This dissertation consists of three major studies. The first study, described in Chapter 3, focuses on the experimental work we carried out; experimental study of the electronic transition dipole moment matrix elements (TDMM) for the and electronic transitions of the sodium dimer molecule. Here we obtained the electronic transition dipole moments through Autler-Townes and resolved fluorescence spectroscopy and compared them to the theory. The second study, described in Chapter 4, is on sodium dimer ion-pair states. In this work, we calculated the radiative lifetimes and electronic transition dipole moments between Na2 ion-pair states ( , , , ) and state. This study was published in 2015. The last study, described in Chapter 5, is the total lifetime (bound-bound plus bound-free) and transition dipole moment calculations of the ion-pair electronic states, , of the lithium dimer molecule. / Physics