A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Materials Science and Engineering of the Nelson Mandela African Institution of Science and TechnologyComputational and theoretical methods were employed to study the structure, vibrational spectra and thermodynamic properties of cluster ions that were detected earlier in saturated vapour over barium dihalides. The equilibrium geometrical parameters and vibrational spectra were computed for the ions BaX3‒, Ba2X3+, Ba3X5+, Ba4X7+ and Ba5X9+ (X= F, Br or I); the DFT/B3P86 and MP2 methods with triple-zeta valence basis sets were used. The ions BaX3‒, Ba2X3+, Ba3X5+ and Ba5X9+ were confirmed to correspond to D3h point group of symmetry and Ba4X7+ to C2v configuration. Alternative structures for the cluster ions have been considered but no isomers were identified. The structural parameters and frequencies calculated with different theoretical approaches appeared to be not much sensitive regarding the methods and basis sets used. The enthalpies of ion molecular reactions were obtained both theoretically through the total energies of participants and based on experimental data through the equilibrium constants measured earlier. The enthalpies of formation ΔfHo(0) of the ions have been determined (in kJ mol–1): ‒1356  4 (BaF3‒); ‒1039  12 (Ba2F3+); ‒2179  16 (Ba3F5+); ‒3277  35 (Ba4F7+); ‒4316  22 (Ba5F9+); ‒858  6 (BaBr3‒); ‒293  10 (Ba2Br3+); ‒982  20 (Ba3Br5+); ‒1644  30 (Ba4Br7+); ‒2282  17 (Ba5Br9+); ‒709  6, (BaI3‒); ‒96  12 (Ba2I3+); ‒654  17 (Ba3I5+); ‒1177  20 (Ba4I7+); ‒1686  20 (Ba5I9+). The dimer molecules existing in vapours over the respective barium dihalides were studied, the thermodynamic properties and vapour compositions of their isomers were computed. For Ba2F4, Ba2Cl4 and Ba2Br4, three isomers of C3v, C2v and C2h symmetries were confirmed to exist while for Ba2I4 only two isomers, C3v and C2h were confirmed. For all isomers, the pyramidal isomer (C3v), was observed to be predominant at lower temperatures up to about 700 K followed by trans- and cis-isomers. The pyramidal isomer possesses higher magnitude of enthalpy of dissociation reaction and hence more stable than other isomers at ambient temperature. The enthalpies of formation of the C3v isomers were obtained (in kJ mol‒1): ‒1874  2 (Ba2F4); ‒1236  7 (Ba2Cl4); ‒1023  8 (Ba2Br4); ‒787  11 (Ba2I4).