Extending Hirshfeld‐I to bulk and periodic materials

In this work, a method is described to extend the iterative Hirshfeld‐I method, generally used for molecules, to periodic systems. The implementation makes use of precalculated pseudopotential‐based electron density distributions, and it is shown that high‐quality results are obtained for both molecules and solids, such as ceria, diamond, and graphite. The use of grids containing (precalculated) electron densities makes the implementation independent of the solid state or quantum chemical code used for studying the system. The extension described here allows for easy calculation of atomic charges and charge transfer in periodic and bulk systems. The conceptual issue of obtaining reference densities for anions is discussed, and the delocalization problem for anionic reference densities originating from the use of a plane wave basis set is identified and handled. © 2012 Wiley Periodicals, Inc.

[1]  P. G. Byrom,et al.  A novel definition of a molecule in a crystal , 1997 .

[2]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[3]  Á. M. Pendás,et al.  Electron number distribution functions with iterative Hirshfeld atoms , 2011 .

[4]  R. S. Mulliken Electronic Structures of Molecules XI. Electroaffinity, Molecular Orbitals and Dipole Moments , 1935 .

[5]  D. L. Cooper,et al.  Anatomy of bond formation. Bond length dependence of the extent of electron sharing in chemical bonds from the analysis of domain-averaged Fermi holes , 2007 .

[6]  Gustavo E Scuseria,et al.  Theoretical study of CeO2 and Ce2O3 using a screened hybrid density functional. , 2006, The Journal of chemical physics.

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

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

[9]  François M. Peeters,et al.  Water on graphene: Hydrophobicity and dipole moment using density functional theory , 2009 .

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

[11]  M. Spackman,et al.  Hirshfeld Surfaces: A New Tool for Visualising and Exploring Molecular Crystals , 1998 .

[12]  Jefferson Z. Liu,et al.  Graphene actuators: quantum-mechanical and electrostatic double-layer effects. , 2011, Journal of the American Chemical Society.

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

[14]  Alexey I. Baranov,et al.  Electron localization and delocalization indices for solids , 2011, J. Comput. Chem..

[15]  E. Wigner,et al.  On the Constitution of Metallic Sodium. II , 1933 .

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

[17]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[18]  P. Ayers Atoms in molecules, an axiomatic approach. I. Maximum transferability , 2000 .

[19]  Alexander J. Norquist,et al.  Beyond Charge Density Matching: The Role of C–H···O Interactions in the Formation of Templated Vanadium Tellurites , 2011 .

[20]  Paul W Ayers,et al.  What is an atom in a molecule? , 2005, The journal of physical chemistry. A.

[21]  Georges Voronoi Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire. Sur quelques propriétés des formes quadratiques positives parfaites. , 1908 .

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

[23]  M. Spackman,et al.  Novel tools for visualizing and exploring intermolecular interactions in molecular crystals. , 2004, Acta crystallographica. Section B, Structural science.

[24]  Blöchl,et al.  Projector augmented-wave method. , 1994, Physical review. B, Condensed matter.

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

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

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

[28]  D. Sholl,et al.  Accurate Treatment of Electrostatics during Molecular Adsorption in Nanoporous Crystals without Assigning Point Charges to Framework Atoms , 2011 .

[29]  Matthias Zeller,et al.  [R-C{sub 7}H{sub 16}N{sub 2}][V{sub 2}Te{sub 2}O{sub 10}] and [S-C{sub 7}H{sub 16}N{sub 2}][V{sub 2}Te{sub 2}O{sub 10}]; new polar templated vanadium tellurite enantiomers , 2011 .

[30]  John C. Slater,et al.  Quantum Theory of Molecules and Solids Vol. 4: The Self‐Consistent Field for Molecules and Solids , 1974 .

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

[32]  T. Verstraelen,et al.  Computation of Charge Distribution and Electrostatic Potential in Silicates with the Use of Chemical Potential Equalization Models , 2012 .

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

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

[35]  Alexander J. Norquist,et al.  [R-C7H16N2][V2Te2O10] and [S-C7H16N2][V2Te2O10]; new polar templated vanadium tellurite enantiomers , 2011 .

[36]  Á. M. Pendás,et al.  Generalized electron number distribution functions: real space versus orbital space descriptions , 2011 .

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

[38]  M. Dolg,et al.  Valence basis sets for lanthanide 4f-in-core pseudopotentials adapted for crystal orbital ab initio calculations , 2005 .

[39]  F. Peeters,et al.  First-principles investigation of graphene fluoride and graphane , 2010, 1009.3847.

[40]  K. Hermansson,et al.  Tuning LDA+U for electron localization and structure at oxygen vacancies in ceria. , 2007, The Journal of chemical physics.

[41]  Dylan Jayatilaka,et al.  Hirshfeld surface analysis , 2009 .

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

[43]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[44]  Stefan Goedecker,et al.  ABINIT: First-principles approach to material and nanosystem properties , 2009, Comput. Phys. Commun..

[45]  Joshua Schrier Fluorinated and nanoporous graphene materials as sorbents for gas separations. , 2011, ACS applied materials & interfaces.

[46]  R. Parr,et al.  Some remarks on the density functional theory of few-electron systems , 1983 .

[47]  Yang,et al.  Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory , 2000, Physical review letters.

[48]  J. Perdew,et al.  Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy , 1982 .

[49]  Fujio Izumi,et al.  VESTA: a three-dimensional visualization system for electronic and structural analysis , 2008 .

[50]  Paul W. Ayers,et al.  A self‐consistent Hirshfeld method for the atom in the molecule based on minimization of information loss , 2011, J. Comput. Chem..

[51]  D. L. Cooper,et al.  Influence of atoms-in-molecules methods on shared-electron distribution indices and domain-averaged Fermi holes. , 2010, The journal of physical chemistry. A.

[52]  F. Peeters,et al.  Paramagnetic adsorbates on graphene: a charge transfer analysis , 2008, 0806.0549.

[53]  David S Sholl,et al.  Chemically Meaningful Atomic Charges That Reproduce the Electrostatic Potential in Periodic and Nonperiodic Materials. , 2010, Journal of chemical theory and computation.

[54]  G. Kresse,et al.  From ultrasoft pseudopotentials to the projector augmented-wave method , 1999 .

[55]  P. Mori-Sánchez,et al.  Hirshfeld surfaces as approximations to interatomic surfaces , 2002 .