Topological Approaches to the Chemical Bond PDF
Preview Topological Approaches to the Chemical Bond
Theoretical Chemistry and Computational Modelling EditorialBoard ManuelAlcami,DepartmentofChemistry,UniversidadAutónomadeMadrid, Madrid,Madrid,Spain RamónSayós,DepartamentdeCiènciadeMaterialsiQuímicaFísica,Universidad deBarcelona(UB),Barcelona,Spain IñakiTuñón,DepartamentodeQuímicaFísica,UniversidaddeValencia,Burjassot -València,Spain StefanoEvangelisti,LaboratoiredeChimieetPhysiqueQuantiques,Université PaulSabatier(ToulouseIII),Toulouse,France NicolasSuaud,LaboratoiredeChimieetPhysiqueQuantiques,IRSAMC, UniversitéPaulSabatier,Toulouse,France MonicaCalatayud,LaboratoiredeChimieThéorique,SorbonneUniversité,Paris Cedex05,France NoeliaFaginasLago,DipartimentodiChimica,BiologiaeBiotecnologie, UniversityofPerugia,Perugia,Italy MauroStener ,DepartmentofChemicalandPharmaceuticalSciences,University ofTrieste,Trieste,Italy ShirinFaraji,DepartmentofTheoretical&ComputationalChemistry, RijksuniversiteitGroningen,Groningen,TheNetherlands DanielEscudero,DepartmentofChemistry,KULeuven,Leuven,Belgium JeremyHarvey,DepartmentofChemistry,KULeuven,Leuven,Belgium MinhThoNguyen,DepartmentofChemistry,KULeuven,Leuven,Belgium Modern Chemistry is unthinkable without the achievements of Theoretical and ComputationalChemistry.Asamatteroffact,thesedisciplinesarenowamandatory tool for the molecular sciences and they will undoubtedly mark the new era that lies ahead of us. To this end, in 2005, experts from several European universities joined forces under the coordination of the Universidad Autónoma de Madrid, to launchtheEuropeanMastersCourseonTheoreticalChemistryandComputational Modeling(TCCM).ThiscourseisrecognizedbytheECTNA(EuropeanChemistry Thematic Network Association) as a Euromaster; it has been part of the Erasmus Mundus Masters Program of the EACEA (European Education, Audiovisual and CultureAgency)since2010.Theaimofthiscourseistodevelopscientistswhoare abletoaddressawiderangeofproblemsinmodernchemical,physical,andbiolog- ical sciences via a combination of theoretical and computational tools. The book series, Theoretical Chemistry and Computational Modeling, has been designed by theeditorialboardtofurtherfacilitatethetrainingandformationofnewgenerations ofcomputationalandtheoreticalchemists. · Ángel Martín Pendás Julia Contreras-García Topological Approaches to the Chemical Bond ÁngelMartínPendás JuliaContreras-García DepartamentodeQuímicaFísicay LaboratoiredeChimieThéorique Analítica SorbonneUniversité UniversidaddeOviedo Paris,France Oviedo,Spain ISSN 2214-4714 ISSN 2214-4722 (electronic) TheoreticalChemistryandComputationalModelling ISBN 978-3-031-13665-8 ISBN 978-3-031-13666-5 (eBook) https://doi.org/10.1007/978-3-031-13666-5 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Cuandonoentiendasunproblema, disminuyesudimensión. EltrabajoenlostiemposdelCOVID19 Foreword WithinthisseriesdedicatedtoTheoreticalChemistryandComputationalModelling (TCCM), the subject developed in this book is of special relevance with regards preciselytocomputationalmodeling,sincethesimulationoftherealworldthrough the use of quantum-chemical methods is unavoidably based on the mathematical itemthatdescribesthatreality,thatis,onthewavefunction.WhentheSchrödinger equationforanychemicalsystem,(cid:2)Hψ = Eψ,issolved,theenergyofthesystem andthewavefunctionthatdescribesit,areobtainedsimultaneously.Theproblem, however, is that the Schrödinger equation can only be solved exactly in very few situations,whichimpliesthatforalmostthetotallyofthesystemswewishtodescribe, bothenergyandwavefunctionareapproximateentitiesThismeansthat,althoughin (cid:2) mostcaseswhentheHamiltonian, H,intheSchrödingerequationistheexactone, thereisnowayofobtainingtheexactwavefunctionofthesystemtobedescribed, andthereforeneithertheexactenergycanbeevaluated.Butitispreciselythewave