Electron correlation in molecules -- ab initio beyond Gaussian quantum chemistry PDF
Preview Electron correlation in molecules -- ab initio beyond Gaussian quantum chemistry
EDITORIAL BOARD FrankJensen(Aarhus,Denmark) MelLevy(Greensboro,NC,USA) JanLinderberg(Aarhus,Denmark) WilliamH.Miller(Berkeley,CA,USA) JohnW.Mintmire(Stillwater,OK,USA) ManojMishra(Mumbai,India) JensOddershede(Odense,Denmark) JosefPaldus(Waterloo,Canada) PekkaPyykko(Helsinki,Finland) MarkRatner(Evanston,IL,USA) DennisR.Salahub(Calgary,Canada) HenryF.SchaeferIII(Athens,GA,USA) JohnStanton(Austin,TX,USA) HarelWeinstein(NewYork,NY,USA) AcademicPressisanimprintofElsevier 50HampshireStreet,5thFloor,Cambridge,MA02139,USA 525BStreet,Suite1800,SanDiego,CA92101-4495,USA TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK 125LondonWall,London,EC2Y5AS,UK Firstedition2016 Copyright©2016ElsevierInc.Allrightsreserved. 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Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgein evaluatingandusinganyinformation,methods,compounds,orexperimentsdescribed herein.Inusingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyand thesafetyofothers,includingpartiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors, assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterof productsliability,negligenceorotherwise,orfromanyuseoroperationofanymethods, products,instructions,orideascontainedinthematerialherein. ISBN:978-0-12-803060-8 ISSN:0065-3276 ForinformationonallAcademicPresspublications visitourwebsiteathttp://store.elsevier.com/ PREFACE This thematic volume of Advances in Quantum Chemistry collects expert topical contributions on electronic structure, regarding the correlation methods and exponential type orbitals. In this respect, it covers “Electron CorrelationinMolecules:AbInitioBeyondGaussianQuantumChemistry.” The first section is on exponential type orbitals (ETO). It therefore covers the eigenfunctions of a one-electron atom (with molecular applica- tions).Theyshowexponentialdecreaseatlongrange,hencethename.They are a challenge to handle for molecules especially, maintaining this funda- mental work at the cutting edge. Often, an approximate expansion in Gaussian functions is used which facilitates application to quantum chemistry at the expense of the physical representation of atomic orbitals. ETO work is a traditional strong point oftheMolecularElectronicStructure(MES)workshopseries.Oneindica- tion of this strong ab initio quantum methodology is that 10 contributions constitute this section, beginning with reviews by Ancarani and Gasaneo, and Nakatsuji and Harris and continuing with research work by Pachucki, Ruiz, Perez, Erturk, Yasui, Ozdogan, and Yu¨kc¸u¨. Contributions of this section were presented in Amasya University (Turkey) in September 2014 and the next workshop is scheduled for Buenos Aires (Argentina) in September 2016. Another indication of this tradition is the Poster award at Amasya to Magdalena Zienkiewicz (Warsaw) for work entitled: Precise Born–Oppenheimer potential for excited states of H molecule. 