A general equation correlating intramolecular rates with 'attack' parameters: distance and angle

Using density functional theory (DFT) at the B3LYP level with the 6-31G(d,p) basis set, a general equation is derived relating activation energy with the distance between the two reactive centers (rGM), and the hydrogen-bonding angle (αGM) in an intramolecular proton transfer process. The strong correlation between the values of rGM and αGM with the activation energy, ΔG‡, which reflects the experimental reaction rate, provides an excellent tool to predict reaction rate based on calculated geometrical parameters for a certain system (ΔH‡, ΔG‡ vs rGM and αGM). The slope of the equation can be used as an indicator of the mode by which the two reacting centers orchestrate in an intramolecular process.

X is O, N or C; αGM is the hydrogen bonding angle; rGM is the distance between the two reactive centers; ΔG‡ and ΔH‡ are the free activation and enthalpic activation energies, respectively.