functiontheentitythatallowsusto“see”,understandandinterpretthepropertiesof thesystem,simplybecauseaccordingtooneofthepostulatesofquantummechanics, although no physical meaning can be associated with the wave function, such a physical meaning can be ascribed to its square, admitting that the square of the wavefunctionhasaprobabilisticinterpretation.Thus,ifonewishestounderstand the properties of the particles, nuclei and electrons ensemble, that make up any chemical system, one must analyze the properties of a mathematical function of manyparticles,whichisthesquareofthewavefunction.Theconsequencesofthis assertionareobvious,sothatinquantummodelingthedifferentwaystowithdraw useful information from the square of the wave function become crucial to obtain a precise view, or at least as precise as possible, of the particles distribution and, consequently,ofthepropertiesofthesystemthatwearetryingtomodel,andthisis preciselytheobjectiveofthebookyouhaveinyourhands,toprovideatimelyand completeoverviewofthedifferentformalismsabletogetusefulinformationfrom thewavefunctionobtainedbysolvingtheSchrödingerequation. Letmeaddthatthemethodologicalcompilationthatisthecontentsofthisbook itisnoteasilyfound,atpresent,inotherpublicationsinthisarea.Here,youwillbe vii viii Foreword abletofollowrigorousdeductionsandexplanationsofthedifferentmathematicaland physicalconceptsbehindasignificantlylargevarietyofthemethodologiesnowadays available,toanalyzeawavefunction,specificallyadaptedforpostgraduatestudents. Onecanconsiderthatthestorybeganinthefiftiesofthepastcentury,whenprof- itingthatintheframeworkoftheBorn–Oppenheimerapproximation,thesquareof thewavefunctionprovidesaprobabilisticdescriptionofthedistributionoftheelec- trons,thefirstmethodsabletocalculatetheprobabilityoffindingelectronsassociated with the different nuclei in the physical space were developed. These formalisms, usuallyknownasPopulationAnalyses,werethefirstattempttounderstandtherules thatgovernthepolaritywithinthedifferentchemicalentities,andtoformulaterules abletounderstandthevaluesofmultipoles(dipoles,quadrupoles,octuples…)within therealmofmolecularchemistry. However,wecannotforgetthat,afterall,theinformationtobeobtainedisasso- ciatedwithamathematicalfunctionthat,asmentionedintheIntroductiondwellsin Hilbert,ratherthaninthephysicalspace.Theconsequenceisthatthemethodology tobeusedtoobtaintheinformationspeaksalanguageverydifferentfromthatused by chemists in their everyday activity, simply because molecules live in the phys- icalspace,butassaidabovethefunctionthatprovidesthatinformationdwellsina Hilbertspace.Thisisoneofthevirtuesofthisbook,toleadusbythehand,without losingthenecessarymathematicalrigorinthedescriptionofthemethodologytobe used,toadeepunderstandingandclearcomprehensionofthepropertiesofatoms, molecules, bonds, non-covalent interactions and other endless “real” world facts. From my personal viewpoint, a paradigmatic example of this virtue would be, for instance,thedeductioninChap.2ofMorse’sequalitythatestablishestherelation- ship between the number of cage points, ring points, bond points and the number ofnucleiforanychemicalsystem;buttherearemanymoreallalongthefollowing chapters. Theorganizationofthebook,ontheotherhand,isperfecttoachievethisgoal, startingwiththeIntroductioninwhich,itismadecleartothereaderthattheanal- ysis of the electron density allows to obtain a very rich information contained in the wavefunction. An introductory chapter on topological spaces, including scalar fields and some very interesting advanced material, such as the section devoted to topologicalinvariants,isindeedessentialtounderstandcorrectlytheanalysisofthe electrondensity,whichispreciselyascalarfieldwhosetopologicalcharacteristics