Correlation between C═O Stretching Vibrational Frequency and pK_a Shift of Carboxylic Acids

Identifying the pK_a values of aspartic acid (Asp) and glutamic acid (Glu) in active sites is essential for understanding enzyme reaction mechanisms. In this study, we investigated the correlation between the C═O stretching vibrational frequency (ν_C═O) of protonated carboxylic acids and the pK_a values using density functional theory calculations. In unsaturated carboxylic acids (e.g., benzoic acid analogues), ν_C═O decreases as the pK_a increases (the negative correlation), whereas in saturated carboxylic acids (e.g., acetic acid analogues, Asp, and Glu), ν_C═O increases as the pK_a increases (the positive correlation) as long as the structure of the H-bond network around the acid is identical. The negative/positive correlation between ν_C═O and pK_a can be rationalized by the presence or absence of the C═C double bond. The pK_a shift was estimated from the ν_C═O shift of Asp and Glu in proteins on the basis of the negative correlation derived from benzoic acids. The previous estimations should be revisited by using the positive correlation derived in this study, as demonstrated by quantum mechanical/molecular mechanical calculations of ν_C═O and electrostatic calculations of pK_a on a key Asp85 in the proton-transfer pathway of bacteriorhodopsin.