Gadolinium endohedral metallofullerenes (EMFs) have shown the potential to become next generation magnetic resonance imaging (MRI) contrast agents due to their significantly improved efficiency and safety, as well as multi-day body retention which allows for a longer surgery and observation compared to current contrast agents. In Chapter 1, I have reviewed the development of gadolinium EMF based MRI contrast agents. In Chapter 2, I have described my study of Gd3N@C80 and Gd3N@C84 metallofullerenols as next generation MRI contrast agents. The metallofullerenols are synthesized and characterized utilizing UV-vis, IR, X-ray photoelectron spectroscopy (XPS) and dynamic light scattering (DLS). In addition, relaxivity data were obtained for the two metallofullerenes, and the results showed that Gd3N@C84 metallofullerenol had enhanced relaxivity compared to Gd3N@C80 metallofullerenol. This result is consistent with the observation of magnetic resonance images of the samples at different concentrations. The enhanced relaxivity was attributed to the special "egg shape" of the Gd3N@C84 cage. In Chapter 3, I have described the relaxivity study of Gd3N@C80 (without functionalization) in oleic acid, which could be used as an MRI contrast agent for more hydrophobic bioenvironments. The results show that Gd3N@C80 has a reasonable relaxation effect (relaxivity ~10 mM-1S-1 at 1.4 T) in oleic acid and could be a viable contrast agent even without functionalization. In Chapter 4, I have discussed the outlook of gadolinium EMF-based MRI contrast agents and suggested several directions for future work. / Master of Science

Endohedral metalofullerenes (EMFs) have emerged as an important class of nanomaterials with vast promise in applications of molecular devices and nanomedicines. This dissertation addresses the EMF research span from synthesis to application, with an emphasis of work on trimetallic nitride template (TNT) EMF and carbide clusterfullerenes (CCFs). As a general introduction, chapter 1 reviews the main literature in TNT EMF studies. Also key works in CCF area are highlighted to show the common feature and uniqueness of this class of EMF in comparison with other EMFs. In the last part of the chapter a list of milestone progress in EMF area has been summarized. Chapter 2 is devoted to the synthetic work on EMFs. Especially, for isotopic modification, the trial and actual EMF syntheses in efforts to introduce 13C, 89Y and 177Lu are described. The next three chapters address the structural characterization of EMFs. Chapter 3 focuses on structural studies of CCFs. With detailed interpretation of 13C NMR and DFT computational results for selected members of the Y2C2@C2n family, the influence of fullerene cage on the size and shape of the yttrium carbide cluster (Y2C2)4+ is investigated. It has also been established that the carbide cluster prefers a linear shape in sufficiently large fullerene cages but adopts a compressed butterfly shape in smaller cages where space is constrained. Chapter 4 presents a systemic examination of dipole moments in TNT EMFs. The first 13C NMR study of M3N@C2(22010)-C78 is achieved on Y3N@C2(22010)-C78. In addition, dipole moments of the M3N@C2n (n=39-44) family are probed by interpretation of chromatographic retention behavior, DFT computational results and single-crystal data. It has been found that TNT EMFs with pentalene motifs exhibit enhanced dipole moments due to the cluster-cage interplay. Chapter 5 provides full characterization of the M2C2@C1(51383)-C84 (M=Y, Gd) molecule, which contains the first example of an asymmetric fullerene cage with fused pentagons. Furthermore, it is suggested that the C1(51383)-C84 cage is capable of a cascade of rearrangements into high symmetry and stable fullerene cages via well-established mechanistic steps, namely, extrusion of C2 units from pentalene or indene motifs and Stone-Wales transformations. As an important intermediate in the formation of high symmetry fullerene cages, the C1(51383)-C84 represents a missing link that implies the "top-down" fullerene formation mechanism. Chapter 6 describes the endeavor to functionalize two exotic EMFs, the room-temperature radical heterometallofullerene Gd2@C79N, and the egg-shaped TNT EMF Gd3N@C84. The reactivity of Gd2@C79N is directly compared to Y2@C79N, Gd3N@C80 and Sc3N@C80 in two reactions and the paramagnetic Gd2@C79N is proven to be very inert toward many known common fullerene cage reactions. Eventually both EMFs have been successfully functionalized via the Bingel reaction, and the derivatives are characterized with HPLC and mass-spectrometry. Chapter 7 compares the effective magnetic moment of Gd3N@C80 and Gd3N@C84, together with the previously reported Gd@C82. The magnetic moment has a second-order contribution to the T1 relaxivity and thereby is an important factor to evaluate an EMF's value in application as MRI contrast agents. Furthermore the influence of cluster motion to magnetic behavior in TNT EMF is discussed. / Ph. D.

