Electron localization and delocalization indices for solids

The electron localization and delocalization indices obtained by the integration of exchange‐correlation part of pair density over chemically meaningful regions of space, e.g., QTAIM atoms are valuable tools for the bonding analysis in molecular systems. However, among periodic systems only few simplest models were analyzed with this approach until now. This contribution reports implementation and evaluation of the localization and delocalization indices on the basis of solid state DFT calculations. A comparison with the results of simple analytical model of Ponec was made. In addition, a small set of compounds with ionic (NaCl), covalent (diamond, graphite), and metallic (Na, Cu) bonding interactions was characterized using this method. Typical features of different types of bonding were discussed using the delocalization indices. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011

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

[2]  J. André,et al.  Self‐Consistent Field Theory for the Electronic Structure of Polymers , 1969 .

[3]  Hanno Essén,et al.  The characterization of atomic interactions , 1984 .

[4]  Miroslav Kohout,et al.  A Measure of Electron Localizability , 2004 .

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

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

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

[8]  M. Solà,et al.  The role of electronic delocalization in transition metal complexes from the electron localization function and the quantum theory of atoms in molecules viewpoints , 2009 .

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

[10]  Miroslav Kohout,et al.  Electron localization function for transition-metal compounds , 2002 .

[11]  Robert Ponec,et al.  Electron pairing and chemical bonds. Electron fluctuation and pair localization in ELF domains , 2005, J. Comput. Chem..

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

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

[14]  Claudia Ambrosch-Draxl,et al.  Augmented Planewave Methods , 2004 .

[15]  K. Pernal,et al.  Electron localizability indicator for correlated wavefunctions. II Antiparallel-spin pairs , 2004 .

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

[17]  M. Nascimento,et al.  The nature of the chemical bond , 2008 .

[18]  B. Silvi,et al.  The Topological Analysis of the Electron Localization Function. A Key for a Position Space Representation of Chemical Bonds , 2005 .

[19]  Andreas Savin,et al.  Analysis of the delocalization in the topological theory of chemical bond , 1998 .

[20]  J. Andrés,et al.  The Nature Of The Chemical Bond In Di- And Polynuclear Metal Cluster Complexes As Depicted By The Analysis Of The Electron Localization Function , 2005 .

[21]  Andreas Savin,et al.  Topological analysis of the electron localization function applied to delocalized bonds , 1996 .

[22]  I. Mayer,et al.  Bond order and valence indices: A personal account , 2007, J. Comput. Chem..

[23]  Y. Grin,et al.  Atomic Shells From the Electron Localizability in Momentum Space , 2006 .

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

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

[26]  R. Bader,et al.  Fluctuation and correlation of electrons in molecular systems , 1974 .

[27]  R. Bochicchio,et al.  On the definition of bond orders at correlated level , 2003 .

[28]  Y. Grin,et al.  Electron localizability indicator for correlated wavefunctions. III: singlet and triplet pairs , 2008 .

[29]  A. Sironi,et al.  Chemical bonding in transition metal carbonyl clusters: complementary analysis of theoretical and experimental electron densities , 2003 .

[30]  Á. M. Pendás,et al.  Non-nuclear Maxima of the Electron Density , 1999 .

[31]  F. Escudero,et al.  Atoms in molecules , 1982 .

[32]  S. T. Mixon,et al.  Comparison of covalent bond indexes and sharing indexes , 1993 .

[33]  István Mayer,et al.  Charge, bond order and valence in the AB initio SCF theory , 1983 .

[34]  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.

[35]  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 .

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

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

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

[39]  M. Kohout.  Bonding indicators from electron pair density functionals. , 2007, Faraday discussions.

[40]  G. V. Chester,et al.  Solid State Physics , 2000 .

[41]  A. Baranov,et al.  Topological analysis of real space properties for the solid-state full-potential APW DFT method , 2010 .

[42]  Evert Jan Baerends,et al.  An approximate exchange-correlation hole density as a functional of the natural orbitals , 2002 .

[43]  R. Ponec.  Chemical bonding in solids. On the generalization of the concept of bond order and valence for infinite periodical structures , 2005 .

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

[45]  Wang,et al.  Accurate and simple analytic representation of the electron-gas correlation energy. , 1992, Physical review. B, Condensed matter.

[46]  János G. Ángyán,et al.  Comparison of ab Initio Hartree−Fock and Kohn−Sham Orbitals in the Calculation of Atomic Charge, Bond Index, and Valence , 2000 .

[47]  Andreas Savin,et al.  Atomic Shell Structure and Electron Numbers , 1996 .

[48]  G. Gutsev,et al.  Toward Understanding the Electron Density Distribution in Magnetic Clusters: Insight from the ELF and AIM Analyses of Ground-State Fe4 , 2004 .

[49]  Y. Grin,et al.  Charge decomposition analysis of the electron localizability indicator: a bridge between the orbital and direct space representation of the chemical bond. , 2007, Chemistry.

[50]  F. Wagner,et al.  Ultrashort metal-metal distances and extreme bond orders. , 2009, Nature chemistry.