FFiigguurree11::VVaalleenncceebboonnddccoommppuutteeddeenneerrggiieess((EE))aassffuunnccttiioonnssoofftthheeiinntteerraattoommiiccddiissttaanncceess((RR))ffoorrssoommeebboonnddss..

PerspectiveNatureChemistry11,443-449(2009)Publishedonline:24August2009|doi:10.1038/nchem.327

SSuubbjjeeccttCCaatteeggoorriieess::GGeenneerraallcchheemmiissttrryy||TThheeoorreettiiccaallcchheemmiissttrryy

Charge-shift bonding and its manifestations in chemistrySasonShaik11,DavidDanovich11,WeiWu22&PhilippeC.Hiberty33

EElleeccttrroonn--ppaaiirrbboonnddiinnggiissaacceennttrraallcchheemmiiccaallppaarraaddiiggmm..HHeerree,,wweesshhoowwtthhaattaalloonnggssiiddeetthheettwwooccllaassssiiccaallccoovvaalleennttaannddiioonniiccbboonnddffaammiilliieess,,tthheerreeeexxiissttssaaccllaassssooffcchhaarrggee--sshhiifftt((CCSS))bboonnddsswwhheerreeiinntthheeeelleeccttrroonn--ppaaiirrfflluuccttuuaattiioonnhhaasstthheeddoommiinnaannttrroollee..CChhaarrggee--sshhiiffttbboonnddiinnggsshhoowwssllaarrggeeccoovvaalleenntt––iioonniiccrreessoonnaanncceeiinntteerraaccttiioonneenneerrggyy,,aannddddeepplleetteeddcchhaarrggeeddeennssiittiieess,,aannddffeeaattuurreessttyyppiiccaallttoorreeppuullssiivveeiinntteerraaccttiioonnss,,aallbbeeiitttthheebboonnddiittsseellffmmaayywweellllbbeessttrroonngg..TThhiissbboonnddiinnggttyyppeeiissrrooootteeddiinnaammeecchhaanniissmmwwhheerreebbyytthheebboonnddaacchhiieevveesseeqquuiilliibbrriiuummddeeffiinneeddbbyytthheevviirriiaallrraattiioo..TThheeCCSSbboonnddiinnggtteerrrriittoorryyiinnvvoollvveess,,ffoorreexxaammppllee,,hhoommooppoollaarrbboonnddssooffccoommppaacctteelleeccttrroonneeggaattiivveeaanndd//oorrlloonnee--ppaaiirr--rriicchheelleemmeennttss,,hheetteerrooppoollaarrbboonnddssoofftthheesseeeelleemmeennttssaammoonnggtthheemmsseellvveessaannddwwiitthhootthheerraattoommss((ffoorreexxaammppllee,,tthheemmeettaallllooiiddss,,ssuucchhaassssiilliiccoonnaannddggeerrmmaanniiuumm)),,hhyyppeerrccoooorrddiinnaatteeddmmoolleeccuulleess,,aannddbboonnddsswwhhoosseeccoovvaalleennttccoommppoonneennttssaarreewweeaakkeenneeddbbyyeexxcchhaannggee--rreeppuullssiioonnssttrraaiinn((aassiinn[[11..11..11]]pprrooppeellllaannee))..HHeerree,,wweeddiissccuusssseexxppeerriimmeennttaallmmaanniiffeessttaattiioonnssooffCCSSbboonnddiinnggiinncchheemmiissttrryy,,aannddoouuttlliinneenneewwddiirreeccttiioonnssddeemmoonnssttrraattiinnggtthheeppoorrttaabbiilliittyyoofftthheenneewwccoonncceepptt..

Thereareprobablyonlyahandfulofconceptsthatareasfundamentalandcentraltochemistryasthatoftheelectron-pairbond.EversincetheingenioushypothesisofLewis11,followedbypioneeringworkofHeitlerandLondon22,ontheoriginsofelectron-pairbonding,andthecolossalintellectualconstructofPauling33,electron-pairbondinghasbeentraditionallyclassifiedintotwomajorfamilies33,,44,,55.Oneisthefamilyofcovalentandpolar-covalentbonds,inwhichthebondingarisespredominantlyfromstabilizationduetothespin-pairinginthecovalentstructureofthebond.Thesecondfamilyinvolvestheionicbonds,inwhichthebondingarisesprimarilyfromtheelectrostaticstabilizationofthetwooppositelychargedfragments.Hence,basedonthistraditionalclassification,thebondingtypecanbecharacterizedbyknowledgeofthestaticelectronicdistributioninthebond,using,forexample,electronegativities,orelectron-densitypopulationanalysesprovidedinstandardquantumchemicalcalculations.However,thesetraditionalclassesofbondingcannotdescribemanyintriguingfeaturesofbonds,ofwhichwementiontwoexamples,oneregarding'ionic'bonds,theotherregarding'covalent'bonds:

