Abstract
The aim of this dissertation is to address the theoretical
challenges of calculating core-excited states within the
framework of orthogonality constrained density functional
theory (OCDFT). OCDFT is a well-established variational, time
independent formulation of DFT for the computation of
electronic excited states. In this work, the theory is
first extended to compute core-excited states and generalized to
calculate multiple excited state solutions. An initial
benchmark is performed on a set of 40 unique
core-excitations, highlighting that OCDFT excitation
energies have a mean absolute error of 1.0 eV. Next, a novel
implementation of the spin-free exact-two-component (X2C)
one-electron treatment of scalar relativistic effects is presented
and combined with OCDFT in an effort to calculate core excited
states of transition metal complexes. The X2C-OCDFT spectra of
three organotitanium complexes (TiCl4,
TiCpCl3, and TiCp2Cl2) are shown
to be in good agreement with experimental results and show a
maximum absolute error of 5-6 eV. Next the issue of assigning core
excited states is addressed by introducing an automated approach to
analyzing the excited state MO by quantifying its local
contributions using a unique orbital basis known as localized
intrinsic valence virtual orbitals (LIVVOs). The utility of this
approach is highlighted by studying sulfur core-excitations in
ethanethiol and benzenethiol, as well as the hydrogen bonding in
the water dimer. Finally, an approach to selectively target specic
core-excited states in OCDFT based on atomic orbital subspace
projection is presented in an effort to target core excited states
of chemisorbed organic molecules. The core excitation spectrum of
pyrazine chemisorbed on Si(100) is calculated using OCDFT and
further characterized using the LIVVO approach.
Table of Contents
1 Introduction and Literature Review. . . . . . . . . . . . . .
1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 1
1.2 Photochemistry and Core Electron Excitations . . . . . . .
. . . . . . 3
1.3 X-Ray Absorption Spectroscopy . . . . . . . . . . . . . .
. . . . . . . 5
1.4 Theoretical Approaches for Calculation of Core Excited
States . . . . 10
1.4.1 Hartree-Fock Static Exchange. . . . . . . . . . . . . .
. . . . . 11
1.4.2 Linear Response Time-Dependent Density Functional
Theory
Approaches . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 13
1.4.3 Coupled Cluster Approaches . . . . . . . . . . . . . . .
. . . . 17
1.5 Orthogonality Constrained Density Functional Theory . . .
. . . . . 20
1.5.1 Original Formulation via Constrained Variational
Minimization 21
1.5.2 Attractive Features of OCDFT for Core Excitations . . .
. . . 22
1.6 Prospectus . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 26
2 Simulation of X-Ray Absorption Spectra with
Orthogonality
Constrained Density Functional Theory . . . . . 33
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 34
2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 37
2.3 Computational Details. . . . . . . . . . . . . . . . . . .
. . . . . . . . 43
2.4 Results and Discussion . . . . . . . . . . . . . . . . . .
. . . . . . . . 45
2.4.1 Calibration of OCDFT core-excitation energies . . . . .
. . . . 45
2.4.2 Application to Nucleobases: Thymine and Adenine
Near-Edge
Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 51
2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 60
2.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 63
3 Predicting Near Edge X-ray Absorption Spectra with
the Spin-Free Exact-Two-Component Hamiltonian and
Orthogonality Constrained Density Functional Theory 73
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 74
3.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 77
3.2.1 One-Electron Spin-Free X2C . . . . . . . . . . . . . . .
. . . . 77
3.2.2 Orthogonality Constrained DFT . . . . . . . . . . . . .
. . . . 79
3.2.3 Comparison of OCDFT and TDDFT for Core Excitations . .
81
3.3 Computational Details. . . . . . . . . . . . . . . . . . .
. . . . . . . . 87
3.4 Results and Discussion . . . . . . . . . . . . . . . . . .
. . . . . . . . 88
3.4.1 Calibration of X2C-OCDFT Core Excitation Energies . . .
. . 88
3.4.2 Ti K-Edge NEXAS of Organotitanium Complexes . . . . . .
. 92
3.5 Discussion and Conclusions . . . . . . . . . . . . . . . .
. . . . . . . . 99
4 Localized Intrinsic Valence Virtual Orbitals as a Tool
for the Automated Classication of Core Excited States108
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 109
4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 112
4.2.1 Construction of Localized Intrinsic Valence Virtual
Orbitals . 113
4.2.2 Determination of the character of the IAOs and LIVVOs .
. . 115
4.2.3 Analysis of OCDFT Particle Orbitals Using LIVVOs . . . .
. 117
4.3 Computational Details. . . . . . . . . . . . . . . . . . .
. . . . . . . . 118
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 119
4.4.1 Analysis of substituent eects in the spectra of thiols .
. . . . 119
4.4.2 Signatures of hydrogen bonding in the NEXAFS spectrum of
the
water dimer . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 124
4.4.3 Basis Set Dependence of LIVVO Analysis . . . . . . . . .
. . . 131
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 133
5 A Maximum Subspace Occupation Approach for the
Study of the NEXAFS Spectra of Chemisorbed Organic
Molecules Using Orthogonality Constrained Density
Functional Theory: Pyrazine on Si(100) a Case
Study . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 141
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 142
5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 148
5.2.1 Assigning Transitions Based on Localized Intrinsic
Valence Virtual
Orbitals . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 151
5.3 Computational Details. . . . . . . . . . . . . . . . . . .
. . . . . . . . 152
5.4 Results and discussion . . . . . . . . . . . . . . . . . .
. . . . . . . . . 154
5.5 Conclusions and Future Work. . . . . . . . . . . . . . . .
. . . . . . . 161
6 Concluding Remarks and Outlook . . . . . . . . . . . . . . .
169
About this Dissertation
Rights statement
- Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.
School |
|
Department |
|
Degree |
|
Submission |
|
Language |
|
Research Field |
|
关键词 |
|
Committee Chair / Thesis Advisor |
|
Committee Members |
|