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VALENCY AND BONDING
Thisgraduate-leveltextpresentsthefirstcomprehensiveoverviewofmodernchem-
ical valency and bonding theory, written by internationally recognized experts in
thefield.TheauthorsbuildonthefoundationofLewis-andPauling-likelocalized
structural and hybridization concepts to present a book that is directly based on
currentabinitiocomputationaltechnology.
The presentation is highly visual and intuitive throughout, being based on the
recognizableandtransferablegraphicalformsofnaturalbondorbitals(NBOs)and
theirspatialoverlapsinthemolecularenvironment.Thebookshowsapplicationsto
abroadrangeofmolecularandsupramolecularspeciesoforganic,inorganic,and
bioorganicinterest.Hundredsoforbitalillustrationshelptoconveytheessenceof
modernNBOconceptsinafacilemannerforthosewithnoextensivebackground
inthemathematicalmachineryoftheSchro¨dingerequation.Thisbookwillappeal
tothosestudyingchemicalbondinginrelationtochemistry,chemicalengineering,
biochemistry,andphysics.
Frank A. Weinhold is Professor of Physical and Theoretical Chemistry at the
UniversityofWisconsin-Madison.HisacademicawardsincludetheAlfredP.Sloan
Fellowship (1970) and the Camille and Henry Dreyfus Foundation Fellowship
(1972)andhehasservedguestappointmentsatmanyprestigiousinstitutesincluding
the Quantum Chemistry Group at the University of Uppsala, Sweden, the Max-
Planck-Institutfu¨rPhysikundAstrophysikinMunich,Germany,andtheUniversity
ofColorado.Hewasthe13thAnnualCharlesA.CoulsonlecturerattheCenterfor
Computational Quantum Chemistry, University of Georgia. Professor Weinhold
has also served on the Honorary Editorial Advisory Boards of the International
JournalofQuantumChemistryandtheRussianJournalofPhysicalChemistryand
istheauthorofover150technicalpublicationsandsoftwarepackages.
Following a brief but influential career as an industrial chemist for Monsanto
Corporation, Clark Landis began his academic career at the University of Col-
orado,Boulder,movingtotheUniversityofWisconsin-Madisonin1990,wherehe
iscurrentlyaProfessorinInorganicChemistry.ProfessorLandiswasco-PIofthe
NewTraditionsSystemicReformProjectinChemicalEducationandisco-author
ofChemistryConcepTests:APathwaytoInteractiveClassroomsandacompanion
videotape.HehaslongservedasaconsultanttoDowChemicalCompanyandis
amemberofitsTechnicalAdvisoryBoard.
VALENCY AND BONDING
A Natural Bond Orbital Donor–Acceptor Perspective
FRANK WEINHOLD AND CLARK R. LANDIS
DepartmentofChemistry,UniversityofWisconsin-Madison,Wisconsin53706
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge ,UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridg e.org /9780521831284
© Cambridge University Press 2005
This book is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2005
- ---- eBook (MyiLibrary)
- --- eBook (MyiLibrary)
- ---- hardback
- --- hardback
Cambridge University Press has no responsibility for the persistence or accuracy of
s for external or third-party internet websites referred to in this book, and does not
guaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.
Contents
Preface pagevii
1 Introductionandtheoreticalbackground 1
1.1 TheSchro¨dingerequationandmodelsofchemistry 1
1.2 Hydrogen-atomorbitals 8
1.3 Many-electronsystems:Hartree–Fockandcorrelatedtreatments 13
1.4 PerturbationtheoryfororbitalsintheHartree–Fock
framework:thedonor–acceptorparadigm 16
1.5 Densitymatrices,naturallocalizedanddelocalizedorbitals,
andtheLewis-structurepicture 21
1.6 Naturalresonancestructuresandweightings 32
1.7 Pauli-exchangeantisymmetryandstericrepulsions 36
1.8 Summary 40
NotesforChapter1 41
2 Electrostaticandionicbonding 45
2.1 Introduction 45
2.2 Atomicandionicorbitals 47
2.3 Chargetransferandhybridizationinionicbonding 49
2.4 Donor–acceptortheoryofhybridizationinionicbonding 55
2.5 Ionic–covalenttransitions 60
2.6 Ion–dipoleanddipole–dipolebonding 64
2.7 Bentioniccompoundsofheavyalkalineearths 73
2.8 Ionicbondingind-blockelements 76
2.9 Summary 86
NotesforChapter2 87
v
vi Contents
3 Molecularbondingins/p-blockelements 89
3.1 Introduction 89
3.2 Covalentandpolarcovalentbonding 90
3.3 Conjugationandaromaticity 182
3.4 Hyperconjugation 215
3.5 Hypervalency:3c/4e“ωbonds” 275
3.6 Hypovalency:3c/2ebridgebonds 306
3.7 Summary 351
NotesforChapter3 353
4 Molecularbondinginthed-blockelements 363
4.1 Introduction 363
4.2 Lewis-likestructuresforthed-blockelements 365
4.3 Hybridizationandmolecularshape 372
4.4 Covalentandpolar-covalentbonding 387
4.5 Coordinativemetal–ligandbonding 434
4.6 Beyondsigmabonding:transition-metalhyperbonding
andpiback/frontbonding 447
4.7 Hypovalency,agosticinteractions,andrelatedaspects
ofcatalyticactivationatmetalcenters 479
4.8 Hyperconjugativeeffects 519
4.9 Multielectroncoordination 522
4.10 Verticaltrendsintransition-metalbonding 545
4.11 Localizedversusdelocalizeddescriptions
oftransition-metalbondingandhyperbonding 563
4.12 Summary 573
NotesforChapter4 575
5 Supramolecularbonding 579
5.1 Anintroductoryoverviewofintermolecularforces 579
5.2 Hydrogenbonding 593
5.3 Charge-transfercomplexes 661
5.4 Transition-statespecies 678
5.5 Couplingofintramolecularandintermolecularinteractions 693
5.6 Summary 702
NotesforChapter5 704
AppendixA.Methodsandbasissets 710
AppendixB.Chemicalperiodicity 715
AppendixC.Units 723
Chemical-speciesindex 727
Authorindex 732
Subjectindex 740
Preface
Twodauntingquestionsfacetheauthorsofprospectivetextbooks.(1)Forwhomis
thebookintended?(2)Whatmakesitdifferentfromotherbooksintendedforthe
sameaudience?Wefirstaddressthesequestions.