Thus,forexample,thebondsH3Si+0.85F-0.85,Li+0.94F-0.94andNa+0.91Cl-0.91,wherethesuperscriptednumbercorrespondstogroupcharges,allhave'ionic'

chargedistribution(determinedbycharge-densityintegrations)55,,66,,77.But,whereasLi+F-andNa+Cl-behavechemicallyasgenuineionicbonds,the'Si+X-'bonds(X-=halide,perchlorate,andotherelectronegativegroups)behavechemicallyascovalentbonds88,,99,,1100.

AnotherstrikingexampleisthedifferencebetweenH2andF2;twohomonuclearbondsthatbyallcriteriashouldbeclassifiedascovalentbonds,butexhibit

fundamentaldifferences.Considertheenergycurves(FFiigg..11)ofthetwobondscalculatedrecently55,,1111,,1122.FFiigguurree11aashowsthattheH–Hbondisindeedcovalent;itscovalentstructureaccountsformostofthebondingenergy(relativetothe'exact'curve).Bycontrast,fortheF–FbondinFFiigg..11bb,thecovalentstructureisentirelyrepulsive,andwhatdeterminesthebondingenergyandtheequilibriumdistanceisthecovalent–ionicmixing.Thismixingleadstoaresonanceenergystabilization,whichwehavetermedthe'charge-shiftresonanceenergy'(RECS).Thus,despitetheirapparentsimilarity,thetwobondsare

verydifferent;whereastheH–Hbondisatruecovalentbond,theF–FbondisaCSbond55,,1122thatiscompletelydeterminedbytheRECSquantity.The

above-mentionedSi–XbondsarealsoCSbonds,andtheoriginalpapers55,,1122,,1133,,1144includeafewmorepuzzlingexamplesthatcounterthetraditionalclassification.Indeed,ourworkoverthepastdecadedemonstratesthatCSbondingconstitutesalargeanddistinctclassofbondingalongsidethetwoclassicalfamilies,andthatitpossessesuniquechemicalandphysicalsignatures55,,1111,,1122,,1133,,1144,,1155,,1166,,1177,,1188.Thefeaturesofthisbondfamily,itsterritoryandchemicalmanifestations,arediscussedinthisPerspective.

TheprincipalVBstructureisshowninblueandtheexactgroundstateinred;thelatteristhecovalent–ioniclinearcombinationdefinedbyeq.(1).aa––ff,TheprincipalVBstructureisthecovalentoneforH–H(aa),F–F(bb),B–H(cc)andF–H(dd),andtheioniconeforNa–F(ee)andNa–Cl(ff).Theenergydifferencebetweentheexact(red)curveandthedominantVB-structurecurve(blue),attheminimumdistanceofthebond,isthecharge-shiftresonanceenergy.Partsaaandbbarereproducedwithpermissionfromref.55,©2005Wiley.

FFuullllssiizzeeiimmaaggee((6600KKBB))

TThheeoorreettiiccaallcchhaarraacctteerriizzaattiioonnooffbboonnddttyyppeess

Theemergenceofthreebondingfamilies—covalent,ionicandnowCS—wasoriginallyderivedfrommodernvalencebond(VB)calculations1122.Asexpressedineq.(1),theVBwavefunction( )ofabondA–Xiscomputedasacombinationofthecovalentform cov(A – X),andtwoionicforms, ion(A+X-)and 'ion(A

-X+):

Thebond-dissociationenergy(De)istheenergyofthiscovalent–ionicwavefunctionrelativetotheseparatefragments(A andX )attheirrelaxedgeometric

andelectronicstructures.Thus,Dehastwocontributions;onecomesfromthebondingenergyoftheprincipalVBstructure,andtheotherfromRECSdueto

thecovalent–ionicmixing.TheprincipalVBstructureistheonehavingthelowestenergy,andhencealsothelargestcoefficientamongthethreestructuresineq.(1).ItscontributiontothebondingenergyisreferredtoasDcovorDion,whereinthesubscriptspecifiesthedominantVBstructure.Inallcases,RECSis

determinedbyreferencetotheprincipalVBstructure,forexample, covinFFiigg..11aa––dd,or ion(FFiigg..11ee,,ff).

