The previous multireference configuration interaction (MRCI) results show that the ground state 4"– of the AlC molecule is basically single configurational in nature. In this paper, the potential energy curve (PEC) of 4"– 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. Our results reveal that the correlation from higher order excitations than doubles is very important for this system