Chemical Reactions: Basic Theory and Computing PDF
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Theoretical Chemistry and Computational Modelling Antonio Laganà Gregory A. Parker Chemical Reactions Basic Theory and Computing Theoretical Chemistry and Computational Modelling Modern Chemistry is unthinkable without the achievements of Theoretical and Computational Chemistry. As a matter of fact, these disciplines are now a mandatory tool for the molecular sciencesandtheywillundoubtedlymarkthenewerathatliesaheadofus.Tothisend,in2005, expertsfromseveralEuropeanuniversitiesjoinedforcesunderthecoordinationoftheUniversidad Autónoma de Madrid, to launch the European Masters Course on Theoretical Chemistry and ComputationalModeling(TCCM).Theaimofthiscourseistodevelopscientistswhoareableto address a wide range of problems in modern chemical, physical, and biological sciences via a combinationoftheoreticalandcomputationaltools.Thebookseries,TheoreticalChemistryand ComputationalModeling,hasbeendesignedbytheeditorialboardtofurtherfacilitatethetraining andformationofnewgenerationsofcomputationalandtheoreticalchemists. Prof.ManuelAlcami Prof.OtiliaMo DepartamentodeQuímica DepartamentodeQuímica FacultaddeCiencias,Módulo13 FacultaddeCiencias,Módulo13 UniversidadAutónomadeMadrid UniversidadAutónomadeMadrid 28049Madrid,Spain 28049Madrid,Spain Prof.RiaBroer Prof.IgnacioNebot TheoreticalChemistry InstitutdeCiènciaMolecular ZernikeInstituteforAdvancedMaterials ParcCientíficdelaUniversitatdeValència RijksuniversiteitGroningen CatedráticoJoséBeltránMartínez,no.2 Nijenborgh4 46980Paterna(Valencia),Spain 9747AGGroningen,TheNetherlands Prof.MinhThoNguyen Dr.MonicaCalatayud DepartementScheikunde LaboratoiredeChimieThéorique KatholiekeUniversiteitLeuven UniversitéPierreetMarieCurie,Paris06 Celestijnenlaan200F 4placeJussieu 3001Leuven,Belgium 75252ParisCedex05,France Prof.MaurizioPersico Prof.ArnoutCeulemans DipartimentodiChimicaeChimica DepartementScheikunde Industriale KatholiekeUniversiteitLeuven UniversitàdiPisa Celestijnenlaan200F ViaRisorgimento35 3001Leuven,Belgium 56126Pisa,Italy Prof.AntonioLaganà Prof.MariaJoaoRamos DipartimentodiChimica ChemistryDepartment UniversitàdegliStudidiPerugia UniversidadedoPorto viaElcediSotto8 RuadoCampoAlegre,687 06123Perugia,Italy 4169-007Porto,Portugal Prof.ColinMarsden Prof.ManuelYáñez LaboratoiredeChimie DepartamentodeQuímica etPhysiqueQuantiques FacultaddeCiencias,Módulo13 UniversitéPaulSabatier,Toulouse3 UniversidadAutónomadeMadrid 118routedeNarbonne 28049Madrid,Spain 31062ToulouseCedex09,France More information about this series at http://www.springer.com/series/10635 à Antonio Lagan Gregory A. Parker (cid:129) Chemical Reactions Basic Theory and Computing 123 AntonioLaganà Gregory A.Parker Dipartimento di Chimica,Biologia e Homer L.Dodge Department of Physics Biotecnologie andAstronomy Universitàdegli Studi diPerugia University of Oklahoma Perugia Norman, OK Italy USA ISSN 2214-4714 ISSN 2214-4722 (electronic) Theoretical Chemistry andComputational Modelling ISBN978-3-319-62355-9 ISBN978-3-319-62356-6 (eBook) https://doi.org/10.1007/978-3-319-62356-6 LibraryofCongressControlNumber:2017947726 ©SpringerInternationalPublishingAG2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland To Giovanna and Jeanene Preface Energy and mass transfers in chemical processes are an intricate land of adventure inwhichatomsandmoleculescompeteandcollaborateondifferentpathsinaway that challenges intellectual abilities when trying to rationalize unexpected outcomes. This book has been designed to help the students of the European Erasmus MundusMasterin“TheoreticalChemistryandComputationalModeling”(TCCM) to familiarize with both theoretical methods and compute techniques useful to handle the microscopic nature of chemical processes. Because of this, the level of references,pseudocodes,andtexthasbeenkeptassimpleandasgeneralaspossible by leveraging on the experience gained by teaching the subject for years at the home University and at the TCCM intensive course. We have also tried to avoid misprints and inaccuracies through repeated cross checks. Despite that, the book mightnotbefreeoferrorsandweaskthereadersthefavoroflettingusknow(our emails are given in the front page) about possible improvements. In the book, the reader is driven to disentangle elementary events out of the kinetics of complex systems in which reactive and nonreactive