ThesequantitiescharacterizethebondingtypeascanbegleanedfromFFiigg..11.ThustheprincipalVBstructureforbothH–HandB–His cov,theRECSquantityissmallandmuchlesssignificantthanthelargeDcov(FFiigg..11aa,,cc);inaccordancewiththis,thesebondsareclassicalandpolar-covalenttypes,

respectively.Bycontrast,F–H(FFiigg..11dd)showsaweaklyboundprincipalstructure cov,whereasthemajorcontributiontothebondcomesfromRECS.An

extremecaseistheF–Fbond(FFiigg..11bb)inwhichtheprincipalstructure covisnotevenbonded,thatis,Dcovisnegative,whereasRECSisevenlargerthan

thetotalbondingenergy.Inagreementwiththis,F–HandF–FarebothCSbonds.Finally,inNa–FandNa–Cl(FFiigg..11ee,,ff)theprincipalVBstructureisnow

ion,andtheRECSquantityisaminorcontributor,makingbothclassicalionicbonds,wheremostofthebondingenergyarisesfromtheionicstructure.

Analternativewaytocharacterizebondinguseselectron-densitytheories,suchasatomsinmolecules(AIM)1199andelectronlocalizationfunction(ELF)2200.TheAIMparameterscanbeeithercalculatedorderivedfromdensitydeterminedexperimentally,andareusedbyexperimentalchemiststocharacterizeinteractionswithinmolecules2211,,2222.Inthistheory,abondisgenerallycharacterizedbyabondpath,whichdefinesamaximumdensitypathconnectingthebondedatoms.Thepointofthepathatwhichthedensityisataminimumiscalledthebondcriticalpoint(BCP),andthevaluesofthedensity, (rc),wherercisthelocusofthebondcriticalpointandtheLaplacian, 2 (rc),atthispointarecharacteristicofthebondingtype.AccordingtoAIM,aclassicalcovalent

bondistypifiedbyasignificant (rc)value,andalargenegative2 (rc).Bycontrast,closed-shellinteractions,whichexperiencePaulirepulsions(also

knownasoverlaprepulsionorexchangerepulsion),asinionicbonds,ortheHe---Heinteraction,havecharacteristicallyasmallcriticaldensityandapositiveLaplacian.

TheLaplacianisespeciallytelling1199,,2233,asitisconnectedtothekineticandpotentialenergydensitiesatBCP,G(rc)andV(rc),respectively,bythefollowing

local-virialtheoremexpression:

Thus,anegativeLaplacianmeansthatthebondingregionisdominatedbytheloweringofthepotentialenergy,whereasapositiveLaplacianmeansthattheinteractionistypifiedbyexcesskineticenergy,andhenceisrepulsive.

TheELFapproachisanothertopologicalmethod,whichusesafunctionrelatedtothePaulirepulsiontocarryoutapartitionofthemolecularspaceintobasinsofattractorsthatcorrespondtothevolumesoccupiedbycoreinnershells,bondsandlonepairs.AsintheLewismodel,avalencebasinmayeitherbelongtoasingleatomicshellorbesharedbyseveral.Inthefirstcase,thebasiniscalledmonosynapticandcorrespondstoalone-pairregion,andinthesecondcaseitispolysynaptic,andspecificallybisynapticforatwo-centrebond.Thebasinpopulation, ,anditsvariance, 22,arecalculatedbyintegratingtheone-electronandthepairdensityoverthevolumesofthecorrespondingbasins.Foraclassicalcovalentbond,thebasinisdisynaptic,itspopulationiscloseto2.0,andthevarianceissignificantlysmallerthanthepopulation,whereasaclassicalionicbondsuchasNaClhasonlycoreandmonosynapticbasins55,,2200,,2244.

Toprovideaglobalpictureofthevariouscategoriesofbonds,27bonds55,,1111,,1122,,1133,,1144,,1155,,1166,,1177,,1188arepresentedinTTaabbllee11,andareorganizedintothreegroups,labelledI–III.ThefirstgroupinvolveshomonuclearbondsfromH–Htothe'inverted'C–Cbondin[1.1.1]propellane(seeFFiigg..22cc)1188.GroupsII

Nature Chemistry

FFiigguurree22::SSoommeeEELLFFrreepprreesseennttaattiioonnssooffeelleeccttrroonnddeennssiittyyiinnaaffeewwttyyppiiccaallccaasseess..

aa,TheELFdisynapticbasin55forH3C–CH3.bb,Themonosynapticbasins55fortheF–Fbond.cc,Disynapticbasinsforthewing

bondsof[1.1.1]propellane,andtwomonosynapticbasinsforthecentralinvertedbond2266.ThenatureofeachbondisfurthercharacterizedbyRECS,theELFbasinpopulation ,anditsvariance

22,thedensity atthebondcriticalpointandthe

correspondingLaplacian 2 (energiesareinkcalmol-1,densitiesinea0-3,Laplaciansinea0

-5).ForH3C–CH3andF–F,the

ELFandAIMparametersaretakenfromRefs55and1111,respectively.For[1.1.1]propellane,theAIMparametersareexperimentalvalues2255(averagedforthewingbonds)fromthestudyofasubstituted[1.1.1]propellanederivative.TheELFdrawingsinaaandbbarereproducedwithpermissionfromref.55,©2005Wiley.TheELFdrawingincisreproducedwithpermissionfromref.2266,©2007Wiley.

