On the performance of some aromaticity indices: A critical assessment using a test set

Aromaticity is a central chemical concept widely used in modern chemistry for the interpretation of molecular structure, stability, reactivity, and magnetic properties of many compounds. As such, its reliable prediction is an important task of computational chemistry. In recent years, many methods to quantify aromaticity based on different physicochemical properties of molecules have been proposed. However, the nonobservable nature of aromaticity makes difficult to assess the performance of the numerous existing indices. In the present work, we introduce a series of fifteen aromaticity tests that can be used to analyze the advantages and drawbacks of a group of aromaticity descriptors. On the basis of the results obtained for a set of ten indicators of aromaticity, we conclude that indices based on the study of electron delocalization in aromatic species are the most accurate among those examined in this work. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008

[1]  P. Fowler,et al.  Trimerization of Ethyne: Growth and Evolution of Ring Currents in the Formation of the Benzene Ring , 2003 .

[2]  I. Gutman,et al.  Graph theory and molecular orbitals. 19. Nonparametric resonance energies of arbitrary conjugated systems , 1977 .

[3]  P. Geerlings,et al.  Local hardness: a critical account , 2007 .

[4]  P. Salvador,et al.  Comparison of the AIM delocalization index and the Mayer and fuzzy atom bond orders. , 2005, The journal of physical chemistry. A.

[5]  Haijun Jiao,et al.  What is aromaticity? , 1996, J. Chem. Inf. Comput. Sci..

[6]  F. Bernardi,et al.  Theoretical Study of the Aromatic Character of the Transition States of Allowed and Forbidden Cycloadditions , 1995 .

[7]  M. Randic.  Aromaticity of polycyclic conjugated hydrocarbons. , 2003, Chemical reviews.

[8]  Siân T. Howard,et al.  Benzenoid hydrocarbon aromaticity in terms of charge density descriptors , 1997 .

[9]  K. Fukui.  The path of chemical reactions - the IRC approach , 1981 .

[10]  Yosadara Ruiz-Morales,et al.  The Agreement between Clar Structures and Nucleus-Independent Chemical Shift Values in Pericondensed Benzenoid Polycyclic Aromatic Hydrocarbons: An Application of the Y-Rule , 2004 .

[11]  P. Schleyer,et al.  An Evaluation of the Aromaticity of Inorganic Rings: Refined Evidence from Magnetic Properties , 1997 .

[12]  X. Fradera,et al.  Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory , 2002 .

[13]  Clémence Corminboeuf,et al.  Nucleus-independent chemical shifts (NICS) as an aromaticity criterion. , 2005, Chemical reviews.

[14]  Roald Hoffmann,et al.  Extended Hückel Theory. II. σ Orbitals in the Azines , 1964 .

[15]  J. Aihara.  Circuit resonance energy: a key quantity that links energetic and magnetic criteria of aromaticity. , 2006, Journal of the American Chemical Society.

[16]  X. Fradera,et al.  An insight into the local aromaticities of polycyclic aromatic hydrocarbons and fullerenes. , 2003, Chemistry.

[17]  A. Moyano,et al.  A simple approach for the evaluation of local aromaticities , 1991 .

[18]  Roald Hoffmann,et al.  Conservation of orbital symmetry , 1968 .

[19]  J. M. Schulman,et al.  Aromatic Character of [n]Helicenes and [n]Phenacenes , 1999 .

[20]  P. Schleyer,et al.  Aromaticity of pericyclic reaction transition structures: magnetic evidence , 1998 .

[21]  S. Sakai.  New Criterion on the Aromaticity of Six-Membered Rings , 2002 .

[22]  M. González-Moa,et al.  Characterization of pericyclic reactions using multicenter electron delocalization analysis. , 2007, Chemphyschem : a European journal of chemical physics and physical chemistry.

[23]  J. M. Bofill,et al.  Are nucleus-independent (NICS) and 1H NMR chemical shifts good indicators of aromaticity in π-stacked polyfluorenes? , 2006 .

