The hardness kernel as the basis for global and local reactivity indices

In a very recent article (Torrent‐Sucarrat et al., J Comput Chem 2007, 28, 574), we have shown how to evaluate the global hardness for polyatomic molecules using a hardness kernel approximation. We present here an extension of this previous work by improving the model used to evaluate the hardness kernel and the Fukui function. In addition, the concept of the local hardness is analyzed in detail, and for the first time, profiles of local hardness with kinetic and exchange‐correlation contributions for polyatomic molecules are reported. Finally, the concept of condensed atomic hardness is introduced and its usefulness as chemical reactivity descriptor is examined. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008

[1]  P. Fuentealba.  Reactivity indices and response functions in density functional theory 1 Dedicated to Professor Yves , 1998 .

[2]  R. Parr,et al.  Aspects of the Softness and Hardness Concepts of Density‐Functional Theory , 1991 .

[3]  P. Kolandaivel,et al.  Condensed Fukui function: dependency on atomic charges , 1997 .

[4]  C. Weizsäcker.  Zur Theorie der Kernmassen , 1935 .

[5]  J. Pople,et al.  Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules , 1972 .

[6]  R. Pearson.  Maximum Chemical and Physical Hardness , 1999 .

[7]  R. Contreras,et al.  BASICITY AND SOLVENT EFFECTS ON HYDROGEN BONDING IN NR3 ... HCOOH (R = H, CH3) MODEL SYSTEMS , 1999 .

[8]  J. Cioslowski,et al.  Atomic Fukui indices from the topological theory of atoms in molecules applied to Hartree-Fock and correlated electron densities , 1993 .

[9]  Paul Geerlings,et al.  Calculation of molecular electrostatic potentials and Fukui functions using density functional methods , 1996 .

[10]  Viktorya Aviyente,et al.  Interpretation of hydrogen bonding in the weak and strong regions using conceptual DFT descriptors. , 2006, The journal of physical chemistry. A.

[11]  R. Parr,et al.  Fukui function from a gradient expansion formula, and estimate of hardness and covalent radius for an atom , 1995 .

[12]  P. Fuentealba,et al.  On the condensed Fukui function , 2000 .

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

[14]  Swapan K. Ghosh,et al.  Simple Density Functional Approach to Polarizability, Hardness, and Covalent Radius of Atomic Systems , 1994 .

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

[16]  P. Geerlings,et al.  Conceptual density functional theory. , 2003, Chemical reviews.

[17]  Sourav Pal,et al.  On non-negativity of Fukui function indices , 1999 .

[18]  P. Ayers,et al.  Computing Fukui functions without differentiating with respect to electron number. II. Calculation of condensed molecular Fukui functions. , 2007, The Journal of chemical physics.

[19]  L. Curtiss,et al.  Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint , 1988 .

[20]  R. Parr.  Density-functional theory of atoms and molecules , 1989 .

[21]  R. Parr,et al.  Electronegativity: The density functional viewpoint , 1978 .

[22]  V. Lebedev,et al.  A QUADRATURE FORMULA FOR THE SPHERE OF THE 131ST ALGEBRAIC ORDER OF ACCURACY , 1999 .

[23]  P. Geerlings,et al.  DEVELOPMENT OF LOCAL HARDNESS RELATED REACTIVITY INDICES : THEIR APPLICATION IN A STUDY OF THE SE AT MONOSUBSTITUTED BENZENES WITHIN THE HSAB CONTEXT , 1995 .

[24]  M. Nguyen,et al.  Nitrous oxide as a 1,3-dipole: a theoretical study of its cycloaddition mechanism. , 2001, The Journal of organic chemistry.

[25]  P. Geerlings,et al.  Effect of the π-π stacking interaction on the acidity of phenol , 2005 .

[26]  Wilfried Langenaeker,et al.  Atomic charges, dipole moments, and Fukui functions using the Hirshfeld partitioning of the electron density , 2002, J. Comput. Chem..

[27]  Darrin M York,et al.  Quantum descriptors for biological macromolecules from linear‐scaling electronic structure methods , 2004, Proteins.

[28]  F. Méndez,et al.  The Hard and Soft Acids and Bases Principle: An Atoms in Molecules Viewpoint , 1994 .

[29]  R. Parr,et al.  Principle of maximum hardness , 1991 .

[30]  P. Ayers,et al.  Computing Fukui functions without differentiating with respect to electron number. I. Fundamentals. , 2007, The Journal of chemical physics.

[31]  R. Parr,et al.  Hardness, softness, and the fukui function in the electronic theory of metals and catalysis. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[32]  P. Geerlings,et al.  Analogies and differences between two ways to evaluate the global hardness. , 2006, The Journal of chemical physics.

[33]  Robert G. Parr,et al.  Density functional approach to the frontier-electron theory of chemical reactivity , 1984 .

[34]  P. Ayers.  Can one oxidize an atom by reducing the molecule that contains it? , 2006, Physical chemistry chemical physics : PCCP.

[35]  M. Berkowitz,et al.  Molecular hardness and softness, local hardness and softness, hardness and softness kernels, and relations among these quantities , 1988 .

[36]  M. Solà,et al.  Global hardness evaluation using simplified models for the hardness kernel , 2002 .

[37]  W. J. Orville-Thomas.  Atoms in Molecules — a Quantum Theory , 1996 .

