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Emmanuel Giner 2019-11-22 15:41:07 +01:00
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\title{Mixing density functional theory and wave function theory for strong correlation: the best of both worlds} \title{Mixing density functional theory and wave function theory for strong correlation: the best of both worlds}
\begin{abstract} \begin{abstract}
bla bla bla youpi tralala The present work proposes an extension to prototypes of strongly correlated systems of the recently proposed basis set correction based on density functional theory (DFT).
We study the potential energy surfaces (PES) of the H$_{10}$, C$_2$, N$_2$, O$_2$ and F$_2$ molecules up to full dissociation limit in increasing basis sets at near full configuration interaction (FCI) level with and without the present basis set correction.
Such basis set correction relies on a mapping between range-separated DFT (RSDFT) and wave function calculations in a finite basis set through the definition of an effective non-divergent interaction mimicking the coulomb operator projected in a finite basis set. From that mapping, RSDFT-types functionals are used to recover the dominant the correlation effects missing in a finite basis set.
The scope of the present work is to develop new approximations for the complementary functionals which are suited to describe strong correlation regimes and which fulfill two very desirable properties: $S_z$ invariance and size extensivity.
In that context, we investigate the dependence of the functionals on different flavours of on-top pair densities and spin-polarizations. An important result is that the explicit dependence on the on-top pair density allows one to completely remove the dependence on any form of spin-polarization without any significant loss of accuracy.
In the general context of multi-configurational DFT, such findings show that one can avoid the use of effective spin polarization whose mathematical definition is rather \textit{ad hoc} and which can become complex valued.
Quantitatively, we show that the basis set correction allows chemical accuracy on atomization energies in a triple-zeta quality for most of the systems studied. Also, the present basis set correction provides smooth curves all along the PES.
\end{abstract} \end{abstract}
\maketitle \maketitle
@ -813,15 +819,14 @@ More precisely, we proposed a new scheme to design functionals fulfilling a) $S_
The development of new $S_z$ invariant and size extensive functionals has lead us to investigate the role of two related quantities: the spin-polarization and the on-top pair density. The development of new $S_z$ invariant and size extensive functionals has lead us to investigate the role of two related quantities: the spin-polarization and the on-top pair density.
One important result of the present study is that by using functionals \textit{explicitly} depending on the on-top pair density, one can avoid dependence to any form of spin-polarization without loos of accuracy. One important result of the present study is that by using functionals \textit{explicitly} depending on the on-top pair density, one can avoid dependence to any form of spin-polarization without loos of accuracy.
From a practical point of view, this allows to avoid the commonly used effective spin-polarization\cite{PerSavBur-PRA-95} with multi-configurational wave function, This avoids the commonly used effective spin-polarization with multi-configurational wave function whose mathematical definition originally proposed by Perdrew and co-workers in Ref. \cite{PerSavBur-PRA-95} has only a clear mathematical ground for a single Slater determinant and can be become complex-valued in the case of multi-configurational wave functions. From a more fundamental aspect, this shows that the spin-polarization in DFT-related frameworks only mimic's the role of the on-top density.
which is satisfying as the definition originally proposed by Perdrew and co-workers in Ref. \cite{PerSavBur-PRA-95} has only a clear mathematical ground for single Slater determinant and can be become complex-valued in the case of multi-configurational wave functions. From a more fundamental aspect, this shows that the spin-polarization in DFT-related frameworks only mimic's the role of the on-top density.
Regarding the results of the present approach, the basis set correction systematically improves the near FCI calculation in a given basis set. More quantitatively, it is shown that the atomization energy $D_0$ is within the chemical accuracy for all systems but C$_2$ within a triple zeta quality basis set, whereas the near FCI values are far from that accuracy within the same basis set. Regarding the results of the present approach, the basis set correction systematically improves the near FCI calculation in a given basis set. More quantitatively, it is shown that the atomization energy $D_0$ is within the chemical accuracy for all systems but C$_2$ within a triple zeta quality basis set, whereas the near FCI values are far from that accuracy within the same basis set.
In the case of C$_2$, an error of 5.5 mH is obtained with respect to the estimated exact $D_0$, and we leave for further study the detailed investigation of the reasons of this relatively unusual poor performance of the basis set correction. In the case of C$_2$, an error of 5.5 mH is obtained with respect to the estimated exact $D_0$, and we leave for further study the detailed investigation of the reasons of this relatively unusual poor performance of the basis set correction.
Also, it is shown that the basis set correction gives substantial differential contribution along the PES only close to the equilibrium geometry, meaning that it cannot recover the dispersion forces missing because the incompleteness of the basis set. Although it can be looked as a failure of the basis set correction, in our context such behaviour is actually preferable as the dispersion forces are long-range effects and the present approach was designed to recover electronic correlation effects near the electron coalescence. Also, it is shown that the basis set correction gives substantial differential contribution along the PES only close to the equilibrium geometry, meaning that it cannot recover the dispersion forces missing because the incompleteness of the basis set. Although it can be looked as a failure of the basis set correction, in our context such behaviour is actually preferable as the dispersion forces are long-range effects and the present approach was designed to recover electronic correlation effects near the electron coalescence.
Finally, regarding the computational cost of the present approach, it should be stressed (see supplementary materials) that it is completely negligible with respect to WFT methods for all systems and basis set studied here. We believe that it opens the road to a significant improvement of the results in WFT for strong correlation. Finally, regarding the computational cost of the present approach, it should be stressed (see supplementary materials) that it is minor with respect to WFT methods for all systems and basis set studied here. We believe that such approach is a significant step towards calculations near the CBS limit for strongly correlated systems.
\bibliography{srDFT_SC} \bibliography{srDFT_SC}