2P121
A LC-DFT+vdW Study of the Diels-Alder Reactions and the Global Hardness
Response Analysis(University of Yamanashi, Japan) ○Raman K. Singh, Takao Tsuneda[Introduction] There have been considerable attentions drawn to the Diels-Alder reactions
especially in chemical reactivity calculations. The development of computational methods for theexploration of reaction energetics, barrier heights, and frontier orbital energies are facilitated by
the benchmark results. Over the past two decades, density functional theory (DFT) has beenfrequently used to investigate Diels-Alder reactions and previous reports indicate that many
conventional DFTs show serious errors to give quantitative thermodynamic properties without
clarifying the underlying reasons. Besides this, these reactions have often been discussed on thefrontier orbital theory and the corresponding frontier orbital energies were used for explaining
their chemical reactivities and kinetics but it is difficult for most quantum chemistry methods toobtain correct orbital energies. In this study, we apply various types of long-range corrected (LC)and other major functionals to the Diels-Alder reactions (Figure 1) to ascertain the reasons forpoor enthalpies and then investigate the accuracy in the barrier height results. Furthermore, themaximum hardness rule on the reaction pathways was explored based on the orbital energies.1

Figure 1: Diels-Alder reactions involving ethylene, acetylene, maleic anhydride and maleimide
as dienophiles.
[Computational Details] We carried out calculations employing various types of DFT
functionals: LC, pure, hybrid and semiempirical functionals. The LC functionals include LCBOP, LCgau-BOP, LC-BLYP, CAM-B3LYP, LC-ωPBE and ωB97X. The LC-BOP and LCBLYP functionals were combined with local response dispersion (LRD) to evaluate thedispersion correlation effects on the Diels-Alder reactions. For comparison, pure BOP, hybrid
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B3LYP, semiempirical dispersion-corrected B97-D, semiempirical hybrid meta BMK and M062x functionals were considered. The geometries have been optimized by each functional using
the cc-pVTZ basis set. All the optimized structures have positive and real frequency. The
Gaussian 09 suite of the program has been used to perform all the computations.
[Results and Discussion] Figure 2 clearly shows that the long-range correction significantly
improves the reaction enthalpies and the LRD correction has no effect on it. However, dispersion
correlation correction is crucial to give accurate barrier heights as can be seen in Fig. 3. Finally
we calculated the global hardness responses (GHRs), which are half of the HOMO-LUMO gaps,
along the intrinsic reaction coordinates (IRCs). Figure 4 depicts the calculated GHRs and thecorresponding total energies along the IRCs, where the GHRs and total energies are set to be zeroat the reactants. These figures show that LC-BOP GHR results first decrease slightly when thereaction proceeds from the reactants to the transition state and after that increase drasticallytoward the product, while B3LYP GHR curves increases monotonically right from the reactants
to the product via transition state. The former results suggest that the minimum GHR in thereaction pathway of such reactions is obtained either at the transition state or when the reacting
species are about to reach the transition state. We also get GHR curves similar to the B3LYP one
by the functionals examined here except for LC-BOP, LCgau-BOP and LC-BLYP. Theseoutcomes demonstrate that LC-DFT results satisfy the maximum hardness rule for overall
reaction paths while conventional functionals violate this rule on the reaction pathways.

Figure 2: Errors in the computed enthalpies (in kcal mol-1) with respect to CBS-QB3 results.

Figure 3: Errors in calculated reaction
Figure 4: GHRs, η and total energies E along thebarrier heights with the experimental
IRC.
results.
[1] Singh, R.K., Tsuneda, T. J. Comput. Chem. 2013, 34, 379–386.
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