SI for QUESTDB

Manuscript/QUEST_WIREs.tex

@@ -297,6 +297,17 @@ where $E_{\text{var}}^{(m)}$ and $E_{\text{rPT2}}^{(m)}$ are calculated with CIP
 This relation is valid in the regime of a sufficiently large number of determinants where the second-order perturbational correction largely dominates.
 In theory, the coefficient $\alpha^{(m)}$ should be equal to one but, in practice, due to the residual higher-order terms, it deviates slightly from unity.
 
+For the largest systems considered here, $\abs{E_{\text{rPT2}}}$ can be as large as 2~eV and, thus,
+the accuracy of the excitation energy estimates strongly depends on our ability to compensate the errors in the calculations.
+Here, we greatly enhance the compensation of errors by making use of
+our selection procedure ensuring that the rPT2 values of both states
+match as well as possible (a trick known as PT2 matching
+\cite{Dash_2018,Dash_2019}), i.e. $E_{\text{rPT2}} =
+E_{\text{rPT2}}^{(0)} \approx E_{\text{rPT2}}^{(m)}$, and
+by using a common set of state-averaged natural orbitals with equal weights for the ground and excited states.
+%This last feature tends to make the values of $\alpha^{(0)}$ and $\alpha^{(m)}$ very close to each other, such that the error on the energy difference is decreased.
+
+
 Using Eq.~\eqref{eqx} the estimated error on the CIPSI energy is calculated as
 \begin{equation}
   E_{\text{CIPSI}}^{(m)} - E_{\text{FCI}}^{(m)}
@@ -312,17 +323,6 @@ state is given by
   + \mathcal{O}\qty[{E_{\text{rPT2}}^2 }]
 \end{equation}
 which evidences that the error in $\Delta E_{\text{FCI}}^{(m)}$ can be expressed as $\qty(\alpha^{(m)}-\alpha^{(0)}) E_{\text{rPT2}} + \mathcal{O}\qty[{E_{\text{rPT2}}^2}]$.
-
-Now, for the largest systems considered here, $\abs{E_{\text{rPT2}}}$ can be as large as 2~eV and, thus,
-the accuracy of the excitation energy estimates strongly depends on our ability to compensate the errors in the calculations.
-Here, we greatly enhance the compensation of errors by making use of
-our selection procedure ensuring that the PT2 values of both states
-match as well as possible (a trick known as PT2 matching
-\cite{Dash_2018,Dash_2019}), i.e. $E_{\text{rPT2}} =
-E_{\text{rPT2}}^{(0)} \approx E_{\text{rPT2}}^{(m)}$, and
-by using a common set of state-averaged natural orbitals with equal weights for the ground and excited states.
-This last feature tends to make the values of $\alpha^{(0)}$ and $\alpha^{(m)}$ very close to each other, such that the error on the energy difference
-is decreased.
 In the ideal case where one is able to fully correlate the CIPSI calculations associated with the ground and excited states, the fluctuations of
 $\Delta E_\text{CIPSI}^{(m)}(n)$ as a function of the iteration number $n$ would completely vanish and the exact excitation energy would be obtained from the first CIPSI iterations.
 Quite remarkably, in practice, numerical experience shows that the fluctuations with respect to the extrapolated value $\Delta E_\text{FCI}^{(m)}$ are small,
@@ -1316,13 +1316,19 @@ Besides this, because computing 500 (or so) excitation energies can be a costly
 We hope to report on this in the near future.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section*{acknowledgements}
+%\section*{acknowledgements}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%AS, MC, and PFL thank the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481) for financial support.
+%Support from the \textit{``Centre National de la Recherche Scientifique''} is acknowledged.
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section*{research resources}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%
 This work was performed using HPC resources from GENCI-TGCC (Grand Challenge 2019-gch0418) and from CALMIP (Toulouse) under allocation 2020-18005.
-AS, MC, and PFL thank the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481) for financial support.
-Funding from the \textit{``Centre National de la Recherche Scientifique''} is also acknowledged.
 DJ acknowledges the \textit{R\'egion des Pays de la Loire} for financial support and the CCIPL computational center for ultra-generous allocation of computational time.
 
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section*{conflict of interest}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%