DEVELOPMENT OF ROBUST AB INITIO METHODS - iOpenShell

309 Pages·2014·7.22 MB·English

DEVELOPMENTOFROBUSTABINITIOMETHODSFORDESCRIPTIONOF
EXCITEDSTATESANDAUTOIONIZINGRESONANCES
by
DmitryZuev
ADissertationPresentedtothe
FACULTYOFTHEUSCGRADUATESCHOOL
UNIVERSITYOFSOUTHERNCALIFORNIA
InPartialFulfillmentofthe
RequirementsfortheDegree
DOCTOROFPHILOSOPHY
(CHEMISTRY)
May2014
Copyright 2014 DmitryZuev
Acknowledgements
First of all I would like to express greatest gratitude to my advisor - Professor Anna
Krylov. It was a great honor for me to be a part of her bright group all these 5 years.
Without her advice, support and motivation throughout all my years in graduate school
this work would not be possible. She was always source of inspiration and I knew that
herdoorisalwaysopenifIneedhelporadvice. AfteralltheseyearsworkingwithAnna
Ilearntthatsheisagreatscientist,leaderandjustagoodperson.
The group under the strict guidance by Anna has always been full with brilliant
and helpful people. I would like to thank Professor Ksenia Bravaya for helping me
with making first steps in mastering the field of quantum chemistry. Her diligence and
willingness to help were one of the determinant factors in succeeding at my projects.
Dr. Zhenya Epifanovsky was the first person who taught me real programming in C++
whichallowedmetogetajobasasoftwaredeveloper. Bylookingathishigh-classcode
I always had an example and motivation to be a good programmer. Dr. Thomas Jagau
wasafreshbloodforourgroupwhohelpedustodevelopnewapproachesindescribing
ii
resonances. His expertise and punctuality allowed us to look at the old problem from
thecompletelydifferentangle.
I would like to thank Dr. Kirill Khistyaev and Nastya Gunina for being good lab-
mates and friends. Besides them I would like to thank other friends outside the lab -
IvanGrishagin,AndreyRudenko,AnatolyDryga,SergeyMukhin. Allofthemtogether
made my life in Los Angeles interesting and enjoyable. I especially would like to
thankmyearlydeceasedfriendMishaVinaykin. WewereverygoodfriendssinceSaint
PetersburgStateUniversityandhewasthepersonwhoencouragedmetoapplytoUSC
forgraduatestudies. Histragicdeathwasabiglossforscientificcommunityandallhis
friends.
I would also like to thank other members of Chemistry Department who taught me
many important things both in classes and outside it. Professor Curt Wittig taught very
interesting class and his lectures were always fun to listen to. Professor Stephen Brad-
forth and Alexander Benderskii taught a very useful class on Molecular Spectroscopy
which helped me to look at the molecules and its properties from a different perspec-
tive. I would like to thank Professor Andrey Vilesov who told me and Misha about
USC Chemistry Department and explained how to enter graduate school. I would like
to thank Michele Dea - the person who is always ready to help with any administrative
mattersandresolveanyproblems.
iii
I would like to thank my parents in Russia who were always supportive and made
it possible for me to attend and graduate from one of the best Physics Departments in
Russia. WithoutthemIwouldneverachievewhatIhavenow.
Graduate school was a time when I was rapidly growing - both intellectually and
personally. It was the time when I met many smart people, made very good friends and
learntveryimportantlifelessons. Iwillalwaysrememberitasoneofthemostimportant
andinterestingchaptersofmylife.
