The use of solid-state NMR and DFT calculations to study Y₂Sn[subscript(x)]Ti[subscript(2-x)]O₇, Y₂Sn[subscript(x)]Zr[subscript(2-x)]O₇ and Y₂Ti[subscript(x)]Zr[subscript(2-x)]O₇, materials with applications for the safe encapsulation of radioactive actinides is investigated. As a result of cation or anion disorder in these materials, NMR spectra are often complex and difficult to interpret. Therefore, an investigation using a range of NMR active nuclei and measurement of a variety of NMR parameters (isotropic chemical shift, δ[subscript(iso)]; span, Ω and quadrupolar coupling, C[subscript(Q)]) were used to provide a full and detailed picture of each material. The measurement of Ω in these disordered compounds with multiple resonances in the NMR spectra, required the use of 2D CSA-amplified PASS (CAPASS) experiments to enable the separation of each of the spinning sideband manifolds. An experimental assessment of the CAPASS experiment showed that although low ν₁/Ω[subscript(Hz)] ratios (as found in ⁸⁹Y NMR) resulted in distortions in the spectra obtained, a modified fitting procedure could be utilised to compensate for this fact, which allowed the accurate measurement of Ω. Despite the difficulties in acquiring the ⁸⁹Y NMR spectra, they were found to be the most informative of the NMR-active nuclei available. ¹¹⁹Sn NMR spectra, although much easier to acquire than ⁸⁹Y, were more complex and harder to analyse, owing to the overlapping resonances. Therefore, ¹¹⁹Sn NMR could only be used to confirm or support the results obtained using ⁸⁹Y NMR. Although ¹⁷O NMR was found to be useful, a full study could not be implemented due to the lack of ¹⁷O enriched samples; an area where future investigation may prove fruitful. Finally, [superscript(47/49)]Ti and ⁹¹Zr NMR spectra were found to be the most difficult to acquire due to their low receptivities and the quadrupolar broadened lineshapes, and as a result, little additional information was obtained. As a result of this analysis, for the Y₂Sn[subscript(x)]Ti[subscript(2-x)]O₇ pyrochlore solid solution, using primarily ⁸⁹Y δ[subscript(iso)] and Ω, and additionally confirmed with ¹¹⁹Sn δ[subscript(iso)], it was found that the Sn and Ti cations were randomly ordered throughout the B-sites. Additionally, ⁸⁹Y Ω could be used to obtain approximate Y-O[subscript(48f)] and Y-O[subscript(8b)] bond lengths for each type of Y environment. The study of Y₂Sn[subscript(x)]Zr[subscript(2-x)]O₇ using ⁸⁹Y NMR showed that although the end members were single phase, pyrochlore (Y₂Sn₂O₇) or defect fluorite (Y₂Zr₂O₇), the intermediate compositions were mostly two phase mixtures, consisting of an ordered pyrochlore (with an average formula of Y₂Sn₁.₈Zr₀.₂O₇) and a disordered phase, where the proportions of the pyrochlore and disordered phases decreased and increased, respectively, with the Zr content. Additionally, although the coordination states of the Y and Sn cations were easily determined using ⁸⁹Y and ¹¹⁹Sn NMR, respectively, the coordination states of the Zr cations could not be confirmed directly by ⁹¹Zr NMR. However, using indirect analysis from results obtained with ⁸⁹Y and ¹¹⁹Sn NMR, it was determined that 6 coordinate Zr was present in each composition, and it was always present in a greater proportion than 8 coordinate Zr. Finally, although ⁸⁹Y NMR spectra of Y₂Ti[subscript(x)]Zr[subscript(2-x)]O₇ were extremely difficult to analyse, it was tentatively proposed that they could be similar to Y₂Sn[subscript(x)]Zr[subscript(2-x)]O₇ due to some similarities observed between the spectra.

