Ab initio calculations up to MP2/aug-cc-pVTZ//MP2/cc-pVTZ level, including natural charge population and natural resonance theory analyses, have been carried out to study the two-way effects between hydrogen bond (H-bond) and the intramolecular resonance effect by using the H-bonded complexes of formamide (FAO) and its derivatives (FAXs, X represents the heavy atoms in the substituent groups, =CH2, =NH, =SiH2, =PH, and =S) with water as models. Unlike NH3 and NH2CH3 which prefer being H-bond acceptors (HA) to form H-bond with water, the amino groups in the six monomers, because of the resonance effect, prefer being H-bond donors (HD) rather HA. Six monomers can all form HD complexes with water, and only two (FAC and FASi) with the weakest resonance effect are able to form HA complexes with water. The HD H-bond and resonance effect enhance each other (positive two-way effects) whereas the HA H-bond and resonance effect weaken each other (negative two-way effects). The H-bond energies in the six HD complexes are nearly linearly correlated with the weights of the dipolar resonance in Pauling's model and the N-C bond lengths; the correlation coefficients are 0.91 and 0.93, respectively. The positive two-way effects also happens in FAO-water complex, in which the FAO CO group serves as HA (HA(co)). Interestingly, when the HD and HA(co) H-bonds are present in FAO H-bond complex simultaneously, the enhancements are much more significant, and the energies of the two types of H-bonds are much larger than those when only one type of H-bond is present, reflecting the cooperative effects. By using the knowledge to the two-way effects, we computationally designed a molecule (FAO-BH3) to increase H-bond energy. Because of the oxygen lone pair donation to the empty pi orbital of BH3, FAO-BH3 has a much stronger resonance effect than FAO. As a result, the H-bond energy (-5.55 kcal/mol) in HD H2O center dot center dot center dot FAO-BH3 complex is much greater than the -3.30 kcal/mol in the HD H2O center dot center dot center dot FAO complex. The two-way effects can be rationalized as follows: the resonance effect leads to intramolecular charge shifts in the monomers which facilitate or prevent the charge donation or acceptation of their H-bond partners. Therefore, the H-bonds are strengthened or weakened. In reverse, the charge donations or acceptations of their H-bond partners facilitate or prevent the intramolecular charge shifts in the monomer moieties, which enhance or weaken the resonance effect. The understanding to the two-way effects may be helpful in drug design and refinement by modulating the H-bond strength and in building empirical H-bond models to study large biological molecules. The study supports Pauling's resonance model.