The investigation of spectroscopic information is important for understanding the mechanisms of molecular photochemical and photophysical reactions. As a prototype to study the electronic structures and spectra of diatomic molecular systems, the vibration-rotational spectra of alkali dimer and its ions have aroused considerable research interest in the last two decades. Single-reference and multi-reference coupled cluster theory in combination with correlation consistent Gaussian basis set are adopted to study the ground-state potential energy curves of ⁷Li₂^{(0,± 1)} molecular systems. The correlation effect and relativistic effect of all the electrons are taken into account in the calculation. And the spectroscopic constants, including the equilibrium internuclear distance R_e, the harmonic vibrational frequency ω_e, the anharmonic constant ω_ex_e, the equilibrium rotational constant B_e, and the dissociation energy D_e of the molecular system and vibration-rotational energy level information of the ground states are obtained by solving the radial Schr dinger equations. The calculated spectroscopic constants of the neutral and positive ion system accord well with the experimental values; however for the negative ion system, the calculation of equilibrium internuclear distance needs further improving, and other spectroscopic constants are consistent well with the experimental values. The present computational results indicate that the ground state wave functions of neutral and positive ion systems have obvious single reference configuration characteristics, while the ground state of negative ion molecule system should be described with multireference configuration wave functions. The vibration-rotational energy levels of ground state with different theoretical methods are in good agreement with the experimental values. The vibrational-rotational energy levels and spectroscopic constants of neutral and positive ion systems are well reproduced, and some experimental information about spectrum is still lacking. Although the difference among the equilibrium internuclear distances for the ground state of the negative ion, obtained from different theoretical methods are still existent, the results of the vibrational level interval accord well with each other. This study provides useful information about spectrum for accurately investigating the electronic structures and spectra of the ground state of Li₂ molecular system and its two isotopic molecules, especially for the negative ion system with little information about spectrum.