This thesis reports the theoretical investigations aimed at understanding the structure, stability and properties of a few inorganic compounds. The first chapter presents an introductory overview of the theories used to solve the questions addressed in the thesis. A brief discussion of the work is also presented here. The second chapter deals with electron reservoirs which have been one of the basic motifs of single-electron device. Mononuclear vinylidene complexes of type Mn(C5H4R’)(R” 2 PCH2CH2PR "2)= C = C(R1)(H) were synthesized and reported [Venkatesan et al, Organometallics 25, 5190 (2006)] as potential electron reservoirs capable of storing and releasing electrons in a reversible fashion. These compounds have been of great interest because their red-ox chemistry (reversible oxidative coupling and reductive decoupling) is governed by the C - C bond. However slow oxidation of the mononuclear vinylidene complexes leads to undesired product. In our model compound Mn(C5H5)(PH3)2 = C = C(R1)(H), we substituted the cyclopentadienyl moiety by isolobal dianionic dicarbollyl ligand Dcab2- (C2B9H2-11 ). This simple substitution could reduce the production of undesired product. Calculations of vertical detachment energy, thermodynamic feasibility and molecular orbital analysis showed that this substitution was thermodynamically feasible and led to easy oxidation and dimerization of the parent compound accompanied with better reversibility of the reaction. The effect of substituents (R = H,Me,Ph) on Cβ atom of our model system was also analyzed. The substituent on β carbon had a great effect on the stability and reactivity of these complexes. Our comparative study between Mn(C5H5)(PH3)2 = C = C(R)(H) and Mn(Dcab)(PH3)2 = C = C(R)(H)−1 (where R = H,Me,Ph) predicted the latter to be a more potential electronic reservoir. Gas-phase observations on MAl 4- (M = Li, Na, Cu) and Li3Al-4 coupled with computations led to the conclusion that Al42− [Boldyrev and Wang et al, Science 291, 859 (2001)] is “aromatic” while Al44- is “antiaromatic” [Boldyrev and Wang et al, Science 300, 522 (2003)]. It has been reported by Pati et al [J. Am. Chem. Soc. 125, 3496 (2005)] that co-ordination with a transition metal can stabilize the “antiaromatic” Al4Li4. In the first section of chapter three, it has been reported that Al4Li4 can also be stabilized by capping it with main group element like C and its isoelectronic species BH. Calculations of binding energy, nuclear independent chemical shift (NICS), energy decomposition analysis and molecular orbital analysis supported the capping induced stability, reduction of bond length alternation and increase of aromaticity of these BH/C capped Al4Li4 systems. The interaction between px and py orbitals of BH/C and the HOMO and LUMO of Al4Li4 was responsible for such stabilization. Calculations suggested that capping might introduce fluxionality in the molecule at room temperature. Al has valence electronic configuration of s2p1 and Al42− has been shown to have multiple aromaticity [Boldyrev and Wang et al, Science 291, 859 (2001)]. Analogy between electronic configuration s2pof Al and d1sof Sc/Y prompted us to explore the aromaticity of M42− clusters (M = Sc, Y ) which have been described in the second section of chapter three. Different geometries of M42− clusters (M = Sc, Y ) were explored, and the planar butterfly-like D2h geometry (two fused triangles) was found to be the most stable isomer. This is unlike the case of Al42− where D4h isomer was the most stable one as reported in the literature. In D2h geometry of M42− clusters (M = Sc, Y ), significant electron delocalization in each wing of the butterfly indicated fused d aromaticity. Atomization energy and chemical hardness supported the preference of D2h geometry over the D4h geometry. Molecular orbital analysis showed that the d-electrons were delocalized in each triangle of D2h geometry. Our interest in the search of new kinds of binuclear sandwich compounds led us to consider sandwiched metal dimers CB5H6M - MCB5H6 (M = Si, Ge, Sn) which are at the minima in the potential energy hypersurface with a characteristic M - M single bond. This work has been described in the first section of chapter four. The NBO analysis and the M - M distances ( ˚A) (2.3, 2.44 and 2.81 for M= Si, Ge, Sn respectively) indicated substantial M - M bonding. Consecutive substitution of two boron atoms in B7H7−2 by M (Si, Ge, Sn) and carbon respectively led to neutral MCB5H7, where M - H bond bent towards the carbon side of