometric features. In most cases geometric contributions play a significant role and variation in GEO-term is the most important factor in variation of HOMA values and their correlation with Birds indices. Aromaticity indices for 24 five- and six-membered, most typical, heterocyclic systems are presented and discussed. Aromaticity index (HOMA) = 1 - [dearomatization term due to bond length alternations (GEO) + energetic term (EN)] is extended for hetero-π-electron systems. All terms are accessible from experimental bond lengths.

Facts and artifacts about aromatic stability estimation

Abstract The stability of a set of 105 five-membered π-electron systems (involving aromatic, non-aromatic and anti-aromatic species) was evaluated using six isodesmic reactions of which two belong to the subclass of homodesmotic reactions, which are based on cyclic and acyclic reference systems. We demonstrate that the ‘Resonance Energies’ derived from isodesmotic schemes have obvious flaws and do not correct or cancel other contributions to the energy, such as the changes of hybridization, homoconjugation of heterosubstituted cyclopentadienes, conjugative interactions of CC or CX (X=N or P) with a π or pseudo π orbital at Y (Y=O, S, NH, PH), strain, etc. as effectively as possible. Likewise, ‘aromatic stabilization energies (ASE)’ derived from homodesmotic schemes based on the acyclic reference compounds do not give satisfactory results. We strongly recommend that only cyclic reference compounds should be used for ASE and other aromaticity evaluations. The analysis is based on ab initio optimized geometries at B3LYP/6-311+G∗∗.

Separation of the Energetic and Geometric Contributions to Aromaticity. 2. Analysis of the Aromatic Character of Benzene Rings in Their Various Topological Environments in the Benzenoid Hydrocarbons. Crystal and Molecular Structure of Coronene

Statistical analysis of the aromatic character and its geometric and energetic contributions of 167 benzene rings embedded in various topological environments in 26 benzenoid hydrocarbons leads to the following conclusions:  the aromatic character of benzene rings with three or fewer fused rings is due mostly to geometric contributions, whereas in other cases energetic contribution is decisive. Aromaticity indices for individual rings (local aromaticity) depend strongly on the kind of topological environment. Terminal rings always exhibit a strong aromatic character, whereas those fused to many rings are often weakly aromatic. The study is based on precisely solved X-ray or neutron crystal structure determination retrieved from Cambridge Structural Database supplemented by our own precise determination of coronene.

Quadrannulene: A Nonclassical Fullerene Fragment

The presence of nonhexagonal rings in an otherwise graphitic lattice induces curvature. Pentagons are common—twelve pentagons surrounded by hexagons make up C60. Larger rings are present in Stone–Wales defects, and the polyhedral formula of Euler mandates their existence in carbon nanotube Y-junctions. Except for a single, partially saturated example, four-membered rings in graphitic structures are, however, unknown. The smallest examples of these graphitic structures are the [n]circulenes, wherein a central n-sided polygon is surrounded by n-fused benzenoid rings. [7]Circulene, first prepared by Yamamoto, Nakazaki, and coworkers in 1983, is saddle shaped. [6]Circulene, or coronene, is the trivial, planar case, and it was first synthesized by Scholl andMeyer in 1932 but also occurs naturally. [5]Circulene, or corannulene, comprises 1/3 of the C60 skeleton and has been intensely studied, and it was first prepared by Lawton and Barth in 1971. Whereas a few pioneering attempts have been reported, [4]circulene has never been synthesized before. We report herein the preparation and characterization of a stable [4]circulene. By analogy with Lawton s naming of corannulene (Latin: cor, heart; annula, ring), we suggest the trivial name quadrannulene (Latin: quadra, square; annula, ring) for the [4]circulene parent. Hence, we name this derivative 1,8,9,16-tetrakis(trimethylsilyl)tetra-cata-tetrabenzoquadrannulene, abbreviated TMS4-TBQ. The IUPAC name and atom numbering are given in the Supporting Information. Our unoptimized five-step synthesis (Scheme1) provides TMS4-TBQ in very low yield. Hopf and co-workers recently summarized two synthetic strategies to the quadrannulene core: making the four-membered ring from [2,2]-paracyclo-

Global and Local Aromaticity of Linear and Angular Polyacenes

Abstract Ab initio (B3LYP/6-311G∗∗) optimisation of seven linear and five angular polyacenes gave us an opportunity to study aromaticity in terms of HOMA index and its components EN and GEO, the energy of the carbon skeleton of these hydrocarbons was calculated from CC bond lengths. Independently, the Cohen–Benson group additivity values were used to estimate the thermochemical aromatic stabilisation energy (ASE). For individual rings the NICS values were computed and compared with HOMA. An increase of size of both linear and angular polyacenes is associated with a substantial decrease in their aromaticity, with a greater decrease for the linear polyacenes. This is well documented by both HOMA and Cohen–Benson ASE.

