Modern Charge-Density Analysis - Springer978-90-481-3836-4/1.pdfContents 1 A Guided Tour Through Modern Charge Density Analysis..... 1 Carlo Gatti and Piero Macchi 2 Electron Densities

Modern Charge-Density Analysis

Carlo Gatti • Piero MacchiEditors

Modern Charge-DensityAnalysis

123

EditorsCarlo GattiCNR-ISTM, Istituto di Scienze e TecnologieMolecolari del CNRc/o Dipartimento di Chimica Fisica edElettrochimicaUniversita degli Studi di MilanoVia Golgi 1920133 MilanoItalycarlo.gatti@istm.cnr.it

Piero MacchiDepartment of Chemistry and BiochemistryUniversity of BernFreiestrasse 3CH3012 BernSwitzerlandpiero.macchi@dcb.unibe.ch

ISBN 978-90-481-3835-7 e-ISBN 978-90-481-3836-4DOI 10.1007/978-90-481-3836-4Springer Dordrecht Heidelberg London New York

Library of Congress Control Number: 2011941749

© Springer Science+Business Media B.V. 2012No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or byany means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without writtenpermission from the Publisher, with the exception of any material supplied specifically for the purposeof being entered and executed on a computer system, for exclusive use by the purchaser of the work.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

This book is dedicated toCarla Roetti, Miguel Alvarez Blanco,Andres Goeta and Cesare PisaniTheir valuable contribution inthe field of charge density has beenan inspiration for many of us andwill remain for the future generationsof scientists

Preface

The contributions in this book manifest the tremendous developments that havetaken place in the last 10–20 years in electron density research in the broadest sense.Although the possibility of measuring the distribution of electrons in crystallinesolids with X-rays was realized soon after the discovery of X-ray diffraction earlyin the twentieth century it was not until half a century later that the first systematicattempts started to bear fruit. This was of course well after the advent of quantummechanics but before the development of fast computers made the calculation ofelectronic structure a tool employed by a large research community in the physicalsciences.

Already in 1922 Bragg realized that measurement of the net charges in NaClwas as yet impossible, but not beyond reach, when he wrote (with James andBosanquest) that ‘it seems that crystal analysis must be pushed to a far greaterdegree of refinement before it can settle the point’ (Phil. Mag44, 433 (1922)). The‘greater degree of refinement’ has now been achieved to a degree well beyond whatcould be envisioned in 1922. This applies to both experiment and theory and tothe broad field of charge spin and momentum densities, all three of which arediscussed in the current volume. The development of radiation sources, detectorsand automation of data collection equipment has been nothing short of dramatic.New theoretical methods and in particular Bader’s development of the density-based Theory of Atoms in Molecules, combined with the exponential increase incomputing power have created a link between theory and experiment which openeda new phase in electron density research in which the emphasis is very much oninterpretation of the results and their application in the understanding of chemical,physical and biological phenomena. The current volume is highly timely in coveringthe advances. Its chapters survey the state of the art and point the way to furtherexciting developments.

Williamsville, NY Philip Coppens

vii

Contents

1 A Guided Tour Through Modern Charge Density Analysis . . . . . . . . . . . 1Carlo Gatti and Piero Macchi

2 Electron Densities and Related Properties from theab-initio Simulation of Crystalline Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Cesare Pisani, Roberto Dovesi, Alessandro Erba,and Paolo Giannozzi

3 Modeling and Analysing Thermal Motion in ExperimentalCharge Density Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Anders Ø. Madsen

4 Spin and the Complementary Worlds of Electron Positionand Momentum Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165Jonathan A. Duffy and Malcom J. Cooper

5 Past, Present and Future of Charge Density and DensityMatrix Refinements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Jean-Michel Gillet and Tibor Koritsanszky

6 Using Wavefunctions to Get More Information Outof Diffraction Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213Dylan Jayatilaka