the five membered ring. Dehydrogenation of two MCB5H7 might lead to our desired CB5H6M - MCB5H6 where similar bending of M -M bond has been observed. The bending of M - M bond in CB5H6M -MCB5H6 was more than the M - H bending in MCB5H7. Molecular orbital analysis has been done to understand the bending. Larger M - M bending observed in CB5H6M - MCB5H6 in comparison to M - H bending observed in MCB5H7 was suspected to be favored by stabilization of one of the M - M π bonding MO’s. Preference of M to occupy the apex of pentagonal skeleton of MCB5H7 over its icosahedral analogue MCB10H11 has been observed. Structures of sandwiched binuclear L- M – M - L where M = Ti, Zr and L = Cp, C3B3H6 were also investigated as described in second section of chapter four. We found that these compounds having bent geometry with short M - M distance (1.87˚A for M=Ti and 2.29˚A for M=Zr) lie at the minima in the potential energy hypersurface. Bending from the linear geometry led to the stabilization of M - L antibonding interaction in L - M – M - L. Molecular orbital analysis, NBO calculations, Wiberg bond index and charge analysis suggested M2+ unit to be embedded in between two L’s in L - M – M - L. Molecules that have the ability to perform interesting mechanical motions have always been of great interest. Umbrella inversion of ammonia is one of the most interesting and well studied phenomena. This study has led to the development of the MASER. The possibility of inversion of the molecule C9H9−Li+ by the movement of Li+ through the C9H9−ring was studied earlier [Das et al, Chem. Phys. Lett. 365, 320 (2002)]. In the fifth chapter theoretical investigation on a B12 cluster has been reported, which could exhibit a through ring umbrella inversion. Calculations showed that a part of the molecule, consisting of a three membered boron ring could invert through the rest, viz., a nine membered boron ring. Using a simple model, the double well potential for the motion was calculated. The barrier for inversion was found to be 4.31 kcal/mol. The vibrational levels and tunneling splitting were calculated using this potential. It was found that the vibrational excitation to the v = 17 level caused large amplitude “inversion oscillation” of the molecule. After considering the tunneling effect, inversion rate at 298K was calculated by using transition state theory and was found to be 1.17 x 1010/s. Finally, in the last chapter the main results of the thesis have been summarized.

This thesis uses solid-state nuclear magnetic resonance (NMR) spectroscopy and density functional theory (DFT) calculations to study local structure and disorder in inorganic materials. Initial work concerns microporous aluminophosphate frameworks, where the importance of semi-empirical dispersion correction (SEDC) schemes in structural optimisation using DFT is evaluated. These schemes provide structures in better agreement with experimental diffraction measurements, but very similar NMR parameters are obtained for any structures where the atomic coordinates are optimised, owing to the similarity of the local geometry. The ³¹P anisotropic shielding parameters (Ω and κ) are then measured using amplified PASS experiments, but there appears to be no strong correlation of these with any single geometrical parameter. In subsequent work, a range of zeolitic imidazolate frameworks (ZIFs) are investigated. Assignment of ¹³C and ¹⁵N NMR spectra, and measurement of the anisotropic NMR parameters, enabled the number and type of linkers present to be determined. For ¹⁵N, differences in Ω may provide information on the framework topology. While ⁶⁷Zn measurements are experimentally challenging and periodic DFT calculations are currently unreliable, calculations on small model clusters provide good agreement with experiment and indicate that ⁶⁷Zn NMR spectra are sensitive to the local structure. Finally, a series of pyrochlore-based ceramics (Y₂Hf₂₋ₓSnₓO₇) is investigated. A phase transformation from pyrochlore to a disordered defect fluorite phase is predicted, but ⁸⁹Y and ¹¹⁹Sn NMR reveal that rather than a solid solution, a significant two-phase region is present, with a maximum of ~12% Hf incorporated into the pyrochlore phase. The use of ¹⁷O NMR to provide insight into the local structure and disorder in these materials is also investigated. Once the different T₁ relaxation and nutation behaviour is considered it is shown that quantitative ¹⁷O enrichment of Y₂Sn₂O₇ is possible, and that ¹⁷O does offer a promising future tool for study.