text: A relatively recent work (2006) by Fernández and Frenking (2006) summarized the trends in hyperconjugation among various groups of acyclic molecules, using energy decomposition analysis or EDA. Fernández and Frenking define this type of analysis as "...a method that uses only the pi orbitals of the interacting fragments in the geometry of the molecule for estimating pi interactions." For this type of analysis, the formation of bonds between various molecular moieties is a combination of three component terms. ΔE represents what Fernández and Frenking call a molecules “quasiclassical electrostatic attractions.” The second term, ΔE, represents the molecules Pauli repulsion. ΔE, the third term, represents stabilizing interactions between orbitals, and is defined as the sum of ΔE and ΔE. The total energy of interaction, ΔE, is the result of the sum of the 3 terms.
  A group whose ΔE values were very thoroughly analyzed were a group of enones that varied in substituent. 
  Fernández and Frenking reported that the methyl, hydroxyl, and amino substituents resulted in a decrease in ΔE from the parent 2-propenal. Conversely, halide substituents of increasing atomic mass resulted in increasing ΔE. Because both the enone study and Hammett analysis study substituent effects (although in different species), Fernández and Frenking felt that comparing the two to investigate possible trends might yield significant insight into their own results. They observed a linear relationship between the ΔE values for the substituted enones and the corresponding Hammett constants. The slope of the graph was found to be -51.67, with a correlation coefficient of -0.97 and a standard deviation of 0.54. Fernández and Frenking conclude from this data that ..."the electronic effects of the substituents R on pi conjugation in homo- and heteroconjugated systems is similar and thus appears to be rather independent of the nature of the conjugating system.".