Atoms in Molecules: An Introduction

93 Pages·1999·17.404 MB·English

by  Paul L Popelier

Atoms in Molecules
An Introduction
Paul Popelier
UMIST, Manchester, UK
An ;mpdnt ot PEARSON EDUCATION
Harlow, England London New York· Reading, Massachusetts San Francisco Toronto Don Mills, Ontario Sydney
rokyo ·Singapore Hong Kong Seoul· Taipei Cape Town Madrid Mexico Crty Amsterdam Munich Paris· Milan
Pearson Education Lilnited
Edinburgh Gate, Harlow
Essex Cl\120 2JE
l'ngland
and A.<;sociated Companies 1hroughout 1he lJ"orld To Fred and Hermine
Pearson Fducation Limited 2000 171yfavourite bond
hTihme rinig ahct coofr dPaanucl eP wopitchl itehre t oC obpey irdigenhtti,f iDede saigs na uatnhdo rP oatfe tnhtiss AWcto r1k9 8h8a.s been asserted by To all researchers
tPpArhchuletlobr itCleroiiysogcahphoJeytp rsrsys iy rigoneshtrgste e, am rL rv,leie icccodeoer;nrn dstncriioenan nggpps ,ac Amrontgirn t eotioentfttdc hit nyehig nniLs v ratiepdnssu.ye,tb r 9iwlfcio0ctir etamThdtio o ocuotntotre pnmebyihytaiahn yameg nrb yieCtn h moreteu heppreatrr n oiURsod,noru iaecwtdleeer,ddic t, tLt Kresoontinnon dirpgceoed,dn ro mm miWnei scIiashs niPsaoy unn' e!i Hcdoa Efbl ,.ty h e PCaosntt,r pibruetsienngt taon AdfIiMttu re
First published 2000
ISBN 0 582 36 798 0
British Libra•·y Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Library of Congress Cataloging-in-Publication Data
A catalog entry for this title is :.wailab.lc from the Library of Congress.
Set by 35 in Times and Melior
Produced by Addison Wesley Longman Singopore (Pte) Ltd.,
Printed in Singapore
•
Contents
List of box contents X
Prej(Jce XI
Acknowledgements XIV
List ol acronyms XV
Software XVll
1 The electron density 1
1.1 The aim of AIM: a metaphor 1
1.2 Quantum mechanics 2
1.3 The electron density 3
1.4 The electron density from theoretical
calculations 6
1.5 The electron density from experiment 11
1.6 Representing the electron density 12
1. 7 Deformation densities 15
Summary 16
References 17
Further reading 17
· 2 The gradient vector field 19
2.1 What is the gradient? 19
2.2 The gradient path 21
2.3 The gradient vector field 24
2.4 Critical points 26
2.5 Some examples of gradient vector fields 28
2.6 Non-nuclear attractors 32
Summary 33
References 34
Further reading 34
viii Contents Contents ix
3 The atom 35 7.3 The virial theorem 100
3.1 The atomic basin 35 7.4 The hypcrvirial theorem 102
3.2 The interatomic surface 38 Summary 108
3.3 The shape of an atom 43 References 109
3.4 Atomic integration 46 Further reading 109
3.5 Atomic additivity 48
3.6 Atomic transferability 49 ', 8 The Laplacian 110
Summary 50 8.1 The Laplacian 110
References 51
8.2 Valence shell charge concentration 112
Further reading 52
8.3 The atomic graph 113
8.4 The VSEPR model 118
c'4 The bond
53 8.5 Lewis and the Laplacian complementarity
4.1 Origin of the bond concept 53
principle 122
4.2 Energy considerations 54
Summary 125
4.3 The bond critical point 56
References 126
4.4 The bond path 58
Further reading 127
4.5 Bonds in typical molecules 61
4.6 Bonds in van der Waals molecules 64
4.7 Bonds in organolithium molecules 65 9 Electrostatics 128
4.8 The agostic bond 66 9.1 The electron population of an atom 128
Summary 68 9.2 The atomic dipole moment 134
References 68 9.3 The atomic quadrupole moment 136
