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Excitation energies and properties of large molecules from ab-initio calculations [Elektronische Ressource] / vorgelegt von Danylo Kats

147 pages
ExcitationEnergiesandPropertiesofLargeMoleculesfromab-initioCalculationsDissertationzurErlangungdesDoktorgrades derNaturwissenschaften (Dr. rer. nat.)derFakulta¨t-ChemieundPharmazie-derUniversita¨tRegensburgvorgelegtvonDanyloKatsausRegensburgRegensburg 2010Promotionsgesuch eingereichtam: 25.01.2010Tagdeskolloquiums: 18.03.2010DieseArbeitwurdeeingeleitetvon: Prof. Dr. MartinSchu¨tzPromotionsausschussVorsitzender: Prof. Dr. Hans-AchimWagenknechtErstgutachter: Prof. Dr. MartinSchu¨tzZweitgutachter: Dr. TatianaKoronaDrittpru¨fer: Prof. Dr. BernhardDickDieErgebnissedieserArbeitsindbereitsvero¨ffentlichtworden:Chapter2D.Kats,T.KoronaandM.Schu¨tz”LocalCC2electronicexcitation energiesforlargemoleculeswithdensityfitting”TheJournalofChemicalPhysics125,104106(2006),doi: 10.1063/1.2339021Chapter3D.Kats,T.KoronaandM.Schu¨tz”Transitionstrengths andfirst-order propertiesofexcitedstatesfromlocalcoupledclusterCC2responsetheorywithdensityfitting”TheJournalofChemicalPhysics127,064107(2007),doi: 10.1063/1.2755778Chapter4D.Kats,D.UsvyatandM.Schu¨tz”OntheuseoftheLaplacetransform inlocalcorrelation methods”PhysicalChemistryChemicalPhysics10,3430(2008),doi: 10.1039/b802993hChapter5D.Kats,D.Usvyat,S.Loibl,T.MerzandM.Schu¨tz”Commenton’Minimaxapproximation forthedecompositionofenergydenominatorsinLaplace-transformedMøller-Plessetperturbationtheories’[J.Chem. Phys. 129,044112(2008)]”TheJournalofChemicalPhysics130,127101(2009),doi: 10.1063/1.
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ExcitationEnergiesandProperties
ofLargeMolecules
fromab-initioCalculations
Dissertation
zurErlangungdesDoktorgrades derNaturwissenschaften (Dr. rer. nat.)
derFakulta¨t
-ChemieundPharmazie-
derUniversita¨tRegensburg
vorgelegtvon
DanyloKats
ausRegensburg
Regensburg 2010Promotionsgesuch eingereichtam: 25.01.2010
Tagdeskolloquiums: 18.03.2010
DieseArbeitwurdeeingeleitetvon: Prof. Dr. MartinSchu¨tz
Promotionsausschuss
Vorsitzender: Prof. Dr. Hans-AchimWagenknecht
Erstgutachter: Prof. Dr. MartinSchu¨tz
Zweitgutachter: Dr. TatianaKorona
Drittpru¨fer: Prof. Dr. BernhardDickDieErgebnissedieserArbeitsindbereitsvero¨ffentlichtworden:
Chapter2
D.Kats,T.KoronaandM.Schu¨tz
”LocalCC2electronicexcitation energiesforlargemoleculeswithdensity
fitting”
TheJournalofChemicalPhysics
125,104106(2006),doi: 10.1063/1.2339021
Chapter3
D.Kats,T.KoronaandM.Schu¨tz
”Transitionstrengths andfirst-order propertiesofexcitedstates
fromlocalcoupledclusterCC2responsetheorywithdensityfitting”
TheJournalofChemicalPhysics
127,064107(2007),doi: 10.1063/1.2755778
Chapter4
D.Kats,D.UsvyatandM.Schu¨tz
”OntheuseoftheLaplacetransform inlocalcorrelation methods”
PhysicalChemistryChemicalPhysics
10,3430(2008),doi: 10.1039/b802993h
Chapter5
D.Kats,D.Usvyat,S.Loibl,T.MerzandM.Schu¨tz
”Commenton’Minimaxapproximation forthedecompositionofenergy
denominatorsinLaplace-transformedMøller-Plessetperturbation
theories’[J.Chem. Phys. 129,044112(2008)]”
TheJournalofChemicalPhysics
130,127101(2009),doi: 10.1063/1.3092982Chapter6
D.KatsandM.Schu¨tz
”AmultistatelocalcoupledclusterCC2responsemethodbasedonthe
Laplacetransform”
TheJournalofChemicalPhysics
131,124117(2009),doi: 10.1063/1.3237134
Chapter7
D.KatsandM.Schu¨tz
”LocalTime-DependentCoupledClusterResponseforpropertiesof
excited
statesinlargemolecules”
Zeitschriftfu¨rphysikalischeChemie
(2010)Acknowledgements
Thisthesiswouldnothavebeencompletedwithoutguidanceandsupport
frommycolleges,friendsandfamily.
FirstofallIwouldliketoexpressmygratitudetomysupervisor,Prof.
Dr. MartinSchu¨tz,forhisexcellentguidance,encouragementandsupport
throughout thewholeperiodofmyPhDstudentship.