7 Local Models for Joint Position and Momentum Density Studies . . . . 259Jean-Michel Gillet

8 Magnetization Densities in Material Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277Beatrice Gillon and Pierre Becker

9 Beyond Standard Charge Density Topological Analyses . . . . . . . . . . . . . . . 303Angel Martın Pendas, Miroslav Kohout,Miguel Alvarez Blanco, and Evelio Francisco

ix

x Contents

10 On the Interplay Between Real and Reciprocal Space Properties . . . . 359Wolfgang Scherer, Georg Eickerling, Christoph Hauf,Manuel Presnitz, Ernst-Wilhelm Scheidt, Volker Eyert,and Rainer Pottgen

11 Intermolecular Interaction Energies from ExperimentalCharge Density Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387Paulina M. Dominiak, Enrique Espinosa,and Janos G. Angyan

12 Chemical Information from Charge Density Studies . . . . . . . . . . . . . . . . . . . 435Ulrike Flierler, Dietmar Stalke, and Louis J. Farrugia

13 Charge Density in Materials and Energy Science . . . . . . . . . . . . . . . . . . . . . . . 469Jacob Overgaard, Yuri Grin, Masaki Takata,and Bo B. Iversen

14 A Generic Force Field Based on Quantum Chemical Topology . . . . . . . 505Paul L.A. Popelier

15 Frontier Applications of Experimental Charge Densityand Electrostatics to Bio-macromolecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527Christian Jelsch, Sławomir Domagała, Benoıt Guillot,Dorothee Liebschner, Bertrand Fournier,Virginie Pichon-Pesme, and Claude Lecomte

16 Charge Densities and Crystal Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553Mark A. Spackman

17 Electron Density Topology of Crystalline Solids at High Pressure . . . . 573John S. Tse and Elena V. Boldyreva

18 Bonding Changes Along Solid-Solid Phase TransitionsUsing the Electron Localization Function Approach . . . . . . . . . . . . . . . . . . . 625Julia Contreras-Garcıa, Miriam Marques, Bernard Silvi,and Jose M. Recio

19 Multi-temperature Electron Density Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659Riccardo Destro, Leonardo Lo Presti, Raffaella Soave,and Andres E. Goeta

20 Transient Charge Density Maps from Femtosecond X-RayDiffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697Thomas Elsaesser and Michael Woerner

21 Charge Density and Chemical Reactions: A Unified Viewfrom Conceptual DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715Paul A. Johnson, Libero J. Bartolotti, Paul W. Ayers,Tim Fievez, and Paul Geerlings

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765

Contributors

Janos G. Angyan CRM2, CNRS and Nancy-University, B.P. 239, F-54506Vandœuvre-les-Nancy, France, angyan@crm2.uhp-nancy.fr

Paul W. Ayers Department of Chemistry, McMaster University, Hamilton, ON,Canada L8S4M1, ayers@mcmaster.ca

Libero J. Bartolotti Department of Chemistry, East Carolina University,Greenville, NC 27858, USA, bartolottil@mail.edu

Pierre Becker Structures, Properties and Modelling of Solids (SPMS) Laboratory,Ecole Centrale Paris, Grande Voie des Vignes, 92295, Chatenay-Malabry, France,pierre.becker@ecp.fr

Miguel Alvarez Blanco Dpto. Quımica Fısica y Analıtica, Universidad de Oviedo,33006 Oviedo, Spain, miguel@carbono.quimica.uniovi.es

Elena V. Boldyreva REC-008 Novosibirsk State University and Institute of SolidState Chemistry and Mechanochemistry SB RAS, ul. Kutateladze, 18, Novosibirsk128, Russia, eboldyreva@yahoo.com

Julia Contreras-Garcıa MALTA-Consolider Team and Departamento de QuımicaFısica, Universidad de Oviedo, E-33006 Oviedo, Spain, contrera@lct.jussieu.fr

Malcom J. Cooper Department of Physics, University of Warwick, Coventry, CV47AL, UK, m.j.cooper@warwick.ac.uk