Further reading 69 9.4 The electrostatic potential 139
Summary 142
·,,,; 5 The full topology 70 References 143
5.1 The ring critical point 70 Further reading 143
5.2 The cage critical point 72
55..34 TRheev iPewoi nocfa arlel -tHypoepsf roufl ec ritical point 7772 ~ '·10 B10o.1n d Icnhtraordaucctteiorinz ation 114444
5.5 Ellipticity 77
10.2 Shared and closed-shell interactions 144
Summary 79
10.3 Bond representation 146
Further reading 80
10.4 BCP properties for a given type of bond 147
,.; I 6 Structural change 10.5 Criteria for hydrogen bonding 150
81
6.1 Structure versus geometry 81 10.6 Cases of hydrogen bonding 153
Summary 155
6.2 Bifurcation mechanism 84
References 156
6.3 Conflict mechanism 88
6.4 Structure diagram 91
Summary 94 Compound index 157
References 94 Subject index 159
Further reading 95
J7
The quantum atom 96
7.1 The rules of the game 96
7.2 The kinetic energy of an atom 99
List of box contents Preface
Listen carefully to Nature for she only H·hispers
1.1 The electron density from the wave function s This book is an invitation. lt is an invitation to participate in the quest to
1.2 Atomic units 7 construct a solid bridge between modem computational quantum mechanics
2.1 The gradient 20 and chemistry. Nowadays, affordable computers run sophisticated quantum
2.2 The gradient path 23 chemical programs yielding the energies and geometries of vast numbers
3.1 Natural atomic coordinates 36 of molecules. The development of chemical insight, however, has lagged
3.2 Zero-flux surfaces 40 behind these spectacular advances. Chemical concepts taught to under
5.1 Eigem alues and eigenvectors of the Hessian 73 graduates are based primarily on knowledge· that was available in times
6.1 Equivalence and homeomorphism 82 when computers did not exist or were rare tools. Although these chemical
7.1 Some vector calculus 97 concepts are undoubtedly valuable, they should constantly be confronted with
7.2 The vi rial theorem 101 modem solutions of the Schrodinger equation obtained by the present
7.3 Commutators 103 day computers. Naive reductionism set aside, we must admit that if the
7.4 An impmiant postulate 104 Schrodinger equation is true, then all of its consequences must be true. As a
7 .S Vectors, tensors and their products 107 result, any chemical concept must be compatible with the Schrodinger equa
8.1 The meaning of the Laplacian 111 tion; it cannot have a life of its own, disconnected from the physics that
8.2 Electron pairing 119 governs Nature. Of course this is a challenging research program, with many
8.3 The Laplacian and acidity 123 battles to fight, but I believe it is wmih it.
9.1 Multipole moments 129 Accepting that Science coerces us to a unified and streamlined picture
of Nature, we face such questions as, how do we recover from quantum
mechanics a chemically meaningful and intuitively appealing atom inside
a molecule? How do we recover a bond in a molecule from quantum mech
anics as a simple and computable object? How do we broadly classify bonds
in terms of their covalent or ionic character based on quantum mechanics?
How do we detect and characterize hydrogen bonding from modem wave
functions? How do we explain the geometry of ligands around a central
atom from the electron density?
