Matta, Boyd. The quantum theory of atoms in molecules
.pdfXXX List of Abbreviations Appearing in this Volume
NBO |
Natural bond orbital(s) (method) |
NCP or ncp |
Nuclear critical point |
NICS |
(Schleyer’s) nucleus-independent chemical shift |
NICS(0) |
(Schleyer’s) nucleus-independent chemical shift in the plane of an |
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aromatic ring at its geometrical center |
NICS(n) |
˚ |
(Schleyer’s) nucleus-independent chemical shift n A above the |
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plane of an aromatic ring at its geometrical center |
NMR |
Nuclear magnetic resonance (spectroscopy) |
NNA |
Non-nuclear attractor |
NNA |
Nearest-neighbor approximation |
NNM |
Non-nuclear maximum (or maxima) |
NPA |
Natural population analysis |
NR |
Newton–Raphson (method/technique) |
ODM |
One-electron density matrix |
OG |
(Gas-phase) optimized geometry (as opposed to crystal geometry) |
PAHB |
Polarization-assisted hydrogen bond(ing) |
PAH(s) |
Polycyclic aromatic hydrocarbon(s) |
PASA |
Promolecular atom shell approximation |
PBH(s) |
Polybenzenoid hydrocarbon(s) |
PDI |
para-Delocalization index (of Sola` et al.) |
PE |
Potential energy |
PES |
Potential energy surface(s) |
PEST |
Property-encoded surface translator |
PH |
Poincare´-Hopf relationship |
ppm |
Part per million |
Pyr |
Pyridine |
QCISD |
Quadratic configuration interaction with single and double excita- |
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tions |
QCISD(T) |
Quadratic configuration interaction with single and double excita- |
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tions (with correction for triple excitations) |
QCT |
Quantum chemical topology |
QSAR |
Quantitative structure–activity relationship(s) |
QSPR |
Quantitative structure–property relationship(s) |
QTAIM |
Quantum theory of atoms in molecules |
QTAMC |
Quantum theory of atoms in molecules and crystals |
RAHB |
Resonance-assisted hydrogen bond(ing) |
RCP or rcp |
Ring critical point |
RECON |
(Rapid TAE) reconstruction (of molecular charge densities) |
RHF |
Restricted Hartree–Fock (method) |
RNA |
Ribonucleic acid |
RSS |
Root summed squares |
R.H.S. |
Right-hand side (of an equation) |
SCF |
Self-consistent field |
SCVS |
Self-consistent virial scaling |
SES |
Sodium electrosodalite |
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List of Abbreviations Appearing in this Volume |
XXXI |
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SF |
Source function |
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SI |
Surface integral |
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SIEP |
Surface integral of the electrostatic potential |
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SIG |
Surface integral of the G kinetic energy density |
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SIK |
Surface integral of the K kinetic energy density |
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SSHB |
Short strong hydrogen bond(ing) |
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std |
Standard deviation |
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STM |
Scanning–tunneling microscope (or microscopy) |
TThymine
TAE |
(Breneman’s) transferable atom equivalent |
TMS |
Transition metal sulfide(s) |
TMS |
Tetramethylsilane |
UUracil
UHF |
Unrestricted Hartree–Fock (method) |
VHTS |
Virtual high-throughput screening |
VSCC |
Valence shell charge concentration |
VSCD |
Valence shell charge depletion |
VSEPR |
Valence-shell electron-pair repulsion model of molecular geometry |
XRD |
X-Ray di raction |
ZFS |
Zero-flux surface |
XXXIII
List of Contributors
Dr. Ibon Alkorta |
Dr. Miguel A. Blanco |
Instituto de Quı´mica Me´dica |
Departamento de Quı´mica Fı´sica |
(CSIC) |
y Analı´tica |
Juan de la Cierva 3 |
Universidad de Oviedo |
28006 Madrid |
33006 Oviedo |
Spain |
Spain |
ibon@iqm.csic.es |
miguel@carbono.quimica.uniovi.es |
Dr. Yosslen Aray |
Prof. Russell J. Boyd |
Centro de Quimica, IVIC |
Department of Chemistry |
Apartado 21827 |
Dalhousie University |
Caracas 1020 A |
Halifax, NS, B3H 4J3 |
Venezuela |
Canada |
yaray@mail.ivic.ve |
russell.boyd@dal.ca |
Prof. Richard F.W. Bader |
Prof. Curt M. Breneman |
Department of Chemistry |
Department of Chemistry and |
McMaster University |
Chemical Biology |
1280 Main Street West |
Rensselaer Polytechnic Institute |
Hamilton, ON, L4S 4M1 |
110 8th St |
Canada |
Troy, NY 12180-3590 |
bader@mcmaster.ca |
USA |
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brenec@rpi.edu |
Prof. Axel D. Becke |
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Department of Chemistry |
Prof. Fernando Corte´s-Guzma´n |
Dalhousie University |
Departamento de Quı´mica Orga´nica |
Halifax, NS, B3H 4J3 |
Facultad de Quı´mica |
Canada |
Universidad Nacional Auto´noma de |
axel.becke@dal.ca |
Me´xico |
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Circuito Escolar, Ciudad Universitaria |
