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High level ab initio potential energy surfaces and vibrational spectroscopy [Elektronische Ressource] / Kiran Sankar Maiti

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Published 01 January 2007
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Lehrstuhl fu¨r Theoretische Chemie
der Technischen Universit¨at Mu¨nchen
High level ab initio potential energy surfaces and
vibrational spectroscopy
Kiran Sankar Maiti
Vollst¨andiger Abdruck der von der Fakult¨at fu¨r Chemie der Technischen Universit¨at
Mu¨nchen zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr. Notker R¨osch
Pru¨fer der Dissertation:
1. Univ.-Prof. Dr. Wolfgang Domcke
2. Univ.-Prof. Dr. Fritz Elmar Ku¨hn
Die Dissertation wurde am 03.07.2007 bei der Technischen Universit¨at Mu¨nchen
eingereicht und durch die Fakult¨at fu¨r Chemie am 31.07.2007 angenommen.Acknowledgment
First of all, my heartiest thanks goes to Dr. Christoph Scheurer for offering me an
interesting and important research topic; for his sincere supervision, guidance and
valuable suggestions throughout this work; for his time and care in correcting the thesis
and also for the personal care and affection, which I received from him.
I am very thankful to Prof. W. Domcke for his care and valuable suggestions in science
and different aspect of life.
I am also thankful to Dr. Tobias Steinel for introducing me to a new field of science, his
valuable discussions and suggestions.
I am grateful to all of my colleagues for their cooperation and helping hands in all
directions. My heartiest thanks to Mr. Andeas Motzke, for his warm friendship and
extensive helpinthebeginningofmylifeinMunich. Alsoaspecial thankstoSabyashachi
for his friendship and extensive help in correcting the thesis.
I would like to thanks Frau M¨osch for her help in all semi-academic matters.
Thanks to Somnath, Lalu, Manish, Shyama, Souradip, Paramita for their friendship and
help.
Above all, I am thankful to my parents, my brother and sisters and my uncle Late
Panchugopal Maiti and all of my well wishers for their love and blessings.
iiiContents
0.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
0.2 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction 1
2 Quantum Chemistry 5
2.1 Quantum Chemical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 The Electronic Problem . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Hartree-Fock Self-Consistent Field Method . . . . . . . . . . . . . . 8
2.1.3 Concept of basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.4 Electron Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.5 Møller-Plesset Perturbation Theory . . . . . . . . . . . . . . . . . . 16
3 Extended scheme of the basis set extrapolation 19
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Correlation energy in the two electron atom . . . . . . . . . . . . . 20
3.2.2 MP2-R12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.3 Cost of different methods. . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Extrapolation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 Exponential extrapolation . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.2 Power-law extrapolation of the total energy . . . . . . . . . . . . . 28
3.3.3 Extrapolation of the correlation energy . . . . . . . . . . . . . . . . 30
3.3.4 Gradient and Hessian calculation for the correlation method . . . . 34
3.3.5 Extrapolation of Gradient and Hessians . . . . . . . . . . . . . . . . 35
3.4 Choice of model systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.6 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.6.1 Choice of the extrapolation method . . . . . . . . . . . . . . . . . . 39
3.6.2 MP2 vs. CCSD(T) parameterization . . . . . . . . . . . . . . . . . 41
3.6.3 Standard MP2 vs RI-MP2 parameterization. . . . . . . . . . . . . . 42
3.6.4 Performance of the X5 method . . . . . . . . . . . . . . . . . . . . 43
3.6.5 The PES calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.6.6 The PES calculation with local parameters . . . . . . . . . . . . . . 48
vvi Contents
