There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The ability to sustain a diatropic ring current is the defining characteristic of aromatic species.1-7 Cyclic electron delocalization results in enhanced stability, bond length equalization, and special magnetic as well as chemical and physical properties.1 In contrast, antiaromatic compounds sustain paratropic ring currents3 despite their localized, destabilized structures.1-7 We have demonstrated the direct, quantitative relationships among energetic, geometrical, and magnetic criteria of aromaticity in a wide-ranging set of aromatic/antiaromatic fivemembered rings.5a While the diamagnetic susceptibility exaltation (Λ) is uniquely associated with aromaticity, it is highly dependent on the ring size (area2) and requires suitable calibration standards.6 Aromatic stabilization energies (ASEs) of strained and more complicated systems are difficult to evaluate. CC bond length variations in polybenzenoid hydrocarbons can be just as large as those in linear conjugated polyenes.2 The abnormal proton chemical shifts of aromatic molecules are the most commonly employed indicators of ring current effects.1 However, the ca. 2-4 ppm displacements of external protons to lower magnetic fields are relatively modest (e.g., δH ) 7.3 for benzene vs 5.6 for dC-H in cyclohexene). In contrast, the upfield chemical shifts of protons located inside aromatic rings are more unusual. The six inner hydrogens of [18]annulene, for example, resonate at -3.0 ppm vs δ ) 9.28 for the outer protons. This relationship is inverted dramatically in the antiaromatic [18]annulene dianion, C18H18, where δ ) 20.8 and 29.5 (in) vs. -1.1 (out).8 Similar demonstrations of paratropic ring currents in antiaromatic compounds are well documented.3,8,9 Chemical shifts of encapsulated 3He atoms are now employed as experimental and computed measures of aromaticity in fullerenes and fullerene derivatives.10 While the rings of most aromatic systems are too small to accommodate atoms internally, the chemical shifts of hydrogens in bridging positions have long been used as aromaticity and antiaromaticity probes.9 δLi+ can be employed similarly, with the advantage that Li+ complexes with individual rings in polycyclic systems can be computed.4,11 We now propose the use of absolute magnetic shieldings, computed at ring centers (nonweighted mean of the heavy atom coordinates) with available quantum mechanics programs,12 as a new aromaticity/antiaromaticity criterion. To correspond to the familiar NMR chemical shift convention, the signs of the computed values are reversed: Negative “nucleus-independent chemical shifts” (NICSs) denote aromaticity; positive NICSs, antiaromaticity (see Table 1 for selected results). Figure 1, a plot of NICSs vs the ASEs for our set of five-membered ring heterocycles,5a provides calibration. The equally good correlations with magnetic susceptibility exaltations and with structural variations establish NICS as an effective aromaticity criterion. Unlike Λ,6 NICS values for [n]annulenes (Table 1) show only a modest dependence on ring size. The 10 π electron systems give significantly higher values than those with 6 π electrons. The antiaromatic 4n π electron compounds, cyclobutadiene (27.6), pentalene (18.1), heptalene (22.7), and planar D4h cyclooctatetraene (30.1), all show highly positive NICSs. Like the Li+-complex probe,4 the NICS evaluates the