Mathematical physics in theoretical chemistry PDF
Preview Mathematical physics in theoretical chemistry
Mathematical Physics in Theoretical Chemistry Developments in Physical & Theoretical Chemistry Series Editor JamesE.House With the new series Developments in Physical & Theoretical Chemistry, Elsevier introducesacollectionofvolumesthathighlighttimelyandimportantdevelopments inthisinterdisciplinaryfield.Theseriesaimstopresentusefulandtimelyreference works dealing with significant areas of research in which there is rapid growth. Through the contributions of specialists, these volumes will provide essential backgroundonappropriateandrelevanttopicsandprovidesurveysoftheliterature ataleveltobeusefultoadvancedstudentsandresearchers.Inthisway,thevolumes will address the underlying theoretical and experimental background on the topics for researchers entering the topic fields and function as useful reference works of lasting value. A primary goal for the volumes in the series is to provide a strong educational thrust for advanced study in particular fields. Each volume will have an editor who is intimately involved in work constituting the topic of the volume. Although contributions to volumes in the series will include those of established scholars,contributionsfromthosewhoarerisinginprominencewillalsobeincluded. 2018 PhysicalChemistryofGas–LiquidInterfaces JenniferA.FaustandJamesE.House,Editors 2019 MathematicalPhysicsinTheoreticalChemistry S.M.BlinderandJ.E.House,Editors Developments in Physical & Theoretical Chemistry J. E. House, Series Editor Mathematical Physics in Theoretical Chemistry Edited by S. M. Blinder UniversityofMichigan,AnnArbor,MIandWolframResearch, Champaign,IL,USA J. E. House Illinois WesleyanUniversity,Bloomington, IL;andIllinoisState University,Normal,IL,USA Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates ©2019ElsevierInc.Allrightsreserved. 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LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ISBN978-0-12-813651-5 ForinformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:SusanDennis AcquisitionEditor:AnnekaHess EditorialProjectManager:AmyM.Clark ProductionProjectManager:PremKumarKaliamoorthi CoverDesigner:VictoriaPearson TypesetbySPiGlobal,India Contributors S.M.Blinder UniversityofMichigan,AnnArbor,MI,UnitedStates CailaBruzzese DepartmentofChemistry,BrockUniversity,St.Catharines,Ontario,Canada KimberlyJordanBurch Department of Mathematics, Indiana University of Pennsylvania, Indiana, PA,UnitedStates AndrewL.Cooksy Department of Chemistry and Biochemistry, San Diego State University, SanDiego,CA,UnitedStates GuidoFano UniversityofBologna,Bologna,Italy JamesW.Furness DepartmentofPhysicsandEngineeringPhysics,TulaneUniversity,NewOrleans, LA,UnitedStates DavidZ.Goodson Department of Chemistry and Biochemistry, University of Massachusetts Dartmouth,NorthDartmouth,MA,UnitedStates JustinK.Kirkland DepartmentofChemistry,UniversityofTennessee,Knoxville,TN,UnitedStates ErrolLewars DepartmentofChemistry,TrentUniversity,Peterborough,ON,Canada DevinA.Matthews InstituteforComputationalEngineeringandSciences,TheUniversityofTexasat Austin,Austin,TX,UnitedStates EgorOspadov Department of Physics, Brock University, St. Catharines; Department of Chem- istry,TheUniversityofWesternOntario,London,Ontario,Canada StuartM.Rothstein DepartmentofPhysics;DepartmentofChemistry,BrockUniversity,St.Catharines, Ontario,Canada JohnF.Stanton DepartmentofChemistry,UniversityofFlorida,Gainesville,FL,UnitedStates JianweiSun DepartmentofPhysicsandEngineeringPhysics,TulaneUniversity,NewOrleans, LA,UnitedStates xi xii Contributors JacobTownsend DepartmentofChemistry,UniversityofTennessee,Knoxville,TN,UnitedStates IngaS.Ulusoy Department of Chemistry, Michigan State University, East Lansing, MI, UnitedStates KonstantinosD.Vogiatzis DepartmentofChemistry,UniversityofTennessee,Knoxville,TN,UnitedStates AngelaK.Wilson Department of Chemistry, Michigan State University, East Lansing, MI, UnitedStates YuboZhang DepartmentofPhysicsandEngineeringPhysics,TulaneUniversity,NewOrleans, LA,UnitedStates Mathematical physics in theoretical chemistry CONTENTS (i) TheHartree-Fockapproximation(S.M.Blinder) (ii) SlaterandGaussianbasisfunctionsandcomputationofmolecularintegrals (A.K.Wilson) (iii) Post-Hartree-Fockmethods:Configurationinteraction,many-body