Transition states for Diels-Alder reactions are strongly correlated, as evidenced by high-to-very-high M diagnostics, and therefore they require treatment by multireference methods. Multiconfiguration pair-density functional theory (MC-PDFT) combines a multiconfiguration wave function with a functional of the electron density and the on-top pair density to calculate the electronic energy for strongly correlated systems at a much lower cost than wave function methods that do not employ density functionals. Here we apply MC-PDFT to the Diels-Alder cycloaddition reaction of 1,3-butadiene with ethylene, where two kinds of reaction paths have been widely studied: concerted synchronous paths and diradical stepwise paths. The lowest-energy reaction path is now known to be a concerted synchronous one, and a method's ability to predict this is an important test. By comparison to the best available theoretical results in the literature, we test the accuracy of MC-PDFT with several choices of on-top functional for geometries and enthalpies of stable structures along both paths and for the transition state geometries. We also calculate the Arrhenius activation energies for both paths and compare these to experiment. We also compare to Kohn-Sham density functional theory (KS-DFT) with selected exchange-correlation functionals. CAS-PDFT gives consistently good energies and geometries for both the concerted and stepwise mechanisms, but none of the KS-DFT functionals gives accurate activation energies for both. The stepwise transition state is very strongly correlated, and MC-PDFT can treat it, but KS-DFT (which involves a single-configuration treatment) has larger errors. The results confirm that using a multiconfigurational reference function for strongly correlated transition states can significantly improve the reliability and that MC-PDFT can provide good accuracy at a much lower computational cost than competing multireference methods.
|Original language||English (US)|
|Number of pages||10|
|Journal||Journal of Physical Chemistry A|
|State||Published - Dec 1 2022|
Bibliographical noteFunding Information:
The authors are grateful to Laura Gagliardi for coadvising the project and to Andrew Sand for contributions to OpenMolcas that made the project possible. We thank the University of Minnesota’s Summer Undergraduate Research Fellowship in Computational and Theoretical Chemistry (SURF-CTC) and the Summer Lando/NSF REU (grant no. CHE-1851990) for funding. We thank the Minnesota Supercomputing Institute for computing resources. T.R.S. acknowledges that this material is based on the work supported by the National Science Foundation Graduate Research Fellowship Program under grant no. CON-75851, project no. 00074041. This work was also supported in part by the National Science Foundation under grant CHE-2054723. The opinions, findings, conclusions, and recommendations expressed in this article are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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