FFuullllssiizzeeiimmaaggee((3399KKBB))

TTaabbllee11::AAccoolllleeccttiioonnooffbboonnddsswwiitthhtthheeiirrVVBBaannddAAIIMMpprrooppeerrttiieess::ggrroouuppIIccoorrrreessppoonnddssttoohhoommoonnuucclleeaarrccoovvaalleennttaannddCCSSbboonnddss,,IIIIttoohheetteerroonnuucclleeaarrccoovvaalleennttaannddCCSSbboonnddss,,aannddIIIIIIttooiioonniiccbboonnddss..

FFuullllttaabbllee

andIIIinvolveheteronuclearbonds,fromC–HtoSi–F.EachbondischaracterizedbyVBproperties;theweightoftheprincipalVBstructure( cov, ion),the

bondingenergyofthatstructure(Dcov,Dion)followedbythefullbond-dissociationenergy(De),andRECS,followedbytherelativeresonanceenergy

(%RECS),whichisthepercentageratioofRECStoDe.ForsomeofthebondsweshowAIM-derivedquantities, and2 aswellastheLaplacian

componentsintheBCPforbondingduetotheprincipalstructureofthebond( 2 covor2ion),andthecovalent–ionicresonance(

2res)1111.

LetusfirstinspectthehomonuclearbondsinpartIofTTaabbllee11,whichbyalldefinitionscouldnotpossessstaticbond-ionicities.Thebondenergiesinentries1–4aredominatedbythecovalentcomponent,withRECSbeingtheminorbondingcontribution(<50%).Bycontrast,thebondsinentries6–10,allhavea

bondingenergydominatedbyRECS(>100%),whereasthecovalentstructureisrepulsive(Dcov<0).TheN–Nbond,entry5,isaborderlinecase,withRECSaccountingfor66.6%ofthetotalbondingenergy.LeavingasidetheweakNa–NaandLi–LibondsforwhichallAIMparametersareclosetozero,thereisanexcellentcorrelationbetweentheRECSquantitiesandtheAIMparameters,especiallywithinthesamerowoftheperiodictable.Thus,fromC–CtoF–F

(entries4–7),theresonancecomponentoftheLaplacian( 2res)ismoreandmorenegative,inagreementwiththeincreaseofRECS,whereasthecovalent

component( 2cov)goesfromnegativetopositivevalues,inagreementwiththerepulsivenatureofthecovalentstructureinCSbonds.Asaresult,the

totalLaplacian 2 islargeandnegativeforclassicallycovalentbondsandeitherasmallnegativeorapositivevalueforCSbonds.Notethat,accordingtoboththeRECSandtheexperimentallyderived

2 values2255,the[1.1.1]propellanemoleculeembodiesthetwocategoriesofbonds,classicallycovalentfor

thewingbonds(entry11)andCSbondforthe'inverted'centralbond(entry10).

ThesamedistinctionbetweenthecovalentandCSbondgroupswasrecentlyshowntoemergefromELFanalysis55.Thus,bondssuchasH–H,C–CandLi–Li,werefoundtopossessdisynapticbasinswithapopulationcloseto2.0andsmallvariances,whereasbondssuchasF–F,Cl–Cl,O–O,Br–Br,N–NandtheinvertedC–Cbondof[1.1.1]propellanepossesssmallbasinpopulations2266( 1.0),withvariancesandcovariancesaslargeasthepopulation.Inthestatisticaltheoryofthebasinpopulations,thecovariances55,,2277gaugedirectlythecovalent–ionicfluctuationsand,usually,arelargefortheCSbondsandsmallforthecovalentbonds55.However,asthecovariancesshowsimilartrendstothevariancesweonlyshowthelatterinthefollowingdiscussion.ThesetrendsaredemonstratedinFFiigg..22,whichshowsthemolecularbasinsforH3C–CH3,F–FandC–Cin[1.1.1]propellane,alongsidetheirVBandAIM

properties.Furthermore,itisseeninFFiigg..22bb,,ccthatthedisynapticbasinsofF–FandtheinvertedC–Cbondofpropellaneareinfacttwomonosynapticbasins,muchlikedissociatedbonds.Thus,thethreemethodsofdiagnosingbondingagreeontheclassificationofhomonuclearbondsintotwofamilies,andtheVBmethodbringsadditionalenergeticinsightthathighlightsthedominantroleoftheRECSenergyintheCSbondgroup.

