Implementation, development and assessment of local hybrid density functionals [Elektronische Ressource] / vorgelegt von Hilke Bahmann

Informations

• Publié par: julius-maximilians-universitat_wurzburg
• Publié le: 01 janvier 2010
• Nombre de lectures: 20
• Langue: English

Extrait

Implementation, Development and Assessment
of Local Hybrid Density Functionals
Dissertation
zur Erlangung des naturwissenschaftlichen Doktorgrades der
Julius-Maximilians-Universitat Wurzburg
vorgelegt von
Hilke Bahmann
aus Duisburg, Deutschland
Oktober, 2010Eingereicht bei der Fakultat fur Chemie und Pharmazie am:
Gutachter der schriftlichen Arbeit
1. Gutachter:
2. Gutachter:
Prufer des o entlichen Promotionskolloquiums
1. Prufer:
2. Prufer:
3. Prufer:CONTENTS
CHAPTER 1: INTRODUCTION : : : : : : : : : : : : : : : : 2
CHAPTER 2: THEORETICAL BACKGROUND : : : : : : 6
2.1 Kohn-Sham and Hartree-Fock theory . . . . . . . . . . . . . . 8
2.2 Adiabatic connection . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Exchange-correlation hole . . . . . . . . . . . . . . . . . . . . 18
2.4 Approximations to the exchange and correlation functional . . 21
2.5 Local hybrid functionals . . . . . . . . . . . . . . . . . . . . . 28
2.6 Exact-exchange energy-density and potential . . . . . . . . . 31
CHAPTER 3: TRAINING AND ASSESSMENT SETS : : 40
3.1 Atomization energies . . . . . . . . . . . . . . . . . . . . . . . 40
3.2 Barriers heights . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3 AE6/BH6 set . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.4 Dissociation of symmetric radical cations . . . . . . . . . . . . 46
3.5 Transition metal compounds . . . . . . . . . . . . . . . . . . . 47
3.6 Isotropic hyperne coupling constants . . . . . . . . . . . . . . 51
CHAPTER 4: CHOICE OF LOCAL MIXING FUNCTION 54
4.1 Local mixing functions . . . . . . . . . . . . . . . . . . . . . . 55
4.2 Optimization procedure . . . . . . . . . . . . . . . . . . . . . 64
CHAPTER 5: IMPLEMENTATION : : : : : : : : : : : : : : 67
5.1 Post-SCF local hybrid functionals . . . . . . . . . . . . . . . . 68
5.2 Self-consistent implementation of local hybrid functionals . . . 69
CHAPTER 6: COMPUTATIONAL DETAILS : : : : : : : : 77v
CHAPTER 7: ASSESSMENT: : : : : : : : : : : : : : : : : : : 80
7.1 Fit results and dependency on the training set . . . . . . . . . 82
7.2 Local hybrids with gradient-corrected functionals . . . . . . . 85
7.3 Thermochemistry . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.4 Reaction barriers . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.5 Dissociation of symmetric radical cations . . . . . . . . . . . . 102
7.6 Transition metal compounds . . . . . . . . . . . . . . . . . . . 106
7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
CHAPTER 8: THE LOCAL HYBRID POTENTIAL : : : : 113
8.1 Total energies . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.2 Isotropic hyperne coupling constants . . . . . . . . . . . . . . 116
8.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
CHAPTER 9: CONCLUSION AND OUTLOOK : : : : : : : 124
CHAPTER 10: SUMMARY : : : : : : : : : : : : : : : : : : : : 127
KAPITEL 11: ZUSAMMENFASSUNG : : : : : : : : : : : : : 132LIST OF ABBREVIATIONS
AC Adiabatic Connection
AO Atomic Orbital
BH Barrier Height
DFT Densitiy Functional Theory
FDO Functional Derivative with respect to the Orbitals
GGA Generalized Gradient Approximation
HFCC Hyperne Coupling Constant
HK Hohenberg-Kohn
HT Hydrogen Transfer
I/O input/output
LDA Local Density Approximation
LMF Local Mixing Function
LSDA Local Spin Density Approximation
KS Kohn-Sham
MAE Mean Absolute Error
MSE Mean Signed Error
MO Molecular Orbital
NHT Non-Hydrogen Transfer
OEP Optimized E ective Potential
RI Resolution of the Identity
SCF Self-Consistent Field
TM Transition Metal
ZPE Zero Point EnergyCHAPTER 1
INTRODUCTION
Electronic structure calculations represent potentially the most important
tool at hand for chemists to explain and predict experimental observations
of quantum phenomena in molecules. The methods that are routinely used
in chemistry can be divided in two main categories: wave function methods
and Density Functional Theory (DFT). The former o er the advantage that
they can systematically converge to more accurate results, at the expense of
a dramatic increase in the computational cost associated with the methods.
The latter, based on an approximate representation of the electron density,
provides an e cient alternative and has so far o ered the best compromise
between accuracy and e ciency. Finding its roots in theoretical physics,
where it is typically used to represent extended systems, DFT has become
very popular amongst chemists in the last twenty years. The importance
of the method was recognized in 1998, when the Nobel Prize for chemistry
was awarded to Walter Kohn [1] and John A. Pople for the development
of density-functional theory and computational methods in quantum chem-
istry, respectively. Although a formally exact method, DFT as specied by
Kohn and Sham in their seminal paper [2] is approximate in practice. In
this theory, all non-classical electron-electron interactions and parts of the
correlated kinetic energy are gathered in the so-called exchange-correlation
energy functional. While the exact form of the exchange-correlation func-
tional is unknown, several exact physical and mathematical constraints have
been found to guide the development of increasingly sophisticated and accu-
rate approximations.