[24]  Ricardo A. Mosquera,et al.  QTAIM n‐center delocalization indices as descriptors of aromaticity in mono and poly heterocycles , 2007, J. Comput. Chem..

[25]  G. Seifert,et al.  Induced magnetic fields in aromatic [n]-annulenes—interpretation of NICS tensor components , 2004 .

[26]  Miquel Solà,et al.  Theoretical evaluation of electron delocalization in aromatic molecules by means of atoms in molecules (AIM) and electron localization function (ELF) topological approaches. , 2005, Chemical reviews.

[27]  M. Solà,et al.  Local aromaticity of the six-membered rings in pyracylene. A difficult case for the NICS indicator of aromaticity. , 2004, The Journal of organic chemistry.

[28]  Patrick Bultinck,et al.  Aromaticity in linear polyacenes: Generalized population analysis and molecular quantum similarity approach , 2007, J. Comput. Chem..

[29]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[30]  F. Feixas,et al.  Aromaticity of distorted benzene rings: exploring the validity of different indicators of aromaticity. , 2007, The journal of physical chemistry. A.

[31]  Michael J. S. Dewar,et al.  Aromaticity and Pericyclic Reactions , 1971 .

[32]  P. Fowler,et al.  Current Densities of Localized and Delocalized Electrons in Molecules , 2002 .

[33]  H. Zimmerman.  Moebius-Hueckel concept in organic chemistry. Application of organic molecules and reactions , 1971 .

[34]  Douglas Lloyd.  What Is Aromaticity? , 1996, J. Chem. Inf. Comput. Sci..

[35]  Paul von Ragué Schleyer,et al.  Introduction: DelocalizationPi and Sigma , 2005 .

[36]  Alan R. Katritzky,et al.  AROMATICITY AS A QUANTITATIVE CONCEPT. 7. AROMATICITY REAFFIRMED AS A MULTIDIMENSIONAL CHARACTERISTIC , 1998 .

[37]  J. Cioslowski,et al.  The concerted trimerization of ethyne to benzene revisited , 2000 .

[38]  R. H. Mitchell,et al.  Effective aromaticity of tricarbonylchromiumbenzene, about 25 enhanced over that of benzene: structural evidence from a complexed benzannulene. , 2002, Journal of the American Chemical Society.

[39]  A. Katritzky,et al.  Aromaticity: a Theoretical Concept of Immense Practical Importance , 2000 .

[40]  S. Lindeman,et al.  Charge-transfer bonding in metal–arene coordination , 2000 .

[41]  A. Katritzky,et al.  To what extent can aromaticity be defined uniquely? , 2002, The Journal of organic chemistry.

[42]  P. Geerlings,et al.  A computational study of aromaticity-controlled Diels–Alder reactions , 2000 .

[43]  Alexandru T. Balaban,et al.  Is aromaticity outmoded? , 1980 .

[44]  R. Carbó-Dorca,et al.  Electron delocalization and aromaticity in linear polyacenes: atoms in molecules multicenter delocalization index. , 2006, The journal of physical chemistry. A.

[45]  Friedrich Biegler-König,et al.  Calculation of the average properties of atoms in molecules. II , 1982 .

[46]  P. Fuentealba,et al.  Sigma-pi separation of the electron localization function and aromaticity. , 2004, The Journal of chemical physics.

[47]  S. Sakai.  Theoretical Analysis of Concerted and Stepwise Mechanisms of Diels−Alder Reaction between Butadiene and Ethylene , 2000 .

[48]  Patrick Bultinck,et al.  Critical analysis of the local aromaticity concept in polyaromatic hydrocarbons. , 2007, Faraday discussions.

[49]  A. Stanger.  Nucleus-independent chemical shifts (NICS): distance dependence and revised criteria for aromaticity and antiaromaticity. , 2006, The Journal of organic chemistry.

[50]  M. Hall,et al.  Benzene chromium tricarbonyl revisited: Theoretical study of the structure and dynamics of (η6-C6H6)Cr(CO)3 , 2000 .

