Magnetic Anisotropy of Transition Metal Complexes Nicholas F. Chilton A thesis submitted to e University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences 2015 School of Chemistry e University of Manchester 2 Contents Contents ....................................................................................................................................... 3 List of abbreviations ................................................................................................................... 5 Abstract ........................................................................................................................................ 7 Declaration .................................................................................................................................. 9 Copyright statement ................................................................................................................. 11 Acknowledgements .................................................................................................................. 13 1. Preface .................................................................................................................................... 15 2. Introduction .......................................................................................................................... 17 Rationale for the alternative format and organization of thesis ..................................... 17 Brief of included works and roles of authors .................................................................... 17 Magnetically anisotropic materials .................................................................................... 21 3. The electronic and magnetic properties of molecules ..................................................... 23 Magnetic properties of the electron ................................................................................... 23 Quantum mechanics and the wavefunction ..................................................................... 24 A single electron: the hydrogen atom ................................................................................ 26 Multi-electron atoms ........................................................................................................... 28 Magnetic and relativistic effects: the Dirac equation ....................................................... 29 Energy scales ......................................................................................................................... 30 Linear algebra ........................................................................................................................ 32 Perturbation theory .............................................................................................................. 34 The spherical harmonics ..................................................................................................... 36 More than one way to skin a cat ......................................................................................... 37 3 The parametric approach: angular momentum in quantum mechanics ....................... 38 The ab initio approach ......................................................................................................... 42 Connection of the ab initio and parametric approaches ................................................. 45 Experimental observables .................................................................................................... 47 Conclusion ............................................................................................................................. 48 References .............................................................................................................................. 48 4. Paper one: “On the Possibility of Magneto-Structural Correlations: Detailed Studies of Dinickel Carboxylate Complexes” .......................................................................................... 51 5. Paper two: “Large Zero-Field Splittings of the Ground Spin State Arising from Antisymmetric Exchange Effects in Heterometallic Triangles” ......................................... 65 6. Paper three: “An electrostatic model for the determination of magnetic anisotropy in dysprosium complexes” ........................................................................................................... 79 7. Paper four: “The first near-linear bis(amide) f-block complex: a blueprint for a high temperature single molecule magnet” .................................................................................. 111 8. Paper five: “Design Criteria for High-Temperature Single-Molecule Magnets” ........ 131 9. Paper six: “Direct measurement of dysprosium(III)···dysprosium(III) interactions in a single-molecule magnet” ........................................................................................................ 149 10. Conclusion ......................................................................................................................... 185 11. Outlook .............................................................................................................................. 187 12. Appendix: Further Ph.D. publications ........................................................................... 189 Total word count: 55,000 4 List of abbreviations AO Atomic Orbital BO Born-Oppenheimer CASPT2 Complete Active Space Second Order Perturbation Theory CASSCF Complete Active Space Self-Consistent Field CF Crystal Field CI Configuration Interaction EPR Electron Paramagnetic Resonance HF Hartree-Fock LCAO Linear Combination of Atomic Orbitals MCSCF Multi-Configurational Self-Consistent Field MF Mean Field MO Molecular Orbital NEVPT2 N-Electron Valence State Perturbation Theory PT Perturbation Theory QM Quantum Mechanics RASSCF Restricted Active Space Self-Consistent Field RASSI Restricted Active Space State Interaction RS Russell-Saunders SCF Self-Consistent Field SMM Single Molecule Magnet SOC Spin-Orbit Coupling ZFS Zero Field Splitting 5 6 Abstract Magnetic Anisotropy of Transition Metal Complexes: a thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences. The study of magnetic anisotropy in molecular systems permeates the physical sciences and finds application in areas as diverse as biomedical imaging and quantum information processing. The ability to understand and subsequently to design improved agents requires a detailed knowledge of their fundamental operation. This work outlines the background theory of the electronic structure of magnetic molecules and provides examples, for elements across the Periodic Table, of how it may be employed to aid in the understanding of magnetically anisotropic molecules. II III II The magnetic anisotropies of a series of dimetallic Ni 2 complexes and a Ru 2Mn triangle are determined through multi-frequency Electron Paramagnetic Resonance (EPR) spectroscopy and ab initio calculations. The magnetic anisotropy of the former is found to be on the same order of magnitude as the isotropic exchange interactions, while that of the latter is found to be caused by large antisymmetric exchange interactions involving the RuIII ions. An intuitive electrostatic strategy for the prediction of the magnetic anisotropy of DyIII complexes is presented, allowing facile determination of magnetic anisotropy for low symmetry molecules. Through the presentation of the first near-linear pseudo-two-coordinate 4f-block complex, a new family of DyIII complexes with unprecedented Single Molecule Magnet (SMM) properties is proposed. Design criteria for such species are elucidated and show that in general any two-coordinate complex of DyIII is an attractive synthetic target. The exchange interaction between two DyIII ions is directly measured with multi- frequency EPR spectroscopy, explaining the quenching of the slow magnetic relaxation in the pure species compared to the SMM properties of the diluted form. The interpretation of this complex system was achieved with supporting ab initio calculations. Nicholas F. Chilton February 2015 7 8 Declaration No portion of the work credited to the author in this thesis has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning. 9 10 Copyright statement The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the “Copyright”) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. 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