Facts and artifacts about aromatic stability estimation

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^∗∗.     

A novel approach in analyzing aromaticity by homo- and isostructural reactions: an ab initio study of fluorobenzenes

The influence of fluorine substitutions on the stability of benzene is examined by using the Hartree-Fock (HF) and MP2 models. It is conclusively demonstrated that homodesmotic reactions based on the open-chain zigzag polyenes are unsatisfactory. A comparison of the intramolecular interactions of educts and products shows that they are not well balanced. Hence, these reactions should be abandoned in discussing aromaticity. A much better vehicle for exploring aromaticity is provided by homostructural reactions, which employ cyclic monoene and diene as reference model compounds. Their heavy atoms are enforced to assume planar geometries to enable sigma/pi separation. The HF/cc-pVTZ calculations show that extrinsic aromaticity of benzene B DeltaE(ease)(B)() arises both from the sigma- and pi-contributions. They are -14.8 and -23.1 in kcal/mol, respectively, if the stockholder energy partitioning scheme is employed. This result implies that both the sigma- and pi-frameworks contribute to the aromatic stabilization of B, the latter being more important. The total aromatic stabilization DeltaE(ease)(B)() is -37.9 kcal/mol. Schleyer's indene-isoindene isomerization approach also strongly indicates that the decisive factor in determining the aromatic stability of the benzene moiety is the pi-electron framework. The origin of extrinsic aromaticity is identified as the increased nuclear-electron attraction of both sigma- and pi-electrons, if 1,3-cyclohexadiene is used as a gauge compound. Further, by using a system of isostructural reactions, it is conclusively demonstrated that fluorobenzenes exhibit a remarkable additivity of the substituent effects, as far as the stability of multiply substituted benzenes is concerned. This additivity rule is so accurate that it enables delineation of the fluorine repulsions and the aromaticity defect DeltaE(AD). It appears that the DeltaE(AD) values increase upon sequential fluorine substitution at the next nearest (vicinal) position thus making multiply fluorinated benzenes less stable.     

Is nucleus-independent chemical shift scan a reliable aromaticity index for planar heteroatomic ring systems?

Density functional theoretical investigation has been performed to explore the reliability of the nucleus-independent chemical shift (NICS) scheme in assessing aromatic behavior of some planar six-membered heteroatomic systems. It has been observed that the NICS scan and the diamagnetic and paramagnetic contributions of the in-plane and out-of-plane components are quite reliable in assessing any aromatic or antiaromatic behavior in borazine. However, for boraphosphabenzene, the aromatic stabilization energy is too small to consider it as an aromatic system but the NICS scans and the homodesmotic reactions suggest an opposite trend. Interestingly, in the case of alumazene, a very shallow minimum is observed for the out-of-plane component, which suggests the presence of weak diamagnetic ring current. However, the diamagnetic and paramagnetic contribution curves to the out-of-plane component for alumazene clearly reveal a net paramagnetic contribution. Thus we may surmise that apart from the single NICS value, the NICS scan also is not a very authentic tool for the assessment of aromaticity of planar six-membered heteroatomic systems.     

On the aromatic stabilization of corannulene and coronene

The application of set of homodesmotic reactions allowed us to estimate the aromatic stabilization energy (ASE) of corannulene and coronene. Appropriate reactions have been applied to balance syn/anti mismatches in di-, tetra- and hexamethylene substituted derivatives. Based on many different polycyclic reference structures that compensate the effect of strain in the corannulene moiety the value of ASE comes to 44.5 kcal mol(-1). Planar corannulene is more stabilized by cyclic π-electron delocalization by ca. 10.7 kcal mol(-1), as compared with a bowl-shaped system. A similar approach for coronene leads to an ASE equal to 58.4 kcal mol(-1).     

