High-level ab initio calculations have been performed on dihydrogen-bonded complexes with hydrogen fluoride (HF) as a proton-donating molecule and simple molecules as proton-accepters (CH4, SiH4, BeH2, MgH2, LiH, and NaH). MP4(SDQ)/6-311++G** and QCISD(T)/6-311++G** results show that H-bond energies for such systems are significant. For example, the H-bond energy is -11.9 kcal/mol for the LiH ... HF complex at the QCISD(T)/G-311++G** level of theory; the basis set superposition error (BSSE) was included, and the geometry of the complex was optimized at the QCISD/6-311++G** level. The relationships between the geometrical parameters of these complexes are in good agreement with those obtained from the bond valence model. The BSSE is taken into account in all levels of calculations. A comparison of the results of the calculations shows that the MP2/6-311++G** level of theory is sufficient for a description of dihydrogen-bonded complexes. Additionally, Bader's theory is included in the analysis of the investigated systems.