Energetic aspects of cyclic pi-electron delocalization: evaluation of the methods of estimating aromatic stabilization energies

Solvent impact on the aromaticity of benzene analogues: implicit versus explicit solvent approach

Solvent impact on the structural index of aromaticity was modelled by polarised continuum field approximation (IEFPCM) and hybrid quantum chemistry (QM/MM) method. Significant solvent related relaxation of the solutes geometries were noticed especially for highly polar species. The significant reduction of the aromaticity was observed for some aromatic compounds in water solution compared to gas phase. The rationale of this fact was provided based on dipole moment changes, energy penalty for polarisation of solute and the distribution of frontier orbital densities. The incoherent predictions of explicit and implicit solvation models are noticed since in some cases the PCM approach artificially exaggerate the geometry relaxation in solution which is not observed if explicit solvent molecules are taken into account.

Direct evaluation of cyclic contributions to the pi energy of conjugated hydrocarbons from strongly localized zero-order pictures

This paper presents a new procedure for identifying that part of the pi electronic energy of conjugated hydrocarbons which results from cyclic circulation of electrons around a ring. It first shows that one may calculate perturbatively the ground state energy of the Hückel Hamiltonian from a strongly localized Kekulé-type zero-order wave function. The contributions due to cyclic circulation of the electrons appear explicitly, in terms of the interatomic hopping integral t, at the second order in cyclobutadiene (where it is equal to -t (antiaromatic)) and at third order in benzene, where its value is 0.5t (aromatic). Conjugated isomers of benzene are also considered. The cyclic circulation contributions for an N-membered ring are shown to depend strongly on the molecular graph in which it is embedded. A general expression is found for the cyclic contribution to the pi energy of a ring, the Kekulé graph of which contains N double bonds alternating with N single bonds. It is the energy of the ring, plus the sum of the energies of the N subsystems that result from one double-bond removal, minus the sum of the energies of the N open systems that result from one single-bond cut. This new aromaticity index, ACE(MC), may be seen as the enthalpy of a hyperhomodesmotic chemical equation. In contrast to the index ACE(DC) previously defined from a double cut of the ring, the multiple-cut ACE(MC) exhibits the expected asymptotic disappearance of the cyclic energy as the ring size tends to infinity. In the multiple-cut approach, aromaticity persists in bond-alternating rings, but, in contrast to the total pi energy, the purely cyclic contribution tends to resist distortion. Extension of the approach to charged, branched and heterosubstituted rings are discussed, as well as its ab initio transcription.

Interplay of pi-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.

Probing intramolecular interactions in arylselenides using a property descriptor based approach

Although a large volume of experimental evidence is available on the existence of intramolecular nonbonding interactions between chalcogen atoms in main group organometallic compounds, the primary focus has been on the contact distances involving the chalcogen atoms. The important class of intramolecular Se...X (where X is O, S, N) nonbonding interaction in a series of organoselenium compounds is quantified using a new scheme based on a molecular property descriptor. In the present study, we have employed the nucleus-independent chemical shift [NICS(0)] values, as a property descriptor to evaluate the strength of exocyclic nonbonding interactions in a series of aryl selenides. The ab initio MP2 as well as density functional theory methods have been used in conjunction with Dunning's cc-pVDZ basis set. The quantified values of Se...X nonbonding interactions are compared with other schemes based on thermochemical equations such as homodesmic and ortho-para methods. The changes in NICS(0) values at the aryl ring center are found to be sensitive to the strength of exocyclic Se...X interaction.

Decabromobiphenyl (PBB-209) activates the aryl hydrocarbon receptor while decachlorobiphenyl (PCB-209) is inactive: experimental evidence and computational rationalization of the different behavior of some halogenated biphenyls

