Covariant density functional theory (CDFT) is one of the modern theoretical tools for describing the nuclear structure physics of finite nuclei. Its performance is defined by underlying covariant energy density functionals (CEDFs). In this dissertation and within the framework of the CDFT, different physical properties of the ground and the excited states of rotating and non-rotating nuclei have been investigated. A systematic global investigation of pairing properties based on all available experimental data on pairing indicators has been performed for the first time in the framework of covariant density functional theory. It is based on separable pairing interaction of Ref.\ \cite{TMR.09}. The optimization of the scaling factors of this interaction to experimental data clearly reveals its isospin dependence in the neutron subsystem. However, the situation is less certain in the proton subsystem since similar accuracy of the description of pairing indicators can be achieved both with isospin-dependent and mass-dependent scaling factors. The differences in the functional dependencies of scaling factors lead to the uncertainties in the prediction of proton and neutron pairing properties which are especially pronounced at high isospin and could have a significant impact on some physical observables. Although the present investigation is based on the NL5(E) covariant energy density functional (CEDF), its general conclusions are expected to be valid also for other CEDFs built at the Hartree level. It is shown for the first time that rotational bands which are proton unbound at zero or low spins can be transformed into proton bound ones at high spin by collective rotation of nuclear systems. This is due to strong Coriolis interaction, which acts on high-$N$ or strongly mixed M orbitals and drives the highest in energy occupied single-particle states of nucleonic configurations into the negative energy domain. Proton emission from such proton bound rotational states is suppressed by the disappearance of static pairing correlations at high spins of interest. These physical mechanisms lead to a substantial extension of the nuclear landscape beyond the spin zero proton drip line. In addition, a new phenomenon of the formation of giant proton halos in rotating nuclei emerges: it is triggered by the occupation of strongly mixed M intruder orbitals. Possible experimental fingerprints of the transition from particle bound to particle unbound part of rotational bands are discussed and compared for proton and neutron rich nuclei near and beyond respective drip lines.

This dissertation focuses on the design and study of charged aromatic molecules where weak π-π interactions synergize with electrostatic interactions to enhance the overall interaction between aromatic moieties. Each chapter investigates some aspect of this hypothetical synergy between electrostatics and π-face aromatic cohesion. The first chapter unveiled the importance of electrostatics in the intramolecular stacking of flexible aromatic molecular templates 1-2Br and 2a. While our previous studies found dicationic molecular template 1-2Br to have intramolecular π-stacking between electron poor pyridinium and electron rich xylylene moieties, no such stacking interaction was observed in the neutral analog 2a. Chapter two systematically explored the stacking pattern of electron poor aromatics in the form of oxygen- and / or nitrogen- substituted triangulenium cations, [1(NR)3]+ and [1(O)3(OH)3]+. As indicated in the chemical literature, triazatriangulenium cations [1(NR)3]+ with N- ethyl (and longer alkyl chains) chains were found to pack as face-to-face dimers. This study found the formation of columnar, face-to-face, n-meric association between aromatic cations in the structures with decreased steric interactions of the side chains in the stacking planes ([1(NMe)3]+ and [1(O)3(OH)3]+). Similar iso-structural triangulene based aromatic anions, (2)- and (3)2- didn’t indicate any facial interactions in the solid states. The possible synergy between unit charge electrostatics and π-face aromatic interactions was explored in aromatic ion pairs 1•2 of triangulene based aromatic cations and aromatic anions. This charge-assisted π-π stacking seems to be the novel way of getting strong π-system interactions where the strongest non-covalent force and the weakest non-covalent force: ionic bonding and π-stacking respectively synergize together. The π-π interaction between ionic aromatics in the solid state was investigated by means of single crystal x-ray diffraction and powder x-ray diffraction (PXRD). The interaction in the solution state was examined by UV-Vis spectroscopy, electrospray ionization mass spectroscopy (ESI-MS) and electrochemical studies. Studies found that optimal synergy was possible only in the ion pairs with no steric interactions of alkyl (or aryl) side chains in the stacking planes (1(O)3•2 & 1(NMe)3•2) and the interaction was found to be comparable with the strongest radical-assisted π-stacking described in the chemical literature.