iv
Table of contents
Acknowledgements ii
Listoftables viii
Listoffigures xii
Abbreviations xvii
Abstract xix
Chapter1: Introductionandoverview 1
1.1 Excitedstatesandresonancesinbiochromophores . . . . . . . . . . . . 1
1.2 Autoionizingresonancestatesinatomicandmolecularsystems . . . . . 3
1.3 Improvementofefficiencyandrobustnessofexcitedstatemethods . . . 9
1.4 Chapter1references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter2: Electronic structure of the two isomers of the anionic form of
p-coumaricacidchromophore 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Computationaldetails . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.1 StructuresandchargedistributionsofpCA− . . . . . . . . . . 28
2.3.2 Ab initio calculations of the electronically excited and ionized
statesofpCA− . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.3 Molecularorbitalframework . . . . . . . . . . . . . . . . . . . 44
2.3.4 Theoryversusexperiment . . . . . . . . . . . . . . . . . . . . 46
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.5 Chapter2references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Chapter3: Effectofmicrohydrationontheelectronicstructureofthechro-
mophoresofthephotoactiveyellowandgreenfluorescentproteins 62
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.2 Computationaldetails . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
v
3.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3.1 Optimized structures and binding energies of the mono- and
dihydratedchromophores . . . . . . . . . . . . . . . . . . . . . 69
3.3.2 ElectronicallyexcitedandionizedstatesofmicrohydratedpCA− 72
3.3.3 Theory versus experiment: microhydrated clusters of the PYP
chromophore . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.5 Chapter3references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Chapter4: Complex-scaledequation-of-motioncoupled-clustermethodwith
singleanddoublesubstitutionsforautoionizingexcitedstates 89
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2 Complex-scalingformalism: GeneraltheoryandEOM-EE-CCSDimple-
mentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.1 C-productversusscalarproduct . . . . . . . . . . . . . . . . . 100
4.2.2 One-andmanyelectronbasissets . . . . . . . . . . . . . . . . 102
4.2.3 Complex-scaledEOM-EE-CCSD . . . . . . . . . . . . . . . . 103
4.3 Resultsanddiscussion . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.3.1 Two-electronsystems: 2s2 resonancesinHeandH− . . . . . . 107
4.3.2 Many-electronssystems: Beatom . . . . . . . . . . . . . . . . 125
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.5 Chapter4references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Chapter5: Complex absorbing potentials within EOM-CC family of meth-
ods: Theory,implementation,andbenchmarks 139
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.4 Benchmarkcalculations . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.4.1 ComputationalDetails . . . . . . . . . . . . . . . . . . . . . . 153
5.4.2 TheImpactoftheCAPOnset . . . . . . . . . . . . . . . . . . 159
5.4.3 TheRoleofDiffuseBasisFunctions . . . . . . . . . . . . . . . 160
5.4.4 TheRoleoftheValenceBasisSet . . . . . . . . . . . . . . . . 163
5.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.5.1 2Π ResonanceinN− . . . . . . . . . . . . . . . . . . . . . . . 169
g 2
5.5.2 2ΠResonanceinCO− . . . . . . . . . . . . . . . . . . . . . . 173
5.5.3 2Π ResonanceinC H− . . . . . . . . . . . . . . . . . . . . . 174
g 2 2
5.5.4 2B ResonanceinC H− . . . . . . . . . . . . . . . . . . . . . 176
2g 2 4
5.5.5 2B ResonanceinCH O− . . . . . . . . . . . . . . . . . . . . 179
1 2
5.5.6 2Π ResonanceinCO− . . . . . . . . . . . . . . . . . . . . . . 181
u 2
5.5.7 2A and2B ResonancesinC H− . . . . . . . . . . . . . . . . 183
u g 4 6
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
vi
5.7 Chapter5references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Chapter6: Cholesky representation of electron-repulsion integrals within
coupled-clusterandequation-of-motionmethods 199
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
6.2 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.2.1 Choleskyalgorithm . . . . . . . . . . . . . . . . . . . . . . . . 202
6.2.2 Resolution-of-the-identityalgorithm . . . . . . . . . . . . . . . 205
6.3 RI/CDCCSDandEOM-CCSDmethods: Theory . . . . . . . . . . . . 206
6.3.1 Coupled-clusterequationswithsingleanddoublesubstitutions . 206
6.3.2 EOM-EE/SF-CCSDandCD/RIEOM-EE/SF-CCSD . . . . . . 211
6.3.3 EOM-IP-CCSDandCD/RIEOM-IP-CCSD . . . . . . . . . . . 215
6.3.4 EOM-EA-CCSDandCD/RIEOM-EA-CCSD . . . . . . . . . . 216
6.4 Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
6.6 Chapter6references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Chapter7: Root-specific eigenvalue solvers in the EOM family of methods:
Implementationandbenchmarks 240
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
7.2 Equation-of-motion(EOM)familyofmethods . . . . . . . . . . . . . . 242
7.3 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
7.3.1 Davidson’smethod . . . . . . . . . . . . . . . . . . . . . . . . 244
7.3.2 GeneralizedPreconditionedLocallyMinimalResidual(GPLMR)
method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
7.4 Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
7.6 Chapter7references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
Chapter8: Futurework 263
8.1 Chapter8references . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Bibliography 269
vii
List of tables
2.1 Verticaldetachmentenergies(VDE,eV)forthetwopCA− isomersesti-
mated by Koopmans theorem (KT, eV) and computed with EOM-IP-
CCSD/6-311+G(df,pd)//RI-MP2/aug-cc-pVDZ.