2 Electronic correlation is a major frontier in quantum chemistry nowa- days. The methods of ab initio quantum chemistry will only give accurate properties for molecules and solids when electron correlation is taken into account. Its treatment ranges from rapid density functional theory (DFT) approaches to almost exact quantum Monte Carlo (QMC) approaches. These methods are covered in the second section. Thesetheoreticaltechniquesincludeelectroncorrelationandareintro- duced with the help of general contributions by Pastorczak, Weatherford, andMusialasfarasDFTisconcernedandbyToulouseandUmrigaraswell as Pederiva regarding fundamental quantum Monte Carlo work and both DFTandQMChavebeenappliedtoquantumchemicaltreatmentofreac- tivity for difficult cases in this section, where correlation needs to be obtained accurately to cater for variation from reactants to products: this xi xii Preface is illustrated by Grabowski et al. in recent work on the noble gas dimers, evaluatingcorrelationeffectsindensityfunctionaltheoryalongthedissoci- ationpath.Early2014alsosawthefirstvalidatedabinitiobenchmarkforthe H dissociation energy barrier on Cu(111), given using QMC by Hoggan: 2 14.79kcal/mol, well within standard error (0.5) of the experimental value 14.48kcal/mol. (see ArXiv). A couple of novel research-reviews close this volume, where theory is used as a very direct complementary approach to experiment, one on X-Ray Constrained Wave Functions: Fundamentals and Effects of the MolecularOrbitalsLocalizationbyGenoniandtheotherregardingElectron Impact Ionization by Saha et al. Hopedfully readers enjoy this volume as much as we have enjoyed editing it! PHILIP E. HOGGAN AND TELHAT OZDOGAN Editors CONTRIBUTORS SeldaAkdemir DepartmentofScienceEducation,FacultyofEducation,SinopUniversity,Sinop,Turkey LorenzoUgoAncarani EquipeTMS,UMRCNRS7565,ICPM,Universite´ deLorraine,57078Metz,France RolandAssaraf SorbonneUniversite´s,UPMCUnivParis06,andCNRS,UMR7616,Laboratoire deChimieThe´orique,Paris,France ArunK.Basak DepartmentofPhysics,UniversityofRajshahi,Rajshahi,Bangladesh AhmedBouferguene Faculte´ Saint-Jean,UniversityofAlberta,Alberta,Canada AdamBuksztel InstituteofPhysics,FacultyofPhysics,AstronomyandInformatics,NicolausCopernicus University,Torun,Poland MelekEraslan DepartmentofPhysics,FacultyofArtsandSciences,AmasyaUniversity,Amasya,Turkey MuratErturk DepartmentofPhysics,Facultyofartsandsciences,OnsekizMartUniversity,C¸anakkale, Turkey,andInstituteofPhysics,NicholasCopernicusUniversity,Torun,Poland AlexeiM.Frolov DepartmentofAppliedMathematics,UniversityofWesternOntario,London,Ontario, Canada GustavoGasaneo DepartamentodeF´ısica,UniversidadNacionaldelSur,8000Bah´ıaBlanca,BuenosAires, andConsejoNacionaldeInvestigacionesCient´ıficasyTe´cnicasCONICET,Argentina DanielH.Gebremedhin DepartmentofPhysics,FloridaA&MUniversity,Florida,USA AlessandroGenoni CNRS,andUniversite´ deLorraine,LaboratoireSRSMC,UMR7565, Vandoeuvre-l(cid:1)es-Nancy,France NikitasI.Gidopoulos DepartmentofPhysics,DurhamUniversity,Durham,UnitedKingdom IreneuszGrabowski InstituteofPhysics,FacultyofPhysics,AstronomyandInformatics,NicolausCopernicus University,Torun,Poland xiii xiv Contributors CarlosMarioGranados-Castro EquipeTMS,UMRCNRS7565,ICPM,Universite´deLorraine,57078Metz,France,and DepartamentodeF´ısica,UniversidadNacionaldelSur,8000Bah´ıaBlanca,BuenosAires, Argentina A.K.FazlulHaque DepartmentofPhysics,UniversityofRajshahi,Rajshahi,Bangladesh FrankE.Harris DepartmentofPhysics,UniversityofUtah,SaltLakeCity,andQuantumTheoryProject, UniversityofFlorida,Gainesville,Florida,USA PhilipE.Hoggan InstitutPacal,UMRCNRS6602,CampusUniversitairedesCe´zeaux,AubiereCedex, France YusakuI.Kurokawa QuantumChemistryResearchInstitute,Kyoto,Japan FedericoLatorre