TurningbacktoheteropolarbondsinpartIIinTTaabbllee11,wenotethefollowingtrends.WhereasthecovalentVBstructureistheprincipaloneforallthesebonds,thebondsstillfallintotwodistinctgroups.Specifically,entries12–15belongtotheclassicalpolar–covalentbondfamilybasedontheir%RECS,which

FFiigguurree33::CCoorrrreellaattiioonnoofftthheecchhaarrggee--sshhiifftt//ccoovvaalleennttbboonnddcchhaarraacctteerrwwiitthhtthheerreeppuullssiivvee//aattttrraaccttiivveennaattuurreeoofftthheeccoovvaalleennttiinntteerraaccttiioonn,,aannddwwiitthhtthheeeelleeccttrroonneeggaattiivviittiieessoofftthheebboonnddeeddaattoommss..

iswellbelow50%.Bycontrast,thebondsinentries16–22allhaveweaklybondedcovalentstructures,andlargeRECSexceeding50%andinsomecases

>100%.InpartIIIofTTaabbllee11theprincipalVBstructureofallbondsisionic.Thebondingenergiesinentries23–26arealldominatedbytheelectrostaticcontributiontobonding(Dion),withsmallRECScontributions.Theseareclassicalionicbonds.Finally,theSi–Fbondinentry27isspecial:itsprincipalVB

structureisionic;itsstaticionicityislarge,butitsRECSissignificant,muchlargerthanthatintheclassicalionicbondsinIII.Valencebondtheorypredicts55

thatthisbondwillbeverydifferentfromionicbonds.Asalreadyalludedtoabove,theSi–Xbondsbehaveasthoughtheywerecovalentdespitetheirlargeionicity88.Here,inIIandIII,thesebondsandtheirheavieranaloguesareclearlymarkedeitherasCSbonds(Si–Cl,Ge–Cl)1144orasbondswithalargeCScharacter(Si–F)55.

TheAIManalysisoftheheteropolarbondsinIIdoesnotdistinguishbetweenthecovalentandCSbonds,buttheLaplaciancomponentsintheBCPshowthattheCSbondshavemorepronounced 2 resvalues

1111comparedwiththeclassicalcovalentbonds,inlinewiththedominantRECSquantity.

Interestingly,theELFanalysis55ofthesebondsshowsbettertheirCSnature;allhavingdepleteddisynapticbasins( =0.86–1.22)withhighvariances(0.64–0.68),andthecaseofSi–FisverysimilartoF–F,withameagrepopulation(0.27)andavariance(0.24)thatisequaltothepopulation.Finally,theAIManalysisoftheclassicalionicbondsinIII(ref.1111)showstheexpectedcharacteristicsfromclosed-shellinteractions;allhavepositiveLaplaciansthataredominatedbytheioniccomponent, 2 ion.Inagreementwiththisclassificationoftheclassicalionicbonds,ELFshows

55thatthesebondsonlypossess

monosynapticbasins.

Insummary,CSbondingemergesasadistinctclassalongsidethecovalentandionicbonds.InVBtheory55,,1111,,1122,,1133,,1144,,1155,,1166,,1177,,1188,CSbondingistypifiedbylargeRECS,andinELF,byadepletedbasinpopulationwithlargevarianceandcovariance

55.Inaddition,homonuclearCSbondingis

characterizedinAIMbyasmallnegativeorapositiveLaplacianoftheelectrondensity1111,,2288.ItshouldbenotedthatthecharacterizationofCSbondingbyAIMandELFelectron-densityanalysesisindependentofthetheoreticalmethodthatisusedtocomputethewavefunctionorelectrondensity;forexample,molecularorbitalbondingtheoryordensityfunctionals55,,1111,showingthatthelattermethodseffectivelyaccountforCSbonding,evenifnotintheexplicitwayachievedbyVBtheory.ThereisofcoursearelationshipbetweentheVBmethodandmolecularorbitalordensity-functional-theory-basedmethodsofenergypartitioning(Kitaura–Morokuma2299,Ziegler–Rauk3300,Baerends–Bickelhaupt3311).Althoughthesemethodsdonot,asyet,makeprovisionstocharacterizeCSbonding,theyshareafewessentialfeatureswiththeVBmodel:themajoroneisthePaulirepulsionthatistheoriginofthelargecovalent–ionicresonanceenergy.InthisrespecttheseenergypartitionmethodsshouldseeadifferencebetweenbondssuchasH2andF2(ref.3322).