EOM-IP-CCSD/6-311+G(df,pd) adiabatic detachment energies (ADE,
eV)computedusingωB97X/aug-cc-pVDZoptimizedgeometriesofthe
neutralsforthefirstionizedstateandIP-CISD/6-31+G(d,p)forthesub-
sequentonesarealsogiven. . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Verticalexcitationenergies(E ,eV)andoscillatorstrengths(f ,inparen-
ex l
thesis) of the carboxylate pCA− isomer. The RI-MP2/aug-cc-pVDZ
optimizedgeometrieswereusedfortheexcitationenergycalculations. . 34
2.3 Verticalexcitationenergies(E ,eV)andoscillatorstrengths(f ,inparen-
ex l
thesis) of the phenolate pCA− isomer. The RI-MP2/aug-cc-pVDZ opti-
mizedgeometrieswereusedfortheexcitationenergycalculations. . . . 36
3.1 Vertical excitation energies (eV), oscillator strengths (f , in parenthesis)
l
and detachment energies (eV) of the microhydrated pCA−. Excitation
energies and transition dipole moments were computed by EOM-EE-
CCSD/6-31+G(d,p) and EOM-EE-CCSD/6-31+G(d), respectively, ion-
izationenergies—byEOM-IP-CCSD/6-311+G(df,pd). . . . . . . . . . 73
3.2 Vertical excitation and detachment energies (eV) of the microhydrated
deprotonatedHBDI.ExcitationenergieswerecomputedbySOS-CIS(D)/cc-
pVTZ,detachmentenergies—byωB97X-D/6-311++G(2df,2pd). . . . 75
4.1 Gaussian basis set exponents (α) of the first basis function and scaling
factors(k,αi+1 =αi/k)usedintheeven-temperedseries. . . . . . . . 109
4.2 Complexenergiesofthe2s2resonanceinheliumcalculatedbycs-EOM-
EE-CCSDindifferentbases. . . . . . . . . . . . . . . . . . . . . . . . 110
viii
4.3 Energies of the 2s2 resonance in H− calculated by cs-EOM-EE-CCSD
in different bases. ∆E is given relative to the 1s ground state of neutral
hydrogencomputedforcorrespondingbasisset. . . . . . . . . . . . . . 111
4.4 Energiesofthe1s22p3sresonanceinBecalculatedindifferentbases. . 128
5.1 EOM-EE-CCSDexcitationenergiesandexpectationvalues(cid:104)R2(cid:105)forsev-
eral excited states of CO and C H computed using the aug-cc-pVTZ
2 4
basis set with additional diffuse basis functions placed at the all heavy
atoms(A)oratthecenterofthemolecule(C). . . . . . . . . . . . . . . 155
5.2 Dependence of resonance positions E and widths Γ of the 2Π reso-
R
nanceofCO− andthe2B resonanceofC H− ontheonsetoftheCAP.
2g 2 4
Values for ηopt, (η·dE/dη)η=ηopt, and (cid:107)W(cid:107) are also reported. All values
computed at the CAP-EOM-EA-CCSD/aug-cc-pVTZ+3s3p3d(C) level
oftheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.3 ResonancepositionsE andwidthsΓaswellasvaluesforη and(cid:107)W(cid:107)
R opt
for the 2Π resonance state of CO− computed by CAP-EOMEA-CCSD
usingtheaug-cc-pVTZbasissetwithdifferentadditionalaugmentation.