aromaticity and antiaromaticity contributions of individual rings in polycyclic systems. Scheme 1 (HF/6-31+G*, data from Table 1) shows NICSs for selected examples. The benzenoid aromatic NICSs provide evidence both for localized and “perimeter” models. The naphthalene (1) NICS (-9.9) resembles that of benzene (-9.7), as do the NICSs for the outer rings of phenanthrene (2) (-10.2) and triphenylene (3); the aromaticity of the central rings of the latter two are reduced. The NICS of the central ring of anthracene (4) (-13.3) exceeds the benzene value in contrast to the outer ring NICS (-8.2). Remarkably, the NICS (-7.0) for the seven-membered ring of azulene (5) is very close to that of the tropylium ion (-7.6 ppm), whereas the azulene five-membered ring NICS (-19.7) is even larger in magnitude than that of the cyclopentadienyl anion (-14.3). The four-membered rings in benzocyclobutadiene (6) (NICS ) 22.5) and in biphenylene (7) (19.0) are antiaromatic, but less so than cyclobutadiene itself (27.6). The six-membered rings in these polycycles are still aromatic, but their NICSs (-2.5 (1) (a) Minkin, V. I.; Glukhovtsev, M. N.; Simkin, B. Y. Aromaticity and Antiaromaticity; Wiley: New York, 1994. (b) Garratt, P. J. Aromaticity; Wiley: New York, 1986. (c) Eluidge, J. A.; Jackman, L. M. J. Chem. Soc. 1961, 859. (2) Schleyer, P. v. R.; Jiao, H. Pure Appl. Chem. 1996, 28, 209. (3) Pople, J. A.; Untch, K. G. J. Am. Chem. Soc. 1966, 88, 4811. (4) Jiao, H; Schleyer, P. v. R. AIP Conference Proceedings 330, E.C.C.C.1, Computational Chemistry; Bernardi, F., Rivail, J.-L., Eds.; American Institute of Physics: Woodbury, New York, 1995; p 107. (5) (a) Schleyer, P. v. R.; Freeman, P.; Jiao, H.; Goldfuss, B. Angew. Chem., Int. Ed. Engl. 1995, 34, 337. (b) Jiao, H.; Schleyer, P. v. R. Unpublished IGLO results. (c) Kutzelnigg, W.; Fleischer, U.; Schindler, M. In NMR: Basic Princ. Prog.; Springer: Berlin, 1990; Vol. 23, p 165. (6) Dauben, H. J., Jr.; Wilson, J. D.; Laity, J. L. In Non-Benzenoid Aromatics; Synder, J., Ed.; Academic Press, 1971; Vol. 2, and references cited. The partitioning of ring current or ring current susceptabilitites among various rings in polycyclic syestems were considered earlier, e.g., by Aihara (Aihara, J. J. Am. Chem. Soc. 1985, 207, 298 and refs cited) and by Mallion (Haigh, C. W.; Mallion, J. Chem. Phys. 1982, 76, 1982). (7) Fleischer, U.; Kutzelnigg, W.; Lazzeretti, P.; Mühlenkamp, V. J. Am. Chem. Soc. 1994, 116, 5298. (8) Sondheimer, F. Acc. Chem. Res. 1972, 5, 81. (9) (a) Hunandi, R. J. J. Am. Chem. Soc. 1983, 105, 6889. (b) Pascal, R. A., Jr.; Winans, C. G.; Van Engen, D. J. Am. Chem. Soc. 1989, 111, 3007. (10) (a) Bühl, M.; Thiel, W.; Jiao, H.; Schleyer, P. v. R.; Saunders, M.; Anet, F. A. L. J. Am. Chem. Soc. 1994, 116, 7429 and references cited. (b) Bühl, M.; van Wüllen, C. Chem. Phys. Lett. 1995, 247, 63. The authors have shown that the negative absolute shielding in the center of C60 is nearly the same as δ3He, computed at the same level. (11) Paquette, L. A.; Bauer, W.; Sivik, M. R.; Bühl, M.; Feigel, M.; Schleyer, P. v. R. J. Am. Chem. Soc. 1990, 112, 8776. (12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, ReVision B.2; Gaussian Inc., Pittsburgh, PA, 1995. Figure 1. Plot of NICSs (ppm) vs the aromatic stabilization energies (ASEs, kcal/mol)5a for a set of five-membered ring heterocycles, C4H4X (X ) as shown) (cc ) 0.966). 6317 J. Am. Chem. Soc. 1996, 118, 6317

Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe

I. Introduction: Conceptual vs Fundamental andComputational Aspects of DFT1793II. Fundamental and Computational Aspects of DFT 1795A. The Basics of DFT: The Hohenberg−KohnTheorems1795B. DFT as a Tool for Calculating Atomic andMolecular Properties: The Kohn−ShamEquations1796C. Electronic Chemical Potential andElectronegativity: Bridging Computational andConceptual DFT1797III. DFT-Based Concepts and Principles 1798A. General Scheme: Nalewajski’s ChargeSensitivity Analysis1798B. Concepts and Their Calculation 18001. Electronegativity and the ElectronicChemical Potential18002. Global Hardness and Softness 18023. The Electronic Fukui Function, LocalSoftness, and Softness Kernel18074. Local Hardness and Hardness Kernel 18135. The Molecular Shape FunctionsSimilarity 18146. The Nuclear Fukui Function and ItsDerivatives18167. Spin-Polarized Generalizations 18198. Solvent Effects 18209. Time Evolution of Reactivity Indices 1821C. Principles 18221. Sanderson’s Electronegativity EqualizationPrinciple18222. Pearson’s Hard and Soft Acids andBases Principle18253. The Maximum Hardness Principle 1829IV. Applications 1833A. Atoms and Functional Groups 1833B. Molecular Properties 18381. Dipole Moment, Hardness, Softness, andRelated Properties18382. Conformation 18403. Aromaticity 1840C. Reactivity 18421. Introduction 18422. Comparison of Intramolecular ReactivitySequences18443. Comparison of Intermolecular ReactivitySequences18494. Excited States 1857D. Clusters and Catalysis 1858V. Conclusions 1860VI. Glossary of Most Important Symbols andAcronyms1860VII. Acknowledgments 1861VIII. Note Added in Proof 1862IX. References 1865

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Conceptual density functional theory.

Acenes have long been the subject of intense study because of the unique electronic properties associated with their pi-bond topology. Recent reports of impressive semiconductor properties of larger homologues have reinvigorated research in this field, leading to new methods for their synthesis, functionalization, and purification, as well as for fabricating organic electronic components. Studies performed on high-purity acene single crystals revealed their intrinsic electronic properties and provide useful benchmarks for thin film device research. New approaches to add functionality were developed to improve the processability of these materials in solution. These new functionalization strategies have recently allowed the synthesis of acenes larger than pentacene, which have hitherto been largely unavailable and poorly studied, as well as investigation of their associated structure/property relationships.

The larger acenes: versatile organic semiconductors.

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

Structural Aspects of Aromaticity

Energetic Aspects of Cyclic Pi-Electron Delocalization: Evaluation of the Methods of Estimating Aromatic Stabilization Energies

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

A short and efficient route to a broad range of imidazo[1,2-a]pyridines from 2-aminopyridines and acetophenones is achieved by a tandem, one-pot process starting with an Ortoleva–King reaction. Optimal conditions for the first step were established after examining various reaction parameters (solvent, reagent ratios, and temperature). The conditions identified (1st step, neat, 2.3 equiv of 2-aminopyridine, 1.20 equiv of I2, 4 h, 110 °C; 2nd step, NaOHaq, 1 h, 100 °C) resulted in the formation of imidazo[1,2-a]pyridines in 40–60% yields. The synthesis is compatible with various functionalities (OH, NMe2, Br, OMe). Products containing a 2-(2′-hydroxyphenyl) substituent undergo excited state intramolecular proton transfer (ESIPT) in nonpolar and polar-aprotic solvents. Although ESIPT-type emission in nonpolar solvents is weak, the Stokes shifts are very high (11000 cm–1). The comparison of the properties of six ESIPT-capable imidazo[1,2-a]pyridines shows the influence of various substituents on emission char...

Michał K. Cyrański

Papers

Structural Aspects of Aromaticity

Energetic Aspects of Cyclic Pi-Electron Delocalization: Evaluation of the Methods of Estimating Aromatic Stabilization Energies

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

Imidazo[1,2-a]pyridines susceptible to excited state intramolecular proton transfer: one-pot synthesis via an Ortoleva-King reaction.

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