Riccardo Destro Department of Physical Chemistry and Electrochemistry, Uni-versita degli Studi di Milano, Via Golgi 19, 20133 Milan, Italy, riccardo.destro@unimi.it

Sławomir Domagała Laboratoire de Cristallographie Resonance Magnetique etModelisations (CRM2) CNRS, UMR 7036, Faculte des Sciences et Techniques,Nancy University. Institut Jean Barriol, BP 70239, 54506 Vandoeuvre-les-Nancy,Cedex, France, SLAWDOM@chem.uw.edu.pl

xi

xii Contributors

Paulina M. Dominiak Department of Chemistry, University of Warsaw, ul. Pas-teura 1, 02-093 Warszawa, Poland, pdomin@chem.uw.edu.pl

Roberto Dovesi Dipartimento di Chimica IFM, and Centre of Excellence NIS(Nanostructured Interfaces and Surfaces), Universita di Torino, via Giuria 5, I-10125Torino, Italy, roberto.dovesi@unito.it

Jonathan A. Duffy Department of Physics, University of Warwick, Coventry, CV47AL, UK, j.a.duffy@warwick.ac.uk

Georg Eickerling Institut fur Physik, Universitat Augsburg, Universitatsstrasse 1,86159 Augsburg, Germany, georg.eickerling@physik.uni-augsburg.de

Thomas Elsaesser Max-Born-Institut fur Nichtlineare Optik und Kurzzeitspek-troskopie, D-12489 Berlin, Germany, elsasser@mbi-berlin.de

Alessandro Erba Dipartimento di Chimica IFM, and Centre of Excellence NIS(Nanostructured Interfaces and Surfaces), Universita di Torino, via Giuria 5, I-10125Torino, Italy, alessandro erba@virgilio.it

Enrique Espinosa CRM2, CNRS and Nancy-University, B.P. 239, F-54506Vandœuvre-les-Nancy, France, enrique.espinosa@crm2.uhp-nancy.fr

Volker Eyert Institut fur Physik, Universitat Augsburg, Universitatsstrasse 1,86159 Augsburg, Germany, veyert@materialsdesign.com

Louis J. Farrugia School of Chemistry, University of Glasgow, G12 8QQ Scot-land, UK, louis.farrugia@glasgow.ac.uk

Tim Fievez Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel(VUB), Pleinlaan 2, 1050 Brussel, Belgium, tfievez@rub.vub.ac.be

Ulrike Flierler Institut fur Anorganische Chemie, Universitat Gottingen, Tam-mannstrasse 4, 37077 Gottingen, Germany, uflierler@chemie.uni-goettingen.de

Bertrand Fournier Laboratoire de Cristallographie Resonance Magnetique etModelisations (CRM2) CNRS, UMR 7036, Faculte des Sciences et Techniques,Nancy University, Institut Jean Barriol, BP 70239, 54506 Vandoeuvre-les-Nancy,Cedex, France, bertrand.fournier@crm2.uhp-nancy.fr

Evelio Francisco Dpto. Quımica Fısica y Analıtica, Universidad de Oviedo, 33006Oviedo, Spain, evelio@carbono.quimica.uniovi.es

Carlo Gatti Istituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM)e Dipartimento di Chimica Fisica ed Elettrochimica, Universita di Milano, Via Golgi19, I-20133 Milan, Italy

Center for Materials Crystallography, Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark, carlo.gatti@istm.cnr.it

Paul Geerlings Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel(VUB), Pleinlaan 2, 1050 Brussel, Belgium, pgeerlin@vub.ac.be

Contributors xiii

Paolo Giannozzi Democritos Simulation Center, CNR-IOM Istituto Officina deiMateriali, I-34151 Trieste, Italy

Dipartimento di Chimica, Fisica e Ambiente, Universita di Udine, via delle Scienze208, I-33100 Udine, Italy, paolo.giannozzi@uniud.it