Nous avons synthétisé différentes dyades donneurs-accepteurs (D-A) π-conjuguées à base de fullerène pour des applications photovoltaïques dans lesquelles les unités D étaient soit des oligophenylenevinylenes (OPV) soit des oligophenyleneethynylene (OPE) et les unités A étaient le C60 ou un endofullerène du type Y3N@C80. Il y avait une exigence supplémentaire pour nos matériaux, à savoir qu’ils devaient s’auto-organiser en phases liquides-cristallines. Pour ce faire, toutes les unités D contenaient un promoteur mésogène afin d'induire le mésomorphisme de la dyade D- et donc de contrôler la morphologie des couches minces nécessaires à l’élaboraiton des cellules photovoltaïques grâce à une organisation supramoléculaire. En dehors de cela, nous avons étudié l’influence de la nature chimique du donneur (par exemple lyophile ou amphiphile), de la longueur des oligomères et de la multiaddition sur les propriétés photophysiques et sur l'auto-assemblage. Nous avons synthétisé une dyade OPE-Y3N@C80 qui est le premier dérive mésomorphe et photosensible de ce type de métallofullerène endohédral. / We have synthesized different π-conjugated system-fullerene dyads for photovoltaic applications, where the donor units were either oligophenylenevinylene (OPV) or oligophenyleneethynylene (OPE) derivatives and for the acceptor, C60 or Y3N@C80 was used. There was an additional requirement for our materials: liquid crystallinity. All the donor units contained a mesogenic promoter in order to induce mesomorphism in the D-A dyad and to control the morphology of the prepared film through supramolecular organization. Apart from that, we investigated the effect of the chemical nature of the donor moiety (ie. lyophilic or amphiphilic), the oligomeric length and multiaddition on the photophysical properties and on the self-assembly. We have synthesized an OPE-Y3N@C80 dyad which is the first trimetallic nitride template endohedral metallofullerene derivative with mesomorphic and photoactive properties.

In this thesis, a series of computational studies based on density functional theory (DFT) and density functional tight-binding (DFTB) is presented to deeply understand experimental results on the synthesis of endohedral fullerenes and graphene/iron hybrids at atomic level. In the first part, a simple and efficient model is proposed to evaluate the strain experienced by clusters encapsulated in endohedral metallofullerenes (EMFs). Calculations for the sole cluster, either in the neutral or the charged state, cannot be used for this goal. However, when the effect of the carbon cage is mimicked by small organic π-systems (such as pentalene and sumanene), the cluster has sufficient freedom to adopt the optimal configuration, and therefore the energetic characteristics of the EMF-induced distortion of the cluster can be evaluated. Both nitride and sulfide clusters were found to be rather flexible. Hence, they can be encapsulated in carbon cages of different size and shape. For carbide M2C2 cluster the situation is more complex. The optimized cluster can adopt either butterfly or linear shapes, and these configurations have substantially different metal-metal distance. Whereas for Sc2C2 both structures are isoenergetic, linear form of the Y2C2 cluster is substantially less stable than the butterfly-shaped configuration. These results show that phenomenon of the “nanoscale fullerene compression” once proposed by Zhang et al. (J. AM. CHEM. SOC. (2012),134(20)) should be “nanoscale fullerene stretching”. Finally, the results also reveal that both Ti2S and Ti2C2 cluster are strained in corresponding EMF molecules, but the origin of the strain is opposite: C78-D3h(5) cage imposes too long Ti···Ti distance for the sulfide cluster and too short distance for the carbide cluster. In the second part of the thesis, possible fullerene geometries and electronic structures have been explored theoretically for the species detected in mass spectra of the Sc-EMF extract synthesized using CH4 as a reactive gas. Two most promising candidates, namely Sc4C@C80-Ih(7) and Sc4C3@C80-Ih(7), have been identified and further studied at the DFT level. For Sc4C@C80, the tetrahedral Sc4 cluster with the central μ4-C atom was found to be 10 kJ/mol more stable than the square cluster. For Sc4C3@C80, the calculation showed that the most stable is the Sc4C3 cluster in which the triangular C3 moiety is η3- and η2-coordinated to Sc atoms. Whereas Sc4C@C80 has rather small HOMO-LUMO gap and low ionization potential, the HOMO-LUMO gap of Sc4C3@C80 is substantially higher and exceeds that of Sc4C2@C80. In the third part, computational studies of structures and reactivity are described for a new type of EMFs with a heptagon that has been produced in the arc-discharge synthesis. