The quadratic force constants of heteronuclear diatomic molecules, LiH, BeH, BH, CH, NH and OH are evaluated by use of the one center function of Bishop et. al. The master formula on which the computation is based was suggested by the previous work of one of the present authors. The results are in good agreement with the experimental values. It is found that around the nucleus of the atom located in the close vicinity of the expansion center of the one center function, the electronic distribution is relatively unrealistic, and the suggested formula would lead an erroneous result when one takes the origin of variables of P_2(cos{ heta})/r_3$ at the atomic nucleus