Jean-Michel Gillet Structures, Proprietes et Modelisation des Solides, UMR8580,Ecole Centrale Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex,France, jean-michel.gillet@ecp.fr

Beatrice Gillon Laboratoire Leon Brillouin (CEA-CNRS), Centre d’Etudes deSaclay, 91191 Gif-sur-Yvette, Cedex, France, Beatrice.gillon@cea.fr

Andres E. Goeta Chemistry Department, Durham University, South Road,Durham, DH1 3LE UK, a.e.goeta@durham.ac.uk

Yuri Grin Max-Planck-Institut fur Chemische Physik fester Stoffe, D-01187Dresden, Germany, grin@cpfs.mpg.de

Benoıt Guillot Laboratoire de Cristallographie Resonance Magnetique etModelisations (CRM2) CNRS, UMR 7036, Faculte des Sciences et Techniques,Nancy University, Institut Jean Barriol, BP 70239, 54506 Vandoeuvre-les-Nancy,Cedex, France, benoit.guillot@lcm3b.uhp-nancy.fr

Christoph Hauf Institut fur Physik, Universitat Augsburg, Universitatsstrasse 1,86159 Augsburg, Germany, christoph.hauf@physik.uni-augsburg.de

Bo B. Iversen Department of Chemistry and iNANO, Aarhus University, DK-8000Arhus C, Denmark, bo@chem.au.dk

Dylan Jayatilaka Chemistry, School of Biomedical, Biological and ChemicalSciences, University of Western Australia, 35 Stirling Highway, Nedlands, 6009WA, Australia, dylan.jayatilaka@uwa.edu.au

Christian Jelsch Laboratoire de Cristallographie Resonance Magnetique etModelisations (CRM2) CNRS, UMR 7036, Faculte des Sciences et Techniques,Nancy University, Institut Jean Barriol, BP 70239, 54506 Vandoeuvre-les-Nancy,Cedex, France, christian.jelsch@crm2.uhp-nancy.fr

Paul A. Johnson Department of Chemistry, McMaster University, Hamilton, ON,Canada L8S4M1, johnsopa@mcmaster.ca

Miroslav Kohout Max Planck Institute for Chemical Physics of Solids, NothnitzerStr. 40, 01187 Dresden, Germany, kohout@cpfs.mpg.de

Tibor Koritsanszky Department of Chemistry, Computational Science Program,Middle Tennessee State University, Murfreesboro, TN 37132, USA, tkoritsa@gmail.com

Claude Lecomte Laboratoire de Cristallographie Resonance Magnetique etModelisations (CRM2) CNRS, UMR 7036, Faculte des Sciences et Techniques,

xiv Contributors

Nancy University, Institut Jean Barriol, BP 70239, 54506 Vandoeuvre-les-Nancy,Cedex, France, claude.lecomte@crm2.uhp-nancy.fr

Dorothee Liebschner Laboratoire de Cristallographie Resonance Magnetique etModelisations (CRM2) CNRS, UMR 7036, Faculte des Sciences et Techniques,Nancy University, Institut Jean Barriol, BP 70239, 54506 Vandoeuvre-les-Nancy,Cedex, France, dorothee.liebschner@crm2.uhp-nancy.fr

Leonardo Lo Presti Department of Physical Chemistry and Electrochemistry,Universita degli Studi di Milano, Via Golgi 19, 20133 Milan, Italy, leonardo.lopresti@unimi.it

Piero Macchi Department of Chemistry and Biochemistry, University of Bern,Freiestrasse 3, CH3012 Bern, Switzerland, piero.macchi@dcb.unibe.it

Anders Ø. Madsen Department of Chemistry, University of Copenhagen, Univer-sitetsparken 5, DK-2100 Copenhagen Ø, Denmark, madsen@chem.ku.dk

Miriam Marques SUPA, School of Physics and Centre for Science at ExtremeConditions, The University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK,mmarques@staffmail.ed.ac.uk