[51]  K. Houk,et al.  Concerted and stepwise mechanisms in cycloaddition reactions: potential surfaces and isotope effects , 1994 .

[52]  Nicolás Otero,et al.  Local aromaticity study of heterocycles using n-center delocalization indices: the role of aromaticity on the relative stability of position isomers , 2006 .

[53]  M. Solà,et al.  Relation between the substituent effect and aromaticity. , 2004, The Journal of organic chemistry.

[54]  P. Schleyer,et al.  Magnetic Properties of Aromatic Transition States: The Diels–Alder Reactions , 1994 .

[55]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[56]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[57]  Paul von Ragué Schleyer,et al.  Nucleus-Independent Chemical Shifts:  A Simple and Efficient Aromaticity Probe. , 1996, Journal of the American Chemical Society.

[58]  Alan R. Katritzky,et al.  Aromaticity as a Quantitative Concept. 1. A Statistical Demonstration of the Orthogonality of "Classical" and "Magnetic" Aromaticity in Five- and Six-Membered Heterocycles , 1989 .

[59]  M. Solà,et al.  Nucleus-independent chemical shift (NICS) profiles in a series of monocyclic planar inorganic compounds , 2006 .

[60]  Tadeusz Marek Krygowski,et al.  Sigma- and pi-electron delocalization: focus on substituent effects. , 2005, Chemical reviews.

[61]  R. Ponec,et al.  Multicenter bond indices as a new measure of aromaticity in polycyclic aromatic hydrocarbons , 2005 .

[62]  Patrick W. Fowler,et al.  Patterns of Ring Currents in Conjugated Molecules: A Few-Electron Model Based on Orbital Contributions , 2001 .

[63]  Juan Andrés,et al.  An electron localization function study of the trimerization of acetylene: Reaction mechanism and development of aromaticity , 2005 .

[64]  R. Bader.  Atoms in molecules : a quantum theory , 1990 .

[65]  Xavier Fradera,et al.  The Lewis Model and Beyond , 1999 .

[66]  J. Aihara,et al.  Local aromaticities in large polyacene molecules. , 2005, The journal of physical chemistry. A.

[67]  M. Solà,et al.  An analysis of the changes in aromaticity and planarity along the reaction path of the simplest Diels–Alder reaction. Exploring the validity of different indicators of aromaticity , 2005 .

[68]  H. Lischka,et al.  The Diels-Alder reaction of ethene and 1,3-butadiene: an extended multireference ab initio investigation. , 2004, Chemphyschem : a European journal of chemical physics and physical chemistry.

[69]  Mercedes Alonso,et al.  Neural networks as a tool to classify compounds according to aromaticity criteria. , 2007, Chemistry.

[70]  Pedro Salvador,et al.  Electron sharing indexes at the correlated level. Application to aromaticity calculations. , 2007, Faraday discussions.

[71]  F. Feixas,et al.  Is the Aromaticity of the Benzene Ring in the (eta6-C6H6)Cr(CO)3 Complex Larger than that of the Isolated Benzene Molecule? , 2007 .

[72]  E. Clar.  The aromatic sextet , 1972 .

[73]  P. Lazzeretti,et al.  Current Density Maps, Magnetizability, and Nuclear Magnetic Shielding Tensors for Anthracene, Phenanthrene, and Triphenylene , 1999 .

[74]  Thomas Heine,et al.  Description of electron delocalization via the analysis of molecular fields. , 2005, Chemical reviews.

[75]  J. Pople,et al.  Self‐consistent molecular orbital methods. XX. A basis set for correlated wave functions , 1980 .

[76]  P. Salvador,et al.  Aromaticity measures from fuzzy-atom bond orders (FBO). The aromatic fluctuation (FLU) and the para-delocalization (PDI) indexes. , 2006, The journal of physical chemistry. A.

[77]  Karl Jug,et al.  Aromaticity as a multi-dimensional phenomenon , 1991 .

[78]  A. Katritzky,et al.  Quantitative measures of aromaticity for mono-, bi-, and tricyclic penta- and hexaatomic heteroaromatic ring systems and their interrelationships. , 2001, Chemical reviews.

