Performance of 3D‐space‐based atoms‐in‐molecules methods for electronic delocalization aromaticity indices

Several definitions of an atom in a molecule (AIM) in three‐dimensional (3D) space, including both fuzzy and disjoint domains, are used to calculate electron sharing indices (ESI) and related electronic aromaticity measures, namely, Iring and multicenter indices (MCI), for a wide set of cyclic planar aromatic and nonaromatic molecules of different ring size. The results obtained using the recent iterative Hirshfeld scheme are compared with those derived from the classical Hirshfeld method and from Bader's quantum theory of atoms in molecules. For bonded atoms, all methods yield ESI values in very good agreement, especially for C–C interactions. In the case of nonbonded interactions, there are relevant deviations, particularly between fuzzy and QTAIM schemes. These discrepancies directly translate into significant differences in the values and the trends of the aromaticity indices. In particular, the chemically expected trends are more consistently found when using disjoint domains. Careful examination of the underlying effects reveals the different reasons why the aromaticity indices investigated give the expected results for binary divisions of 3D space. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011.

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

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

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

[4]  R. Fulton.  Sharing of electrons in molecules , 1993 .

[5]  M. Solà,et al.  Erratum: “The aromatic fluctuation index (FLU): A new aromaticity index based on electron delocalization” [J. Chem Phys. 122, 014109 (2005)] , 2006 .

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

[7]  R. Wheatley,et al.  Redefining the atom: atomic charge densities produced by an iterative stockholder approach. , 2008, Chemical communications.

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

[9]  K. C. Mundim,et al.  Definition of a multicenter bond index , 1990 .

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

[11]  Robert Ponec,et al.  Investigation of Some Properties of Multicenter Bond Indices , 1997 .

[12]  R. Ponec,et al.  Multicenter bond indices as a new means for the quantitative characterization of homoaromaticity. , 2005, The journal of physical chemistry. A.

[13]  A. Savin,et al.  Classification of chemical bonds based on topological analysis of electron localization functions , 1994, Nature.

[14]  K. Tiels,et al.  Uniqueness and basis set dependence of iterative Hirshfeld charges , 2007 .

[15]  R. Wheatley,et al.  Atomic charge densities generated using an iterative stockholder procedure. , 2009, The Journal of chemical physics.

[16]  Robert S. Mulliken,et al.  Electronic Population Analysis on LCAO‐MO Molecular Wave Functions. IV. Bonding and Antibonding in LCAO and Valence‐Bond Theories , 1955 .

[17]  Miquel Solà,et al.  On the performance of some aromaticity indices: A critical assessment using a test set , 2008, J. Comput. Chem..

[18]  D. L. Cooper,et al.  Comparison of the Hirshfeld-I and iterated stockholder atoms in molecules schemes. , 2009, Physical chemistry chemical physics : PCCP.

[19]  Georges Voronoi.  Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .

[20]  Robert S. Mulliken,et al.  Electronic Population Analysis on LCAO‐MO Molecular Wave Functions. III. Effects of Hybridization on Overlap and Gross AO Populations , 1955 .

[21]  Kenneth B. Wiberg,et al.  Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane , 1968 .

[22]  Gilbert N. Lewis,et al.  The Atom and the Molecule , 1916, Resonance.

[23]  E. Francisco,et al.  A Molecular Energy Decomposition Scheme for Atoms in Molecules. , 2006, Journal of chemical theory and computation.

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

[25]  C. G. Bollini,et al.  Graphical Linking of MO Multicenter Bond Index and VB Structures. II- 5-c Rings and 6-c Heterocyclic Rings , 2001 .

[26]  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.

[27]  R. Daudel,et al.  Localizability of Electrons in Atoms and Molecules—Application to the Study of the Notion of Shell and of the Nature of Chemical Bonds , 1955 .

[28]  Axel D. Becke,et al.  A Simple Measure of Electron Localization in Atomic and Molecular-Systems , 1990 .

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

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

[31]  Robert S. Mulliken,et al.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. II. Overlap Populations, Bond Orders, and Covalent Bond Energies , 1955 .

[32]  I. Gutman,et al.  THE CLOSE RELATION BETWEEN CYCLIC DELOCALIZATION, ENERGY EFFECTS OF CYCLES AND AROMATICITY , 2009 .

[33]  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.

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

[35]  Chérif F. Matta,et al.  Atomic Charges Are Measurable Quantum Expectation Values: A Rebuttal of Criticisms of QTAIM Charges , 2004 .

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

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

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

[39]  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 .

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

[41]  J. Ángyán,et al.  COVALENT BOND ORDERS AND ATOMIC VALENCE INDICES IN THE TOPOLOGICAL THEORY OF ATOMS IN MOLECULES , 1994 .

[42]  F. L. Hirshfeld.  Bonded-atom fragments for describing molecular charge densities , 1977 .

[43]  Chérif F Matta,et al.  An experimentalist's reply to "What is an atom in a molecule?". , 2006, The journal of physical chemistry. A.

[44]  N. Koga,et al.  A Consistent Approach toward Atomic Radii , 2001 .

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

[46]  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.

[47]  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.

[48]  P. Salvador,et al.  Overlap populations, bond orders and valences for fuzzy atoms , 2004 .

[49]  István Mayer,et al.  Towards a “Chemical” Hamiltonian , 1983 .

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

[51]  A. Becke.  A multicenter numerical integration scheme for polyatomic molecules , 1988 .

[52]  Ernest R. Davidson,et al.  A test of the Hirshfeld definition of atomic charges and moments , 1992 .

[53]  R. Bader,et al.  Spatial localization of the electronic pair and number distributions in molecules , 1975 .

[54]  Patrick Bultinck,et al.  Critical analysis and extension of the Hirshfeld atoms in molecules. , 2007, The Journal of chemical physics.

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

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

[57]  Miquel Solà,et al.  Electron localization function at the correlated level. , 2006, The Journal of chemical physics.

[58]  R. S. Mulliken.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .

[59]  Andrew Streitwieser,et al.  Electron Delocalization and the Fermi Hole , 1996 .

[60]  F. Sondheimer.  Recent advances in the chemistry of large-ring conjugated systems , 1963 .

[61]  Patrick Bultinck,et al.  Electrostatic Potentials from Self-Consistent Hirshfeld Atomic Charges. , 2009, Journal of chemical theory and computation.