Jacob Overgaard Department of Chemistry and iNANO, Aarhus University, DK-8000 Arhus C, Denmark, jacobo@chem.au.dk

Angel Martın Pendas Dpto. Quımica Fısica y Analıtica, Universidad de Oviedo,33006 Oviedo, Spain, angel@fluor.quimica.uniovi.es

Virginie Pichon-Pesme Laboratoire de Cristallographie Resonance Magnetique etModelisations (CRM2) CNRS, UMR 7036, Faculte des Sciences et Techniques,Nancy University, Institut Jean Barriol, BP 70239, 54506 Vandoeuvre-les-Nancy,Cedex, France, Virginie.Pichon@crm2.uhp-nancy.fr

Cesare Pisani Dipartimento di Chimica IFM, and Centre of Excellence NIS(Nanostructured Interfaces and Surfaces), Universita di Torino, via Giuria 5, I-10125Torino, Italy, cesare.pisani@unito.it

Paul L.A. Popelier Manchester Interdisciplinary Biocentre (MIB), 131 PrincessStreet, Manchester M1 7DN, UK

School of Chemistry, University of Manchester, Oxford Road, Manchester M139PL, UK, pla@manchester.ac.uk

Rainer Pottgen Institut fur Anorganische und Analytische Chemie, UniversitatMunster, Corrensstrasse 30, 48149 Munster, Germany, pottgen@uni-muenster.de

Manuel Presnitz Institut fur Physik, Universitat Augsburg, Universitatsstrasse 1,86159 Augsburg, Germany, manuel.presnitz@physik.uni-augsburg.de

Jose M. Recio MALTA-Consolider Team and Departamento de Quımica Fısica,Universidad de Oviedo, E-33006 Oviedo, Spain, mateo@fluor.quimica.uniovi.es

Contributors xv

Ernst-Wilhelm Scheidt Institut fur Physik, Universitat Augsburg,Universitatsstrasse 1, 86159 Augsburg, Germany, ernst-wilhelm.scheidt@physik.uni-augsburg.de

Wolfgang Scherer Institut fur Physik, Universitat Augsburg, Universitatsstrasse 1,86159 Augsburg, Germany, wolfgang.scherer@physik.uni-augsburg.de

Bernard Silvi Laboratoire de Chimie Theorique (UMR-CNRS 7616), UniversitePierre et Marie Curie, 3 rue Galilee, 94200 Ivry sur Seine, France, silvi@lct.jussieu.fr

Raffaella Soave Istituto di Scienze e Tecnologie Molecolari (ISTM), ItalianNational Reseearch Council (CNR), Via Golgi 19, 20133 Milan, Italy, raffaella.soave@istm.cnr.it

Mark A. Spackman School of Biomedical, Biomolecular & Chemical Sciences,University of Western Australia, Crawley, WA 6009, Australia, mark.spackman@uwa.edu.au

Dietmar Stalke Institut fur Anorganische Chemie, Universitat Gottingen, Tam-mannstrasse 4, 37077 Gottingen, Germany, dstalke@chemie.uni-goettingen.de

Masaki Takata SPring8 Synchrotron Facility, Koto 1-1-1, Sayo-cho, Sayo, Hy-ougo 679-5148, Japan, takatama@spring8.or.jp

John S. Tse Department of Physics and Engineering Physics, University ofSaskatchewan, Saskatoon, SK, Canada S7N 5E2, John.Tse@usask.ca

Michael Woerner Max-Born-Institut fur Nichtlineare Optik und Kurzzeitspek-troskopie, D-12489 Berlin, Germany, woerner@mbi-berlin.de

Abbreviations

1-RDM 1-electron Reduced Density Matrix2-RDM 2-electron Reduced Density Matrix3D three dimensionalAcG N-acetylglycineACP Anisotropic Compton ProfileADF Amsterdam Density Functional ab-initio packageADF2004 Amsterdam Density Functional ab-initio package (2004 version)ADPs Anisotropic Displacement ParametersADPs Atomic Displacement ParametersAE All-ElectronAF antiferromagneticAFM AntiferromagneticAIM Atom’s in Molecules (analogous to QTAIM, Quantum Theory of

