DFT study of the Diels–Alder reactions between ethylene with buta-1,3-diene and cyclopentadiene

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Abstract
A set of DFT methods (Xa, HFB, S-VWN, B–LYP; B–HandH and Becke3-LYP) has been used for the calculation of the transition states and energy barriers of the Diels–Alder reaction of ethylene with buta-1,3-diene and cyclopentadiene. The pure DFT methods overestimate the bond lengths, while the hybrid methods give values much closer to those obtained by conventional ab initio methods. The ratio of the σ-forming bonds to the π-breaking bonds is in excellent correlation to the predicted electronic energy barriers for these reactions. The local spin density approximation (S–VWN) fails completely giving a negative value for the classical energy barrier height for the addition of ethylene to buta-1,3-diene. On the other hand, the vibrational adiabatic barrier heights predicted by B-LYP/6-31G** and the hybrid Becke3-LYP/6-31G** theoretical models are in excellent agreement with available experimental data for both reactions.