Are 1,2-dihydrodiazetes aromatic? An experimental and computational investigation

A thorough experimental and computational investigation of the aromaticity of the 1,2-dihydrodiazete ring system was carried out. The X-ray crystal structure of 1,2-dihydrodiazete 6 is reported, and the alkene-like reactivity of compound 6 is described. The compound's structure and reactivity suggest that 6 is not aromatic. This conclusion is corroborated by computational results on 6 and related compounds including homodesmotic reactions to test for aromatic stabilization, NICS calculations, and NBO calculations. Compound 6, and 1,2-dihydrodiazetes in general, are concluded to be strained heterocycles with no indication for aromatic stabilization.     

Homodesmotic reaction for fullerenes

The ASE (aromatic stabilization energy) for C₆₀ and C₇₀ have been evaluated by a new homodesmotic reaction and the results support the early established fact that C₇₀ is more stable than C₆₀.     

Aromatic stabilization energy calculations for the antiaromatic fluorenyl cation. Issues in the choice of reference systems for positively charged species

Aromatic stabilization energy (ASE) calculations for the fluorenyl cation show substantial destabilization in comparison to suitable reference systems (16.3 +/- 1.6 kcal/mol), supporting its categorization as an antiaromatic species. The choice of appropriate reference systems is exacting for cationic systems because of the need to match strain energies, convolved with allylic-type resonance terms and other potential structural effects that stabilize charge. Several homodesmotic ASE reaction systems are examined to demonstrate the role played by these factors in the calculation of an ASE value for the fluorenyl cation. The magnitudes of the derived ASE are quite similar for four very different determinative, homodesmotic reaction systems, giving strong support to the inherent accuracy of the final derived ASE value. The results of nucleus independent chemical shift calculations for the components of each one of the ASE reactions add additional weight to this conclusion.     

3,4-二硫方酸芳香性和气相酸性的理论研究

在RHF/6-311G^**,RHF/6-311+G^**和B3LYP/6-311+G^**水平优化得到3,4-二硫方酸(3,4-二巯基-3-环丁烯-1,2-二酮)三种平面构象异构体的平衡几何构型.用MP2(Full)/6-311G^**//RHF/6-311G^**方法计算单点能量,发现ZZ型异构体是能量最低构象,且ZZ和ZE型能量非常接近.用优化的最稳定构象ZZ型异构体在RHF/6-311G^**//RHF/6-311G^**,RHF/6-311G^**//RHF/6-311G^**,MP2(Full)/6-311G^**//RHF/6-311G^**和B3LYP/6-311G^**//B3LYP/6-311G^**水平计算其气相酸性(ΔG⁰)和同键反应芳香性稳定化能(HASE).用基团加和法(Group Increment Approach)在RHF/6-311G^**//RHF/6-311G^**和B3LYP/6-311G^**//B3LYP/6-311G^**水平计算其磁化率增量(Λ).计算结果表明,标题化合物的同键反应芳香性稳定化能和磁化率增量均为负值,表明它具有芳香性,实现了标题化合物芳香性的几何、能量和磁性的判定.     

Stability and aromaticity of the cyclopenta-fused pyrene congeners

The aromaticity of all possible cyclopenta-fused pyrene congeners has been investigated at various levels of theory. On the basis of the calculated resonance energies and magnetic properties (delta(1)H data, magnetic susceptibility anisotropies, and NICS values), the overall aromaticity of these compounds is found to decrease gradually with increasing number of externally fused five-membered rings. The relatively small differences (<5 kcal/mol) in thermodynamic stability of the isomeric dicyclopentapyrenes (E(tot): dicyclopenta[cd,fg]- > dicyclopenta[cd,jk]- > dicyclopenta[cd,mn]pyrene), which differs from the aromaticity order based on the magnetic criteria (dicyclopenta[cd,mn]- > dicyclopenta[cd,fg]- > dicyclopenta[cd,jk]pyrene), is shown by model calculations to be dominated by sigma-strain imposed on the pyrene skeleton by sequential cyclopenta-fusion. This is supported by the computed homodesmotic reaction energies and aromatic stabilization energy (ASE(isom)) from isodesmic aromatic-nonaromatic isomerization, and by the model calculations on "distorted" cyclopenta[cd]pyrenes. The elusive tetracyclopenta[cd,fg,jk,mn]pyrene is computed to be bowl-shaped; its corresponding planar geometry is the transition state for bowl-bowl interconversion.     