In rat H4IIE cells permanently transfected with a luciferase gene under the control of AhR, incubation with PBB-209 led to a statistically significant increase of luminescence. In this system, PCB-209 only caused a small induction of luciferase activity. In a fish cell line, only PBB-209 was able to provoke an induction of ethoxyresorufin- O-deethylase activity. Ligand binding to the AhR was studied by means of a cell-free in vitro system in which the activation of AhR is very unlikely to occur without ligand binding. None of the biphenyls studied provoked any activation of AhR in this system. To rationalize the results and to get insight into the molecular mechanism of activation of AhR by PBB-209 as compared with PCB-209, a comprehensive computational study was carried out on these congeners as well as on PCB-126 and PCB-169, two potent AhR activators through ligand binding. The calculations include (i) conformational analysis and dipole moments of each conformer, (ii) aromaticity indices, (iii) molecular electrostatic potentials, (iv) quadrupole moments, (v) electronic and reactivity descriptors, and (vi) dissociation energies of C-Cl and C-Br bonds in model aromatic compounds. It was found that some molecular features of PBB-209, such as the electrostatic potential (EP) and EP-derived descriptors (Politzer's parameters), indicate that PBB-209 is more similar to PCB-126 and PCB-169 than to PCB-209, which share quite similar geometries based on the substitution pattern. The similarity between PBB-209, PCB-126, and PCB-169 seems to hint that these three compounds can share, at least partially, similar mechanisms of activation of AhR. It is unquestionable that PCB-126 and PCB-169 directly bind AhR and PBB-209 does not. We hypothesize that there are several simultaneous mechanisms for activation of AhR, and the most active compounds act for more than one mechanism.

A Hückel-Level Kinetic-Stability-Based Approach to Aromaticity: Cyclic Even Alternant Hydrocarbons

A graph-theoretical procedure is described that relates Hückel-level expectations for the kinetic stabilities of even, alternant hydrocarbons to their Lewis structures. New parameters Ac and T are developed. A universal kinetic-stability-based standard is proposed for classifying alternant hydrocarbons as aromatic, non-aromatic, or anti-aromatic.

Application of AIM parameters at ring critical points for estimation of pi-electron delocalization in six-membered aromatic and quasi-aromatic rings

The AIM parameters at the ring critical point (the electron density and its Laplacian, the total electron energy density and both its components, potential and kinetic electron energy densities), have been intercorrelated with aromaticity indices: the geometry-based HOMA and the magnetism-based NICS, NICS(1), and NICS(1)(zz). A set of 33 phenylic rings having possibly a diversified aromatic character, and a set of 20 quasi-rings formed by intramolecular hydrogen and lithium bonds, have been taken into consideration. It has been found that the density of total electron energy, H, may serve as a new quantitative characteristic of pi-electron delocalization. The dependences between H values and aromaticity indices are correlated (cc(H/HOMA)=0.99, cc(H/NICS(1)zz)=0.95).

The question of aromaticity in open-shell cations and anions as ion-radical offsprings of polycyclic aromatic and antiaromatic hydrocarbons

Arene cation-radicals and anion-radicals result directly from the one-electron oxidation and reduction of many aromatic hydrocarbons, yet virtually nothing is known of their intrinsic (thermodynamic) stability and hence "aromatic character". Since such paramagnetic ion radicals lie intermediate between aromatic (Hückel) hydrocarbons with 4n + 2-electrons and antiaromatic analogues with 4n-electrons, we can now address the question of pi-delocalization in these odd-electron counterparts. Application of the structure-based "harmonic oscillator model of aromaticity" or the HOMA method leads to the surprising conclusion that the aromaticity of these rather reactive, kinetically unstable arene cation and anion radicals (as measured by the HOMA index) is actually higher than that of their (diamagnetic) parent-contrary to conventional expectations.

The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations

Branched alkanes like isobutane and neopentane are more stable than their straight chain isomers, n-butane and n-pentane (by 2 and 5 kcal mol(-1), respectively). Electron correlation is largely responsible. Branched alkanes have a greater number of net attractive 1,3-alkyl-alkyl group interactions, there are three such stabilizing 1,3 "protobranching" dispositions in isobutane, but only two in n-butane. Neopentane has six protobranches but n-pentane only three. Propane has one protobranch and is stabilized appreciably, by 2.8 kcal mol(-1), relative to methane and ethane. This value per protobranch also applies to the n-alkanes and cyclohexane. Consequently, energy evaluations employing alkane reference standards, for example, of small ring strain and stabilizations due to conjugation, hyperconjugation, and aromaticity, should be corrected for protobranching, for example, by employing Pople's isodesmic bond separation reaction method. This reduces the ring strain of cyclopropane to 19.2 from the conventional 27.7 kcal mol(-1), while the stabilization energies of alkenes and alkynes due to hyperconjugation (5.5 and 7.7 kcal mol(-1) for propene and propyne) and conjugation (14.8 and 27.1 kcal mol(-1) for butadiene and butadiyne) are considerably larger than the traditional estimates. Widely diverging literature evaluations of benzene resonance energy all give approximately 65 kcal mol(-1) after adjusting for conjugation, hyperconjugation, and protobranching "contaminations." The BLW (block localized wavefunction) method, which localizes pi bonds and precludes their interactions, largely confirms these stabilization estimates for hyperconjugation, conjugation, and aromaticity. Protobranching is seriously underestimated by theoretical computations at the HF and most DFT levels, which do not account for electron correlation satisfactorily. Such levels give bond separation energies, which can differ greatly from experimental values.

