Classical Reaction\nBarriers in DFT: An Adiabatic-Connection\nPerspective

Classical reaction barriers in density-functional theory\nare considered\nfrom the perspective of the density-fixed adiabatic connection. A\n‘reaction adiabatic-connection integrand’, Rλ, is introduced, where λ is the electron–electron\ninteraction strength, for which ∫01Rλdλ equals the barrier, meaning the barrier\ncan be easily visualized as the area under a plot of Rλ vs λ. For five chemical reactions,\nplots of reference Rλ, calculated from Lieb maximizations at\nthe coupled-cluster level of theory, are compared with approximate Rλ, calculated from common exchange–correlation\nfunctionals using coordinate scaling, for coupled-cluster densities.\nThe comparison provides a simple way to visualize and understand functional-driven\nerrors and trends in barriers from approximate functionals, while\nallowing a clean separation of the role of exchange and correlation\ncontributions to the barrier. Specifically, the accuracy of R0 is determined entirely by the accuracy\nof the exchange functional, while the shape of Rλ is determined entirely by the correlation\nfunctional. The results clearly illustrate why the optimal amount\nof exact (orbital) exchange in hybrid functionals differs between\nreactions, including forward and reverse directions in the same reaction,\nand hence why simply introducing larger amounts of exact exchange\nmay not be a reliable approach for improving barriers. Instead, the\nshape of Rλ must be captured more accurately through\nmore accurate correlation functionals, and the numerical data presented\nmay be useful for this purpose. Density-driven errors are then considered,\nand possible cancellation with functional-driven errors in barriersnoted\nin prior studies when Hartree–Fock densities are usedis\nillustrated from the perspective of Rλ.