Direct estimate of the strength of conjugation and hyperconjugation by the energy decomposition analysis method

The intrinsic strength of π interactions in conjugated and hyperconjugated molecules has been calculated using density functional theory by energy decomposition analysis (EDA) of the interaction energy between the conjugating fragments. The results of the EDA of the trans-polyenes H ₂C= CH - (HC=CH)₁₁ - CH=CH₂ (n=1-3) show that the strength of π conjugation for each C=C moiety is higher than in trans-1,3-butadiene. The absolute values for the conjugation between Si= Si π bonds are around two-thirds of the conjugation between C=C bonds but the relative contributions of ΔE_π to ΔE_orb in the all-silicon systems are higher than in the carbon compounds. The π conjugation between C=C and C=O or C=NH bonds in H₂C=CH-C(H)=O and H₂C=CH-C(H)=NH is comparable to the strength of the conjugation between C=C bonds. The π conjugation in H₂C=CH-C(R)=O decreases when R = Me, OH, and NH₂ while it increases when R = halogen. The hyperconjugation in ethane is around a quarter as strong as the it conjugation in ethyne. Very strong hyperconjugation is found in the central C - C bonds in cubylcubane and tetrahedranyltetrahedrane. The hyperconjugation in substituted ethanes X₃C-CY₃ (X,Y = Me, SiH₃, F, Cl) is stronger than in the parent compound particularly when X,Y = SiH₃ and Cl. The hyperconjugation in donor-acceptor-substituted ethanes may be very strong; the largest ΔE_π, value was calculated for (SiH ₃)₃C-CCl₃, in which the hyperconjugation is stronger than the conjugation in ethene. The breakdown of the hyperconjugation in X₃C-CY₃ shows that donation of the donor-substituted moiety to the acceptor group is as expected the most important contribution but the reverse interaction is not negligible. The relative strengths of the π interactions between two C=C double bonds, one C=C double bond and CH ₃ or CMe₃ substituents, and between two CH₃ or CMe₃ groups, which are separated by one C - C single bond, are in a ratio of 4:2:1. Very strong hyperconjugation is found in HC≡C - C(SiH ₃)₃ and HC≡C - CCl₃. The extra stabilization of alkenes and alkynes with central multiple bonds over their terminal isomers coming from hyperconjugation is bigger than the total energy difference between the isomeric species. The hyperconjugation in Me - C(R)=O is half as strong as the conjugation in H₂C= CH - C(R)=O and shows the same trend for different substituents R. Bond energies and lengths should not be used as indicators of the strength of hyperconjugation because the effect of ö interactions and electrostatic forces may compensate for the hyperconjugative effect.