PPhhyyssiiccaalloorriiggiinnssooffCCSSbboonnddiinngg

ThelargeRECSquantityofCSbondsisanoutcomeofthemechanismnecessarytoestablishequilibriumandoptimumbondingduringbondformation.This

mechanismhasbeenanalysedbeforeindetail55,,1122,,3333;herewepresentasimpleranalysis.Bycomparingtheatomicandcovalentradiiintheperiodictable,onefindsthatgenerallyrATOM<rcov.Thismeansthatasatoms(fragments)bindtheyshrink.Theshrinkagecausesasteepincreaseinthekineticenergyof

thefragments,whichexceedstheloweringofthepotentialenergyduetothediminishedsize3344,,3355,,3366,,3377,,3388,,3399,,4400.Thus,theshrinkagetipsthevirialratioofthekinetic(T)versuspotential(V)energiesoff-equilibrium(V/T=-2atequilibrium).Thecovalent–ionicresonanceisthemeanswherebythekineticenergycanbereducedtorestorethevirialratio1122,,3344,andthisistrueinallbonds.Thekineticenergyriseduetoshrinkageisproportionaltothecompactnessofbondingpartners,andtherefore,asthefragmentsinbondingbecomemoreelectronegative,andhencemorecompact,thekineticenergyriseduetoshrinkagewillgetsteeper.Moreover,whentheatoms(fragments)bearlone-pairs,athree-electronrepulsionappearsbetweenthe lone-pairofonefragmentandthebondingelectronoftheother.Thiseffectwilldestabilizethecovalentstructure,asenvisagedoriginallybySanderson4411,whotermedthisasthelone-pairbond-weakeningeffect(LPBWE);thisPaulirepulsionraisesthekineticenergyofthebond,andtheeffectbecomesmoresevereasthenumberoflonepairsontheatomincreases.Aselectronegativefragmentsarealsolone-pairrich,thecombinationofatomicshrinkageandLPBWEcausesahighexcesskineticenergy.Insuchcases,theresonanceenergythatwillberequiredtorestorethevirialratiobecomesnecessarilyverylarge,andonefindsbondswithweakenedcovalentstructuresandlargeRECSquantities.Thus,farfrombeingamerephenomenologicalmodel,CSbondingisafundamental

mechanismthatisnecessarytoadjustthekineticandpotentialenergytothevirialratioatequilibrium,inresponsetothePaulirepulsivestrainexertedonthebond.

TheaboverelationshipsareillustratedinFFiigg..33;partashowsaplotofthecovalentpartoftheLaplacianagainstDcovforhomonuclearbonds1111.Intheright

lowerquadrant,whereDcov>0and2cov<0,arethebondswithstabilizedcovalentbonding.Thesecondgroup,intheupperleftquadrant,involves

electronegativeandlone-pair-richatomsand'invertedcarbons',whichundergoCSbonding.Itcanbeseenthatthisbonding-typeisassociatedwithweakenedcovalentspinpairing(Dcov<0),owingtolone-pairrepulsion,whichraisesthekineticenergy,asseenfromthepositivesignof

2cov.

aa,ThecovalentLaplacian, 2 cov,versusthecovalentbondenergy,Dcovforaseriesofhomonuclearbonds.bb,RECS(A–A)

versustheelectronegativityofA( A).cc,RECSforA–AandA–Xbondsversustheaverageelectronegativityofthebond.dd,

RECSfor -bondsversustheaverageelectronegativityofthebond.ee,AplotoftheresonanceLaplacianversustheaverage

electronegativityofthebond.Partsaaandeereproducedwithpermissionfromref.1111,©2009Wiley.Partsbb––ddreproducedwithpermissionfromref.55,©2005Wiley.

FFuullllssiizzeeiimmaaggee((3399KKBB))

FFiigguurree33bbshowstheRECSquantitiesforhomonuclearA–Abonds,plottedagainsttheelectronegativity( A)ofA.Itisseenthatineachperiod,RECSincreasesastheelectronegativtyincreases.FFiigguurree33ccshowsasimilarplotbutnowusingbothhomonuclearandheteronuclearbonds55,andFFiigg..33ddshowsthesametrendfor -bonds1155.ItisapparentthattheRECSquantityofthebondgenerallyincreasesastheaverageelectronegativityofthebond

partnersincreases.Finally,FFiigg..33eeshowsthattheresonancecomponentoftheLaplacianthatgaugestheloweringofthekineticenergybycovalent–ionicmixingalsocorrelateswiththeaverageelectronegativityofthebond1111.InthisrespectwenotethatwhatdeterminestheRECSquantityisnotthesimple

orbitaloverlap,andinfact,theRECSincreasesastheoverlapbecomessmaller55,,1122.Forexample,theorbitaloverlapinH2ismuchlargerthaninF2,

whereasthecovalent–ionicresonanceenergybehavesintheoppositeway.ThisunderscorestherelationshipofRECStotheexchange–repulsiondecrease

inthebondingregionratherthantothesimple'sharingofdensity'asincovalency.

