Computational aspects of the energy derivative multi-reference double-excitation configuraiton interactions approach to calculations of the electric field gradient (EFG) tensor are discussed. Special attention is paid to those features of the method which are essential for a physically relevant description of the nuclear quadrupole coupling in low-lying rovibronic states of diatomic molecules. The 2H and 7Li quadrupole coupling constants (QCCs) of rovibrational levels of 7Li 2H in its X 1∑ and A 1∑ + electronic states are calculated by this approach and compared with those based on the standard expectation value approach to the evaluation of the EFG tensor. The scheme might become useful in theoretical interpretation of the quadrupole hyperfine structure of excited rovibrational levels of diatomic molecules in their ground and excited electronic states.