processes combine and compete in different ways depending on the interactions and momenta of the speciesinvolved.Outofsuchcomplexity,wegraduallysingleoutanddealwiththe key features (by leveraging preferentially on elementary gas phase processes) of two-, three-, four-, and many-body collisions. Then, complexity is regained to extend the treatment to large systems by introducing some approximations. Thebookstartsinchapteronebyconsideringthemodelingofratecoefficientsin termsofthetransitionstate(TS)approach.Fromtheanalysisoftheweaknessofthe TS model (useful for a phenomenological systematization of experimental data although useless for predictions), the efficiency of chemical processes is rational- ized in terms of collisions of two structureless bodies using classical mechanics (inwhichatomsareconsideredasmasspoints)andsimplemodelinteractions(like pure Coulomb attraction and/or repulsion, hard sphere, mixed attraction at long range plus repulsion at short range (Sutherland, Morse, and Lennard-Jones)). Classical mechanics computational machinery, relying on both analytical and numerical procedures tailored to solve related Newton, Hamilton, and Lagrange vii viii Preface equations, are analyzed in this chapter by associating a set of trajectories starting fromdifferentinitialconditionstothefateofthecollisionprocess(liketheangleof deflection) and working out the value of quantities of experimental relevance (like cross sections and rate coefficients). Theobservedfailureoftheclassicalmechanicstreatmenttoreproducesomekey features of measured data (like the elastic differential cross section in two body collisions) is traced back to the quantum nature of molecular processes and to the related uncertainty principle. This drives the reader in chapter two to the use of quantum techniques for evaluating the properties of both bound and elastically scattered atom–atom systems. Related quantum treatments are then discussed and analytical solutions are first worked out for some prototype cases to the end of guiding the reader to use of special functions. Then, some basic numerical tech- niques and related pseudocodes useful for integrating the corresponding Schrödingerequationforgenericatom–atominteractions,areillustratedandapplied in order to compare related results with corresponding classical ones. At this point, the reader is ready to abandon the constraint that atoms are structurelessbodiesanddealinchapterthreewiththeelectronicstructureofatoms and molecules. To move in this direction, we discuss some techniques used for carryingoutabinitiocalculationsofelectronicenergiesanddiscusstheadoptionof bothoneelectronfunctionsandvariationalprinciple.Alongthisline,theelectronic structure of polyatomic molecules, molecular orbitals, Hartree–Fock, and self-consistent field (SCF) molecular orbital (MO) models are discussed in some detail.Then,weendupbyillustratingpostHartree–Fockconfigurationinteraction, multiconfiguration self-consistent fields, and perturbation methods for the calcu- lation of electronic energies and other molecular properties. To better deal with largersystems,mentionismadealsotosomeempiricalcorrectionssimplifyingthe electronicstructurecalculationsforlargesetsofatomsaswellasforalargenumber of molecular geometries of the same molecule and a large number of molecules. Finally, the techniques used to shape potential energy global and local functional formulations to fit the distinctive features of computed ab initio values are dis- cussed with the specific intention of attributing to related parameters a physical correspondence. Next, in chapter four, concepts and techniques to be used for carrying out dynamical calculations of reactive systems starting from atom–diatom elementary processesareconsidered.Tothisend,themotionofnucleiisdisentangledfromthat of the electrons by introducing the Born–Oppenheimer approximation. Then, for atom–diatom systems, different sets of coordinates are discussed for singling out those better suited for representing the interaction and for integrating dynamics equations. For the latter, different choices are discussed for classical and quantum treatments as well as for time-dependent and time-independent techniques. The integration of dynamics equations allows to figure out the typical features of the atomistic phenomenology of atom–diatom systems such as the effect of a different allocation of energy to the