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Coyoaca´n, Me´xico D.F. 04510 |
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fercor@servidor.unam.mx |
XXXIV |
List of Contributors |
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Dr. Aurora Costales |
Prof. Jose´ Elguero |
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Departamento de Quı´mica Fı´sica |
Instituto de Quı´mica Me´dica (CSIC) |
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y Analı´tica |
Juan de la Cierva 3 |
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Universidad de Oviedo |
28006 Madrid |
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33006 Oviedo |
Spain |
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Spain |
iqmbe17@iqm.csic.es |
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yoyi@carbono.quimica.uniovi.es |
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Prof. Enrique Espinosa |
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Prof. Gabriel Cuevas |
Laboratoire de Cristallographie et |
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Departamento de Fisicoquı´mica |
Mode´lisation des Mate´riaux Mine´raux |
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Instituto de Quı´mica |
et Biologiques |
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Universidad Nacional Auto´noma |
Faculte´ des Sciences et Techniques |
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de Me´xico |
Universite´ Henri Poincare´ |
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Circuito Escolar, Ciudad |
Nancy 1 |
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Universitaria |
BP 239, 54506 Vandoeuvre-le´s- |
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Coyoaca´n, Me´xico D.F. 04510 |
Nancy, Cedex |
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Me´xico |
France |
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gecgb@servidor.unam |
Enrique.Espinosa@lcm3b.uhp-nancy.fr |
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Dr. Richard Dawes |
Dr. Carlo Gatti |
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Department of Chemistry |
CNR-ISTM Istituto di Scienze e |
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University of Missouri-Columbia |
Tecnologie Molecolari |
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Columbia, MO 65211 |
Via Golgi 19 |
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USA |
20133 Milano |
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dawesr@missouri.edu |
Italy |
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c.gatti@istm.cnr.it |
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Dr. Birger Dittrich |
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School of Biomedical & Chemical |
Prof. Ronald J. Gillespie |
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Sciences |
Department of Chemistry |
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The University of Western |
McMaster University |
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Australia |
1280 Main Street West |
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35 Stirling Highway |
Hamilton, ON, L4S 4M1 |
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Crawley WA 6009 |
Canada |
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Australia |
ronald.gillespie@sympatico.ca |
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birger@chemie.fu-berlin.de |
gillespi@mcmaster.ca |
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birger@cyllene.uwa.edu.au |
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Prof. Kathleen M. Gough |
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Dr. Jason R. Dwyer |
Department of Chemistry |
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Max-Born-Institut fu¨r |
University of Manitoba |
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Nichtlineare Optik und |
Winnipeg, MB, R3T 2N2 |
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Kurzzeitspektroskopie |
Canada |
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Max-Born-Strasse 2A |
kmgough@cc.umanitoba.ca |
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12489 Berlin |
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Germany |
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dwyer@mbi-berlin.de |
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List of Contributors XXXV
Prof. Sławomir J. Grabowski
Department of Physics and Chemistry
University of Ło´dz´ ul.Pomorska 149/153 90-236 Ło´dz´
Poland slagra@ccmsi.us
Dr. Benoıˆt Guillot
Laboratoire de Cristallographie et Mode´lisation des Mate´riaux Mine´raux et Biologiques
LCM3B (UMR UHP-CNRS 7036) Faculte´ des Sciences et Techniques
Universite´ Henri Poincare´ BP 239, Boulevard des Aiguillettes
54506 Vandoeuvre-le`s-Nancy CEDEX
France benoit.guillot@lcm3b.uhp-nancy.fr
Dr. Christopher E. Henze
MS T27-A
