Clusters constitute an intermediate state of matter between molecules and solids whose properties are size dependent and can be tailored. In recent years, cluster science has become one of the most exciting areas of research since their study can not only bridge our understanding between atoms and their bulk but also between various disciplines. In addition, clusters can serve as a source of new materials with uncommon properties. This dissertation deals with an in-depth study of clusters as a bridge across physics, chemistry, and materials science and provides a fundamental understanding of the structure-property relationships by focusing on three different topics. The first topic deals with superatoms which are clusters that mimic the chemistry of atoms. I show that superhalogens and superalkalis can be designed to mimic the chemistry of halogen and alkali atoms, respectively. An entirely new class of salts can then be synthesized by using these superatoms as the building blocks. I have also explored the possibility of designing highly electronegative species called hyperhalogens by using superhalogens as ligands or superalkalis as core and a combination of both. Another aspect of my work on superatom is to examine if traditional catalysts (namely Pd) can be replaced by clusters composed of earthabundant elements (namely Zr and O). This is accomplished by comparing the electronic structure and reactivity of Pd clusters with isoelectronic ZrO clusters. The second topic deals with a study of the electronic structure of coinage metal (Cu and Ag) clusters and see if they remain unchanged when a metal atom is replaced by an isoelectronic hydrogen atom as is the case with Au-H clusters. The third topic deals with clusters as model of polymeric materials to understand their gas storage and sequestration properties. This is accomplished by studying the trapping of H2, CO2, CH4 and SO2 molecules in borazine-linked polymers (BLPs) and benzimidazole-linked polymers (BILPs). The first two topics provide a bridge between physics and chemistry, while the third topic provides a bridge to materials science.

Fullerenes have highly excited electronic states with interesting properties for possible wide ranging applications including in electronics. These highly excited, Rydberg-like states, so-called superatom molecular orbitals (SAMOs), are diffuse low-angular momenta states with molecular orbitals centred on the hollow fullerene core. The SAMOs can be detected by femtosecond photoelectron spectroscopy (PES) and characterised by photoelectron angular distributions (PADs) combined with time-dependent density functional theory (TD-DFT) calculations. The photoelectron spectra of C60 and C70 show a peak structure below kinetic energies corresponding to the photon energy, superimposed on a thermal electron background. This peak structure was assigned to one-photon ionisation of the SAMO states based on PAD and TD-DFT. In this thesis, studies of the fullerene species C82 and Sc3N@C80 revealed PES and PAD with similar features to C60 and C70. The SAMO peaks became less prominent compared to the thermal electron background for increasing molecular size and decreasing symmetry, and were almost absent for the endohedral species. To provide more information about the influence of encapsulated atoms in the fullerene cage on the SAMO states, experiments on Li@C60 have been carried out. A lower thermal electron emission temperature and a splitting of the SAMO peaks has been observed for Li@C60 compared to C60. Nevertheless the binding energies are remarkably similar in all investigated fullerenes, which is important for any applications. Since the binding energies are about the same, but the ionisation potentials of the fullerenes are different, the excitation energy to the SAMOs scales with the ionisation energy. The reasons for the well-pronounced peak structure of the SAMO states in the PES of C60 could be explained by the similarity of the SAMOs to Rydberg states along with the higher photoionisation probabilities compared to valence states which were modelled by Benoît Mignolet and Françoise Remacle. As the SAMOs are highly excited electronic states, like Rydberg states, the potential energy surface of the neutral molecule and the ionised molecule are similar. Therefore the vibrational energy is conserved in the molecule during the photoionisation on the femtosecond time scale. The TD-DFT calculations on C60, carried out by Benoît Mignolet and Françoise Remacle, revealed the photoionisation probabilities of the SAMOs to be at least three orders of magnitude higher than for non-SAMOs for the applied experimental conditions. To test the prediction of the model, the relative photoionisation probabilities of the s-SAMO to p-SAMO and the s-SAMO to d-SAMO were obtained experimentally from the PES at various photon energies (2-3.5 eV) within this work. The analysis indicates remarkable agreement between the experiment and the theoretical values. Further quantum chemical calculations on a series of polycyclic aromatic hydrocarbons (PAHs) were carried out within this thesis, which revealed similar Rydberg-like molecular orbitals in analogy to the SAMOs in fullerenes. The first series included benzene, naphthalene, anthracene, tetracene, pentacene and hexacene. The second series consisted of phenanthrene, pyrene and coronene. Finally, the third series covered cubane, adamantane and dodecahedral C20. All modelled molecules showed diffuse, excited electronic states similar to the SAMOs. Within each series the binding energies of these states decrease with increasing molecular size as well as the ionisation energies, except for the 3rd series. A comparison between all series shows that the binding energies of the states for the 3rd series (the 3-D series) are slightly higher than for the 1st and 2nd series in relation to similar molecular size. The results of the coronene calculations are compared to experimental photoelectron spectra and are shown to be in good agreement with the experiments.

