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The influence of the hydrogen bond formation on the nuclear magnetic resonance parameters has been investigated for the binary (1:1) and ternary (1:2) glycine-HCN complexes in the gas phase using high-level density functional theory with the B3LYP/6-31++G(2d,2p)//B3LYP/6-31++G(d,p) model of quantum chemistry. The calculated isotropic/anisotropic shielding parameters of the isolated glycine and HCN molecules are reported and compared with other theoretical results and experimental measurements. Six different conformations of hydrogen-bonded clusters have considered for both 1:1 and 1:2 glycine-HCN complexes. The isotropic and anisotropic chemical shifts for all the constituent atoms of the complexes have been calculated. The spin-spin coupling constants and the Fermi contact terms have also been analyzed in the context of hydrogen-bond formation.