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, so the former should be synthesized in much higher yield than observed. This disagreement may be ascribed to the kinetic factors rather than thermodynamic stability. Because of prospective applications of this EMFs by introducing functional groups, the influence of the heptagon on the chemical properties have been further evaluated. Thermodynamically and kinetically preferred reaction sites are studied computationally for Prato and Bingel-Hirsch cycloaddition reactions. In both types of reactions the heptagon is not affected, and chemical reactivity is determined by the adjacent pentalene units. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon edges, whereas the most reactive sites in kinetically-controlled Bingel-Hirsch reaction are the carbon atoms next to the pentagon/pentagon edge. Fourth, although various EMFs have been successfully synthesized and characterized, the formation mechanism is still not known in details, and hence control of the synthesis products is rather poor. Therefore, EMF self-assembly process in Sc/carbon vapor in the presence and absence of cooling gas (helium) and reactive gas (NH3 and CH4) is systematically investigated using quantum chemical molecular dynamics (QM/MD) simulations based on the DFTB potentials. The cooling gas effect is that the presence of He atoms accelerates formation of pentagons and hexagons and reduces the size of formed carbon cages in comparison to the analogous He-free simulations. As a result, the Sc/C/He system yields a large number of successful trajectories (i.e. leading to the Sc-EMFs) with more realistic cage-size distribution than the Sc/C system. Encapsulation of Sc atoms within the carbon cage was found to proceed via two parallel mechanisms. The main mechanism involves nucleation of the several hexagons and pentagons with Sc atoms already at the early stages of the carbon vapor condensation. In such proto-cages, both Sc–C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at high temperatures. Further growth of the carbon cage results in encapsulation of one or two Sc atoms within the forming fullerene. Another encapsulation mechanism is observed in rare cases. In this process, the closed cage is formed with Sc being a part of the carbon network, i.e. being bonded by three or four Sc–C σ-bonds. However, such intermediates are found to be unstable, and transform into the endohedral fullerenes within few picoseconds of annealing. In perfect agreement with experimental studies, extension of the simulation to Fe and Ti showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3). The role of “reactive gas” in the EMF synthesis is revealed in dedicated simulations of the fullerene formation in the presence of several molecules of CH4 or NH3. When concentration of reactive gas is high, carbon vapor tends to form graphene flakes or other carbon species terminated by hydrogen atoms, whereas the yield of empty fullerenes is very low. Conversely, with additional metal atoms (Sc) and the same number of NH3 molecules, the yield of fullerenes constantly increase from 5 to 65% which is ascribed to the catalytic activity of metal atoms in the nucleation of carbon cages already at early stage. Moreover, due to the presence of hydrogen atoms from the reactive gas, the carbon cage formation requires much longer time, which provides sufficient reaction time to encapsulate 3 or 4 Sc atoms within one cage. It explains preferential formation of clusterfullerenes in experiments with reactive gas. At the same time, monometallofullerenes and dimetallofullerenes are the main products in absence of reactive gas. We