DepartmentofTheoreticalChemistry,Friedrich-AlexanderUniversityErlangen–Nu¨rnberg, Erlangen,Germany,andInstituteofTheoreticalChemistry,UniversityofVienna,Vienna, Austria LeszekMeissner InstituteofPhysics,NicholasCopernicusUniversity,Torun,Poland BenjaminMeyer CNRS,andUniversite´ deLorraine,LaboratoireSRSMC,UMR7565,Vandoeuvre-l(cid:1)es- Nancy,France DarioM.Mitnik ConsejoNacionaldeInvestigacionesCient´ıficasyTe´cnicasCONICET,andInstitutode Astronom´ıayF´ısicadelEspacio(IAFE)andDepartamentodeF´ısica,UniversidaddeBuenos Aires,C1428EGABuenosAires,Argentina PaoloMori DipartimentodiFisica,UniversitàdiTrento,Trento,Italy AnnaMotyl InstituteofChemistry,UniversityofSilesia,Katowice,Poland AbhishekMukherjee ECT*,StradadelleTabarelle286,Trento,Italy,andClusterVisionB.V., Nieuw-Zeelandweg15B,Amsterdam,Netherlands MonikaMusiał InstituteofChemistry,UniversityofSilesia,Katowice,Poland HiroyukiNakashima QuantumChemistryResearchInstitute,Kyoto,Japan HiroshiNakatsuji QuantumChemistryResearchInstitute,Kyoto,Japan Contributors xv TelhatOzdogan Department of Physics, Faculty of Arts and Sciences, Amasya University, Amasya, Turkey € EminOztekin DepartmentofPhysics,FacultyofScienceandArts,OndokuzMayısUniversity,Samsun, Turkey KrzysztofPachucki FacultyofPhysics,UniversityofWarsaw,Warsaw,Poland EwaPastorczak InstituteofPhysics,LodzUniversityofTechnology,Lodz,Poland M.AtiqurR.Patoary DepartmentofPhysics,UniversityofRajshahi,Rajshahi,Bangladesh FrancescoPederiva DipartimentodiFisica,UniversitàdiTrento,andINFN-TIFPA,TrentoInstitutefor FundamentalPhysicsandApplications,Trento,Italy JorgeE.Pe´rez DepartamentodeF´ısica,FacultaddeCienciasExactasFco-QcasyNaturales,Universidad NacionaldeR´ıoCuarto,R´ıoCuarto,Argentina KatarzynaPernal InstituteofPhysics,LodzUniversityofTechnology,Lodz,Poland AlessandroRoggero InstituteforNuclearTheory,UniversityofWashington,Seattle,Washington,USA Mar´ıaBele´nRuiz DepartmentofTheoreticalChemistry,Friedrich-AlexanderUniversityErlangen–Nu¨rnberg, Erlangen,Germany BidhanC.Saha DepartmentofPhysics,FloridaA&MUniversity,Tallahassee,Florida,USA PatrycjaSkupin InstituteofChemistry,UniversityofSilesia,Katowice,Poland SzymonS´miga InstituteofPhysics,FacultyofPhysics,AstronomyandInformatics,NicolausCopernicus University,Torun,Poland JulienToulouse SorbonneUniversite´s,UPMCUnivParis06,andCNRS,UMR7616,Laboratoirede ChimieThe´orique,Paris,France M.AlfazUddin DepartmentofPhysics,UniversityofRajshahi,Rajshahi,Bangladesh CyrusJ.Umrigar LaboratoryofAtomicandSolidStatePhysics,CornellUniversity,Ithaca,NewYork,USA xvi Contributors CharlesA.Weatherford DepartmentofPhysics,FloridaA&MUniversity,Florida,USA JunYasui RIKENInnovationCenter,Hirosawa,Wako,Saitama,andFrontierResearchCenter, CanonInc.,Ohta-ku,Tokyo,Japan NiyaziYu¨kc¸u¨ DepartmentofEnergySystemsEngineering,FacultyofTechnology,AdıyamanUniversity, Adıyaman,Turkey MagdalenaZientkiewicz FacultyofPhysics,UniversityofWarsaw,Warsaw,Poland CHAPTER ONE A Sturmian Approach to Photoionization of Molecules Carlos Mario Granados-Castro*,†,1, Lorenzo Ugo Ancarani*,1, Gustavo Gasaneo†,{, Dario M. Mitnik{,} *EquipeTMS,UMRCNRS7565,ICPM,Universite´deLorraine,57078Metz,France †DepartamentodeF´ısica,UniversidadNacionaldelSur,8000Bah´ıaBlanca,BuenosAires,Argentina {ConsejoNacionaldeInvestigacionesCient´ıficasyTe´cnicasCONICET,Argentina }InstitutodeAstronom´ıayF´ısicadelEspacio(IAFE)andDepartamentodeF´ısica,UniversidaddeBuenosAires, C1428EGABuenosAires,Argentina 1Correspondingauthors:e-mailaddress:[email