Theexchange–repulsionpressurethatisassociatedwiththelonepairsofelectronegativefragmentsisnottheonlyfactorthatcanpromoteCSbonding.Arecentlyidentifiedadditionalfactor55,,1122,,1133,,1144,,1177wasexpressedinbondsbetweenmetalloidsofgroup14andelectronegativegroups,forexamplealltheSi–F,Si–ClandGe–ClbondsinTTaabbllee11.TheVBcalculationsforthesebondsshowthatthecorrespondingioniccurvefortheMe3Si–Clbond,forexample,

ismuchdeeperthanthatforthecorrespondingMe3C–Clbond1177.Moreover,theioniccurveMe3Si

+Cl-hasatighterminimumthanMe3C+Cl-.Thismeans

thattheMe3Si+ionissmallerthantheMe3C

+ionalongthelineofapproachtothecentralatom(siliconorcarbon),inharmonywiththefactthatthechargeis

completelylocalizedonSiinMe3Si+,whereasitishighlydelocalizedinMe3C

+.Thiscausestheionicandcovalentstructurestobecloseinenergyin

Me3SiCl,thusleadingtoahighRECSquantity,whichisapparentfromTTaabbllee11fortheSi–Clbond1177.

MMaanniiffeessttaattiioonnssooffCCSSbboonnddiinngg

HavingshowntheemergenceofCSbondinganditspromotingfactors,herewefollowwithsomeevidenceforthesignatureofthisbondtypeinthechemicalbehaviour.

EEvviiddeenncceeooffCCSSbboonnddiinnggffrroommeelleeccttrroonn--ddeennssiittyymmeeaassuurreemmeennttss.TheexistenceoftheCSbondfamilywilleventuallybeconsolidatedbyexperimentaldeterminationoftheLaplacianofvariousbonds,asalreadydonefor[1.1.1]propellanederivatives2255,N2O4(ref.4422)andothers

2211.Inthe

meantime,theexistenceoftwodistinctfamiliesalreadyemergesfromelectron-density-differencemaps(measurableexperimentally),whichplotthedifferencebetweentheactualmoleculardensityandthedensityofareferencestatemadefromsphericalatoms( = Mol- Ref),atthesamegeometryas

themolecule.Thesedata4433,,4444,,4455,,4466clearlyshowabond-groupwith >0,whichcoincideswiththeclassicalcovalentbond,andasecondgroupof'no-densitybonds'with <0,whichcoincideswiththeCSbondingfamily.Theexampleof[1.1.1]propellaneshowsthetwobondtypes2255;theC–Cbondsinthewingsarenormalcovalentbondswith >0,whereasthe'inverted'(C–C)has <0.Althoughthedeformationdensitydependsonthedefinitionofthereferenceatomicstate4477,theexampleofpropellanes4433,,4444,,4455,wherethesamemoleculedisplaystwoC–Cbonds,onehavingnegativeandtheotherpositivedeformationdensities,isfreeofthislimitation.

EEvviiddeenncceeffoorrCCSSbboonnddiinnggiinncchheemmiiccaallrreeaaccttiivviittyy.Thefindingsthathalogen-transferreactions(andespeciallyoffluorine)havemuchlargerbarriers(by>20kcalmol-1forX=F)thanthecorrespondinghydrogen-transferprocesses,isassociatedwiththeRECSquantityofthebond

1166.Asweshowed

recently1166,thebarrierdifferencebetweenthetwoseriesfollowsaverysimplerelationship:

NotethatmeasurementofthebarrierdifferenceforthetwoseriesenablesquantificationoftheCSresonanceenergyfromexperimentalbarriers.

RRaarriittyyooffssiilliicceenniiuummiioonnssiinnccoonnddeennsseeddpphhaasseess.AsSi–XbondshavelargeRECSvalues,theirchemicalbehaviourcanbecontrastedwithcarbon,

whichdoesnotgenerallyinvolveCSbonds.Oneofthemanifestationsistherareionicchemistryofsiliconincondensedphases88,comparedwiththeubiquityincarbon.ArecentVBstudyshowed1177thattheMe3Si

+Cl-structureinaqueoussolutionretainsthetightion-pairminimum,andthusmixesstrongly

withthecovalentstructureandacquireslargeRECS.ThislargeRECSisthemajorreasonwhythebondwillnotundergoheterolysisinsolution(butwillprefer

associativeprocesses),andwhyinthesolidstateevenPh3Si–OClO3isacovalentsolid1100bycontrasttothecarbonanalogue,whichhasanNa+Cl--type

latticewithPh3C+andClO4

-ions4488andothers4499.