Onemightthinkfromcountingthemathematicalequationsthatthebookisin-
tended for a theoretical physicist. This is partially true, for indeed we hope the
subject is presented in a way that will satisfy a rigorously inclined mathemati-
cal physicist that “valency and bonding” is not just murky chemical voodoo, but
authenticsciencegroundedinthedeepesttenetsoftheoreticalphysics.
Beyond Chapter 1 the reader may be relieved to find few if any equations that
would challenge even a moderately gifted high-school student. The emphasis on
orbitaldiagramsand“doingquantummechanicswithpictures”mightthensuggest
thatthebookisintendedforundergraduatechemistrystudents.Thisisalsopartially
true.Forexample,webelievethatourtreatmentofhomonucleardiatomicmolecules
(Section 3.2.9) should be accessible to undergraduates who commonly encounter
thetopicinintroductorychemistrycourses.
Our principal goal has been to translate the deepest truths of the Schro¨dinger
equationintoavisualizable,intuitiveformthat“makessense”evenforbeginning
students,andcanhelpchemistryteacherstopresentbondingandvalencyconceptsin
amannermoreconsistentwithmodernchemicalresearch.Chemistryteacherswill
findherearatherwideselectionofelementarytopicsdiscussedfromahigh-level
viewpoint. The book includes a considerable amount of previously unpublished
material that we believe to be of broad pedagogical interest, such as the novel
Lewis-likepictureoftransition-metalbondingpresentedinChapter4.
Because we are both computational chemistry researchers, we have naturally
directed the book also to specialists in this field, particularly those wishing to in-
corporatenaturalbondorbital(NBO)andnaturalresonancetheory(NRT)analysis
into their methodological and conceptual toolbox. Researchers will find here a
vii
viii Preface
ratherbroadsamplingofNBO/NRTapplicationstorepresentativechemicalprob-
lems throughout the periodic table, touching on many areas of modern chemical,
biochemical,andmaterialsresearch.
But,weexpectthatthemajorityofreaderswillbethosewithonlyarudimentary
commandofquantumchemistryandchemicalbondingtheory(e.g.,atthelevelof
junior-yearphysicalchemistrycourse)whowishtolearnmoreabouttheemerging
abinitioanddensity-functionalviewofmolecularandsupramolecularinteractions.
Whilethisisnota“textbookinquantumchemistry”perse,webelievethatthebook
canserveasasupplementbothinupper-levelundergraduatecoursesandingraduate
coursesonmoderncomputationalchemistryandbondingtheory.
Inidentifyingthefeaturesthatdistinguishthisbookfrommanypredecessors,we
donotattempttoconcealtheenormousdebtofinspirationowedtosuchclassicsas
Pauling’s Nature of the Chemical Bond and Coulson’s Valence. We aspire neither
to supplant these classics nor to alter substantially the concepts they expounded.
Rather,ourgoalistotakeasimilarlyglobalview,butdevelopamorecurrentand
quantitative perspective on valency and bonding concepts such as hybridization,
electronegativity, and resonance, capitalizing on the many advances in wavefunc-
tioncalculationandanalysisthathavesubsequentlyoccurred.Wehopetherebyto
sharpen,revitalize,andenhancetheusefulnessofqualitativebondingconceptsby
presentinga“twenty-first-centuryview”ofthenatureofchemicalbonding.
Readerswhoareaccustomedtoseeingchemicaltheorizingbuttressedbycompar-
isonswithexperimentsmaybesurprisedtofindlittleofthelatterhere.Throughout
thisbook,computersolutionsofSchro¨dinger’sequation(ratherthanexperiments)
are regarded as the primary “oracle” of chemical information. We specifically as-
sume that high-level calculations (e.g., at the hybrid density-functional B3LYP/
6-311++G∗∗ level) can be relied upon to describe molecular electronic distribu-
tions, geometries, and energetics to a sufficient degree of chemical accuracy for
ourpurposes.(Infact,theaccuracyisoftencomparabletothatofthebestavailable
experimentaldata,morethanadequateforqualitativepedagogicalpurposes.)The
viewpointofthisbookisthatmodernabinitiotheorynolongerrequiresextensive
experimentalcomparisonsinorderforittobeconsideredseriously,andindeed,the-
orycanbeexpectedtosupplanttraditionalexperimentalmethodsinanincreasing
numberofchemicalinvestigations.Inthedeepestsense,thisisa“theorybook.”
Dual authorship naturally brings a distinctive blend of perspectives. The book
reflectstheinfluenceofa“donor–acceptor”perspectivebasedonNBO/NRTwave-
function analysis methods developed in the research group of F. W. (a physical
chemist).WhileNBOanalysesarenowrathercommoninthechemicalliterature,
thepresentworkprovidesthefirstbroadoverviewoforganicandinorganicchemi-
calphenomenafromthisgeneralviewpoint.Thebookalsoincorporateskeyinsights
gainedfromconstructingvalence-bond-based(VALBOND)molecular-mechanics
