figs and abstract

benzene.tex

@@ -36,6 +36,12 @@
 \email{scemama@irsamc.ups-tlse.fr}
 \affiliation{\LCPQ}
 
+% Abstract
+\begin{abstract}
+Following the recent work of Eriksen \textit{et al.} [\href{https://arxiv.org/abs/2008.02678}{arXiv:2008.02678 [physics.chem-ph]}], we report the performance of the \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) method on the non-relativistic frozen-core correlation energy of the ground state of the benzene molecule in the cc-pVDZ basis. Following our usual protocol, we obtain a correlation energy of $-8xx.xx$ m$E_h$ which agrees with the best theoretical estimate of $-863$ m$E_h$ proposed by Eriksen \textit{et al.} using an extensive array of highly-accurate new electronic structure methods.
+\end{abstract}
+
+% Title
 \maketitle
 
 % Intro
@@ -57,7 +63,7 @@ We refer the interested reader to Ref.~\onlinecite{Eriksen_2020} and its support
 Soon after, Lee \textit{et al.} reported phaseless auxiliary-field quantum Monte Carlo \cite{Motta_2018} (ph-AFQMC) correlation energies for the very same problem. \cite{Lee_2020}
 
 % The system
-The target application is the non-relativistic frozen-core correlation energy of the benzene molecule in the cc-pVDZ basis.
+The target application is the non-relativistic frozen-core correlation energy of the ground state of the benzene molecule in the cc-pVDZ basis.
 The geometry of benzene has been computed at the MP2/6-31G* level and it can be found in the supporting information of Ref.~\onlinecite{Eriksen_2020}.
 This corresponds to an active space of 30 electrons and 108 orbitals, \ie, the Hilbert space of benzene is of the order of $10^{35}$ Slater determinants.
 Needless to say that this size of Hilbert space cannot be tackled by exact diagonalization with current architectures.
@@ -100,7 +106,7 @@ However, performing SCI calculations rapidly becomes extremely tedious when one
 From an historical point of view, CIPSI is probably one of the oldest SCI algorithm. 
 It was developed in 1973 by Huron, Rancurel, and Malrieu \cite{Huron_1973} (see also Ref.~\onlinecite{Evangelisti_1983}).
 Recently, the determinant-driven CIPSI algorithm has been efficiently implemented \cite{Giner_2013,Giner_2015} in the open-source programming environment {\QP} by one of us (AS) enabling to perform massively parallel computations. \cite{Garniron_2017,Garniron_2018,Garniron_2019}
-In particular, we were able to compute highly-accurate calculations of ground- and excited-state energies of small- and medium-sized molecules. \cite{Loos_2018a,Loos_2019,Loos_2020a,Loos_2020b,Loos_2020c}
+In particular, we were able to compute highly-accurate calculations of ground- and excited-state energies of small- and medium-sized molecules (including benzene). \cite{Loos_2018a,Loos_2019,Loos_2020a,Loos_2020b,Loos_2020c}
 CIPSI is also frequently use to provide accurate trial wave function for QMC calculations. \cite{Caffarel_2014,Caffarel_2016a,Caffarel_2016b,Giner_2013,Giner_2015,Scemama_2015,Scemama_2016,Scemama_2018,Scemama_2018b,Scemama_2019,Dash_2018,Dash_2019} 
 The particularity of the current implementation is that the selection step and the PT2 correction are computed \textit{simultaneously} via a hybrid semistochastic algorithm. \cite{Garniron_2017,Garniron_2019}
 Moreover, a renormalized version of the PT2 correction (dubbed rPT2 in the following) has been recently implemented for a more efficient extrapolation to the FCI limit (see below). \cite{Garniron_2019}
@@ -124,7 +130,9 @@ We believe that it provides a very safe estimate of the extrapolation error.
 
 The three flavours of SCI fall into an interval ranging from $-863.7$ to $-862.8$ m$E_h$.
 The CIPSI number is ?
+\titou{Note that, even though benzene is big, we have already reported excitation energies of benzene with the 6-31+G(d) basis in Ref.~\onlinecite{Loos_2019}.}
 
+%%% TABLE II %%%
 \begin{table}
 	\caption{Extrapolation distances, $\Delta E_{\text{dist}}$ (in m$E_{\text{H}}$), involved in computing the final ASCI, iCI, SHCI, CIPSI, and DMRG results. 
 	These are defined by the difference between the final computed energy, $\Delta E_{\text{final}}$, and the extrapolated energy, $\Delta E_{\text{extrap.}}$ (final variational energies, that is, in the absence of perturbation theory, are presented as $\Delta E_{\text{var.}}$). For the SCI methods, extrapolations are performed toward the limit of vanishing perturbative correction, while the variational DMRG energy is extrapolated toward an infinite bond dimension.
@@ -143,8 +151,23 @@ The CIPSI number is ?
 	\end{ruledtabular}
 \end{table}
 
+%%$ FIG. 1 %%%
+\begin{figure*}
+	\includegraphics[width=0.45\linewidth]{fig1a}
+	\hspace{0.08\linewidth}
+	\includegraphics[width=0.45\linewidth]{fig1b}
+	\caption{
+	Convergence of the CIPSI correlation energy for benzene.
+	Left: $\Delta E_\text{var.}$, $\Delta E_\text{var.} + E_\text{PT2}$, and $\Delta E_\text{var.} + E_\text{rPT2}$ (in m$E_h$) as functions of the number of determinants in the variational space.
+	Right: $\Delta E_\text{var.} + E_\text{PT2}$ and $\Delta E_\text{var.} + E_\text{rPT2}$ (in m$E_h$) as functions of $E_\text{PT2}$ or $E_\text{rPT2}$.
+	The two-point linear extrapolation curves (dashed lines) are also reported.
+	The theoretical best estimate of $-863$ m$E_h$ from Ref.~\onlinecite{Eriksen_2020} is reported for comparison purposes.
+	\label{fig:CIPSI}
+	}
+\end{figure*}
+
 % Acknowledgements
-This work was performed using HPC resources from GENCI-TGCC (Grand Challenge 2019-gch0418) and from CALMIP (Toulouse) under allocation 2019-0510.
+This work was performed using HPC resources from GENCI-TGCC (Grand Challenge 2019-gch0418) and from CALMIP (Toulouse) under allocation 2020-18005.
 
 \bibliography{benzene}