Cobalt-Mediated [2+2+2] Cycloaddition versus CH and NH Activation of 2-Pyridones and Pyrazinones with Alkynes: A Theoretical Study

DFT computations have been executed aimed at illuminating the variety of pathways by which pyridones react with alkynes in the presence of [CpCoL(2)]: NH-2-pyridones furnish N-dienylated ligands (N-H activation pathway), N-methyl-2-pyridones are converted into ligated cyclohexadienes ([2+2+2] cocycloaddition pathway), and N-alkynyl-2-pyridones may undergo either [2+2+2] cocycloaddition or C-dienylation (C-H activation), depending on the length of the tether. The calculations predict the formation of the experimentally observed products, including their regio- and stereochemical make up. In addition, the unusual regiochemical outcome of the all-intramolecular [2+2+2] cycloaddition of N,N'-dipentynylpyrazinedione was rationalized by computation, which led to the discovery of a new mechanism.

Structure of the Vinyldiazomethyl Anion and Energetic Comparison to the Cyclic Isomers

The 351.1 nm photoelectron spectrum of the vinyldiazomethyl anion has been measured. The ion is generated through the reaction of the allyl anion with N(2)O in helium buffer gas in a flowing afterglow source. The spectrum exhibits the vibronic structure of the vinyldiazomethyl radical in its electronic ground state as well as in the first excited state. Electronic structure calculations have been performed for these molecules at the B3LYP/6-311++G(d,p) level of theory. A Franck-Condon simulation of the X (2)A'' state portion of the spectrum has been carried out using the geometries and normal modes of the anion and radical obtained from these calculations. The simulation unambiguously shows that the ions predominantly have an E conformation. The electron affinity (EA) of the radical has been determined to be 1.864 +/- 0.007 eV. Vibrational frequencies of 185 +/- 10 and 415 +/- 20 cm(-1) observed in the spectrum have been identified as in-plane CCN bending and CCC bending modes, respectively, for the X (2)A'' state. The spectrum for the A (2)A' state is broad and structureless, reflecting large geometry differences between the anion and the radical, particularly in the CCN angle, as well as vibronic coupling with the X (2)A'' state. The DFT calculations have also been used to better understand the mechanism of the allyl anion reaction with N(2)O. Collision-induced dissociation of the structural isomer of the vinyldiazomethyl anion, the 1-pyrazolide ion, has been examined, and energetics of the structural isomers is discussed.

Tautomeric equilibria and pi electron delocalization for some monohydroxyarenes--quantum chemical studies

Keto-enol tautomeric interconversions and variations of the pi-electron distribution were studied for 11 isolated monohydroxyarenes at the DFT(B3LYP)/6-311++G(2df,2p) level. For two monohydroxyarenes (phenol and 9-anthrol), the PCM model of solvation (water) was also applied to the DFT geometries. The geometry-based HOMA index was applied to estimate pi-electron delocalization in the keto and enol tautomeric forms. Thermodynamic parameters of tautomeric interconversions (DeltaET, DeltaGT, TDeltaST, pKT) were calculated to estimate relative stabilities of individual tautomers and their percentage contents in the tautomeric mixtures. In almost all cases, the aromatic enol forms are strongly favored. An exception is 9-anthrol, which prefers its keto form. The resonance stabilization of this form comes from the central ring. Generally, aromaticity is the main factor that influences tautomeric equilibria in monohydroxyarenes. Hydration effect is considerably smaller and it does not change the tautomeric preference.