[79]  R. H. Mitchell,et al.  The Synthesis, Aromaticity, and NMR Properties of [14]Annulene Fused Organometallics. Determination of the Effective Bond Localizing Ability (“Relative Aromaticity”) and Diamagnetic Anisotropy of Several Organometallic Moieties , 1998 .

[80]  J. V. Lenthe,et al.  Aromaticity of Pyrene and Its Cyclopentafused CongenersResonance and NICS Criteria. An Ab Initio Valence Bond Analysis in Terms of Kekulé Resonance Structures , 2001 .

[81]  M. Cyrański.  Energetic aspects of cyclic pi-electron delocalization: evaluation of the methods of estimating aromatic stabilization energies. , 2005, Chemical reviews.

[82]  Miquel Solà,et al.  Polycyclic benzenoids: why kinked is more stable than straight. , 2007, The Journal of organic chemistry.

[83]  Yuansheng Jiang,et al.  The valence bond calculations for conjugated hydrocarbons having 24–28 π‐electrons , 2000 .

[84]  S. Bachrach,et al.  Towards assessing the aromaticity of the Diels–Alder transition state , 2007 .

[85]  P. Fuentealba,et al.  An Aromaticity Scale Based on the Topological Analysis of the Electron Localization Function Including σ and π Contributions. , 2005, Journal of chemical theory and computation.

[86]  Alexandru T Balaban,et al.  Aromaticity as a cornerstone of heterocyclic chemistry. , 2004, Chemical reviews.

[87]  Michael J. Frisch,et al.  Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets , 1984 .

[88]  Jesús Hernández-Trujillo,et al.  Bonding in Polycyclic Aromatic Hydrocarbons in Terms of the Electron Density and of Electron Delocalization , 2003 .

[89]  Iñaki Morao,et al.  A Simple Ring Current Model for Describing In-Plane Aromaticity in Pericyclic Reactions. , 1999, The Journal of organic chemistry.

[90]  S. Pati,et al.  Ring currents in condensed ring systems , 1998 .

[91]  Mikhail N. Glukhovtsev,et al.  Aromaticity and Antiaromaticity: Electronic and Structural Aspects , 1994 .

[92]  Mario Giambiagi,et al.  Multicenter bond indices as a measure of aromaticity , 2000 .

[93]  Kendall N. Houk,et al.  Pericyclic Reaction Transition States: Passions and Punctilios, 1935-1995 , 1995 .

[94]  P. Bultinck,et al.  The pseudo-π method examined for the computation of multicenter aromaticity indices , 2008 .

[95]  R. Hoffmann,et al.  Haptotropic rearrangements of polyene―MLn complexes. II: Bicyclic polyene―MCp, ―M(CO)3 systems , 1983 .

[96]  Tadeusz Marek Krygowski,et al.  Crystallographic studies of inter- and intramolecular interactions reflected in aromatic character of .pi.-electron systems , 1993, J. Chem. Inf. Comput. Sci..

[97]  A. Toro‐Labbé.  Theoretical aspects of chemical reactivity , 2007 .

[98]  Peter Pulay,et al.  Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations , 1990 .

[99]  P. Schleyer,et al.  Dissected Nucleus-Independent Chemical Shift Analysis of π-Aromaticity and Antiaromaticity. , 2001, Organic letters.

[100]  C. Pittman,et al.  Nucleus independent chemical shift evaluation of the aromaticity of pentafulvene and its exocyclic Si, Ge, and Sn derivatives , 2001 .

[101]  P. Schleyer,et al.  Which NICS aromaticity index for planar pi rings is best? , 2006, Organic letters.

[102]  Richard F. W. Bader.  A quantum theory of molecular structure and its applications , 1991 .

[103]  M. G. Evans,et al.  The activation energy of diene association reactions , 1938 .

[104]  R. H. Mitchell.  Measuring aromaticity by NMR. , 2001, Chemical reviews.

