The nuclear quadrupole coupling constant was calculated as a function of inter nuclear distance for nine quadrupolar nuclei in eight diatomic molecules by the STO 321G method. From the value of the field-gradient and its first and second derivatives the vibrational dependence of the coupling constants were calculated and shown to compare satisfactorily with experiment. The behaviour of the field-gradient as a function of inter nuclear distance can in most cases be rationalized in terms of the field-gradient that will arise for the infinitely separated atoms