NASA Advanced Supercomputing Division
NASA Ames Research Center Mo ett Field, CA 94035 USA
chenze@nas.nasa.gov
Prof. Jesu´s Herna´ndez-Trujillo
Departamento de Fı´sica y Quı´mica Teo´rica Facultad de Quı´mica
Universidad Nacional Auto´noma de Me´xico
Circuito Escolar, Ciudad Universitaria Coyoaca´n, Me´xico D.F. Me´xico 04510
jesus.hernandez@correo.unam.mx
Dr. Christian Jelsch
Laboratoire de Cristallographie et Modelisation des Mate´riaux Mine´raux et Biologiques Unive´rsite´ Henri Poincare´ LCM3B (UMR UHP-CNRS 7036) Faculte´ des Sciences et Techniques Universite´ Henri Poincare´
BP 239, Boulevard des Aiguillettes 54506 Vandoeuvre-le`s-Nancy CEDEX France christian.jelsch@lcm3b.uhp-nancy.fr
Dr. Todd A. Keith
Department of Chemistry University of Missouri – Kansas City 5100 Rockhill Road
Kansas City, MO 64110 USA keithta@umkc.edu
Dr. Ange´lique Lagoutte
Laboratoire de Cristallographie et Modelisation des Mate´riaux Mine´raux et Biologiques Unive´rsite´ Henri Poincare´ LCM3B (UMR UHP-CNRS 7036) Faculte´ des Sciences et Techniques Universite´ Henri Poincare´
BP 239, Boulevard des Aiguillettes 54506 Vandoeuvre-le`s-Nancy CEDEX France angelique.lagoutte@lcm3b.uhpnancy.fr
Prof. Claude Lecomte
Laboratoire de Cristallographie et Modelisation des Mate´riaux Mine´raux et Biologiques Unive´rsite´ Henri Poincare´ LCM3B (UMR UHP-CNRS 7036) Faculte´ des Sciences et Techniques Universite´ Henri Poincare´
BP 239, Boulevard des Aiguillettes 54506 Vandoeuvre-le`s-Nancy CEDEX France claude.lecomte@lcm3b.uhp-nancy.fr
XXXVI List of Contributors
Prof. Laurence Leherte
Laboratoire de Physico-Clinic Informatique (PCI)
Faculte´s Universitaires NotreDame de la Paix
Rue de Bruxelles 61 5000 Namur Belgium
laurence.leherte@fundp.ac.be
Prof. Vı´ctor Luan˜a
Departamento de Quı´mica Fı´sica y Analı´tica
Universidad de Oviedo 33006 Oviedo
Spain victor@carbono.quimica.uniovi.es
Prof. Peter Luger
Institute for Chemistry/ Crystallography
Free University of Berlin Takustr. 6
14195 Berlin Germany
luger@chemie.fu-berlin.de
Dr. Piero Macchi
Dipartimento di Chimica Strutturale e Stereochimica Inorganica
Universita` di Milano Via Venezian 21 20133 Milano
Italy
and
CNR – Istituto di Scienze e Tecnologie Molecolari
Via Golgi 19 Milano Italy
piero.macchi@istm.cnr.it
Prof. Preston J. MacDougall
Department of Chemistry
Middle Tennessee State University 1301 E. Main St.
Murfreesboro, TN 37132 USA pmacdougall@mtsu.edu
preston.macdougall@gmail.com
Dr. Ignasi Mata
Institut de Cie`ncia de Materials de Barcelona (CSIC)
Campus UAB
08193 Bellaterra Spain imata@icmab.es
Dr. Eduard Matito
Institut de Quı´mica Computacional Departament de Quı´mica Universitat de Girona
Campus de Montilivi 17071 Girona Catalonia
Spain eduard@iqc.udg.es
Prof. Che´rif F. Matta
Department of Chemistry & Physics
Mount Saint Vincent University
Halifax, NS, B3M 2J6
Canada
and
Department of Chemistry Dalhousie University Halifax, NS, B3H 4J3 Canada cherif.matta@msvu.ca quantumjazz@hotmail.com
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List of Contributors |
XXXVII |
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Prof. Elies Molins |
Dr. Jordi Poater |
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Institut de Cie`ncia de Materials |
Afdeling Theoretische Chemie |
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de Barcelona (CSIC) |
Scheikundig Laboratorium der Vrije |
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Campus UAB |
Universiteit |
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08193 Bellaterra |
De Boelelaan 1083 |
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Spain |
NL-1081 HV Amsterdam |
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elies.molins@icmab.es |
The Netherlands |
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J.Poater@few.vu.nl |
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Dr. Paula Mori-Sa´nchez |
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Departamento de Quı´mica Fı´sica |
Dr. Paul L. A. Popelier |
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y Analı´tica |
School of Chemistry |
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Universidad de Oviedo |
University of Manchester |
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33006 Oviedo |
Faraday Building, North Campus |
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Spain |
Manchester M60 1QD |
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paula@carbono.quimica.uniovi.es |
UK |
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paul.popelier@manchester.ac.uk |
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Prof. Angel Martı´n Penda´s |
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Departamento de Quı´mica Fı´sica |
Dr. Michel Rafat |
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y Analı´tica |
School of Chemistry |
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Universidad de Oviedo |
University of Manchester |