also provide possible growth mechanisms of carbide and cyano-clusterfullerenes in details to elucidate how the intracluster goes into the cage. A possible growth mechanism of nitride clusterfullerenes has been proposed based on DFT results. In the last part, a free-standing crystalline single-atom thick layer of Fe has been studied theoretically. By investigating the energy difference, ΔE, between a suspended Fe monolayer and a nanoparticle using the equivalent number of Fe atoms, one can estimate that the largest stable membrane should be ca. 12 atoms wide or 3 × 3 nm2 which is in excellent agreement with the experimental observation. Otherwise, the possibility of C, O, N atoms embedded into the Fe membrane can been fully excluded by DFTB and DFT simulations, which agrees with electron energy loss spectroscopy (EELS) measurement. A significantly enhanced magnetic moment for single atom thick Fe membranes (3.08 μB) is predicted by DFT as compared to the bulk BCC Fe (2.1 μB), which originates from the 2D nature of the Fe membrane since the dz2 orbital is out-of-plane while the dxy orbital is in-plane.

This work describes theoretical studies on molecular and electronic structures of lanthanide-based single-molecule magnets focusing on their magnetic properties. In this work, two main problems are covered: the structural ordering of endohedral fullerenes in different supramolecular arrangements, and the magnetic anisotropy of lanthanides in different charge coordinations. The basic methodes used in this work are density functional theory and multiconfigurational self-consistent field.:CHAPTER 1. THEORETICAL FOUNDATIONS OF RARE-EARTH MAGNETISM 12 1.1. Single-molecule magnetism and 4f-elements 14 1.1.1. Electronic structure of 4f-elements 16 1.1.2. LS-coupling scheme 19 1.1.3. Parameterization of the Crystal-Field splitting effect. 20 1.1.4. Zeeman splitting for a free ion 24 1.1.5. Spin Hamiltonian and pseudospin approximation 24 1.1.6. Kramers theorem 25 1.1.7. Weak and strong molecular interactions. 26 1.2. Computational methods in application to Ln-based SMMs 27 1.2.1. Density functional theory (DFT). 28 1.2.2. Multiconfigurational methods in quantum chemistry 33 1.3. Role of molecular structure in single-molecular magnetism 41 1.3.1. Complexes of SMMs with organic molecules 45 1.3.2. SMMs deposited on surfaces 46 CHAPTER 2. STRUCTURAL ORDERING IN COCRYSTALS OF EMFs AND Ni(OEP) 49 2.1. Ordering in endohedral metallofullerenes 49 2.2. Modeling details 51 2.3. Conformer analysis 54 2.4. Electrostatic potential 58 CHAPTER 3. ISOMERISM OF Dy2ScN@C80 DEPOSITED ON SURFACES 61 3.1. Modeling details 62 3.2. Cluster conformation analysis 69 3.3. Charge density analysis 75 CHAPTER 4. Ho|MgO AS A SINGLE-ATOMIC MAGNET. FV-MAGNETISM. 80 4.1. DFT description of Ln|MgO 85 4.2. Ho|MgO system: ab initio calculations 92 4.3. Magnetic properties of lanthanides with FV magnetism 99 4.4. Generalized ligand field and spin Hamiltonians for FV systems. 101 CHAPTER 5. FV-MAGNETISM IN [Ln2+] METALLOCENE COMPLEXES 107 5.1. TbII(CpiPr5)2 DFT-model 108 5.2. FV-interaction in terms of ab initio multiconfigurational approach 113 5.3. Point-charge model 115

In this thesis, a series of computational studies based on density functional theory (DFT) and density functional tight-binding (DFTB) is presented to deeply understand experimental results on the synthesis of endohedral fullerenes and graphene/iron hybrids at atomic level. In the first part, a simple and efficient model is proposed to evaluate the strain experienced by clusters encapsulated in endohedral metallofullerenes (EMFs). Calculations for the sole cluster, either in the neutral or the charged state, cannot be used for this goal. However, when the effect of the carbon cage is mimicked by small organic π-systems (such as pentalene and sumanene), the cluster has sufficient freedom to adopt the optimal configuration, and therefore the energetic characteristics of the EMF-induced distortion of the cluster can be evaluated. Both nitride and sulfide clusters were found to be rather flexible. Hence, they can be encapsulated in carbon cages of different size and shape. For carbide M2C2 cluster the situation is more complex. The optimized