Quantitative relationships between bond lengths, stretching vibrational frequencies, bond force constants, and bond orders in the hydrogen-bonded complexes involving hydrogen halides

To uncover the correlation between the bond length change and the corresponding stretching frequency shift of the proton donor D–H upon hydrogen bond formation, a series of hydrogen-bonded complexes involving HF and HCl which exhibit the characteristics of red-shifted hydrogen bond were investigated at the MP2/aug-cc-pVTZ, M062X/aug-cc-pVTZ, and B3LYP/aug-cc-pVTZ(GD3) levels of theory with CP optimizations. A statistical analysis of these complexes leads to the quantitative illustrations of the relations between bond length and stretching vibrational frequency, between bond length and bond force constant, between stretching vibrational frequency and bond force constant, between bond length and bond order for hydrohalides in a mathematical way, which would provide valuable insights into the explanation of the geometrical and spectroscopic behaviors during hydrogen bond formation.