Promising, rigorous and elegant answers to these and other important ques
tions can be obtained from a theory caiJed 'atoms in molecules' (AIM). This
theory uses the electron density as its starting point. The electron density is
on a par with the energy in the same way that eigenvalues and eigenfunctions
go hand in hand. Nevertheless, the quantum chemical community has focused
most of its attention on the energy and its derivatives and often describes
xii Preface
Preface xiii
eIgapouisscm rtcnxrzTpirihashterspihrnecohaoepggntpeailyhaeav audetnfdTt ohaftrtsecdliv-e dueu u oc ntcsih tcaeeaAe rcrsyrrleauaiieonlenlele eousic ertc rleIsn aatssme onm teiechMoavatteeissutscc t's.ftu a l eos. ra.r nttyh.tt a pmiIidouotlo nrredcTTnechn t Toce imnr sf owaem eeedcchshnohun, hckrnd nhdh eo eeapa n iiupgeeeto cdeejs s mtsdlcwaslroromdsite ne um eiteavpisb supmo eoisalncnm,daeeofsdiooic urnsystcot suciiun nriuioc ytelbn cabiritasomaactyartt ayk oll oeityaltnsyhclt ge lo.e imat sh is la os oiosht,dnay.dnf Tsi ithh nt pnaaisnrsae rebyaneaIh ftiu ulaa el nn dosaio brkaalislnsctdno csd sos i r aoitusov gwwcieii ynareftgetiotdccsmairrhninn ,gyrdretre eieeki ot hteai v.,telk,iwpw sba tnu lmopiitiniiseTnuh ssemsahtdahs nhi cuauaoo tiocwol taeti,beaseas tpric wawhcfntaitortse goIoeh u orheiw tss cttel nioooy rh ahhs, n e ynhovha bitcnr.ekpeeid cdehee ses afsu ota o aga acm oaoeri pIrlenoAilsbn,rtee trl r nso x hsa eki aneno tcaI tfadtg pth a obnnoMthhooooptryw-iretaeeyte etafzpsrka fimrlt m msat meoenet y l ibtqoabhtA seile nn a pepsuatdfiita ienaddekesn Ihfs teltairncjcMaei taie en eaenuxorhwtajerpccsb sgloyotss.n Adidocyhepyru h t,in y rTve n siter mrsIotgisafkhra obaameehMhubiae nunetp ene atAeeiencshtir mtdoscdrc c redhsh oee eiaI aewieh,ta aae mlmloM nlcAsfu ae oreatcdtnt,octfcbessc eao ocsIehi .rer he otfnMs tb tkr efaesfr'iirb erDortptdoaiicnons oIeheoroaon rrd oiraanies.ng g s ab tcgec slmulhc wtho haamllh-t A shdd siyea rytpfnoo edheee ehd oa n teaiwepms iiconinneeciiratnnntvnkonor misnsds rieg dct psaeig nisa dshma tctpiu euth nvt y ypsooisanshhenonliotfid . aronnano ceaid unt fwom atsarm idiovae cpitituraitnkbnhnnsre rohtela legdye yyt.ealg ed deryo h s, s . ~Aaeawtwiptmlptncawvwtetheahrcfhr mooeniIehoferruateocoeeMrtIcen piioauyi pvwlacrtozvmecrtrttr l,lsinlee rre i te d dyeiaedicyolf is lb sitnt.sw avwitieb real v bnuts.)eyla ceodA enl"aieuthatesaueesadAt , p r efOls idl pdrdinhses alvp ctmrAlemJhri oA i.ral srhreJe de-iayataiuivIooImCIhirIs tnn steCMr tateya,pMae eqieatccdt arSai tn erd, idopu ee.i i rngrpi cd cdn n isi amooaS Iirrbnslhalb g sktv laltyyeociya eoneetlhoeyltnli; h,goycnu .emtnde aga h oret mf IIno iw .ovti o uipaatxuoezatcdtenhehp m mrlhaerg sra ex ocdoaarlmm m e hoileemraotoip~vvferf nb brfx~szm p.esee~ toclii t o si.s,hrnem ls hIlaoo n eplpe<odjn cjeIibsydnlgrfulstsrkpet ~ :' uvve si e d dtls l~ltibbvtfbtteaiaisaiyyssgea! brcendnaeort cmanoe} n teiciirkn