areofaparamountimportancetoachieveasoundandcompleteviewofaconcept centraltochemistry:thechemicalbond.Inthissensethesectiondedicatedtotopo- logicalinvariantsconstitutesanoveltythatisdifficulttofindcompletelydeveloped inpreviouspublications,whichthroughtheanalysisofthecriticalpointsofadynam- ical systems provides a perfect background to understand the basis of the QTAIM (QuantumTheoryofAtomsinMolecules)developedinthefollowingchapter,and thatculminateswiththedeductionofMorse’sequalityImentionedabove. Very interesting isthe presentation of chemical reality as afascinating game in whichboth,localizationanddelocalizationoftheelectrondensity,playfundamental roles, and how they are connected with other pioneering ideas as, for instance, the theory of loges of R. Daudel, the link between localization criteria and the Foreword ix formationofelectronpairs,theequivalencebetweenhole-localizationandelectron- localization, the usefulness of the localization and delocalization indexes, or how theseeffectscharacterizewell-knownchemicalconcepts,amongthemtheinductive andthemesomericeffects,orwhyratheroldmodels,suchastheBerlin’sregions, arerecoveredwhenmanyofthesenewformalismsareapplied. Manypeople,amongthemmanychemists,arecompelledtothinkthationicand covalent bonding are the fundamental necessary concepts to rationalize the whole chemical world, and the analysis of chemical bonding inthis book is really a nice and complete piece of work, but in this book emphasis is made on the fact that nowadays is more and more evident that it is impossible to understand chemical reality ignoring the non-covalent interactions. However, non-covalent interactions alwaysrepresentachallengebecause,bynature,theyareweakandthereforevery difficulttobeadequatelyandaccuratelydescribedbytheory.Theyareforsureessen- tialtounderstandmanybiochemicalphenomena,amongotherreasonsbecausethey are behind chemical recognition and molecular assembly; but more recently they were also found to play important roles in material science and crystals, as well asinatmosphericchemistryandastrochemistry.Anotherrichnessofthebookyou have in your hands is that it explores advanced methodology for the analysis of non-covalentinteractionswhichcannotbefoundinotherbooksontheoreticaland computational chemistry. Indeed, some of the approaches described here are very recentcontributionsinthefield.TothisgroupbelongmethodssuchastheLocalized OrbitalLocator(LOL)formulatedintheyear2000,theElectronLocalizationIndi- cator(ELI)proposedfouryearslater,theElectronPairLocalizationFunction(EPLF) firstdefinedin2004,butmodifiedin2011tomakeitanalyticallycomputablewith standard wavefunctions, obtained with both DFT or ab initio methods, the Local- ized Electron Detector (LED) initially proposed in 2010, or the Density Overlap Regions Indicator (DORI) formulated in 2014; but the book also presents the first successfulattemptstowelldescribeandclassifyintermolecularinteractionsthrough the use of the Quantum Theory of Atoms in Molecules (QTAIM), the Electron Localization Function (ELF) and the Non-Covalent Interactions (NCI) formalism, inwhosedevelopment,oneoftheauthorsofthisbook(J.C.-G.)hadanimportant role. To complete this perspective, the authors were able to describe in detail how theseformalismschangetheperspectiveofmodernchemistryusingrepresentative casesofweakinteractionssuchashydrogenbonds,thecoordinationofbiomolecules aroundmetalcenters,stericrepulsionsorvanderWaalsinteractions. AlthoughQTAIMhasbeen,Iwouldsay,heavilyusedbytheoreticalandcompu- tationalchemistsalongthelasttwodecadesofthelastcenturyandalongthefirsttwo decadesofthepresentoneand,thereforeitcouldbeconsidereda“wellknown”tool inthisdomain,thepresentationofsuchaformalisminthisbookisoriginalindeed and very rigorous. Many readers perhaps are aware that