perturbationtheory,couple-clustertheory(K.D.Vogiatzis) (iv) Density-functionaltheory(J.Sun) (v) Vibrationalenergiesandpartitionfunctions(A.L.Cooksy) (vi) QuantumMonte-Carlo(S.M.Rothstein) (vii) Computationalchemistryonpersonalcomputers(E.G.Lewars) (viii) Chemicalapplicationsofgraphtheory(K.J.Burch) (ix) Singularityanalysisinquantumchemistry(D.Z.Goodson) (x) Diagrammaticmethodsinquantumchemistry(J.F.Stanton) (xi) Quantumchemistryonaquantumcomputer(G.FanoandS.M.Blinder) INTRODUCTION Theoreticalchemistryprovidesasystematicaccountofthelawsgoverningchemical phenomenainmatter.Itappliesphysicsandmathematicstodescribethestructureand interactionofatomsandmolecules,thefundamentalunitsofmatter.Throughtheend of the 19th century, chemistry remained predominantly a descriptive and empirical science.1True,therehadbeendevelopedbythenaconsistentquantitativefoundation based on the notions of atomic and molecular weights, combining proportions, thermodynamicquantities,andthefundamentalideasofmolecularstereochemistry. Chemistrywascertainlyfarmorerationalthanitsancientrootsinalchemybutwas still largely a collection of empirical facts about the behavior of matter. Immanuel Kant,inhisCritiqueofPureReason,claimedthat“inanyspecialdoctrineofnature there can be only as much proper science as there is mathematics therein.”2 This canserveasourphilosophicalrationalizationforemphasizingmathematicalmethods (specificallythefielddesignatedmathematicalphysics)intheoreticalchemistry. 1AveryintriguingaccountofthehistoricaldevelopmentofmodernchemistryisgivenbyMaryJo Nye[1]. 2QuotedintheonlineStanfordEncyclopediaofPhilosophy. xiii xiv Mathematical physics in theoretical chemistry Thedevelopmentsofphysicsinthe20thcenturymadeallofchemistryexplicable, in principle, by quantum mechanics. As summarized by Dirac: “The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble” [2]. By its very nature, quantum mechanics is mathematical physics and therebyweestablishtheconnectionwhichisthethemeofthisvolume.However,the loophole noted by Dirac, the existence of chemical problems too mathematically complex to be solved exactly, justifies the survival of parts of chemistry as an empiricalscience.Inthiscategoryaresemiempiricalconceptsofchemicalbonding and reactivity. This has also led to computational models promoting rational drug design. These have also stimulated applications of other branches of mathematics, forexample,informationtheoryandgraphtheoryappliedtothedefinitionofvarious chemicalindices. The primary objective of theoretical chemistry is to provide a coherent account for the structure and properties of atomic and molecular systems. Techniques adaptedfrommathematicsandtheoreticalphysicsareappliedinattemptstoexplain and correlate the structures and dynamics of chemical systems. In view of the immense complexity of chemical systems, theoretical chemistry, in contrast to theoreticalphysics,generallyusesmoreapproximatemathematicaltechniques,often supplementedbyempiricalorsemiempiricalmethods. This volume begins with an introduction to the quantum theory for atoms and smallmolecules, expanding upon the originalapplications of mathematical physics in chemistry. This field is now largely subsumed within a subdiscipline known as computationalchemistry.Chapter1beginswithanintroductiontotheHartree-Fock method,whichistheconceptualfoundationforcomputationalchemistry.Chapter2 discussesthebasisfunctionsemployedinthesecomputations,nowlargelydominated byGaussianfunctions.Chapter3describessomepost-Hartree-Fockmethods,which seektoattain“chemicalaccuracy”inatomicandmolecularcomputations,inpartic- ular, configuration interaction, many-body perturbation theory, and coupled-cluster theory. Chapter 10 discusses diagrammatic techniques borrowed from theoretical physics,whichcanenhancetheefficiencyofcomputations.Chapter7isanaccount of the development of personal computers and their applications to computational chemistry. For larger molecules and condensed matter, alternative approaches, including density functional theory (Chapter 4) and quantum Monte-Carlo (Chapter 6), are becoming popular computational methods. Some additional topics covered in this volumearevibrationalpartitionfunctions(Chapter5),singularityanalysisofpertur- bationtheories(Chapter9),andchemicalapplicationsofgraphtheory(Chapter8). Finally,Chapter11introducestheprinciplesofthequantumcomputer,whichhas the speculative possibility of exponential enhancement of computational power for theoreticalchemistry,aswellasmanyotherapplications. Mathematical physics in theoretical chemistry xv REFERENCES [1] Nye MJ. From chemical philosophy to theoretical chemistry. Berkeley: University of CaliforniaPress;1993. [2] Dirac PAM. Quantum mechanics of many-electron systems. Proc R Soc A (Lond) 1929;123:714–33.
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