CChhaarrttiinnggtthheetteerrrriittoorryyooffCCSSbboonnddiinngg

CSbondingoriginatesfromtheequilibriumconditionofthebond,definedbythevirialratio.Itispromotedbytwomainfactors.

First,byexchangerepulsionthatweakensthecovalencyofthebondandinduceslargeRECSvalues.Thisexcessiveexchangerepulsionistypicalto

electronegativeandlone-pair-richatoms,orbondsweakenedbyexchange–repulsionpressure,asthebridgeheadC–Cbondin[1.1.1]propellane1188,andmanyothersmall-ringpropellanes.

Second,fragmentsthatformextremelysmallcations,whichresembleaproton,withallthepositivechargelocatedatthecentralatom,likeinthesiliceniumcation,R3Si

+,willpromoteCSbondingespeciallywithelectronegativeandlone-pair-richatoms55,,1144,,1177.

Withthesepromoters,CSbondingformsadistinctgroupofbondingthattranscendsconsiderationofstaticchargedistribution,andthatpossessesuniquechemicalsignatures.SomeofthesebondsarecollectedinTTaabbllee11.Butthereareothers,forexample, -bonds,indoublyandtriplybondedmolecules1155,,5500,andinmanyhypercoordinatedcompounds(forexample,PCl5,XeFnandsoon)

55.ClearlymanymoreCSbondsarewaitingtobeidentifiedinnew

molecules.

Futuredirectionsaremany.Afruitfuloneishypercoordinationandaggregation.Thus,forexample,thesmallsizeofR3Si+,andheavieranalogues,mean

thattheywilltendtoformhypercoordinatedcompounds;insolution,inthesolidstate5511andeveninthegasphase,wheresomeunusualmoleculeshavebeenreported5522,,5533,andbridged(Si---X---Si)+systems,whichparticipateincatalyticbondexchangereactions5544.Metal–metalbondsinsomebimetalliccomplexescouldwellbeCSbonds,asinM2(formamidinate)4complexes(M=Nb,Mo,Tc,Ru,Rh,Pd)wherelargepositivevaluesof

2 (rc)havebeen

reported5555.Otherdirectionsinvolvethegenerationof[1.1.1]propellaneinwhichtheCH2wingsaresubstitutedbyheteroatomsthatexertexchangerepulsion

pressureontheinvertedC–Cbond,forexample,HN,OandS(ref.1188).Thein-plane -typebondinortho-benzyneisanotherbondthatisaffectedbyexchange–repulsionpressure.Protonationormethylation(byMe+)ofC–NbondsmayconvertthemintoCSbonds5566,afactthatmayconcernDNAbases,andmayhavemechanisticeffects,asintheprotonatedarginineinthemechanismofnitricoxidesynthase5577.Mostbondsunderimmenseexternalpressure5588arelikelytobeCSbonds,andencapsulatedhighlypositiveionswillbeCS-bound5599,,6600.

Thus,CSbondingisnotmerelyanacademicabstraction.AsnewexamplesorexperimentalmanifestationsofCSbondingwillstarttoaccumulateandberecognized,theconceptofCSbondingwillgraduallybeacceptedbythechemicalcommunity,andwillfindmoreapplications.

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60.

InstituteofChemistryandTheLiseMeitner-MinervaCenterforComputationalQuantumChemistry,TheHebrewUniversityofJerusalem,91904,Jerusalem,Israel.

1.

StateKeyLaboratoryofPhysicalChemistryofSolidSurfacesandCollegeofChemistryandChemicalEngineering,XiamenUniversity,Xiamen361005,P.R.China.

2.

LaboratoiredeChimiePhysique,GroupedeChimieThéorique,CNRSUMR8000,UniversitédeParis-Sud,91405OrsayCédex,France.3.

Correspondenceto:SasonShaik11e-mail:ssaassoonn@@yyffaaaatt..cchh..hhuujjii..aacc..iill

Correspondenceto:WeiWu22e-mail:wweeiiwwuu@@xxmmuu..eedduu..ccnn

Correspondenceto:PhilippeC.Hiberty33e-mail:pphhiilliippppee..hhiibbeerrttyy@@llccpp..uu--ppssuudd..ffrr

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