Previous studies have revealed significant discrepancies between density functional theory (DFT)-calculated and experimental nuclear quadrupolar coupling constants (CQ) for chlorine atoms, particularly in ionic solids. Various aspects of the computations are systematically investigated here, including the choice of the DFT functional, basis set convergence, and geometry optimization protocol. The effects of fast (fs) time-scale dynamics are probed using molecular dynamics (MD) and nuclear quantum effects (NQEs) are considered using path-integral MD calculations. It is shown that the functional choice is the most important factor related to improving the accuracy of the quadrupolar coupling calculations, and that functionals beyond the generalized gradient approximation (GGA) level, such as hybrid and meta-GGA functionals, are required for good correlations with experiment. The influence of molecular dynamics and NQEs is less important than the functional choice in the studied systems. A method which involves scaling the calculated quadrupolar coupling constant is proposed here; its application leads to good agreement with experimental data.