cluster can adopt either butterfly or linear shapes, and these configurations have substantially different metal-metal distance. Whereas for Sc2C2 both structures are isoenergetic, linear form of the Y2C2 cluster is substantially less stable than the butterfly-shaped configuration. These results show that phenomenon of the “nanoscale fullerene compression” once proposed by Zhang et al. (J. AM. CHEM. SOC. (2012),134(20)) should be “nanoscale fullerene stretching”. Finally, the results also reveal that both Ti2S and Ti2C2 cluster are strained in corresponding EMF molecules, but the origin of the strain is opposite: C78-D3h(5) cage imposes too long Ti···Ti distance for the sulfide cluster and too short distance for the carbide cluster. In the second part of the thesis, possible fullerene geometries and electronic structures have been explored theoretically for the species detected in mass spectra of the Sc-EMF extract synthesized using CH4 as a reactive gas. Two most promising candidates, namely Sc4C@C80-Ih(7) and Sc4C3@C80-Ih(7), have been identified and further studied at the DFT level. For Sc4C@C80, the tetrahedral Sc4 cluster with the central μ4-C atom was found to be 10 kJ/mol more stable than the square cluster. For Sc4C3@C80, the calculation showed that the most stable is the Sc4C3 cluster in which the triangular C3 moiety is η3- and η2-coordinated to Sc atoms. Whereas Sc4C@C80 has rather small HOMO-LUMO gap and low ionization potential, the HOMO-LUMO gap of Sc4C3@C80 is substantially higher and exceeds that of Sc4C2@C80. In the third part, computational studies of structures and reactivity are described for a new type of EMFs with a heptagon that has been produced in the arc-discharge synthesis. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, so the former should be synthesized in much higher yield than observed. This disagreement may be ascribed to the kinetic factors rather than thermodynamic stability. Because of prospective applications of this EMFs by introducing functional groups, the influence of the heptagon on the chemical properties have been further evaluated. Thermodynamically and kinetically preferred reaction sites are studied computationally for Prato and Bingel-Hirsch cycloaddition reactions. In both types of reactions the heptagon is not affected, and chemical reactivity is determined by the adjacent pentalene units. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon edges, whereas the most reactive sites in kinetically-controlled Bingel-Hirsch reaction are the carbon atoms next to the pentagon/pentagon edge. Fourth, although various EMFs have been successfully synthesized and characterized, the formation mechanism is still not known in details, and hence control of the synthesis products is rather poor. Therefore, EMF self-assembly process in Sc/carbon vapor in the presence and absence of cooling gas (helium) and reactive gas (NH3 and CH4) is systematically investigated using quantum chemical molecular dynamics (QM/MD) simulations based on the DFTB potentials. The cooling gas effect is that the presence of He atoms accelerates formation of pentagons and hexagons and reduces the size of formed carbon cages in comparison to the analogous He-free simulations. As a result, the Sc/C/He system yields a large number of successful trajectories (i.e. leading to the Sc-EMFs) with more realistic cage-size distribution than the Sc/C system. Encapsulation of Sc atoms within the carbon cage was found to proceed via two parallel mechanisms. The main mechanism involves nucleation of the several hexagons and pentagons with Sc atoms already at the early stages of the carbon vapor condensation. In such proto-cages, both Sc–C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at high temperatures. Further growth of the carbon cage results in encapsulation of one or two Sc atoms within the forming fullerene. Another encapsulation mechanism is observed in rare cases. In this process, the closed cage is formed with Sc being a part of the carbon network, i.e. being bonded by three or four Sc–C σ-bonds. However, such intermediates are found to be unstable, and transform into the endohedral fullerenes within few picoseconds of annealing. In perfect