Kinetics of proton transfer from benzo[b]-2,3-dihydrofuran-2-one and benzo[b]-2,3-dihydrothiophene-2-one. Effect of anion aromaticity on intrinsic barriers

Rates of the reversible deprotonation of benzo[b]-2,3-dihydrofuran-2-one (6H-O) and benzo[b]-2,3-dihydrothiophene-2-one (6H-S) by OH-, primary aliphatic amines, secondary alicyclic amines, and carboxylate ions have been determined in water at 25 degrees C. As noted earlier by Kresge and Meng, 6H-S (pKa = 8.82) is considerably more acidic than 6H-O (pKa = 11.68), which mainly reflects the greater aromatic stabilization of the conjugate base of 6H-S (thiophene derivative) compared to that of 6H-O (furan derivative). The main focus of this paper is to assess how the difference in the aromaticity of the two enolate ions affects the intrinsic barrier to the proton transfer. These intrinsic barriers were determined from Br?nsted plots for the reactions with the amines and carboxylate ions or calculated on the basis of the Marcus equation for the reactions with OH-. They are consistently somewhat higher for the reactions of 6H-S than for the reactions of 6H-O, implying that the aromaticity in the anion enhances the intrinsic barrier. This contrasts with a previous report on the deprotonation of some cyclic rhenium Fischer-type carbene complexes where the reaction that leads to the most aromatic conjugate base (thiophene derivative) has a lower intrinsic barrier than the reaction that leads to the less aromatic furan analogue. We are offering a detailed analysis of other potential factors that may affect the intrinsic barriers and which could explain these contradictory results.     

Circuit resonance energy: a key quantity that links energetic and magnetic criteria of aromaticity

Energetic and magnetic criteria of aromaticity are different in nature and sometimes make different predictions as to the aromaticity of a polycyclic pi-system. Thus, some charged polycyclic pi-systems are aromatic but paratropic. We derived the individual circuit contributions to aromaticity from the magnetic response of a polycyclic pi-system and named them circuit resonance energies (CREs). Each CRE has the same sign and essentially the same magnitude as the corresponding cyclic conjugation energy (CCE) defined by Bosanac and Gutman. Such CREs were found to play a crucial role in associating the energetic criteria for determining the degree of aromaticity with the magnetic ones. We can now interpret both energetic and magnetic criteria of aromaticity consistently in terms of CREs. Ring-current diamagnetism proved to be the tendency of a cyclic pi-system to retain aromatic stabilization energy (ASE) at the level of individual circuits.     

The origin of aromaticity: important role of the sigma framework in benzene.

The physical nature of aromaticity is addressed at a high ab initio level. It is conclusively shown that the extrinsic aromatic stabilization energy of benzene E(ease)B, estimated relative to its linear polyene counterpart(s), is very well-reproduced at the Hartree-Fock (HF) level. This is a consequence of the fact that the contributions arising from the zero-point vibrational energy (ZPVE) and electron correlation are rather small. More specifically, they yield together 2.0 kcalmol(-1) to the destabilization of benzene. A careful scrutiny of the HF energies by virial theorem shows further that the kinetic energies of the sigma and pi electrons E(T)HF(sigma) and E(T)HF(pi) are strictly additive in the gauge linear zig-zag polyenes, which also holds for their sum Et(T)HF This finding has the important corollary that E(ease)B is little dependent on the choice of the homodesmic reactions involving zig-zag polyenes. A detailed physical analysis of the sigma- and pi-electron contributions to extrinsic aromaticity requires explicit introduction of the potential energy terms Vne, Vee, and Vnn, which signify Coulomb interactions between the electrons and the nuclei. The Vee term involves repulsive interaction Vee(sigmapi) between the sigma and pi electrons, which cannot be unequivocally resolved into sigma and pi contributions. The same holds for the Vnn energy, which implicitly depends on the electron density distribution via the Born-Oppenheimer (BO) potential energy surface. Several possibilities for partitioning Vee(sigmapi) and Vnn terms into sigma and pi components are examined. It is argued that the stockholder principle is the most realistic, which strongly indicates that E(ease)B is a result of favorable sigma-framework interactions. In contrast, the pi-electron framework prefers the open-chain linear polyenes.     

