Development and Applications of Orthogonality Constrained Density Functional Theory for the Accurate Simulation of X-Ray Absorption Spectroscopy Open Access

Derricotte, Wallace (2017)

Permanent URL: https://etd.library.emory.edu/concern/etds/fj236288r?locale=en
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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

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