Atoms in Molecules, in other chapters of the book)AMM Anions in metallic matrixAO Atomic OrbitalAS Ammonium SulfateA–TCNB anthracene-tectracyanobenzeneaug-cc-pVTZ Dunning’s correlation consistent triple-zeta basis sets with added

diffuse functionsB3LYP Becke’s 3 parameter functional (in density functional theory

calculations)bcc body centered cubicbcp, BCP bond critical pointbct body centered tetragonalBDC benzene dicarboxylateBF Bloch FunctionBLYP Becke’s 1988 exchange functional and Lee, Yang and Parr corre-

lation functional (in density functional theory calculations)BOMD Born-Oppenheimer Molecular DynamicsBP bond path

xvii

xviii Abbreviations

bpe (E)-1,2-bis(4-pyridyl)ethylenebpNO 4,40-dipyridyl-N,N0-dioxideBS Basis SetBSSE Basis Set Superposition Errorbtr 4,40-bis-1,2,4-triazoleBvK Born-vonKarman (cyclic conditions)BZ Brillouin ZoneCA chloranilCASSCF Complete Active Space Self-Consistent methodCBED Convergent Beam Electron DiffractionCCD Charge Coupled DeviceCCSD Coupled Cluster calculation with both Single and Double Substi-

tutions from the Hartree-Fock determinantCCSD(T) coupled cluster method with single and double excitations with

singles/triples coupling termCD Charge (nuclearCelectronic) densityCDASE Comprehensive Decomposition Analysis of Stabilization EnergyCDM charge density mapsCHD 1,3-cyclohexanedioneCI Configuration InteractionCIF Crystallographic Information FileCISD Configuration Interaction with Single and Double substitutions

from the Hartree-Fock reference determinantCMOS Complementary Metal Oxides SemiconductorsCO Crystalline OrbitalCP,CPF Compton Profile (Function)CPHF Coupled Perturbed Hartree-FockCPL-1 Coordination Polymer 1CRYSTAL Crystal ab initio package (any version)CRYSTAL03 Crystal03 ab initio packageCRYSTAL-XX ab-initio package for the calculation of the electronic structure of

periodic systems (XXD98, 03, 09, according to 1998, 2003, 2009version)

CSD Cambridge Structural DatabaseCSO Crystalline Spin-OrbitalCWM Constrained Wavefunction MethodDAFH Domain Averaged Fermi HoleDCD Dewar-Chatt-Duncanson ModelDCH Dirac-Coulomb HamiltonianDCP Directional Compton ProfileDEA DiEthylAmineDEF DiEthylFormamideDF Density Function (charge, spin or momentum density)DFPT Density Functional Perturbation TheoryDFT Density Functional Theory

Abbreviations xix

dhcp double hexagonal closed packedDIABN 4-(diisopropylamino)benzonitrileDKH Douglas, Kroll and Hess (DKH) (relativistic Hamiltonian ap-

proach)DM Density MatrixDMA DiMethylAcetamideDMA Distributed Multipole AnalysisDMF DiMethylFormamidedmpe dimethyl-phosphinoethaneDM-TTF 2,6-dimethyltetrathiofulvaleneDNA deoxyribonucleic acidDOS Density of Statesdppen cis-1,2-bis(diphenylphosphino)ethyleneDZP Double-zeta plus Polarization (basis set)DZPT Double-Zeta plus Triple Polarization (basis set)ECP Effective Core PotentialED Electron DensityESD Electron Spin DensityEDD Electron density distributionEDF Electron population Distribution FunctionEDI ELF delocalization indexEF Electric FieldEFG Electric Field GradientELF Electron Localization FunctionELI Electron Localizability IndicatorELMAM Experimental Library of Multipolar Atom ModelEM ElectromagneticEMAC Extended Metal Atom Chain (compounds)EMD Electron Momentum DensityEP Exact Potential (Exact evaluation of the electrostatic interaction

