Excited states and transition metal compounds with quantum Monte Carlo [Elektronische Ressource] / vorgelegt von Annika Bande

Annika Bande

Informations

• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2007
• Nombre de lectures: 18
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Excited States and Transition Metal Compounds
with Quantum Monte Carlo
Von der Fakult¨at fur¨ Mathematik, Informatik und Naturwissenschaften der
Rheinisch-Westf¨alischen Technischen Hochschule Aachen zur Erlangung des
akademischen Grades einer Doktorin der Naturwissenschaften genehmigte
Dissertation
vorgelegt von
Diplom-Chemikerin
Annika Bande
aus
Duisburg
Berichter: Universit¨atsprofessor: Dr.rer.nat. Arne Luc¨ how
Universit¨a Dr.rer.nat. Wolfgang Stahl
Tag der mundlic¨ hen Prufung:¨ 14. Dezember 2007
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfugba¨ r.This work is dedicated to
Tante Ille
Ilse Marie Neilson (12/31/1914-02/01/2004), gentely called Tante Ille, was my nanny.
She always dreamed of joining me, when I get the academic degree of a doctor of
science. I have to thank her a lot for what she taught me: to meet life with humor
and confidence.Before all others I owe Prof. Dr. Arne Luc¨ how a dept of gratitude. His nonstop
support made a success of the time in his group. I am especially thankful for having
had many opportunities to take my time for personal studies and to attend inspiring
conferences.
I thank Prof. Dr. Wolfgang Stahl as the second referee of this thesis.
I am thankful to Prof. Dr. Andreas G¨orling and Dr. Fabio Della Sala for their
collaboration in the work on the Rydberg excitations. I further want to acknowledge
the “Gesellschaft Deuscher Chemiker” (GdCh) for providing a fellowship to travel to
stthe 1 European Chemistry Congress. Though not by names I wish to mention all the
organizers of conferences and seminars who offered me the opportunity to present my
work. Furthermore I want to thank the reseachers I became acquainted with.
Many thanks to Hanno Heeskens who guaranteed a smooth course for all computa-
tional concerns as well as to the people from the “Rechenzentrum” of RWTH Aachen
University.
The correction of this thesis has been done by Martina Peters, Clemens Minnich,
and Raphael Berner, to whom I am grateful.
I am very thankful to have had Anja Simon as a colleague and roommate from the
beginning of my Ph.D. studies. She has always been and is still interested in my work
and, which is most important, has become a very close friend of mine.
Furthermore I wish to express my thanks to my other three roommates Jan Sielk,
Sandra Kut¨ tner, and Thomas Wieland to the other two quantum Monte Carlo grad-
uate students Raphael Berner and Annett Schwarz, as well as to Michaela Braun for
fruitful discussions and good collaborations. I offer my thanks to the research students
Michael Wessel, Jens Burghaus, and Jaswinder Singh who worked on the vanadium
oxide compounds. I am grateful to Iwona Mennicken for her help on all non-scientific
questions. My gratitude shall be expressed to the colleagues from the “Institut fur¨
Physikalische Chemie” for a good working climate.
I very much appreciate my close friends, my family and my husband for their never
ending emotional support.Contents
Abstract 1
1 Introduction 2
2 Electron Structure Calculations 5
2.1 Orbital Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Hartree-Fock Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Configuration Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 Multi-Configuration Self Consistent Field Methods . . . . . . . . . . . 13
2.1.4 Coupled Cluster Methods . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.5 Møller-Plesset Perturbation Theory . . . . . . . . . . . . . . . . . . . 17
2.2 Density Functional Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Famous Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Open Shell Localized Hartree-Fock . . . . . . . . . . . . . . . . . . . . 24
2.3 Quantum Monte Carlo Methods . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Statistical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Variational Quantum Monte Carlo . . . . . . . . . . . . . . . . . . . . 32
2.3.3 Diffusion Quantum Monte Carlo . . . . . . . . . . . . . . . . . . . . . 34
2.3.4 Wave Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
i2.4 Effective Core Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Rydberg Excited States 52
3.1 Excited States in Quantum Chemistry . . . . . . . . . . . . . . . . . . . . . . 52
3.2 Excited States with Quantum Monte Carlo . . . . . . . . . . . . . . . . . . . 54
3.3 The Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.5.1 The Carbon Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.5.2 Carbon Monoxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Vanadium Oxide Compounds 70
4.1 Transition Metals in Quantum Chemistry . . . . . . . . . . . . . . . . . . . . 70
4.2 Transition Metals with Quantum Monte Carlo . . . . . . . . . . . . . . . . . 72
4.3 Transition Metal Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4 Technical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.1 Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4.2 Geometry Optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4.3 Zero Point Vibrational Energies . . . . . . . . . . . . . . . . . . . . . . 83
4.4.4 Reference Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.5 Generation of a Guide Wave Function . . . . . . . . . . . . . . . . . . 84
4.4.6 Quantum Monte Carlo Calculations . . . . . . . . . . . . . . . . . . . 95
4.5 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.5.1 The Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.5.2 Excitation Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
ii4.5.3 Ionization Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.5.4 Atomization Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.5.5 Oxygen Abstraction Energies . . . . . . . . . . . . . . . . . . . . . . . 129
4.5.6 Reaction Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.5.7 Estimation of Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.6 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5 Conclusion 141
References 157
Appendix A: Tables 158
Appendix B: Symbols 173
Appendix C: Abbreviations 180
Curriculum Vitae 185
iiiAbstract
To the most challenging electron structure calculations belong weak interactions, excited state
calculations, transition metals and properties. In this work the performance of variational
quantum Monte Carlo (VMC) and fixed-node diffusion quantum Monte Carlo (FN-DMC) is
tested for challenging electron structure problems using the quantum Monte Carlo amolqc
code by Luc¨ how et al..
The transition metal compounds under consideration are vanadium oxides. Here excita-
tion, ionization, oxygen atom and molecule abstraction, and atomization energies have been
+/0
studied for the vanadium oxide clusters VO withn = 0−4. The reaction energy of V O →n 2 5
VO +VO was calculated. The complete FN-DMC procedure established includes geometry3 2
optimization and calculation of zero point corrections using BP86/TZVP, single point cal-
culation of the BP86/SB type, and optimization of Jastrow parameters in the framework of
VMC variance minimization to obtain a suitable guide wave function. A careful adjustment
of the pseudopotential evaluation and of the time steps was done to obtain reliable FN-DMC
results that proved at least as accurate as results from CCSD(T)/cc-pVTZ calculations in-
cluding scalar relativistic corrections. This FN-DMC procedure will easily be extendible to
larger systems. For the oxygen abstraction and the atomization where experimental data is
available for comparison, FN-DMC/BP86/SB always renders the best results of all calcula-
tions performed. The dissociation of VO, its vertical ionization and the oxygen abstraction
+
from VO are obtained in excellent agreement to experiment using FN-DMC/BP86/SB.2
Rydberg excitation energies and singlet triplet splittings are calculated for the carbon
3atom and carbon monoxide. The considered excitations were from the P ground state into
3 1 1 1 3the P and P 2pns (n=3-6) Rydberg states and from Σ into Σ and Σ 5σmσ (m=6-7),
respectively. The wave functions used are described in terms of configuration state functions
from OSLHF orbitals which are particularly well-suited for the construction of QMC guide
and trial functions for Rydberg states. The OSLHF excitation energies are improved with
VMC and FN-DMC, respectively. However, fixed-node DMC does not describe the singlet
triplet splittings reliably whereas VMC results are in excellent agreement with the experi-
ment. Regional analyses and the newly established we