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

[39]  S. Pal,et al.  The influence of electric field on the global and local reactivity descriptors: reactivity and stability of weakly bonded complexes. , 2007, Journal of Physical Chemistry A.

[40]  P. Salvador,et al.  One- and two-center physical space partitioning of the energy in the density functional theory. , 2007, The Journal of chemical physics.

[41]  L. Pacios.  Study of a gradient expansion approach to compute the Fukui function in atoms , 1997 .

[42]  M. Solà,et al.  An assessment of a simple hardness kernel approximation for the calculation of the global hardness in a series of Lewis acids and bases , 2005 .

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

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

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

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

[47]  P. Kollman,et al.  An approach to computing electrostatic charges for molecules , 1984 .

[48]  Ralph G. Pearson,et al.  Absolute Electronegativity and Hardness: Application to Inorganic Chemistry , 1988 .

[49]  E. Wigner.  On the Interaction of Electrons in Metals , 1934 .

[50]  John C. Slater,et al.  Atomic Radii in Crystals , 1964 .

[51]  Robert G. Parr,et al.  Variational Principles for Describing Chemical Reactions: The Fukui Function and Chemical Hardness Revisited , 2000 .

[52]  Hasse Fredriksson,et al.  Theory of Atoms and Molecules , 2008 .

[53]  E. Fermi.  Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des periodischen Systems der Elemente , 1928 .

[54]  Swapan K. Ghosh.  Energy derivatives in density-functional theory , 1990 .

[55]  Paul Geerlings,et al.  On the quality of the hardness kernel and the Fukui function to evaluate the global hardness , 2007, J. Comput. Chem..

[56]  H. Chermette,et al.  Reactivity Indices in Density Functional Theory: A New Evaluation of the Condensed Fukui Function by Numerical Integration , 1998 .

[57]  Wolfram Koch,et al.  A Chemist's Guide to Density Functional Theory , 2000 .

[58]  Ralph G. Pearson,et al.  Chemical Hardness: PEARSON:CHEM.HARDNESS O-BK , 1997 .

[59]  Henry Chermette,et al.  Chemical reactivity indexes in density functional theory , 1999 .

[60]  P. Dirac.  Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.

[61]  P. Fuentealba.  A local model for the hardness kernel and related reactivity parameters in density functional theory , 1995 .

[62]  R. Parr,et al.  Simplified Models for Hardness Kernel and Calculations of Global Hardness , 1997 .

[63]  M. Berkowitz,et al.  On the concept of local hardness in chemistry , 1985 .

[64]  C. Breneman,et al.  Determining atom‐centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis , 1990 .

[65]  L. H. Thomas.  The calculation of atomic fields , 1927, Mathematical Proceedings of the Cambridge Philosophical Society.

[66]  P. Geerlings,et al.  Quantum similarity study of atoms: a bridge between hardness and similarity indices. , 2007, The Journal of chemical physics.

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

[68]  R. Parr,et al.  Variational method for determining the Fukui function and chemical hardness of an electronic system , 1995 .

[69]  P. Geerlings,et al.  Interplay between π–π interactions and the H-bonding ability of aromatic nitrogen bases , 2005 .

[70]  G. Goode,et al.  Negative ions and the magnetron , 1969 .

[71]  P. Geerlings,et al.  Understanding the concept of basicity in zeolites. A DFT study of the methylation of Al-O-Si bridging oxygen atoms. , 2006, The journal of physical chemistry. B.

[72]  J. Steyaert,et al.  Influence of the π–π interaction on the hydrogen bonding capacity of stacked DNA/RNA bases , 2005, Nucleic acids research.

[73]  A. Cedillo,et al.  Global and Local Reactivity and Activation Patterns of HOOX (X = H, NO2, CO2-, SO3-) Peroxides with Solvent Effects , 2003 .

[74]  P. Fuentealba,et al.  Further exploration of the Fukui function, hardness, and other reactivity indices and its relationships within the Kohn-Sham scheme , 2007 .

[75]  R. Carbó-Dorca,et al.  Negative Fukui functions: New insights based on electronegativity equalization , 2003 .

[76]  Weitao Yang,et al.  The use of global and local molecular parameters for the analysis of the gas-phase basicity of amines. , 1986, Journal of the American Chemical Society.

[77]  P. Salvador,et al.  Energy partitioning for "fuzzy" atoms. , 2004, The Journal of chemical physics.

[78]  R. C. Morrison,et al.  Variational principles for describing chemical reactions: Condensed reactivity indices , 2002 .

[79]  P. Geerlings,et al.  AB INITIO AND DENSITY FUNCTIONAL THEORY STUDY OF THE GEOMETRY AND REACTIVITY OF BENZYNE, 3-FLUOROBENZYNE, 4-FLUOROBENZYNE, AND 4,5-DIDEHYDROPYRIMIDINE , 1998 .

[80]  R. Carbó-Dorca,et al.  Critical thoughts on computing atom condensed Fukui functions. , 2007, The Journal of chemical physics.

[81]  O. Tishchenko,et al.  Protonation of Gaseous Halogenated Phenols and Anisoles and Its Interpretation Using DFT-Based Local Reactivity Indices , 2001 .

[82]  Warren J. Hehre,et al.  AB INITIO Molecular Orbital Theory , 1986 .

[83]  P W Ayers,et al.  Variational principles for describing chemical reactions. Reactivity indices based on the external potential. , 2001, Journal of the American Chemical Society.