IwouldliketothankDr. TatianaKoronafordeepandextremelyfruitful
collaboration andalsohavinggoodtimeduringseveralconferences.
I am obliged to many of my colleagues from the theoretical chemistry
group of the University Regensburg who supported me throughout the
past few years, especially Dr. Denis Usvyat for interesting and fruitful
discussions and Dr. Keyarash Sadeghian for his tricky test molecules,
whichneverworkedfromthefirsttime.
Iamgratefultoallmycollegesforunderstandingandpatienceduring
our ”russian” conversations, for the nice atmosphere here in our cozy
corridor on the third floor of the chemistry building, and for pleasant tea
rounds.
I also would like to thank my parents and sisters for their patience,
believeinmeandencouragingmewiththeirbestwishes.
ThisprojectwasfundedbytheDeutscheForschungsgemeinschaft(DFG)
in the context of the priority program SPP1145, which is gratefully ac-
knowledged.
viContents
1 Introduction 3
1.1 CoupledClusterTheoryandDiagrams . . . . . . . . . . . . 4
1.1.1 FundamentalsoftheCoupledClusterTheory . . . . 4
1.1.2 Diagrammatictechniqueforspatialorbitals . . . . . . 5
1.1.3 MP2andCC2methods . . . . . . . . . . . . . . . . . 7
1.2 LinearResponsetheory. . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Time-dependentformalism . . . . . . . . . . . . . . . 8
1.2.2 Time-averagingandresponsefunctions . . . . . . . . 10
1.2.3 Excitationenergies . . . . . . . . . . . . . . . . . . . . 12
1.3 Densityfittingapproximation . . . . . . . . . . . . . . . . . . 13
1.4 Localmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Laplacetransform . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.6 Structure ofthethesis . . . . . . . . . . . . . . . . . . . . . . . 17
2 LocalCC2 18
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 ThelocalCC2model . . . . . . . . . . . . . . . . . . . 21
2.2.2 LocalCC2excitationenergies . . . . . . . . . . . . . . 26
2.3 TestCalculations . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3 Propertiesofexcitedstates 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.1 Transitionstrengths . . . . . . . . . . . . . . . . . . . 49
3.2.2 First-orderproperties . . . . . . . . . . . . . . . . . . 52
3.2.3 CPdomainsforpropertycalculations . . . . . . . . . 53
3.3 TestCalculations . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
1CONTENTS 2
4 LaplaceTransforminlocalmethods 66
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3 TestCalculations . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5 IntegrationPointsforLaplaceTransform 89
6 LocalCC2withLaplaceTransform 94
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2.1 DirectdiagonalizationoftheJacobian . . . . . . . . . 98
6.2.2 Therightmatrix-vectorproduct . . . . . . . . . . . . 100
6.2.3 Localapproximations forexcitedstates . . . . . . . . 102
6.2.4 Complexeigenvaluesand-vectors . . . . . . . . . . . 104
6.2.5 Rescalingofmatrix-vector productafterrefresh . . . 106
6.3 TestCalculations . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7 LCC2vs. LT-LCC2 115
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.1 Excitationenergies . . . . . . . . . . . . . . . . . . . . 117
7.2.2 Transitionstrengths andfirst-orderproperties . . . . 121
7.3 TestCalculations . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
8 Summary 129
Bibliography 131Chapter1
Introduction
Electronic excitations playanimportant role in thephysical andchemical
processes in the universe, from chemistry taking place in all life-forms to
Fraunhofer lines in the optical spectrum of the Sun, etc. Itis evident, that
we need reliable theoretical methods to study properties of electronically
excitedstates,whichcanbeusedtointerpretexperimentaldata,tounder-
standmechanismsofcomplexphoto-reactions,topredictspectrafromnot
(yet) synthesized molecules etc. Over the last decades an arsenal of dif-
ferent ab initio methods for excited state calculations has been developed,
rangingfromratherinexpensivebutoftenunreliableapproaches(likeCon-
figuration Interaction Singles, CIS [1]) to highly accurate but very expen-
sive methods (like multi-reference CI [2–5] or Coupled Cluster (CC) [6]
withtheinclusionoftriplesexcitations). Oneofthemostcommonlyused
methods for calculating the excitation spectra of large molecules is the
Time-Dependent Density Functional Theory (TD–DFT) [7,8]. However
TD–DFT, used with the common exchange-correlation functionals based
onthegeneralizedgradientapproximation(includinghybridslikeB3LYP),
is not capable to provide a qualitatively correct spectrum of a molecular
system, as concerns charge transfer (CT) or Rydberg states, or excitations
of larger π systems play a role [8,9]. Errors in excitation energies of CT
states can easily exceed 2 eV [10], with TD-DFT drawing a picture of the
photophysics of a system which is quite different from that provided by
morereliablemethodsandincompatibletoexperimentalfindings[11]. Al-
though veryrecently several newfunctionals haveappeared,which were
especiallytailoredtoovercomethesedeficiences(seee.g. theCAM-B3LYP
method[12]),theTD-DFTapproachshouldbestillusedwithcaution and
is far from being a black-box method. For instance the CAM-B3LYP func-
tional was reported to reproduce the correct behaviour of a low-lying CT
band of the zincbacteriochlorin-bacteriochlorin complex [13], yet another
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