The structural changes, dipole moments, and interaction energies for a series of C–H⋯X hydrogen bonded complexes involving F3CH as proton donor and NH3, OH2, NCH, and FH as proton acceptors have been studied using ab initio calculations including electron correlation effect for various basis sets. The NH3 shows a conventional hydrogen bond, while the other molecules show improper hydrogen bonds as evidenced by the C–H bond length shortening and the blue-shift of C–H stretching vibrational frequency. In the complex of F3CH⋯NCH, both C–H and N–C bonds are contracted, and their corresponding stretching vibrational frequencies are blue-shifted compared with monomers. The blue-shifted stretching vibration in the proton acceptor molecule has not been much addressed until now. Both conventional and improper hydrogen bonds are noted in the nonlinear complex of F3CH⋯FH, where FH molecule plays a dual role of proton acceptor and donor at the same time. The interaction energies are almost equivalent for HF and MP2 calculations, which does not support a recent proposition that the dispersive interaction is the origin of improper H-bonding.