[105]  F. Feixas,et al.  Electron delocalization and aromaticity measures within the Hückel molecular orbital method , 2007 .

[106]  Gernot Frenking,et al.  Unicorns in the world of chemical bonding models , 2007, J. Comput. Chem..

[107]  T. M. Krygowski,et al.  Structural aspects of aromaticity. , 2001, Chemical reviews.

[108]  J. Cioslowski,et al.  Properties of aromaticity indices based on the one-electron density matrix. , 2007, The journal of physical chemistry. A.

[109]  Kendall N. Houk,et al.  Density functional theory calculations of pericyclic reaction transition structures , 1996 .

[110]  Xavier Fradera,et al.  The calculation of electron localization and delocalization indices at the Hartree–Fock, density functional and post-Hartree–Fock levels of theory , 2002 .

[111]  R. H. Mitchell,et al.  Synthesis of the first metal-complexed benzannulene. An estimate of the aromaticity of tricarbonylchromium-complexed benzene relative to the aromaticity of benzene itself , 1990 .

[112]  Paolo Lazzeretti.  Assessment of aromaticity via molecular response properties , 2004 .

[113]  P. Fowler,et al.  Ring currents in aromatic hydrocarbons , 1996 .

[114]  Miquel Solà,et al.  Assessment of Clar's aromatic π-sextet rule by means of PDI, NICS and HOMA indicators of local aromaticity† , 2005 .

[115]  Alexander I Boldyrev,et al.  All-metal aromaticity and antiaromaticity. , 2005, Chemical reviews.

[116]  C. Glidewell,et al.  Mndo study of bond orders in some conjugated BI- and tri-cyclic hydrocarbons , 1984 .

[117]  T. M. Krygowski,et al.  Definition of aromaticity basing on the harmonic oscillator model , 1972 .

[118]  K. Fukui.  Formulation of the reaction coordinate , 1970 .

[119]  Ranbir Singh,et al.  J. Mol. Struct. (Theochem) , 1996 .

[120]  J. W. Emsley,et al.  Progress in Nuclear Magnetic Resonance Spectroscopy , 1984 .

[121]  G. Portella,et al.  Local aromaticity of [n]acenes, [n]phenacenes, and [n]helicenes (n = 1-9). , 2005, The Journal of organic chemistry.

[122]  P. Fuentealba,et al.  Chapter 5 Understanding and using the electron localization function , 2007 .

[123]  L. Radom,et al.  Fulvalenes, Fulvenes, and Related Molecules: An ab Initio Study. , 1997, The Journal of organic chemistry.

[124]  Xavier Fradera,et al.  The delocalization index as an electronic aromaticity criterion: application to a series of planar polycyclic aromatic hydrocarbons. , 2003, Chemistry.

[125]  I. Gutman,et al.  On the distribution of π-electrons in large polycyclic aromatic hydrocarbons , 2004 .

[126]  H. Bernhard Schlegel,et al.  An improved algorithm for reaction path following , 1989 .

[127]  Miquel Solà,et al.  The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization. , 2005, The Journal of chemical physics.

[128]  P. Fowler,et al.  Substituent effects on induced current densities in penta- and heptafulvenes , 2002 .

[129]  M. Randic,et al.  Partitioning of π -electrons in rings of polycyclic conjugated hydrocarbons: Part 6. Comparison with other methods for estimating the local aromaticity of rings in polycyclic benzenoids , 2005 .

[130]  R. Ponec,et al.  Local aromaticity in polycyclic aromatic hydrocarbons: electron delocalization versus magnetic indices. , 2006, Chemistry.

[131]  C. Tsipis.  DFT study of “all-metal” aromatic compounds , 2005 .

[132]  M. Cyrański,et al.  Global and Local Aromaticity of Linear and Angular Polyacenes , 2000 .

[133]  R. Gobetto,et al.  Synthesis, Structural and Spectroscopic Characterization of Four [(η6‐PAH)Cr(CO)3] Complexes (PAH = Pyrene, Perylene, Chrysene, 1,2‐Benzanthracene) , 2004 .