近年來密度泛函理論(DFT)所計算出來的親電性以及親核性已經被用來當作反應活化能的重要指標，因此我們藉由DFT來了解到Diels-Alder (DA) 反應的機制。其中文獻利用不同取代基修飾的乙烯和固定的diene分子進行DA反應，發現增加dienophile缺電子的特性，而增加diene多電子特性時可以降低反應的活化能。
　　首先利用DFT來計算取代基如何影響分子的最高佔有分子軌域(HOMO)以及最低未佔有分子軌域(LUMO)的能階分布。當乙烯上的取代基具有低的LUMO能階時會壓低乙烯(dienophile)的LUMO，當壓低的程度越大則會增加dienophile的親電性能力。而dienophile的LUMO能階壓低，使得diene分子HOMO能階的電子更容易轉移到dienophile的LUMO能階上面，因此降低了DA反應的活化能。這也解釋到當路易士酸和取代基形成氫鍵的時候會降低DA反應的活化能。
　　該研究已發展到取代基具有π type的孤對電子對，結果發現這類的取代基會推高dienophile的HOMO和LUMO能階因此造成DA的反應性變差。但是不穩定的HOMO能階卻能增加diene的親核性能力,因此具有π type孤對電子對的取代基適合取代在diene分子上。
　　此結論驗證本篇論文所提到的自身DA反應，烯胺分子{pyrrolidinyl-substituted (E)-buta-1,3-dien-1ylbenzene}可以當作diene以及dienophile，其中pyrrolidine主要是推高HOMO的能階以降低DA反應活化能。並在pyrrolidine上修飾取代基藉此影響分子HOMO和LUMO能階，最後發現結果如預期所想，影響邊界軌域變動的主要原因是取代基的誘導效應。

　　In the course of understanding Diels-Alder (DA) reaction mechanism, the global electrophiliciy and empirical nucleophilicity defined within the density functional theory (DFT) have been adopted as reaction indices to account for the relative activation energies found experimentally. These published results are accomplished by DA reactions of a specified diene with substituted ethylene series. One general rule can be summarized by the statement that the increase of the electron-deficiency character of the dienophile, together with the increase of the electron-rich character of diene, would lead to lower activation energy.
　　In this work we have first employed DFT calculations to investigate the electronic nature of substituents with the aim to understand how chemical substitution affects the energy levels of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). Substituents having low-LUMO can press down the LUMO of an ethylene derivative (dienophile), which in return increases the magnitude of electrophiliciy of this dienophile. This effect is corresponding to the electron-deficiency argument for the dienophile, which enables the DA reactions to proceed with low activation energies. This also explains the low activation energy found for reaction systems involving hydrogen-bonding formation between the Lewis acid and the substituent.
　　　　The studies have been extended to substituents having pi-type electron lone-pair orbital(s). It is found that those substituents would elevate levels of both HOMO and LUMO of the dienophile, the latter results in un-favored DA reactions.Since the destabilization of HOMO is corresponding to enhance the nucleophilicity, the substitution conducted on a diene would favor the charge transfer from diene to dienophile. In other words, chemical substitution using those substitutents conducted on “dienes” can also make DA reactions fast.This conclusion can be verified by the reported DA reactions, in which enamine {pyrrolidinyl-substituted (E)-buta-1,3-dien-1ylbenzene} was used as diene and dienophile. The role of the pyrrolidine moiety is to elevate the HOMO and enable a favored DA reaction. Effects of chemical substitution, performed on the pyrrolidinyl carbon, on HOMO/LUMO energies have also been investigated. It is found that, as expected, the inductive effects exerted by the substituents prevail.

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