ceottateedammtroiun) epte~s knmfeam 'tegrn~ ddlaa p,htt drtdy!I tpy etcnie ooee u .thlmh c.lot vyph on A~ rlynoieyo mntse. eanatdg fnaqm.Ifa stlrnva~g BoesaMnro cumhT~avyetvo inltitaptaaab\rdh oh ereo_ydemgnp)tbwuoeeeiel e o aeoedostecte,ndt a ei su enir etpecxrwut oem.nob gdtemihd anmptgnowtmiaf~a hs e~ alrstg efy sdediatob ioromsuo~ eonn Iniieeery ulrw nsmntntsgaeltvdae p§hghc ls c .fe~Asowp teutifuf thi@eov~latao thfTszsIor~hhaven eiss riaMae~Alphrndoaea c icdaJtettn!maiirt si Ih. h crcIs ema AtgmMib~~. ikoe sebnlnj ~~sby I.aun iatIl _, oifMrsioa s!y dpltTntufesMa~rpa fo i~Aghe h lsus f ~c netlk kseeiiiefe{eh s~IScnsceen: alimnsMcet ~au,ide fwmor rsn;o ~or-Id lwcoe :hcSwc ea omtmp1h nh ndnh.oooht!vtlaw _eoto-1ge me1nepwi c9gm- ·ntle oedcht!ebtrayf runalshowg iey f~ohbal mnt st nf e eneph ushtoe iaTiearh: .~eonoeaptIaxure Irneey­CSdedt tItf s t
Iarpbetami edtebTentposrnaah hrmeario fd onhcaceaWmmw_pdnoeetkneeaaW vtetixkodas ssahtt ohren ieiom . hretyiirgc s rgsoay t ionat,ieAe aIrioat'ta nfun na vllifI hli lltist anr ospg eleitumhrodaeehlstsegvhec rlnei efrv taara o vvue w.eto tdaAa vee leaslmielbrtA efxr e eetdtieuc !mcoi orl cwa ahntg rro aposomemreen bececaltm nuep kp lalfuuoiiosae afcutaen tnnps irca ett efirdrng ychdadrhlrbtiIt pelee er heAat iiia otcntibcd neMdhwnnhesppiaucIum grae,sc aentMlteo etil cn e lewl b heepaa nlem ltasrse.uitwrfiahlwidds i t ci cn anrvtr aoeas cR au odce'deodetrsnntroas ol aa aefeie vayltneti bzct tndxy eoitone csuchmaetoottita lm :heeri,eanb nmwpo c mterpepoAirogehselhka.n hap tse xo ewat . iIi OerelcliQa a.nakn atiaen nhTr s bsmshr.t bIuidmegame t i ethoao laa gih pp raeheuitgvessotniattslhattn atonveem elt vl esatesturte amaeashetih , cbsl mrl natn mealleeny,uaoaetsoyg on r soolnxs iiTcw eio et d.navIeneewte onBhl s bisdee d.dmitmmm'de e 'ene al. b Irl i tmmexaedt maalpnAeooohe nnxtleyaa ayfynbx aola yaards r msltvd os'n'pv m aieno h(safeseeo udiCoyr i ee tltnpd kgsmIizi mph fw l dgl io uba ztmrrewnptomo m orroeleofsuwtoeerenh asae o an repsns ewoadkinidekit enrcsdnygngheietf o.as ehnio et.ectelr co vs hceCcy anrnia hW oInidederlrpu ,er daerod e nseo zihnrtdhlea1atsau iacolon.ai eletar9ed lgecnl eov h rrrnp9aestahRB'om eoymefht gr0rrlo u oii at g.oaaia)rmd rmo uftrn edetvip eThiwat t nogfal aihepe ttbepleh dhw.hi ttudrerrol itrahheiee'onehI,s r nssnre n . t aCitIluhbtiba'athanoif hnriegasn teahioe ciedxenmvedfstsr aFnoroee · eh ie paaiincosdesrrcf-canrllteehmisondieo laeoptac.viyex.m tcnr mmdlsp uhte mTplod AaeyelylrIoemlosohk yr ati a, art hsI wufeel tumt b A itoh bi os pnmtct'inuste sih a tIuafihergsglhs oMsaceu dstiecehrai kmh ahs isottt do cpteefehhthe tnii auiha sosoaetadaomdsaocs.l es rptt nd w ?n t erm eAotfco m a gbatth ailbooilIhrininttiocec es 1tmohener iaagtt ati i s i or'all_cipmmttnnma py crpi~ obbtavbomr ta6hp henihratirisvsnlsehcooinotescoe ~e sao earkAe trkosfrllottits ti qbeiyaigrao y nn Imco~y uc·cwnrMnoo ,vo§tn,okleb:tphe ~u-feane un e lpdiff sCi ot cyancsct:aomwo htewn fes oomdctr antphi' isa tmu.ihrelvn1oee t naleelleaTs£yeg nwoprtdtxi tnkt e snh tu wf aht_~ l i tntrtih timemcsJhhaepesheeoT.e&ahsa esrr' ariapbw~ rpb etot csTstu:n lfe tomr behi eoha-~Ahneelowar~l, ~ieyiidfdteii rrakI_ss oah1e l mt otMrlt yt1lhar ooaherhluaf y k.ydet bvatag ae b se eh rrscteAng rIltsanao ent eaorepdbeconiatIp hqsdwhnni iet~MrdLp reuoshlaQy ee eay nitei_pdebrts nanallr tlhawiw lyeilbcMerig sl pcetweft cse ii~t ii saa tghlae snce?rfuwh aolls ainpeo dninsotPattnHceses tcooitl stfatteotnaenaaech mdoaerh n ntns gemupauerv tfhte ci nfs o les'ocetc ea-moe iwtmtt ooctP c trlhue rsut ao m.pule.corhoiorata rl nmt,rlhnioIeedelnpf o ees eaidf msdy1 epa,ss tAtcr roeyy9.vl wthugibut nei vwIs9oe eotteIeo~iuloMater8ioulnoerssnnstrt l r ·
Acknowledgements List of acronyms
I thank my parents for their support and the opportunity they have given me
to become a more complete mind. Many thanks to Richard Bader who has 3D three dimensional
initiated, led and guarded the development of the theory of 'atoms in mole AIL atomic interaction line
cules'. I am grateful to all of his co-workers who have painstakingly ex AIM atoms in molecules
plored the foundations and applications of the theory, and to all researchers AO atomic orbital
who have contributed to it. I owe my students Fiona Aicken and Sean O'Brien B3LYP Becke~3~Lee~ Yang~Parr
for their valuable feedback on the whole manuscript and their help with BCP bond critical point
some calculations, to Ron Gillespie for his extensive comments, construct BP bond path
ive criticism and support, Ian Bytheway for his thorough reading of Chap CP critical point
ters 1~4, Richard Bone for feedback on Chapter 8, and Frank Mair. Many CCP cage critical point . .
thanks to Alexandra Seabrook, Pearson Education's senior commissioning DCI doubly excited configuration mteractwn
editor whose belief in this book has freed AIM from the oyster of special DFT density functional theory
ization. I thank the independent reviewer for his considerable effort. Finally, HF Hartree~Fock
I thank all readers who have accepted the invitation. HOMO highest occupied molecular orbital
lAS interatomic surface
IR infra red
Permissions acknowledgements LCAO linear combination of atomic orbitals
LCP ligand close packing
Grateful acknowledgement is made for pennission to reproduce material in MG molecular graph
this book previously published elsewhere. Every effort has been made to 1vi0 molecular orbital
trace the correct copyright holders, but if any have been inadvertently over MP2 second-order M01ler~Plesset perturbation theory
looked the publisher will be pleased to make the necessary arrangement at (N)NA (non)-nuclear attractor
the first opportunity. NMR nuclear magnetic resonance
RCP ring critical point
We are grateful to the following for permission to reproduce copyright SCF self-consistent field . . .