various degrees offreedom in promoting reactivity, the importance of providing an accurate representation ofthe potential energy surface, themerits anddemerits ofadopting reduced dimensionalityapproaches,ordealing Preface ix quantally with some degrees of freedom (while handling classically the others). Then, the discussion is extended also to the usefulness of singling out the periodic orbits of dynamical systems for rationalizing their reactive behavior (including the categorization of transition state effects)and designing proper statistical treatments for long living processes. Atthispoint,theroadispavedforconsideringinchapterfivesystemsofhigher complexity starting with the four and more atom ones and ending with those for which the atomistic granularity is difficult to manage with sufficient accuracy. The introductionofadditionaldegreesoffreedom,infact,impactsonthestructureand, accordingly, on the formulation of the potential. For this reason, the definition of the quantities to be computed, the computational techniques adopted and the observables to be simulated are also reconsidered. The progress made in this direction is strictly related to the evolution of compute platforms and the level of concurrency and distribution achieved. This has led to a radical change of the organizationofmolecularsciencestowardservice-orientedprocedures,competitive collaboration, data reuse, and openness. Accordingly,thebookisarticulatedasfollows:inthefirstchapter,wedealwith theclassicalmechanics conceptsandtheirapplicationtothetwo-body problem;in the second chapter, we deal with the corresponding (two body) quantum mechanical concepts and treatments; in the third chapter, we move toward the description polyelectronic and polyatomic systems, the calculations of related eigenenergies, and the construction of potential energy surfaces connecting the differentarrangementsofthemolecularsystem;inthefourthchapter,wetacklethe problem of describing the atom–diatom reactive systems and properties and illus- trateaswellthedifferentmethodsforrationalizingrelatedmechanisms;inthefifth chapter, we move toward more complex (up to many atoms and many molecules) systemsandfocusonsynergisticmultiscalecompetitivecollaborationinthecontext ofrecentprogressmadeindistributedcomputing.Eventually,particularimportance isalsogiventothepresentevolutiontowardOpenSciencebyreferringtoaHorizon 2020 funding proposal for establishing a Molecular science European research infrastructure. Perugia, Italy Antonio Laganà Norman, USA Gregory A. Parker Acknowledgements ALthankshisparents(VincenzoandGiuseppina)fortheirsupporttohiseducation even during the difficult times of thepost-Second World War of themid-twentieth century,hiswifeGiovannaforherlovingunderstandingofhisdedicationtoscience and education, his son Leonardo for his commitment to both work and family, his relatives and friends for their love. AL also thanks the large number of colleagues he worked with (see J. Phys. Chem 120 (27) 4595 (2016)). The book itself is coauthored and is the result of variouslong-lastingcollaborations.Mostoftheconceptsillustratedinitwerebetter understood by him thanks tosuch collaborations. Particular help for this book was given by Ernesto Garcia and Stefano Crocchianti not only for producing a large fraction of the jointly published numerical results used as illustrative examples in the book but also for adapting them as figures of the book and by Leonardo Belpassiforrevisingtheelectronicstructuresection.Importantforthewritingofthe book was also the continuous interaction with the students of the Theoretical Chemistry and Computational Modeling (TCCM) Erasmus Mundus Master during the classes on “Mechanisms and Dynamics of Reactive Systems.” GAP thanks his two wonderful parents (Byron and Edna) who taught him the importanceofaneducation.Hethankshisdedicatedwife(Jeanene)andtheireight wonderful children (Steven, Michael, Sheryl, Jennifer, Tamara, Marilyn, William, and Christopher) for their love, patience and example. GAP thanks his Ph.D. advisor, lifelong mentor, and friend Professor Russell T Pack for many fruitful collaborations. GAP also thanks his postdoctoral advisors ProfessorsAronKuppermannandJohnC.Lightfortheirmentorshipandguidance. This book is part of the series that the teachers of the TCCM Master have planned to publish with Springer. xi
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