Table Of Content

Computational Chemistry . Errol G. Lewars Computational Chemistry Introduction to the Theory and Applications of Molecular and Quantum Mechanics Second Edition Prof.ErrolG.Lewars TrentUniversity Dept.Chemistry WestBankDrive1600 K9J7B8PeterboroughOntario Canada [email protected] ISBN978-90-481-3860-9 e-ISBN978-90-481-3862-3 DOI10.1007/978-90-481-3862-3 SpringerDordrechtHeidelbergLondonNewYork LibraryofCongressControlNumber:2010938715 #SpringerScience BusinessMediaB.V.2011 Nopartofthisworkþmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyany means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurpose ofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework. Coverdesign:KuenkelLopkaGmbH Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) ToAnneandJohn, whoknowwhattheircontributionswere . Preface Everyattempttoemploymathematicalmethodsinthestudyofchemicalquestions mustbeconsideredprofoundlyirrationalandcontrarytothespiritofchemistry.If mathematical analysis should ever hold a prominent place in chemistry – an aberration which is happily almost impossible – it would occasion a rapid and widespreaddegenerationofthatscience. Augustus Compte, French philosopher, 1798–1857; in Philosophie Positive, 1830. Adissentingview: The more progress the physical sciences make, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge the degree of perfection to which a science has arrived by the facilitytowhichitmaybesubmittedtocalculation. AdolpheQuetelet,Frenchastronomer,mathematician,statistician,andsociolo- gist,1796–1874,writingin1828. Thissecondeditiondiffersfromthefirstintheseways: 1. Thetypographicalerrorsthatwerefoundinthefirsteditionhavebeen(Ihope) corrected. 2. Those equations that should be memorized are marked by an asterisk, for example*(2.1). 3. Sentencesandparagraphshavefrequentlybeenalteredtoclarifyanexplanation. 4. Thebiographicalfootnoteshavebeenupdatedasnecessary. 5. Significantdevelopmentssince2003,uptonearmid-2010,havebeenaddedand referencedintherelevantplaces. 6. Some topics notin first edition, solvation effects, how to do CASSCF calcula- tions,andtransitionelements,havebeenadded. AsmightbeinferredfromthewordIntroduction,thepurposeofthisbookisto teachthebasicsofthecoreconceptsandmethodsofcomputationalchemistry.This is a textbook, and no attempt has been made to please every reviewer by dealing with esoteric “advanced” topics. Some fundamental concepts are the idea of a vii viii Preface potentialenergysurface,themechanicalpictureofamoleculeasusedinmolecular mechanics, and the Schro¨dinger equation and its elegant taming with matrix methodstogiveenergylevelsandmolecularorbitals.Alltheneededmatrixalgebra isexplainedbeforeitisused.Thefundamentalmethodsofcomputationalchemistry aremolecularmechanics,abinitio,semiempirical,anddensityfunctionalmethods. MoleculardynamicsandMonteCarlomethodsareonlymentioned;whiletheseare important,theyutilizefundamentalconceptsandmethodstreatedhere.Iwrotethe book because there seemed to be no text quite right for an introductory course in computational chemistry suitablefor a fairly general chemical audience;I hope it will be useful to anyone who wants to learn enough about the subject to start readingtheliteratureandtostartdoingcomputationalchemistry.Thereareexcel- lent books on the field, but evidently none that seeks to familiarize the general studentofchemistrywithcomputationalchemistryinthesamesensethatstandard textbooksofthosesubjectsmakeorganicorphysicalchemistryaccessible.Tothat end the mathematics has been held on a leash; no attempt is made to prove that molecular orbitals are vectors in Hilbert space, or that a finite-dimensional inner- product space must have an orthonormal basis, and the only sections that the nonspecialistmayjustifiablyviewwithsometrepidationarethe(outlined)deriva- tionoftheHartree–FockandKohn–Shamequations.Thesesectionsshouldberead, ifonlytogettheflavoroftheprocedures,butshouldnotstopanyonefromgetting onwiththerestofthebook. Computational chemistry has become a tool used in much the same spirit as infraredorNMRspectroscopy,andtouseitsensiblyitisnomorenecessarytobe abletowriteyourownprogramsthanthefruitfuluseofinfraredorNMRspectros- copyrequiresyoutobeabletoabletobuildyourownspectrometer.Ihavetriedto giveenoughtheorytoprovideareasonablygoodideaofhowtheprogramswork.In this regard, the concept of constructing and diagonalizing a Fock matrix is intro- duced early, and there is little talk of secular determinants (except for historical reasons in connection with the simple Hu¨ckel method). Many results of actual computations, most of them specifically for this book, are given. Almost all the assertions in these pages are accompanied by literature references, which should makethetextusefultoresearcherswhoneedtotrackdownmethodsorresults,and students(i.e.anyonewhoisstilllearninganything)whowishtodelvedeeper.The materialshouldbesuitableforseniorundergraduates,graduatestudents,andnovice researchers incomputational chemistry. Aknowledgeofthe shapes ofmolecules, covalentandionicbonds,spectroscopy,andsomefamiliaritywiththermodynamics at about the level provided by second- or third-year undergraduate courses is assumed. Some readers may wish to review basic concepts from physical and organicchemistry. Thereader,then,shouldbeabletoacquirethebasictheoryandafairideaofthe kindsofresults tobeobtainedfromthe common computationalchemistrytechni- ques.Youwilllearnhowonecancalculatethegeometryofamolecule,itsIRand UV spectra and its thermodynamic and kinetic stability, and other information neededtomakeaplausibleguessatitschemistry. Preface ix Computationalchemistryisaccessible.Hardwarehasbecomefarcheaperthanit was even a few years ago, and powerful programs previously available only for expensiveworkstationshavebeenadaptedtorunonrelativelyinexpensivepersonal computers. The actual use of a program is best explained by its manuals and by books written for a specific program, and the actual directions for setting up the various computations are not given here. Information on various programs is provided in Chapter 9. Read the book, get some programs and go out and do computationalchemistry. You may make mistakes, but they are unlikely to put you in the same kind of dangerthatamistakeinawetlabmight. Itisapleasureacknowledgethehelpof: Professor Imre Csizmadia of the University of Toronto, who gave unstintingly of histimeandexperience, Thestudentsinmycomputationalandothercourses, ThegenerousandknowledgeablepeoplewhosubscribetoCCL,thecomputational chemistry list, an exceedingly helpful forum anyone seriously interested in the subject, MyeditorforthefirsteditionatKluwer,DrEmmaRoberts,whowasalwaysmost helpfulandencouraging, ProfessorRoaldHoffmannofCornellUniversity,forhisinsightandknowledgeon sometimesarcanematters, Professor Joel Liebman of the University of Maryland, Baltimore County for stimulatingdiscussions, ProfessorMatthewThompsonofTrentUniversity,forstimulatingdiscussions ThestaffatSpringerforthesecondedition:DrSoniaOjowhohelpedmetoinitiate theproject,andMrsClaudiaCulieratwhoassumedthetaskofcontinuingtoassist meinthisventureandwasalwaysextremelyhelpful. No doubt some names have been, unjustly, inadvertently omitted, for which I tendermyapologies. Ontario,Canada E.Lewars April2010