Low-energy molecular experiments for precision measurements are considered to be a potential alternative to accelerator-based (i.e., high-energy) experiments for probing fundamental physics. The highly celebrated theory of particle physics-the Standard Model (SM) of elementary particles miserably fails to explain the matter-antimatter asymmetry and the existence of dark energy and dark matter of our universe. That is why, physicists are searching for new theories, often referred to as beyond Standard Model (BSM) theories. New sources of CP -violation (i.e., those originating beyond the SM) are very important to explore the BSM physics, where C and P mean two fundamental symmetries: charge conjugation and spatial parity invariance, respectively. The time-reversal invariance (T ) is another fundamental symmetry in physics and our universe is considered to be invariant under CP T symmetry according to the CP T theorem. The existence of non-zero electric dipole moment (EDM) of elementary or composite particles can only be possible if P and T (equivalently, CP ) symmetries are simultaneously violated . Thus, an experimental search of non-zero permanent EDM of the electron, proton, neutron, etc., has become crucial for the development of BSM theories. In recent years, many experiments have been performed or designed to search for new sources of CP violation using atoms and molecules . Because of a few additional advantages, polar molecules are usually preferred over atoms for P, T -violating EDM experiments . Electronic and nuclear structure study of such molecules play a very important role in designing the high-precision molecular experiments. Especially accurate knowledge of the electronic structure of any molecular system of interest is necessary to predict the laser coolability and the P, T -odd electronic structure parameters of the molecule. Large P, T -odd molecular parameter and laser coolability are two of the desired qualities for identifying suitable candidates for P, T -odd molecular EDM experiments. In recent times, a number of notable attempts have been made to measure the electron's EDM (eEDM) using ultracold heavy polar diatomic molecules such as YbF , ThO , BaF , and HfF + . In addition to the eEDM, there are a few significant sources of CP violation, viz., (i) intrinsic EDM of nucleons, (ii) P, T -odd electron-nucleon interaction, (iii) P, T -odd nucleon-nucleon interactions, etc., which results in the permanent EDM of a molecule . That is why, providing robust limits on the fundamental constants corresponding to these P, T -odd sources from molecular EDM experiments is not an easy task. However, it is argued in Refs. that suitable complementary molecules with moderately heavy nuclei could be useful in determining the limits on fundamental P, T -odd constants from the experiments on heavy polar molecules, and authors also enlightened the probable special role of lighter molecules in future searches of CP violation. Thus, detailed studies on lighter or moderately heavy ultracold molecular systems towards this goal could be demanding in coming days.