Restricted Geometry Optimization: A Different Way To Estimate Stabilization Energies for Aromatic Molecules of Various Types

At RHF, MPn, and DFT levels, a procedure of geometry optimization under the restrictions of pi-orbital interactions (GOR) was developed, thus providing a conjugated molecule with the following two types of localized reference geometries: a "GL" geometry where all double bonds are localized, and n different "GE-n" geometries, in each of which only two double bonds were permitted to conjugate. Interestingly, the molecular energy differences between the corresponding pairs of GE-n and GL geometries were found to be additive in each of the acyclic polyenes, and these were not additive for benzene. As a result, an extra stabilization energy (ESE) value of -39.0 kcal/mol was found in benzene. Afterward, GOR was applied to benzene- and furan-like species, strained aromatic molecules, and substituted benzenes, and the calculated ESEs for these molecules were found to be in reasonable ranges. The GOR can isolate a specific group from other groups, and it has several special functions. First, with regard to the substituent effect, the ESE difference between substituted benzene and benzene can be partitioned into conjugative and inductive parts. Second, the behavior of strained aromatic molecules can be ascertained from the roles of their resonance interactions, strained-induced bond localization (SIBL), and inductive effects, indicating that it is resonance interactions, rather than SIBL, which are responsible for localizing double bonds. Emphatically, it is the GL and GE-n geometries of aromatic molecules, rather than nonaromatic compounds, which can be used as the reference structures for calculating ESE. Particularly, these localized geometries are no longer arbitrary.

Electron sharing indexes at the correlated level. Application to aromaticity calculations

Electron sharing indexes (ESI) have been applied to numerous bonding situations to provide an insight into the nature of the molecular electronic structures. Some of the most popular ESI given in the literature, namely, the delocalization index (DI), defined in the context of the quantum theory of atoms in molecules (QTAIM), and the Fuzzy-Atom bond order (FBO), are here calculated at a correlated level for a wide set of molecules. Both approaches are based on the same quantity, the exchange-correlation density, to recover the electron sharing extent, and their differences lie in the definition of an atom in a molecule. In addition, while FBO atomic regions enable accurate and fast integrations, QTAIM definition of an atom leads to atomic domains that occasionally make the integration over these ones rather cumbersome. Besides, when working with a many-body wavefunction one can decide whether to calculate the ESI from first-order density matrices, or from second-order ones. The former way is usually preferred, since it avoids the calculation of the second-order density matrix, which is difficult to handle. Results from both definitions are discussed. Although these indexes are quite similar in their definition and give similar descriptions, when analyzed in greater detail, they reproduce different features of the bonding. In this manuscript DI is shown to explain certain bonding situations that FBO fails to cope with. Finally, these indexes are applied to the description of the aromaticity, through the aromatic fluctuation (FLU) and the para-DI (PDI) indexes. FLU and PDI indexes have been successfully applied using the DI measures, but other ESI based on other partitions such as Fuzzy-Atom can be used. The results provided in this manuscript for carbon skeleton molecules encourage the use of FBO for FLU and PDI indexes even at the correlated level.

Neural Networks as a Tool To Classify Compounds According to Aromaticity Criteria

Aromaticity is a fundamental concept in chemistry, with many theoretical and practical implications. Although most organic compounds can be categorized as aromatic, non-aromatic, or antiaromatic, it is often difficult to classify borderline compounds as well as to quantify this property. Many aromaticity criteria have been proposed, although none of them gives an entirely satisfactory solution. The inability to fully arrange organic compounds according to a single criterion arises from the fact that aromaticity is a multidimensional phenomenon. Neural networks are computational techniques that allow one to treat a large amount of data, thereby reducing the dimensionality of the input set to a bidimensional output. We present the successful applications of Kohonen's self-organizing maps to classify organic compounds according to aromaticity criteria, showing a good correlation between the aromaticity of a compound and its placement in a particular neuron. Although the input data for the training of the network were different aromaticity criteria (stabilization energy, diamagnetic susceptibility, NICS, NICS(1), and HOMA) for five-membered heterocycles, the method can be extended to other organic compounds. Some useful features of this method are: 1) it is very fast, requiring less than one minute of computational time to place a new compound in the map; 2) the placement of the different compounds in the map is conveniently visualized; 3) the position of a compound in the map depends on its aromatic character, thus allowing us to establish a quantitative scale of aromaticity, based on Euclidean distances between neurons, 4) it has predictive power. Overall, the results reported herein constitute a significant contribution to the longstanding debate on the quantitative treatment of aromaticity.