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33006 Oviedo |
Faraday Building, North Campus |
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Spain |
Manchester M60 1QD |
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angel@carbono.quimica.uniovi.es |
UK |
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m-rafat@inbox.com |
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Dr. Virginie Pichon-Pesme |
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Laboratoire de Cristallographie et |
Dr. Jesus Rodrı´guez |
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Mode´lisation des Mate´riaux |
Centro de Quimica, IVIC |
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Mine´raux et Biologiques |
Apartado 21827 |
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LCM3B (UMR UHP-CNRS 7036) |
Caracas 1020 A |
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Faculte´ des Sciences et |
Venezuela |
|
Techniques |
jrodrigu@ivic.ve |
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Universite´ Henri Poincare´ |
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BP 239, Boulevard des |
Prof. Bernard Silvi |
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Aiguillettes |
Laboratoire de Chimie The´orique |
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54506 Vandoeuvre-le`s-Nancy |
UMR (CNRS) 7616 |
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CEDEX |
Universite´ Pierre et Marie Curie |
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France |
3, Rue Galile´e |
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virginie.pichon@lcm3b.uhp- |
94200 Ivry sur Seine |
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nancy.fr |
France |
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silvi@lct.jussieu.fr |
XXXVIII List of Contributors
Prof. Angelo Sironi
Dipartimento di Chimica Strutturale e Stereochimica Inorganica
Universita` di Milano Via Venezian 21 20133 Milano
Italy
and
CNR – Istituto di Scienze e Tecnologie Molecolari
Via Golgi 19 Milano Italy
angelo.sironi@istm.cnr.it
Prof. Miquel Sola`
Institut de Quı´mica Computacional Departament de Quı´mica Universitat de Girona Campus de Montilivi 17071 Girona
Catalonia Spain
miquel.sola@udg.es
Dr. Nagamani Sukumar
Department of Chemistry and Biological Chemistry
Center for Biotechnology and Interdisciplinary Studies Rensselaer Polytechnic Institute 110 8th St.
Troy, NY 12180-3590 USA nagams@rpi.edu
Prof. Vladimir G. Tsirelson
Quantum Chemistry Department Mendeleev University of Chemical Technology
Miusskaya Sq. 9
Moscow 125047 Russia tsirel@muctr.edu.ru vtsirelson@yandex.ru
Dr. David Vega
Departamento de Quı´mica
Facultad Experimental de Ciencias y Tecnologı´a (FACYT)
Universidad de Carabobo Valencia, Edo. Carabobo Venezuela dvega@uc.edu.ve
Prof. Daniel P. Vercauteren
Laboratoire de Physico-Clinic Informatique (PCI)
Faculte´s Universitaires Notre-Dame de la Paix (FUNDP)
Rue de Bruxelles 61 5000 Namur Belgium
daniel.vercauteren@fundp.ac.be
Dr. Tammy L. Welshman
Department of Chemistry University of Manitoba Winnipeg, MB, R3T 2N2 Canada welshman@cc.umanitoba.ca
1
1
An Introduction to the Quantum Theory of Atoms in Molecules
Che´rif F. Matta and Russell J. Boyd
1.1 Introduction
The observation that some properties attributed to atoms and functional groups are transferable from one molecule to another has played a key role in the development of chemistry. This observation provides a basis for group additivity schemes and is exemplified by the constancy of group contributions to thermodynamic and spectroscopic properties. But what is the electronic basis of this empirical transferability? The quantum theory of atoms in molecules (QTAIM) [1], developed by Professor Richard F. W. Bader and his coworkers, relies on quantum observables such as the electron density rðrÞ and energy densities to answer such a question. Other important (related) questions addressed by QTAIM include:
What is an atom in a molecule or a crystal?
How can an atom or a group of atoms be transferable sometimes in very di erent external potentials?
Can one define bonding in molecules unambiguously especially in borderline cases?
This chapter contains a summary of some of the main concepts of QTAIM. A more comprehensive and mathematically elegant treatment can be found in Bader’s book [1].
(Often in this chapter, the word ‘‘molecule’’ includes extended systems such as polymers, weakly bonded molecular complexes, and molecular and ionic crystals, in addition to its more traditional meaning of a single, finite, isolated chemically bonded group of atoms. It will be clear from the context when this term is used in its traditional or in its larger sense.)
1.2
The Topology of the Electron Density
The topology of the electron density is dominated by the attractive forces of the nuclei imparting it with its principal topological feature – a substantial local max-