energy)EPMM Exact Potential and Multipole Moment (Volkov’s method for eval-

uating the electrostatic interaction energy of a pair of molecules)EPR Electron Pair RepulsionESD Electron Spin Densityesd estimated standard deviationsESP ElectroStatic PotentialESRF European Synchrotron Radiation FacilityF4DBB 1,4-dibromotetrafluorobenzene, C6F4Br2

F4DIB 1,4-diiodotetrafluorobenzene, C6F4I2

fcc,FCC Face Centered CubicFLAPW Full Potential Linearized Augmented PlaneWave (code, method)FM FerromagneticFMO Frontier Molecular OrbitalFMs Ferromagnets

xx Abbreviations

FT Fourier TransformFFT Fast Fourier transformFull-CI Full Configuration Interaction methodFWHM Full width at half maximumG03 Gaussian-03 (ab-initio program)G98 Gaussian-98 (ab-initio program)GGA Generalized Gradient ApproximationGly ’-glycineGTF Gaussian-Type-FunctionGTO Gaussian Type OrbitalhAR human aldose reductaseHB Hydrogen BondHC Hansen-Coppens formalism (in multipole models refinements)hcp hexagonal close packingHF Hartree-FockUHF Unrestricted Hartree-FockHIV Human Immunodeficiency VirusHM Halet’s and Mingos’ model on metal carbidesHMs Half-MetalsHOMO Highest Occupied Molecular OrbitalHS High spinHS Hirshfeld surfaceIA Impulse Approximation (in inelastic scattering)IAM Independent Atom ModelInvariom Invariant atom (database)IQA Interacting Quantum AtomsIUCr International Union of CrystallographyKS Kohn-ShamUKS Unrestricted Kohn-ShamKS-DFT Kohn-Sham Density Functional Theory approachLac L-(C)-lactic acidLCAO Linear Combination of Atomic OrbitalsLDA Local Density ApproximationLICC Ligand Induced Charge ConcentrationLIESST Light-Induced Excited-Spin-State TrappingLMP2 Local Møller Plesset perturbation theory truncated at second orderLMTO Linearized Muffin-Tin OrbitalLOCCC Ligand Opposed Core Charge ConcentrationLOL Localized Orbital LocatorLS Least-Squares (procedure)LS Local SourceLS Low spinLUMO Lowest Unoccupied Molecular OrbitalMCP Magnetic Compton ProfileMCPD 2-methyl-1,3-cyclopentanedione

Abbreviations xxi

MCS Magnetic Compton ScatteringMCSCF Multi Configuration Self Consistent FieldMD Magnetization densityMD Molecular DynamicsMEM Maximum Entropy MethodMESP Molecular ElectroStatic PotentialMK Merz-KollmanMM Multipole ModelMMFF94 Molecular Mechanics Force Field package (1994 version)MNA 2-methul-4-nitroanilineMO Molecular OrbitalMOF Metal Organic FrameworkMOON Molecular Orbitals with variable Occupation Numbers (refine-

ment)MOON Molecular Orbitals with variable Occupation Numbers (method)MP2 Møller-Plesset perturbation theory truncated at second orderMP4SDQ Møller-Plesset correlation energy correction truncated at fourth-

order in the space of single, double and quadruple substitutionsfrom the Hartree-Fock determinant