3.6.7 The gradient and the Hessians . . . . . . . . . . . . . . . . . . . . . 50
4 Vibrational Spectroscopy of Methyl benzoate 53
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.1 Normal-mode analysis . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.2 Different approaches for normal-mode analysis . . . . . . . . . . . . 58
4.2.3 The VSCF Approximation . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.4 Configuration interaction VSCF . . . . . . . . . . . . . . . . . . . . 62
4.2.5 Correlation Corrected VSCF . . . . . . . . . . . . . . . . . . . . . . 63
4.2.6 Anharmonicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3 Computational methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4.1 Description of normal modes . . . . . . . . . . . . . . . . . . . . . . 70
4.4.2 Vibrational spectrum of Methyl benzoate . . . . . . . . . . . . . . . 72
4.4.3 Deuterated Methyl benzoate . . . . . . . . . . . . . . . . . . . . . . 80
4.4.4 Anharmonicity observed in the VSCF calculations . . . . . . . . . . 91
4.4.5 Assignment of vibrational frequencies . . . . . . . . . . . . . . . . . 93
5 Conclusions 97
A 101
A.1 Calculation of A and A . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1011 2
A.2 The gradient and Hessian extrapolation with the X5 method . . . . . . . . 102
B 105
B.1 Convergence of diagonal frequency with grid size. . . . . . . . . . . . . . . 105
B.2 Vibrational frequencies for anti-deutero-oDMB . . . . . . . . . . . . . . . . 107
Reference 109List of Abbreviations
1D one dimension
2D two dimension
AO atomic orbital
anti-o-DMB anti-o-deutero-methyl-benzoate
aug-cc-pVXZ augmented correlation consistent polarized valence X-tuple zeta
B3LYP Becke’s 3-parameter LYP (DFT functional)
CC coupled cluster
cc-pVXZ correlation consistent polarized valence X-tuple zeta
CI configuration interaction
CCSD(T) CC singles, doubles, and perturbative triples
DF-L-CCSD(T) density fitting local CCSD(T)
DF-MP2 density fitting MP2
DF-SCS density fitting spin-component scaled
DFT density functional theory
HF Hartree-Fock
IR infrared
MB methyl benzoate
MP2-R12 MP2 with linear r terms12
PES potential energy surface
syn-o-DMB syn-o-deutero-methyl-benzoate
V-MP2 vibrational MP2
VC-MP2 vibrational corrected MP2
VSCF vibrational self consistent fieldviii Chapter 0.1. Summary
0.1 Summary
An extended scheme for basis set extrapolation of the correlation energy is presented
and analyzed for a large number of atoms and molecules. The focus in the development
is on the use in generating high level potential energy surfaces (PES) for multidimen-
sional IR spectroscopy. Methyl benzoate (MB) is studied as a model compound for the
development of new IR pulse schemes with possible applicability to biomolecules. Anhar-
monic vibrational modes of MB are calculated on different level (MP2, SCS, CCSD(T)
with varying basis sets) ab-initio PESs using the vibrational self-consistent field (VSCF)
method and its correlated extensions. Dual level schemes, combining different quantum
chemical methods for diagonal and coupling potentials, are systematically studied and
applied successfully to reduce the computational cost.Chapter 0.2. Zusammenfassung ix
0.2 Zusammenfassung
EinerweitertesSchemazurExtrapolationderKorrelationsenergiezumBasissatzlimitwird
vorgestellt und fu¨r eine umfangreiche Anzahl von Atomen und Moleku¨len analysiert. Das
Ziel der Entwicklung liegt in der Anwendung zur Berechnung von exakten Potentialen-
ergiefl¨achen (PES) fu¨r die Simulation multidimensionaler IR-Spektroskopie. Methylben-
zoat (MB) wurde als Modellsystem zur Entwicklung neuer IR Pulssequenzen, mit dem
HintergrundderAnwendbarkeitaufBiomoleku¨le,untersucht. AnharmonischeSchwingun-
gsmoden fu¨r MB wurden auf ab-initio PES unterschiedlicher Gu¨te (MP2, SCS, CCSD(T)
mitvariierendenBasiss¨atzen) mittels der”vibrationalself-consistent field”(VSCF)Meth-
ode und Ihrer korrelierten Erweiterungen berechnet. Gemischte Ans¨atze, welche ver-
schiedenequantenchemischeMethodenfu¨rdieDiagonal-undKopplungspotentialeverknu¨-
pfen, wurden systematisch analysiert und erfolgreich zur Reduzierung des Rechenaufwan-
des verwendet.