Does aromaticity in a reaction product increase or decrease the intrinsic barrier? Kinetics of the reversible deprotonation of benzofuran-3(2H)-one and benzothiophene-3(2H)-one

A kinetic study of the reversible deprotonation of benzofuran-3(2H)-one (3H-O) and benzothiophene-3(2H)-one (3H-S) by amines and hydroxide ion in water at 25 degrees C is reported. The respective conjugate bases, 3--O and 3--S, represent benzofuran and benzothiophene derivatives, respectively, and thus are aromatic. The main question addressed in this paper is whether this aromaticity has the effect of enhancing or lowering intrinsic barriers to proton transfer. These intrinsic barriers were either determined from Br?nsted plots for the reactions with amines or calculated on the basis of the Marcus equation for the reaction with OH-; they were found to be lower for the more highly aromatic benzothiophene derivative, indicating that aromaticity lowers the intrinsic barrier. It is shown that the reduction in the intrinsic barrier is not an artifact of other factors such as inductive, steric, resonance, polarizability, and pi-donor effects, although these factors affect the intrinsic barriers in a major way. Our results imply that aromatic stabilization of the transition state is ahead of proton transfer; this contrasts with simple resonance effects, which typically lag behind proton transfer at the transition state, thereby increasing intrinsic barriers.     

To what extent can aromaticity be defined uniquely?

Statistical analyses of quantitative definitions of aromaticity, ASE (aromatic stabilization energies), RE (resonance energies), Lambda (magnetic susceptibility exaltation), NICS, HOMA, I5, and A(J), evaluated for a set of 75 five-membered pi-electron systems: aza and phospha derivatives of furan, thiophene, pyrrole, and phosphole (aromatic systems), and a set of 30 ring-monosubstituted compounds (aromatic, nonaromatic, and antiaromatic systems) revealed statistically significant correlations among the various aromaticity criteria, provided the whole set of compounds is involved. Hence, broadly considered, the various manifestations of aromaticity are related and aromaticity can be regarded statistically as a one-dimensional phenomenon. In contrast, when comparisons are restricted to some regions or groups of compounds, e.g., aromatic compounds with ASE > 5 kcal/mol or polyhetero-five-membered rings, the quality of the correlations can deteriorate or even vanish. In practical applications, energetic, geometric, and magnetic desriptors of aromaticity do not speak with the same voice. Thus, in this sense, the phenomenon of aromaticity is regarded as being statistically multidimensional.     

Control of kinetics and thermodynamics of [1,5]-shifts by aromaticity: a view through the prism of Marcus theory

The effects of aromatic stabilization on the rates of [1,5]-hydrogen shifts in a series of carbo- and heterocyclic dihydroaromatic compounds were estimated by B3LYP/6-31G computations. The aromatic stabilization energy of the product is directly translated into increased exothermicity of these reactions. Relative trends for a significant range of endothermic and exothermic [1,5]-shifts with different intrinsic activation energies are reliably described by Marcus theory. The effects of aromaticity or antiaromaticity are very large and can lead to dramatic acceleration or deceleration of [1,5]-hydrogen shifts and even to complete disappearance of the reaction barrier. Not only the activation energy but the shape and position of the reaction barrier can be efficiently controlled by changes in the aromaticity of the products, making these systems interesting models for studying hydrogen tunneling. Marcus theory can also be applied successfully to other pericyclic shifts such as [1,5]-shifts which involve chlorine and methyl transfer.     

