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@ -715,7 +715,8 @@ In other words, smooth potential energy surfaces are obtained with the present b
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More quantitatively, the values of $D_0$ are within chemical accuracy (\ie, an error below $1.4$ mHa) from the cc-pVTZ basis set when using the $\pbeontXi$ and $\pbeontns$ functionals, whereas such an accuracy is not even reached at the standard MRCI+Q/cc-pVQZ level of theory.
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Analyzing more carefully the performance of the different types of approximate density functionals, the results show that $\pbeontXi$ and $\pbeontns$ are very similar (the maximal difference on $D_0$ being 0.3 mHa), and that they give slightly more accurate results than $\pbeuegXi$. These findings provide two important clues on the role of the different physical ingredients used in these functionals: i) the explicit use of the on-top pair density coming from the CASSCF wave function [see Eq.~\eqref{eq:def_n2extrap}] is preferable over the use of the UEG on-top pair density [see Eq.~\eqref{eq:def_n2ueg}] which is somehow understandable, and ii) removing the dependency on any kind of spin polarization does not lead to significant loss of accuracy providing that one employs a qualitatively correct on-top pair density. The latter point is crucial as it shows that the spin polarization in density-functional approximations essentially plays the same role as the on-top pair density.
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This could have significant implications for the construction of more robust families of density-functional approximations within DFT.
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This could have significant implications for the construction of more robust families of density-functional approximations within DFT.
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\manu{Also, we did not report the performance of the $\pbeuegns$ as the latter gave much poorer performance than the three other functionals. The essential reason for these bad performance comes from the fact the $\pbeuegns$ has no direct or indirect knowledge of the on-top pair density of the system. Therefore, it gives a correlation energy for the totally dissociated H$_{10}$ chain even if the on-top pair density is vanishing in that case, which necessary lowers the value of $D_0$. Therefore, from thereon we simply discard the $\pbeuegns$ functional. }
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\PFL{The functional $\pbeuegns$ is not mentioned and should be discarded at this stage (and explain why).}
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\subsection{Dissociation of diatomics}
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2.60 -150.12002711
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3.00 -150.06398251
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4.00 -149.96272858
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5.00 -149.88630151
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10.00 -149.95859616
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