protected]; [email protected] Contents 1. Introduction 4 2. Generalities 6 3. ExamplesTakenfromtheLiterature 8 3.1 H 9 2 3.2 N 10 2 3.3 CO 11 2 3.4 C H 12 6 6 4. SurveyofTheoreticalMethods 13 4.1 CI 13 4.2 Hartree–FockMethods 13 4.3 DensityFunctionalTheory 14 4.4 ComplexMethods 15 4.5 LinearAlgebraicMethod 16 4.6 Multi-Scattering 17 4.7 Plane-Wave-BasedMethods 18 4.8 R-MatrixMethod 19 4.9 RandomPhaseApproximation 20 4.10 Stieltjes–TchebycheffTechnique 21 4.11 TheKohnVariationalMethod 21 4.12 TheSchwingerVariationalMethod 23 4.13 Crank–Nicolson 25 5. SturmianApproach 25 5.1 GeneralizedSturmianFunctions 25 5.2 SturmianApproachtoPhotoionizationProcess 27 5.3 ResultsforMolecules 34 6. Conclusions 39 AdvancesinQuantumChemistry,Volume73 #2016ElsevierInc. 3 ISSN0065-3276 Allrightsreserved. http://dx.doi.org/10.1016/bs.aiq.2015.06.002 4 CarlosMarioGranados-Castroetal. Acknowledgments 41 Appendix.ListofPhotoionizationCalculationsforDifferentMolecules 42 References 44 Abstract Anaccuratetheoreticaldescriptionofphotoionizationprocessesisnecessaryinorderto understandawidevarietyofphysicalandchemicalphenomenaandallowsonetotest correlationeffectsofthetarget.Comparedtothecaseofmany-electronatomsseveral extrachallengesoccurformolecules.Thescatteringproblemisgenerallymulticenter and highly noncentral. The molecular orientation with respect to the polarization of theradiationfieldmustalsobetakenintoaccount.Thesefeaturesmakethecomputa- tionaltaskmuchmorecumbersomeandexpensivethanforatomictargets.Inorderto calculatecrosssections,oneneedstodescribetheejectedelectronwithacontinuum wavefunctionwithappropriateCoulombasymptoticconditions.Makinganumberof initialapproximations, manydifferent theoretical/numerical methodshavebeenpro- posedovertheyears.However,dependingonthecomplexityofthemolecule,agree- mentamongthemisnotuniformandmanyfeaturesoftheexperimentaldataarenotso wellreproduced.Thisisillustratedthroughanumberofexamples.Inordertohavea globaltheoreticaloverview,wepresentasurveyofmostofthemethodsavailablein the literature, indicating their application to different molecules. Within a Born– Oppenheimer,one-centerexpansionandsingleactiveelectronapproximation,wethen introduceaSturmianapproachtodescribephotoionizationofmoleculartargets.The methodisbasedontheuseofgeneralizedSturmianfunctionsforwhichcorrectbound- aryconditionscanbechosen.Thispropertymakesthemethodcomputationallyeffi- cient,asillustratedwithresultsforH O,NH ,andCH . 2 3 4 1. INTRODUCTION Thequantumdescriptionofbothboundandunboundorbitalsisnec- essarytostudycollisionswithatomsandmolecules.Thestudyofsinglepho- toionization(PI)providesanindirecttooltotestourcapacitytodescribethe target before and after the interaction correctly and thus correlation and many-bodyeffects.PIplaysanimportantrolebeyondatomicandmolecular physics, since it has a wide variety of applications, such as astrophysics, 1–3 planetary,4–6 atmospheric,7–8 plasma,9–11 or medical physics.12,13 Also PI helpstounderstanddifferentprocessesinsurfaces,suchasstructuralchanges upon surface adsorption, quantifying the relationship between shape reso- nances and the bond lengths14–17; or to characterize the relation between gas, chemisorbed and solid-state phases in surface reactions.18–21 In the last few years, a Sturmian approach22–23 has been introduced to study single and double ionization of atoms induced by electron24 or
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