An investigation of the aromaticity of transition metal heterocyclic complexes by conventional criteria and indices of aromaticity

Conventional criteria and indices of aromaticity, including electronic, geometric, energetic and magnetic aspects have been applied to examine the aromaticity of five typical transition metal heterocyclic complexes, i.e. six-membered osmabezene 1 and iridabenzene 2, five-membered cobaltacyclopentadiene 3 and iridacyclopentadiene 4, and four-membered tungstacyclobutadiene 5. The results show that the cyclic, planar, conjugated and Hückel 4n+2 rule’s criteria in the transition-metal-containing heterocycles of the five complexes studied are all met. Five quantitative aromaticity indices, including Bird aromatic index (I_n), homodesmotic reaction aromatic stabilization energy (HASE), absolute hardness (η), diamagnetic susceptibility exaltation (Λ) and NMR chemical shift (δH), qualitatively lead to a consistent and affirmative conclusion that all of them are aromatic. However, they fail to draw a common conclusion for their relative magnitudes of aromaticity, which proves once again the multidimensional character of aromaticity.     

Analysis of electron delocalization in aromatic systems: individual molecular orbital contributions to para-delocalization indexes (PDI)

Our research group has recently defined two new aromaticity indexes based on the analysis of electron delocalization in aromatic species using the quantum theory of atoms-in-molecules. One of these indexes is the para-delocalization index (PDI) that measures the electronic delocalization between para-related carbon atoms in six-membered rings. In this paper, we show that this index can be partitioned into individual molecular orbital contributions. We have applied this PDI decomposition to several polycyclic aromatic hydrocarbons showing that this partitioning provides new insight into the origin of aromaticity.     

Aromaticity of the Bergman, Myers-Saito, Schmittel, and directly related cyclizations of enediynes

Aromaticity criteria (magnetic susceptibility exaltations, nucleus independent chemical shifts (NICS), and aromatic stabilization energy (ASE) evaluations) for enediyne and enyne-allene cyclizations evaluated at (UBS)-BLYP/6-31G* all agree that the degrees of cyclic electron delocalization of the benzenoid systems formed by the Bergman (3) and Myers-Saito reactions (5) are comparable to benzene. The reaction enthalpy differences between the parent cyclizations and their benzannelated analogues are not entirely due to disparities in gained ASE during the reactions. The alternative formation of fulvene biradicals is not accompanied by favorable aromatic effects.     

Aromaticity interplay between quinodimethanes and C(60) in diels-alder reactions: insights from a theoretical study

A theoretical study is performed of the Diels-Alder reactions of various o-quinodimethanes (QDM) with C(60) by the AM1 model and limited ab initio and DFT techniques. All reactions are shown to proceed through a concerted transition state possessing a considerable net aromaticity as evidenced from bond orders and magnetic criteria such as the magnetic susceptibility exhaltations (MSE) and nucleus independent chemical shifts (NICS) and produce different kinds of aromatic stabilized fullerene cycloadducts. Computations show that a strong LUMO-dienophile control of C(60) is realized by the influence of pyramidalization, but its high reactivity over alkene appears to be governed by the global aromaticity on fullerene rather than its strain. The aromatic functionalization occurring in QDM upon cycloaddition drastically increases the reaction rate and exothermicity of all QDM-C(60) reactions as compared to the butadiene-C(60) reaction. In fact, the simultaneously existing aromatic destabilization in fullerene indicates its opposite effect to the resonance stabilization in diene; it is thus fully restricted when the gained aromaticity is transmitted from the nucleophilic QDM to the fullerene electrophile in a push-pull manner. However, the overall aromaticity effect shown by the aromatization as well as the aromaticity of C(60) seems to accelerate these reactions at an increased rate.