This work opens a series of studies on the water complexes of adenines. We use a similar approach as used in our earlier studies of cytosine-water complexes (i.e., first we investigate the LR spectral manifestations of hydrogen-bonding at selected interaction sites of the stable amino N9H tautomeric form of adenine by studying simpler model molecules which have only a single or a very few selected hydrogen-bond interaction sites typical for adenine). The present study concerns the first two of such model molecules, benzimidazole and 1-CH3-benzimidazole. LR vibrational spectra of matrix-isolated benzimidazole, 1-CH3-benzimidazole, and their complexes with water are analyzed and assigned by comparing the experimental spectra with the IR frequencies and intensities computed with the use of ab initio and density functional theory (DFT) methods. When the DFT/B3LYP/6-31++G** monomer frequencies are scaled with three different scaling factors, the mean differences between the experimental and calculated frequencies are only 10 and 8 cm(-1) for benzimidazole and 1-CH3-benzimidazole, respectively. The calculated, MP2/6-31++G**//RHF/6-31++G** (MP2 denotes the second-order Moller-Plesset Perturbation Theory, RHF denotes the restricted Hartree-Fock method, and notation MP2//RHF denotes that the molecular geometries were optimized at the RHF level and then used to calculate total energies using the MP2 method), H-bond interaction energies, with the basis set superposition error accounted for, are -22.6, -21.2, and -22.0 kJ/mol for the benzimidazole N-1-H ... OH2 and N-3... H-OH complexes and the 1-CH3-benzimidazole N-3... H-OH complex, respectively. The DFT/B3LYP/6-31++G** method yields similar H-bond interaction energies. The frequency shifts of the vibrational modes directly involved in the H-bond interactions are better predicted by the DFT method than by the RHF method. For other vibrational modes not directly involved in the H-bonds, the two methods provide a similar level of accuracy in predicting the shifts of the fundamental modes caused by H-bonding interactions. In this work we also establish correlations between experimental and theoretical characteristics of the N-H ... OH2 H-bonding in water complexes of benzimidazole and 1-CH3-benzimidazole, and these correlations will be used in future elucidation of FT-IR spectra of water complexes of adenine.