QTAIM theory is related withthetopologicalanalysisoftheelectrondensity,ρ,ofamolecularsystem,but perhaps notmany people isconscious that ρ isnotatrulydifferentiable field,due tothecuspsofthisfunctionatthepositionofthenuclei,whichinprincipleshould be a serious problem when trying to analyze its topology. Details like this, which are currently omitted in other analyses, make this work particularly attractive and x Foreword rigorous. Beautiful are also the illustrations used to explain the link between the chemicalconceptofbondandthe(3,−1)criticalpointsofthedensity,andtheway inwhichthemoleculargraphs,whichareveryusefulcomponentsofthetopological analysisofρarebuiltup.Veryimportantly,however,theauthorsalsowarnthereader aboutthecasesinwhichthemoleculargraphdoesnotnecessarilycoincidewiththe chemicalgraph,indicatingalsothatsituationmayeasilyappearwhendealingwith molecularstructuresoutsideequilibrium.Alongthisline,itisalsoveryinteresting thedistinction,outlinedbytheauthorsfollowingthesuggestionsofProf.PaulPope- lier,anauthorityinthisfield,betweenbondpath,bondinteractionlineandtheplain chemicalconceptofbond.Itisalsoacharmingnoveltytheparallelismestablished, inoneofthesectionsofthesamechapter,ofthefluxoftheelectrondensitywiththe flux of an incompressible fluid. No less interesting is the discussion of relativistic effectsinthisformalism,oritsextensiontothedescriptionofthetimeevolutionof open quantum subsystems. All this background will allow in subsequent sections todiscussconceptslikemomentumdensityanforcedensitythat,onlyinthisbook, areanalyzedindeepshowingthattheyconstitutethefundamentalideasofwhatis nowadaysknownasquantumfielddynamics. Something similar can be said as far as the chapter devoted to the ELF (Elec- tron Localization Function) is concerned, in the sense that the authors provide the reader beautiful arguments justifying the model, that are not easy to find in other presentationsofthetheory,playingwiththeintrinsicinteractionsbetweenfermions and the symmetry requirements the wavefunction that represent them must fulfill, oraddressingquestionslike‘ifelectronsaredelocalized,whydoweobserveLewis pairs?’tobuildabridgebetweenthistheoreticalschemeandtheclassicalideasof Lewis and Linnet, and the fundamental role of the spin concept. As a matter of fact,tobehonestImustsaythatthehistoricalintroductiontothismethodologyisa wonderfulpieceofwork. Anotherimportantfeatureofthisbookconcerningthetopicofnon-covalentinter- actions is the section dedicated to very recent developments aiming at providing a quantification of the formalisms normally used to analyze them. In general the differentmethodsmentionedabove,inthispreface,providedifferentwaystolookat theelectronredistributionsassociatedwiththeappearanceofnon-covalentinterac- tions,butstillitisachallengetoestablishaquantitativerelationshipbetweenthem andtheenergeticsoftheinteraction.Asectionofthebookaddressesthisimportant question, even if this quantification remains still limited. It is also remarkable the sectiondevotedtotheuseofNCIformalismstoanalyzenon-covalentinteractionsby revealingelectronlocalizationthroughtherelationshipbetweenNCIandthekinetic energydensity.Theexamplesprovidedtoillustratethispointarereallybeautiful. The last section of the book dedicated to applications was carefully designed, tryingtopresentawidescopeoffieldsinwhichtheuseofthemethodologydescribed intheprevioussixchaptersmaybecomeanalmostmandatorytooltowellunderstand manyfeaturesofthesystemsunderscrutiny.OneimportantaddedvalueofChap.7, thefirstchapterofthissection,wastheabilityoftheauthorstoinclude,amongthe different examples chosen to illustrate the potentiality of these theoretical tools to helpintheunderstandingofthestructure,bonding,reactivityandagreatvarietyof
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