MQM Molecular Quantum MechanicsMSD Mean Square DisplacementMSO Molecular Spin-OrbitalMSR Mean-Square ResidualMTA Multi-Temperature AnalysisMV Mixed ValenceNADPC Nicotinamide Adenine Dinucleotide Phosphate (oxidized form)NADPH Nicotinamide Adenine Dinucleotide Phosphate (reduced form)NBO natural bond orbitalNCI NonCovalent InteractionND Neutron DiffractionNLO Non Linear OpticalNMR Nuclear Magnetic ResonanceNPA Natural Population AnalysisNPP N-4-nitrophenyl-L-prolinoln-RDM n-electron Reduced Density MatrixNRT natural resonance theoryNSO Natural Spin OrbitalsOCM Outer Core Maximap.d.f. probability density functionPAW Projected Augmented WavesPBC Periodic Boundary ConditionsPCAR Point Contact Andreev Reflectionpdf probability distribution function

xxii Abbreviations

PDZ2 Second PDZ domain. PDZ is a common structural domain of 80–90 amino-acids found in the signaling proteins of bacteria, yeast,plant, viruses and animals

PEECM Periodic Electrostatic Embedded Cluster ModelPES Potential Energy SurfacePGEC Phonon-Glass – Electron CrystalPIXEL Gavezzotti’s method for evaluating the electrostatic interaction

energy of a pair of moleculespNA 4-nitroanilinePND Polarised Neutron DiffractionPNP 2-(N-(L)-prolinol)-5-nitropyridinePOM 3-methyl-4-nitropyridine-N-oxidePP Pseudo-PotentialPSD Position Sensitive DetectorPU Partition of the Unit methodologyPW Plane WavesQCISD Quadratic Configuration Interaction calculation including single

and double substitutionsQCT Quantum Chemical TopologyQM Quantum Mechanics or Quantum-MechanicalQSAR Quantitative Structure Activity RelationshipsQSPR Quantitative Structure Property RelationshipsQTAIM Quantum Theory of Atoms in MoleculesQZ4P core triple zeta, valence quadruple zeta, plus four polarization

functions basis set (in the ADF, Amsterdam Density Functionalab-initio package)

r.m.s. root mean squarer.m.s.d. root mean square deviationRBFNN radial basis function neural networksrcp ring critical pointRDF RaDial Functions (in the multipole models pseudoatom formal-

ism)RFF Reciprocal Form FactorRIET Redox Induced Electron TransferRLFT Rigorous Local Field TheoryRT Room TemperatureSAPT Symmetry Adapted Perturbation TheorySAPT2002 Ab initio program based on Symmetry Adapted Perturbation

Theory (2002 version)SCDS SemiClassic Density Sums (in Gavezzotti’s pixel method)SCMP Self Consistent Madelung PotentialSCO Spin Cross OverSDS H-atom form factor developed by Stewart, Davidson and SimpsonSF Source Functionsh simple hexagonal

Abbreviations xxiii

SIBFA Sum of Interactions Between Fragments computed Ab InitioSP Spin PolarisationSPDFG Volkov, King and Coppens code for evaluating the electrostatic

repulsion in terms of the monomer charge distributionsSTF Slater-Type-FunctionTAAD Transferred Aspherical Atom ModeltBu tert-butylTE ThermoElectricTLS Translation/Libration/Screw model (rigid body model for thermal

motion)TM transition metalTPEP Topological Partitioning of Electronic PropertiesTS Transition StateTTF tetrathiofulvaleneTtr transition temperatureTZP Triple-zeta plus Polarization (basis set)UBDB University at Buffalo DataBankUSPP Ultra-Soft Pseudo-PotentialVB Valence BondVE Valence electronsVOM Valence Orbital ModelVSCC Valence Shell Charge ConcentrationVSCD Valence Shell Charge DepletionVSCP Valence Shell Charge PolarizationVSEPR Valence Shell Electron Pair RepulsionWF Wannier FunctionXAO X-ray Atomic Orbital methodXCDFT X-ray Constrained DFTXCHF X-ray Constrained Hartree-FockXCW X-Ray Constrained (Hartree-Fock) WavefunctionXMCD X-ray Magnetic Circular DichroismXMD X-ray Magnetic DiffractionXRD X-Ray DiffractionZORA quasi-relativistic two-component Zeroth-Order Regular Approxi-

mation