Correlation of Infrared Stretching Frequencies and Hydrogen Bond Distances in Crystals

Empirical correlations between X–H≡Y distance R and frequency shift of the X–H stretching motion Δv are presented for O–H≡O, N–H≡O, and N–H≡N hydrogen bonds. A linear correlation is possible provided a distinct straight line is assumed for each hydrogen bond type. The equations of the best straight lines and standard deviations are: $$\begin{array}{c}\mathrm{O}-\mathrm{H}\mathrm{···}\mathrm{O}\mathrm{\hspace{0.17em}\hspace{0.17em}\Delta \nu (}{\mathrm{cm}}^{\text{−1}}{\text{)=4.43·10}}^3\text{(2.84−R)\hspace{0.17em}σ(Δν)=199}{\mathrm{cm}}^{\text{−1}}\\ \mathrm{N}-\mathrm{H}\mathrm{···}\mathrm{O}\mathrm{\hspace{0.17em}\hspace{0.17em}\Delta \nu (}{\mathrm{cm}}^{\text{−1}}{\text{)=0.548·10}}^3\text{(3.21−R)σ(Δν)=24}{\mathrm{cm}}^{\text{−1}}\\ \mathrm{N}-\mathrm{H}\mathrm{···}\mathrm{N}\mathrm{\hspace{0.17em}\hspace{0.17em}\Delta \nu (}{\mathrm{cm}}^{\text{−1}}{\text{)=1.05·10}}^3\text{(3.38−R)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}?}\end{array}$$