material: International Union of Crystallography for Figs 1.4 and 2.11; SDTCI singly, doubly and triply excite~ configuratiOn mteractwn
Addison-Wesley Publishing Company for Fig. 2.1; National Research Council vscc valence shell charge concentration
Canada/NRC Research Press for Fig. 3.4; Angewandte Chemie for Fig. 3.5; VSEPR valence shell electron pair repulsion
International Journal of Quantum Chemistry for Fig. 3.6; Institute of Phy
sics for Figs 4.4, 4.5, 6.6 and 6.7; American Chemical Society for Figs 4.2,
4.6, I 0.4, I 0.5 (Plate section), 10.6 and I 0. 7; Elsevier Science for Figs 4.8
and 9.5; Taylor & Francis for Fig. 9.6.
Software
New wave functions have been generated with the program GAUSSIAN
(Gaussian 94, Revision B.l, M. J. Frisch, G. W. Trucks, H. B. Schlegel,
P. M. W. GiiJ, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith,
G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham,
V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov,
A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen,
M. W. Wong, J. L. Andres, E. S. Replogle, R. Gompcrts, R. L. Martin,
D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head
Gordon, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Pittsburgh P A, 1995).
New AIM data have been obtained with the commercial computer
program MORPHY98, which is available from http://www.ch.umist.ac.uk/
morphy. Most figures were generated by MORPHY98, except for a few that
can only be obtained from a future release version of MORPHY.
The original AIMPAC suite of programs, developed in Professor Bader's
laboratory at McMaster University (Canada) can be freely obtained from
http://www.chemistry.mcmaster.ca/aimpac.
Since 1994 the well known commercial program GAUSSIAN has pro
vided an option to perform a restricted set of AIM utilities. Interested users
should consult http://www.gaussian.com. However, in our experience the
atomic integration subroutines can provide erroneous results, an uncritical
interpretation 0f which may unjustly damage the reputation of AIM.
Chapter 1
The electron density
There will he another shock,
1vlzcn H'e finally understand ;vhat it really means
1.1 The aim of AIM: a metaphor
Let us make a comparison between the weather and chemistry. Both encom
pass a complex world of phenomena which arc nrled by a handful of phys
ical laws. In the case of chemistry these physical laws are part of quantum
mechanics, while in the case of the weather they are part of fluid dynamics
and thermodynamics. Both quantum mechanics and fluid dynamics provide
us with equations which are very hard to solve for real systems in spite of
their appealing simplicity. The advent of sufficiently powerful computers
has made possible predictions in both the world of chemistry and that of the
weather. Solving the basic equations governing these systems requires elabor
ate and sophisticated computational schemes which typically yield millions of
numbers. In turn, these numbers may be hard to interpret in terms of simple
concepts such as, is this bond ionic or is it going to be foggy tomorrow?
How did chemists make predictions before the advent of computers? They
gathered vast amounts of data on the phenomena they observed. Rationaliz
ing these data led to rules which existed in their own right, disconnected
from the physics of molecules. Strictly speaking, these rules could be applied
only for the set of molecules for which they were originally observed. Sim
ilarly, at the dawn of meteorology, scientists perceived the weather as a com
plex reality imposing its own patterns and rules apparently independently of
the physics that govern them. Parallel to this early scientific development,
people (especially fam1ers) had been carefully observing the weather for
centuries in an attempt to understand its behaviour. This knowledge, often
expressed in colourful proverbs, could be vital, for example, to make a good
decision when to harvest.
In summary, chemical concepts and explanations arise from observations
at an 'upper' level, close to human experience and perception. In other words,
chemical concepts emerged by looking at the world of chemistry itself, not
the underlying world of physics. In a similar vein, weather types and pro
verbs arise from observations at this upper level, that of human experience,