Calculations have been carried out to investigate the stability and electronic structure of aluminum iodide clusters using first principles gradient-corrected density functional theory. Analysis of A113Ix-, A114Ix-, and A17I- clusters reveals that their stability is governed by the geometrically unperturbed A113-, A1142+, and A17+ units, respectively, that are demonstrated to constitute the compact cores of the clusters upon significant iodine content. The compact, icosahedral A113, icosahedral-like A1 14, and capped square bi-pyramid A17 superatom structures of the stable aluminum cores have an analogous electronic configuration to that of halogen, alkaline-earth, and alkaline atoms, respectively. Novel chemistry is demonstrated in superatoms, arising from two primary sources. Firstly, the calculations demonstrate the preference to break molecular I2 bonds in favor of iodine atoms individually adsorbing onto the aluminum sites of the central aluminum core surface. Secondly, the calculation show that observations of alternating stability trends dependent on the number of iodine ligands are connected to the formation and quenching of active sites. The significance of the induced active centers on aluminum iodide clusters upon association to alkenes is addressed, demonstrating a method towards predicting the location and extent of binding hydrocarbons. The novel chemistry of superatoms allows for a host of possible applications that integrate their unique properties in original ways and some key examples are described. Superatoms are the analogs to atoms and subsequently, just as the periodic table of elements lists atoms that can assemble into molecules and lattice structures, there exists the fathomable possibility to incorporate superatoms into extended structures such that they maintain their unique properties and result in a new class of materials. Initiation of such cluster-materials insinuates that cluster-mediated periodic table may be a proper extension to allow for a simple means for conveying fundamental information about clusters.

