In this paper, the potential energy curve (PEC) of 4T– is calculated with the Brueckner coupled-cluster doubles with perturbative triple and quadruple corrections [BD(TQ)]. <...> Basis set extrapolations with the correlation-consistent basis sets are performed. <...> The efficiency and precision of the methods with different basis sets are compared. <...> The calculated spectroscopic constants are in excellent agreement with the experimental ones. <...> Nevertheless, it seems that the basic diatomic species have not attracted wide attention of the scientific community. <...> They identified correctly that the ground state was X4T–. <...> Bauschlicher et al. [ 6 ] studied the low-lying doublet and quartet electronic states of AlC using the multireference CI methodology. <...> From the calculation they drew the conclusion that B4T–—X4T– is the strongest, which was in agreement with the experimental results of Knight et al. [ 2 ]. <...> Gutsev et al. [ 7 ] determined De, the bond length (re), and harmonic frequency (e) using the CCSD(T) method. <...> Tzeli and coworkers investigated the ground-state [ 8 ] and the excited-state [ 9 ] electronic structures using multireference variational methods and large correlation consistent basis sets. <...> The Level8.0 program can solve the radial or one-dimensional Schrцdinger equation for bound and/or quasibound levels of any smooth single or double-minimum potential, and calculate inertial rotation and centrifugal distortion constants, expectation values, and/or Franck—Condon factors and other off-diagonal matrix elements, either for levels of a single potential or between the levels of two different potentials. <...> In this work the spectroscopic constants are calculated with Le Roys LEVEL [ 12 ] program. <...> Using a series of increasing size correlation consistent basis sets and the multireference CI approach, we have investigated the ground state of the AlC molecule. <...> We discussed the reasons that make the MRCI method not good for the calculation of spectroscopic constants of the AlC ground state. <...> The deviation must come from the correlation energy. <...> To improve the level of the correlation energy, we used the BD(TQ) method to calculate the spectroscopic constants. <...> For both Al and C atoms, and the AlC system, the ground state geometry, optimization, and single point energy were calculated at the Brueckner coupled-cluster doubles level with perturbative triples and quadruples [BD(TQ)] [ 13 ] using <...>