Aromaticity strongly affected by substituents in fulvene and heptafulvene as a new method of estimating the resonance effect

Abstract Very good dependences of the variation in π-electron delocalisation expressed by the aromatic character of the ring, defined by the geometry-based HOMA model and NICS index in mono 6-substituted fulvene and 8-substituted heptafulvene derivatives on the nature of substituent allows us for defining the substituent through resonance effect (by means of σp+ and σp− scale of the substituent effect). The analysis is based on 35 optimised systems at DFT B3LYP/6-311+G** level of theory.

Unidirectional Molecular Stacking of Tribenzotriquinacenes in the Solid State: A Combined X‐ray and Theoretical Study

A combined X-ray diffraction and theoretical study of the solid-state molecular and crystal structures of tribenzotriquinacene (TBTQ, 2) and its centro-methyl derivative (3) is presented. The molecular structure of the parent hydrocarbon displays C3v symmetry and the three indane wings adopt mutually orthogonal orientations, similar to the case in its previously reported methyl derivative (3). Also similarly to the latter structure, the bowl-shaped molecules of compound 2 form infinite molecular stacks with perfectly axial, face-to-back (convex-concave) packing and with parallel and unidirectional orientation of the stacks. The experimentally determined intra-stack molecular distance is 4.75 Å for compound 2 and 5.95 Å for compound 3. Whereas the molecules of compound 2 show a slight alternating rotation (±6°) about the common axis of each stack, those of compound 3 show perfect translational symmetry within the stacks. We used dispersion-corrected density functional theory to compute the crystal structures of tribenzotriquinacenes 2 and 3. The London dispersion correction was crucial for obtaining an accurate description of the crystallization of both analyzed systems and the calculated results agreed excellently with the experimental measurements. We also obtained reasonable sublimation energies for both compounds. In addition, the geometries and dimerization energies of oligomeric stacks of compound 2 were computed and showed smooth convergence to the properties of the infinite polymeric stack.

Interplay of π-Electron Delocalization and Strain in [n](2,7)Pyrenophanes

The geometries of a series of [n](2,7)pyrenophanes (n = 6-12) were optimized at the B3LYP/6-311G** DFT level. The X-ray crystal structures determined for the [9](2,7)- and [10](2,7)pyrenophanes agreed excellently with the computed structures. The degree of nonplanarity of the pyrene moiety depends on the number of CH2 groups in the aliphatic bridge and, as analyzed theoretically, influences the strain energy and the extent of pi-electron delocalization in the pyrene fragment. Various indices, e.g., the relative aromatic stabilization energies (DeltaASE), magnetic susceptibility exaltations (Lambda), nucleus-independent chemical shifts (NICS), and the harmonic oscillator model of aromaticity (HOMA) were used to quantify the change in aromatic character of the pyrene fragment. DeltaASE and relative Lambda values (with respect to planar pyrene) were evaluated by homodesmotic equations comparing the bent pyrene unit with its bent quinoid dimethylene-substituted analog. The bend angle, alpha, DeltaASE, and Lambda were linearly related. The aromaticity decreases smoothly and regularly over a wide range of bending, but the magnitude of the change is not large. The differences between planar pyrene (alpha = 0 degrees) and the most distorted pyrene unit (alpha = 39.7 degrees in [6](2,7)pyrenophane) are only 15.8 kcal/mol (DeltaASE) and 18.8 cgs-ppm (Lambda). Also, the geometry-based HOMA descriptor changes by only 0.07 unit. The local NICS descriptors of aromatic character also correlate very well with the global indices of aromaticity. In line with the known reactivity of pyrenophanes, the variations of NICS(1), a measure of pi-electron delocalization, were largest for the outer, biphenyl-type rings. The strain energies of the pyrene fragments were much larger and varied more than those evaluated for the bridge. Both strain energies were interrelated (correlation coefficient R = 0.979) and depend on the bend angle, alpha.

Two sources of the decrease of aromaticity: Bond length alternation and bond elongation. Part I. An analysis based on benzene ring deformations

Abstract Decrease of aromaticity of the π-electron system may be described by two different and independent mechanisms: (i) an increase of the bond length alternation and (ii) an extension of the mean bond length (bond elongation). These two mechanisms are described by two contributions to the HOMA index: GEO and EN, respectively. These contributions correlate very well with the total Hartree-Fock energy of the benzene ring deformed in two ways: (i) when all CC bond lengths are set equal and their length is gradually increased, and (ii) when the mean CC bond length is fixed, and the difference in length between adjacent CC bonds gradually increases. Both changes in geometry bear the changes in the aromatic character of the ring, and the HOMA-values as well as the Hartree Fock energies correlate excellently with Schleyers NICS values.