In the present investigation, we performed a thorough study of potential energy curves, rovibrational spectra, and spectroscopic constants for complexes pairing via dihydrogen bonds. In particular, we dealt with LiH···HX (X = F, CN, CCH, CCF, CCCl) complexes by employing accurate electronic energy calculations at the MP2/aug-cc-pVDZ level of theory. Following this, the Numerov method was applied to solve the nuclear Schrödinger equation, thus obtaining spectroscopic constants and rovibrational spectra. Good linear correlation between the magnitudes of the interaction energies for interaction of HX with LiH, and the most positive electrostatic potentials of hydrogen in HX, was established.