Density Functional Studies on EPR Parameters and Spin-Density Distributions

Density Functional Studies on EPR Parameters and Spin-Density Distributions of Transition Metal Complexes DISSERTATION ZUR ERLANGUNG DES NATURWISSENSCHAFTLICHEN DOKTORGRADES DER BAYERISCHEN JULIUS-MAXIMILIANS-UNIVERSITÄT WÜRZBURG VORGELEGT VON CHRISTIAN REMENYI AUS NECKARSULM WÜRZBURG 2006 Eingereicht am: ___________________________________ bei der Fakultät für Chemie und Pharmazie Gutachter: ___________________________________ Gutachter: ___________________________________ der Dissertation Prüfer: ___________________________________ Prüfer: ___________________________________ Prüfer: ___________________________________ des Öffentlichen Promotionskolloquiums Tag des Öffentlichen Promotionskolloquiums: __________ Doktorurkunde ausgehändigt am: ____________________ Contents Introduction 1 Background and Motivation 1 Objectives of the Study 3 Acknowledgements 5 Chapter 1: Density Functional Theory 7 1.1. Density Functional Theory: Relevance and History 7 1.2. The Fundamentals: Elementary Quantum Chemistry and the Hartree-Fock Approximation 7 1.2.1. The Schrödinger Equation 7 1.2.2. The Hartree-Fock Method 8 1.3. Density Functional Theory – The Principles 10 1.3.1. The Hohenberg-Kohn Theorems 10 1.3.2. The Kohn-Sham Approach 11 1.4. Density Functional Theory – The Machinery 12 1.4.1. Functionals 12 1.4.2. The LCAO Approach 14 1.4.3. Basis Sets and Pseudopotentials 15 Chapter 2: Electron Paramagnetic Resonance 17 2.1. The Electron Spin 17 2.1.1. Where does it come from? – The Electron Spin as a Theoretical Concept 17 2.1.2. The Effective Spin Hamiltonian 18 2.1.3. Measuring the Electronic Spin 19 2.2. From an Effective Spin Hamiltonian to a Quantum Mechanical One 20 2.2.1. The Breit-Pauli Hamiltonian 20 2.2.2. Operators Relevant for the Electron-Zeeman and the Hyperfine Interaction 22 2.3. Calculation of g- and A-Tensors: Perturbation Theory 25 2.3.2. Perturbation Theory Expressions for the Electronic g-Tensor 27 2.3.3. Perturbation Theory Expressions for the A-Tensor 28 2.4. SO Operators and the Gauge Origin of the g-Tensor 29 2.5. More than one Spin Center: Exchange Interaction 29 2.5.1. The Heisenberg-Dirac-van-Vleck Hamiltonian 29 i CONTENTS 2.5.2. The Broken-Symmetry Approach for Calculating J Values 30 Chapter 3: Spin-Orbit Corrections to Hyperfine Coupling Constants 33 3.1. Introduction 33 3.2. Computational Details 34 3.3. Results and Discussion 34 3.3.1. Carbonyl Complexes: Comparison to Semiempirical SO Corrections 34 3.3.2. Copper Complexes 36 3.3.3. Manganese Complexes 41 3.3.4. Use of SO-ECPs on Heavy Atoms 41 3.4. Conclusions 44 Chapter 4: Amavadin as a Test Case for the Calculation of EPR Parameters 45 4.1. Introduction 45 4.2. Computational Details 46 4.3. Results and Discussion 46 4.3.1. g-Tensor 47 4.3.2. A-Tensor in the First-Order Approximation 48 4.3.3. Second-Order SO Corrections to the A-Tensor. 49 4.3.4. Orientation of the Tensors 50 4.3.5. Understanding the Effect of Exchange-Correlation Functional on Bonding and EPR Parameters 51 4.4. Conclusions 54 Chapter 5: EPR Parameters and Spin-Density Distributions of Azurin and other Blue-Copper Proteins 57 5.1. Introduction 57 5.2. Computational Details 59 5.3. Results and Discussion 60 5.3.1. Spin-density Distribution 60 5.3.2. Relevance of the Axial Ligands in Azurin for Spin-Density Distribution 63 5.3.3. The g-Tensor of Azurin 64 5.3.4. 65Cu Hyperfine Coupling Constants 67 5.3.5. Histidine Nitrogen Hyperfine Coupling Constants 73 5.3.6. Tensor Orientations 74 5.3.7. The EPR Parameters of a Selenocysteine-Substituted Azurin 74 5.4. Conclusions 76 ii CONTENTS Chapter 6: Where is the Spin? Understanding Electronic Structure and g-Tensors for Ruthenium Complexes with Redox-Active Quinonoid Ligands 79 6.1. Introduction 79 6.2. Computational Details 82 6.3. Results and Discussion 83 6.3.1. Molecular Structures 83 6.3.2. Spin Density Analyses 85 6.3.3. NPA Charges, Improved Assignments of Formal Oxidation States 90 6.3.4. g-Tensor Values and Orientations 93 6.3.5. Analysis of g-Tensors 99 6.3.6. The Origin of Spin Contamination. A Closer Look at the Bonding Situation 107 6.4. Conclusions 111 Chapter 7: EPR Paramaters and Spin-Density Distributions of Dicopper(I) Complexes with bridging Azo and Tetrazine Radical Anion Ligands 113 7.1. Introduction 113 7.2. Computational Details 115 7.3. Results and Discussion 116 7.3.1. Structures 116 7.3.2. Spin-Density Distribution 117 7.3.3. Metal Hyperfine Coupling Tensors; Comparison with Experiment 120 7.3.4. Metal Hyperfine Couplings; Orbital Analysis 122 7.3.5. Ligand Hyperfine Couplings 125 7.3.6. g-Tensors: Comparison with Experiment and Dependence on Functional 129 7.3.7. Effect of the Phosphine Co-Ligands, Comparison of L = PH3 and L = PPh3. 