The variations reported for E and Γ refer to the change of these quan-
R
tities upon varying the most important CAP onset parameter by 0.5 a.u.
(seeSection5.4.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
5.4 Resonance positions E and widths Γ as well as values for η and
R opt
(cid:107)W(cid:107)forthe2B resonancestateofC H− computedbyCAP-EOMEA-
2g 2 4
CCSD using the aug-cc-pVTZ basis set with different additional aug-
mentation. The variations reported for E and Γ refer to the change of
R
these quantities upon varying the most important CAP onset parameter
by0.5a.u. (seeSection5.4.2). . . . . . . . . . . . . . . . . . . . . . . 158
5.5 Resonance positions E and widths Γ as well as values for η for the
R opt
2Π resonance state of CO− computed by CAP-EOMEA-CCSD using
different valence basis sets. For comparison purposes, EOMEE-CCSD
excitationenergiesforseveralboundstatesofCOarereportedaswell. . 164
5.6 Resonance positions E and widths Γ as well as values for η for the
R opt
2B resonancestateofC H− computedbyCAP-EOMEA-CCSDusing
2g 2 4
different valence basis sets. For comparison purposes, EOMEE-CCSD
excitationenergiesforseveralboundstatesofC H arereportedaswell. 165
2 4
ix
5.7 Energy decomposition analysis for the real and imaginary parts of the
energiesa of the 2Π resonance of CO− and the 2B resonance of C H−
2g 2 4
computed by CAP-EOM-EA-CCSD using different valence basis sets.
Allvaluesinatomicunits. . . . . . . . . . . . . . . . . . . . . . . . . . 166
5.8 ComputationaldetailsofCAP-EOM-EA-CCSDcalculationsonN−,CO−,
2
C H−,C H−,CH O−,CO−,andC H−. . . . . . . . . . . . . . . . . . 168
2 2 2 4 2 2 4 6
5.9 ResonancepositionsE andwidthsΓforthe2Π resonancestateofN−
R g 2
obtainedusingdifferenttheoreticalmethods. . . . . . . . . . . . . . . . 172
5.10 ResonancepositionsE andwidthsΓforthe2ΠresonancestateofCO−
R
obtainedusingdifferentmethods. . . . . . . . . . . . . . . . . . . . . 173
5.11 Resonance positions E and widths Γ for the 2Π resonance state of
R g
C H− obtainedusingdifferentmethods. . . . . . . . . . . . . . . . . . 175
2 2
5.12 Resonance positions E and widths Γ for the 2B resonance state of
R 2g
C H− obtainedusingdifferentmethods. . . . . . . . . . . . . . . . . . 178
2 4
5.13 Resonance positions E and widths Γ for the 2B resonance state of
R 1
CH O− obtainedusingdifferentmethods. . . . . . . . . . . . . . . . . 180
2
5.14 Resonance positions E and widths Γ for the 2Π resonance state of
R u
CO− obtainedusingdifferentmethods. . . . . . . . . . . . . . . . . . . 182
2
5.15 Resonance positions E and widths Γ for the 2A and 2B resonance
R u g
statesofC H− (1,3-butadieneanion)obtainedusingdifferentmethods. . 184
4 6
6.1 Intermediates for CCSD calculations and estimates to store and com-
putethem(closed-shellcase). . . . . . . . . . . . . . . . . . . . . . . . 209
6.2 I and T intermediates for EOM-CCSD and estimated cost to store and
computethem(closed-shellcase). . . . . . . . . . . . . . . . . . . . . 213
6.3 Test systems used for benchmarks, converged CCSD correlation ener-
gies(hartree),andnumberofCCiterations. . . . . . . . . . . . . . . . 221
6.4 CCSDerrorsandwalltimes(sec)using12coresfortest1-test3 . . . . . 222
6.5 CCSDerrorsandwalltimes(sec)using12coresfortest4-test6. . . . . 223
6.6 WalltimeperCCSDiteration(sec)using80GBRAM. . . . . . . . . . 225
6.7 EOM-CCSD energies for the 2 lowest states in each irrep and errors in
energydifferences(eV),andwalltimesforEOM(sec)using12cores. . 228
x