Ab-initio calculations of nano-sized (1 nm) amorphous-TiO₂cluster and dye molecules (N3 and N719) have been carried out. Optimized structures of amorphous cluster and dye molecules have been obtained via molecular dynamics (MD) and density functional theory (DFT) calculations, respectively. The lowest excited state energies of the TiO₂ cluster and the dye molecules have been obtained using time-dependent DFT. The calculations show that HOMO–LUMO gap and singlet–singlet excited state energies for amorphous cluster are very similar to that of a crystalline TiO₂ cluster. Our calculations also show that the energy levels of the molecular dyes are well aligned with those of the amorphous cluster.

The computations of structural, electronic, bonding nature, dynamical, optical, thermoelectric, and elastic properties of the theoretically predicted 1T-Rb₂Se monolayer are effectuated. The 1T-Rb₂Se monolayer displays a semiconducting nature with the energy gap quantified using various exchange-correlational potentials. The phonon and CPMD was deployed for the conclusions on the dynamical and thermal stabilities. With indirect band gap and good thermal response, the material will have possible applications in photovoltaics and thermoelectrics. Positive Poisson’s ratio and elastic tensors validates the elastic strength of the monolayer. The effective masses of charge carriers and its relative ratio are determined from the energy band paraboloids with the deformation potentials for the accuracy of the relaxation time. The 1T-Rb2Se is electronically, ionically, dynamically, thermally, and elastically stable that confirms its feasibility for experimental studies.

The ground-state properties of the disodium helide (Na₂He) in the cubic structure was calculated using the WIEN2k package within GGA, LDA, and mBJ potentials. From our results, the GGA and LDA predict the material to be semiconductor, while mBJ predicts the material to be insulator. The calculated results from the electronic structure show that Na₂He is a direct bandgap semiconductor. 2D structure (monolayer) for this compound is undertaken and phonon calculations were performed. The result indicates that the compound is dynamically unstable. The compound Na₂He will be formed only under high pressure, although the optical properties for Na₂He were studied to provide benchmark studies for unstable compounds. Also, Na K edge x-ray absorption near edge structure (XANES) for Na₂He were computed and discussed.