agreement with experimental studies, extension of the simulation to Fe and Ti showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3). The role of “reactive gas” in the EMF synthesis is revealed in dedicated simulations of the fullerene formation in the presence of several molecules of CH4 or NH3. When concentration of reactive gas is high, carbon vapor tends to form graphene flakes or other carbon species terminated by hydrogen atoms, whereas the yield of empty fullerenes is very low. Conversely, with additional metal atoms (Sc) and the same number of NH3 molecules, the yield of fullerenes constantly increase from 5 to 65% which is ascribed to the catalytic activity of metal atoms in the nucleation of carbon cages already at early stage. Moreover, due to the presence of hydrogen atoms from the reactive gas, the carbon cage formation requires much longer time, which provides sufficient reaction time to encapsulate 3 or 4 Sc atoms within one cage. It explains preferential formation of clusterfullerenes in experiments with reactive gas. At the same time, monometallofullerenes and dimetallofullerenes are the main products in absence of reactive gas. We also provide possible growth mechanisms of carbide and cyano-clusterfullerenes in details to elucidate how the intracluster goes into the cage. A possible growth mechanism of nitride clusterfullerenes has been proposed based on DFT results. In the last part, a free-standing crystalline single-atom thick layer of Fe has been studied theoretically. By investigating the energy difference, ΔE, between a suspended Fe monolayer and a nanoparticle using the equivalent number of Fe atoms, one can estimate that the largest stable membrane should be ca. 12 atoms wide or 3 × 3 nm2 which is in excellent agreement with the experimental observation. Otherwise, the possibility of C, O, N atoms embedded into the Fe membrane can been fully excluded by DFTB and DFT simulations, which agrees with electron energy loss spectroscopy (EELS) measurement. A significantly enhanced magnetic moment for single atom thick Fe membranes (3.08 μB) is predicted by DFT as compared to the bulk BCC Fe (2.1 μB), which originates from the 2D nature of the Fe membrane since the dz2 orbital is out-of-plane while the dxy orbital is in-plane.

Conventional computing faces a huge technical challenge as traditional transistors will soon reach their size limitations. This will halt progress in reaching faster processing speeds and to overcome this problem, require an entirely new approach. Quantum computing (QC) is a natural solution offering a route to miniaturisation by, for example, storing information in electron or nuclear spin states, whilst harnessing the power of quantum physics to perform certain calculations exponentially faster than its classical counterpart. However, QCs face many difficulties, such as, protecting the quantum-bit (qubit) from the environment and its irreversible loss through the process of decoherence. Hybrid systems provide a route to harnessing the benefits of multiple degrees of freedom through the coherent transfer of quantum information between them. In this thesis I show coherent qubit transfer between electron and nuclear spin states in a ¹⁵N@C₆₀ molecular system (comprising a nitrogen atom encapsulated in a carbon cage) and a solid state system, using phosphorous donors in silicon (Si:P). The propagation uses a series of resonant mi- crowave and radiofrequency pulses and is shown with a two-way fidelity of around 90% for an arbitrary qubit state. The transfer allows quantum information to be held in the nuclear spin for up to 3 orders of magnitude longer than in the electron spin, producing a ¹⁵N@C₆₀ and Si:P ‘quantum memory’ of up to 130 ms and 1.75 s, respectively. I show electron and nuclear spin relaxation (T₁), in both systems, is dominated by a two-phonon process resonant with an excited state, with a constant electron/nuclear T₁ ratio. The thesis further investigates the decoherence and relaxation properties of metal atoms encapsulated in a carbon cage, termed metallofullerenes, discovering that exceptionally long electron spin decoherence times are possible, such that these can be considered a viable QC candidate.