Long-Distance Structural Consequences of H-Bonding. How H-Bonding Affects Aromaticity of the Ring in Variously Substituted Aniline/Anilinium/Anilide Complexes with Bases and Acids

The aromaticity of the ring in variously substituted aniline/anilinium/anilide derivatives in their H-bonded complexes with various Broensted acids and bases was a subject of an analysis based on 332 experimental geometries retrieved from the Cambridge Structural Database and geometries optimized at the B3LYP/6-311+G** and MP2/aug-cc-pVDZ levels of theory. Ab initio modeling was applied to the para-substituted aniline, anilinium cation, and anilide anion derivatives (X = NO, NO2, CN, CHO, H, CH3, OCH3, and OH) and their H-bonded complexes (only for X = NO, NO2, CHO, H, and OH) with B (B = F- and CN-) or HB (HB = HF and HCN). In both cases, the harmonic oscillator model of aromaticity index (HOMA) was used, whereas for computational geometries, additionally, the magnetism-based indices NICS, NICS(1), and NICS(1)zz were also applied (NICS = nucleus-independent chemical shift). There is an equivalent prediction of aromaticity by NICSs and HOMA and approximate monotonic dependences of HOMA and NICS on the C-N bond length. The strongest changes in aromaticity estimated by HOMA and NICSs were found for aniline derivatives with NH2...B and anilide derivatives without and with NH-...HB interactions. The changes observed for two other kinds of interactions, NH2...HB and NH3+...base (for anilinium cations), are much smaller. For all four kinds of interactions, the relationships between ipso-bond angle, mean ipso-ortho bond length, and C-N bond length follow the Bent-Walsh rule.

Aromaticity-controlled tautomerism and resonance-assisted hydrogen bonding in heterocyclic enaminone-iminoenol systems

The contribution of aromaticity and intramolecular hydrogen bonding to relative stability, for a set of (1H-azahetero-2-ylidene)-acetaldehyde and 2-azahetero-2-yl-ethanol tautomeric pairs, has been investigated by means of quantum chemical DFT and ab initio methods up to the MP4(SDTQ)/AUG-cc-pVDZ and MP2/AUG-cc-pVTZ levels of theory. It is found that the relative energy of the tautomers is governed by the change in the degree of heterocycle aromaticity upon intramolecular hydrogen transfer. An analysis of geometrical parameters of a hydrogen-bonded system reveals a clear relationship between the aromaticity of the heterocycle, the conjugation in a resonant spacer, and the strengths of the intramolecular hydrogen bonds. This allows the conclusion to be drawn that intramolecular N-H...O and O-H...N hydrogen bonds formed are found to be resonance-assisted and their strength is dependent on the pi-donating/accepting properties of the heterocycle. On the basis of the results of the calculations, a simple model describing the mechanism of resonance assistance of hydrogen bonding has been suggested.

On the Cycle-Dependence of Topological Resonance Energy

The topological resonance energy (TRE) was conceived in the 1970s. From the very beginning, it was known that TRE is equal to the collective energy-effect of all cycles present in a conjugated molecule. Also in the 1970s a theory of cyclic conjugation was elaborated, by means of which it was possible to compute the energy-effect ef(Z) of each individual cycle Z present in a conjugated molecule. Yet, the connection between TRE and the ef(Z)-values was, until now, not studied. We now show that TRE and the sum of the ef(Z)-values are closely correlated but that a certain correction needs to be made by taking into account the energy-effects of pairs, triplets, quartets, etc. of cycles.

The Phenalenyl Motif: A Magnetic Chameleon

The 12pi cation (3) and 14pi anion (4) derived from the phenalenyl radical (2) support diatropic ("aromatic") perimeter ring currents, but isoelectronic replacement of the central atom by either boron (5) or nitrogen (6) leads to paratropic ("antiaromatic") current; the ipsocentric approach to molecular magnetic response accounts for all four patterns in terms of competition between translationally and rotationally allowed virtual pi-pi* excitations.