A simple model for the energy surface of a reacting system permits the calculation of the free energies of activation. A chemical reaction is analyzed in terms of the simple processes (bond making/breaking or atom transfer; geometry changes) which must take place to achieve the overall transformation. When only one (or two, or three, …) of these processes has progressed to the full extent required for reaction, one has a ‘corner intermediate.’ The reaction diagram is viewed as a square (2D) or cube (3D) or hypercube (4D), etc., and energies at intermediate points on the energy surface or hypersurface are calculated by interpolation. Suitable equations have been obtained for this purpose. Along any section parallel to an axis the energy is given by an upward opening parabola centered at the lower energy end. This paper deals with the application of these ideas to proton transfer reactions involving carbon acids. For mono- or dicarbonyl compounds, with pKas ranging from 7 to 25.6, and rate constants for water or hydroxide ranging from 10−9.3 to 104.6, rate constants can be predicted with an r.m.s. error in log k of 0.99 for 51 reactions.
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J. Peter Guthrie (1998) studied this question.