This thesis is a theoretical study of configurational disorder in icosahedral boron-rich solids, in particular boron carbide, including also the development of a methodological framework for treating configurational disorder in such materials, namely superatom-special quasirandom structure (SA-SQS). In terms of its practical implementations, the SA-SQS method is demonstrated to be capable of efficiently modeling configurational disorder in icosahedral boron-rich solids, whiles the thermodynamic stability as well as the properties of the configurationally disordered icosahedral boron-rich solids, modeled from the SA-SQS method, can be directly investigated, using the density functional theory (DFT). In case of boron carbide, especially B4C and B13C2 compositions, the SA-SQS method is used for modeling configurational disorder, arising from a high concentration of low-energy B/C substitutional defects. The results, obtained from the DFT-based calculations, demonstrate that configurational disorder of B and C atoms in boron carbide is not only thermodynamically favored at high temperature, but it also plays an important role in altering the properties of boron carbide − for example, restoration of higher rhombohedral symmetry of B4C, a metal-to-nonmetal transition and a drastic increase in the elastic moduli of B13C2. The configurational disorder can also explain large discrepancies, regarding the proper- ties of boron carbide, between experiments and previous theoretical calculations, having been a long standing controversial issue in the field of icosahedral boron- rich solids, as the calculated properties of the disordered boron carbides are found to be in qualitatively good agreement with those, observed in experiments. In order to investigate the configurational evolution of B4C as a function of temperature, beyond the SA-SQS level, a brute-force cluster-expansion method in combination with Monte Carlo simulations is implemented. The results demonstrate that configurational disorder in B4C indeed essentially takes place within the icosahedra in a way that justifies the focus on lowenergy defect patterns of the superatom picture. The investigation of the thermodynamic stability of icosahedral carbon-rich boron carbides beyond the believed solubility limit of carbon (20 at.% C) demonstrates that, apart from B4C generally addressed in the literature, B2.5C represented by B10Cp2(CC) is predicted to be thermodynamically stable with respect to B4C as well as pure boron and carbon under high pressure, ranging between 40 and 67 GPa, and also at elevated temperature. B2.5C is expected to be metastable at ambient pressure, as indicated by its dynamical and mechanical stabilities at 0 GPa. A possible synthesis route of B2.5C and a fingerprint for its characterization from the simulations of x-ray powder diffraction pattern are suggested. Besides modeling configurational disorder in boron carbide, the SA-SQS method also opens up for theoretical studies of new alloys between different icosahedral boron-rich solids − for example, (B6O)1−x(B13C2)x and B12(As1−xPx)2. As for the pseudo-binary (B6O)1−x(B13C2)x alloy, it is predicted to display a miscibility gap resulting in B6O-rich and either ordered or disordered B13C2-rich domains for intermediate global compositions at all temperatures up to melting points of the materials. However, some intermixing of B6O and B13C2 to form solid solutions is also predicted at high temperature. A noticeable mutual solubility of icosahedral B12As2 and B12P2 in each other to form B12(As1−xPx)2 disordered alloy is predicted even at room temperature, and a complete closure of a pseudo-binary miscibility gap is achieved at around 900 K. Apart from B12(As1−xPx)2, the thermodynamic stability of other compounds and alloys in the ternary B-As-P system is also investigated. For the binary B-As system, zincblende BAs is found to be thermodynamically unstable with respect to icosahedral B12As2 and gray arsenic at 0 K and increasingly so at higher temperature, indicating that BAs may merely exist as a metastable phase. This is in contrast to the binary B-P system, in which zinc-blende BP and icosahedral B12P2 are both predicted to be stable. Owing to the instability of BAs with respect to B12As2 and gray arsenic, only a tiny amount of BAs is predicted to be able to dissolve in BP to form BAs1−xPx disordered alloy at elevated temperature. For example, less than 5% BAs can dissolve in BP at 1000 K. As for the binary As-P system, As1−xPx disordered alloys are predicted at elevated temperature − for example, a disordered solid solution of up to ∼75% As in black phosphorus as well as a small solubility of ∼1% P in gray arsenic at 750 K, together with the presence of miscibility gaps. The thermodynamic stability of three different compositions of α-rhombohedral boron-like boron subnitride, having been proposed so far in the literature, is investigated. Those are, B6N, B13N2, and B38N6, represented respectively by B12(N-N), B12(NBN), and [B12(N-N)]0.33[B12(NBN)]0.67. It is found that, out of these sub- nitrides, only B38N6 is thermodynamically stable from 0 GPa up to ∼7.5 GPa, depending on the temperature, and is thus concluded as a stable composition of α-rhombohedral boron-like boron subnitride.

Theoretical studies using the Kohn-Sham density functional formalism have been carried out to identify and investigate the stability of a variety of atomic clusters for their use in cluster assembled materials. The stable behavior found in a cluster system provides a way to classify inorganic clusters. The clusters in this study can be categorized in one of the following, jellium, all-metal aromatic, Zintl analogue or as a covalent metal-carbide. By understanding the electronic structure and ultimately the stable nature of a cluster first, it is proposed one can construct assemblies based on the stable cluster. The methodology presented is a viable way to design future nanomaterials with a variety of architectures and precise control over properties based on stable cluster motifs.

Quantum confinement in small metal clusters leads to a bunching of states into electronic shells reminiscent of shells in atoms. The addition of ligands can tune the valence electron count and electron distribution in metal clusters. A combined experimental and theoretical study of the reactivity of methanol with AlnIm− clusters reveals that ligands can enhance the stability of clusters. In some cases the electronegative ligand may perturb the charge density of the metallic core generating active sites that can lead to the etching of the cluster. Also, an investigation is conducted to understand how the bonding scheme of a magnetic dopant evolves as the electronic structure of the host material is varied. By considering VCun+, VAgn+, and VAun+ clusters, we find that the electronic and atomic structure of the cluster plays a major role in determining how an impurity will couple to its surroundings.