The results of DFT calculations of harmonic and anharmonic frequencies of the dihydrogen bonded (DHB) complexes H3EH-center dot center dot center dot HOR (E = B, Al, Ga and HOR = CH3OH, CF3CH2OH) in gas phase and in low polar medium (by CPCM model) in comparison with the partners are presented. Normal coordinate analysis of the low-frequency modes was carried out to assign the new vibrations induced by DHB formation by the potential energy distribution values. Among them, the intermolecular H center dot center dot center dot H stretching vibrations only have individual modes. The influence of central atom mass and isotope and the strength of the proton donor effects were determined. The systems convenient for IR studies were chosen from the calculation predictions. The spectral investigation was made on the BH4-/ROH complexes (RCH = CH2FCH2OH (MFE), CF3CH2OH (TFE), (CF3)(2)CHOH (HFIP)). The results of temperature dependence, isotope substitution, and influence of the proton-donor strength studies agree with the theoretical conclusions. Combination of experimental and theoretical approaches allowed determining for the first time the intermolecular stretching mode characterizing intrinsic DHB vibrations.