133 7.3.8. Molecular-Orbital and Atomic Spin-Orbit Analyses of g-Tensors 135 7.4. Conclusions 137 Chapter 8: Bis(semiquinonato)copper Complexes – Change of Spin State by Twisting the Ring System 139 8.1. Introduction 139 8.2. Computational Details 140 8.3. Results and Discussion 141 8.3.1. The g-Tensor as a Probe of the Electronic Structure 141 8.3.2. Spin-Density Distribution 144 iii CONTENTS 8.3.3. The Change of Spin State: Geometrical or Electronic Effect? 145 8.3.4. Other Q-Cu-Q Systems 147 8.3.5. Exchange Coupling 148 8.4. Conclusions 149 Bibliography 151 Summary 161 Zusammenfassung 165 Curriculum Vitae 169 List of Publications 170 iv Introduction Background and Motivation In the awareness of many chemists Electron mentioned field of bioinorganic chemistry fre- Paramagnetic Resonance (EPR) spectroscopy quently reaction steps and species with unpaired leads a shadowy existence. In contrast to Nuclear electrons occur.[8-10] magnetic resonance (NMR) spectroscopy, which In view of that, accurate quantum-chemical is today one of the standard tools for the struc- calculations of EPR parameters of transition ture determination especially for organic com- metal complexes are of considerable importance pounds, EPR is regarded mostly as an exotic in the prediction and analysis of EPR spectra.[11] technique limited to very special cases such as Hyperfine coupling (HFC) and g-tensors provide paramagnetic organotransition metals and coor- a large part of the information of an EPR spec- dination complexes or some curious organic trum and are regarded as sensitive probes of the radicals. However, modern sciences have more spin-density distribution in molecules.[12] and more focused on the understanding of the Spin density, in contrast to the electron den- underlying principles of how life in general sity, is the density of unpaired electrons and can works. Surprisingly, compounds which belong to therefore possess negative or positive values. By the branch of chemistry, which is named the convention, the density which is associated with inorganic one, turned out to be the driving mo- spins aligned parallel to the applied field (a tors for many biologically relevant reactions. spins) is taken as positive and the corresponding Literally each form of life is based on transition b-spin density is regarded as negative.[13] EPR metal ions – 40% of all known enzymes are met- spectroscopy has often been used to estimate the [1] alloproteins. spin distribution from experimental data. In con- Among these we want to mention only three trast, quantum chemical calculations provide examples which will clarify the outstanding im- independent access to spin-density distributions portance of these compounds: (a) proteins con- (and also to the total electron density). They [2, 3] [4, 5] taining iron-sulfur or “blue” copper sites therefore are particularly valuable tools for in- are the main electron transfer agents in organ- vestigating the electronic structure. isms, (b) the water oxidation to oxygen is cata- The g-tensor is the property that probably pro- [6, 7] lyzed by a polynuclear manganese complex. vides the most compact experimental image of Hence EPR spectroscopy has gained renewed the spin-density distribution in a molecule. (HFC interest due to the fact that in the above- constants are different for each atom, whereas 1 INTRODUCTION the g-tensor is a collective quantity of the whole which is found for organic main group radicals. molecule). Simple models relating g-tensor data For transition metal complexes a rather pro- to spin-density distribution and thus to electronic nounced dependence of the results on the ex- structure exist for “normal” transition metal change-correlation functional is found. For ex- complexes with metal-centered spin density as ample, gradient-corrected or local functionals well as for organic p-radicals. For such simple underestimate core-shell spin polarization at the cases some theories exist to interpret the data: metal, which is important in the calculation of ligand-field theory[14-16] for the former case and isotropic metal hyperfine coupling constants Stone’s MO[17] model for the latter. However, no (HFCC). [23, 24] In particular, the isotropic hyper- similarly intuitive rules exist as yet for more fine couplings are frequently difficult to calcu- complicated transition metal complexes, and late, due to the need to describe accurately the therefore things turn out to be more complicated. important core-shell spin polarization without For that difficulty are two mechanisms respon- introducing spin contamination due to exagger- sible, namely spin delocalization and spin polari- ated valence-shell spin polarization. The second zation. Both of them transfer a certain amount of problem to be dealt with are relativistic effects spin density from the transition metal center to on the HFC tensors, including both scalar (spin- other atoms of the molecule.[13] Both of these are free) relativistic (SR) and spin-orbit (SO) effects. present, for example, in redox-active ligands, These are known to influence the HFC results which will discussed later in this work.

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