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Pierre-Francois Loos 2020-08-23 14:26:47 +02:00
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benzene.tex
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@ -43,7 +43,7 @@
% 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.
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 \titou{$-8xx.xx$} 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
@ -128,11 +128,11 @@ As mentioned above, SCI+PT2 methods rely heavily on extrapolation, especially wh
We then linearly extrapolate the total SCI energy to $E_\text{PT2} = 0$ (which effectively corresponds to the FCI limit) using the two largest SCI wave functions.
Although it is not possible to provide a theoretically sound error bar, we estimate the extrapolation error by \titou{the difference in excitation energy between the largest SCI wave function and its corresponding extrapolated value.}
We believe that it provides a very safe estimate of the extrapolation error.
Note that, unlike excited-state calculations where it is important to enforce that the wave functions are `eigenfunctions of the $\Hat{S}^2$ spin operator, \cite{Applencourt_2018} the present wave functions do not fulfil this property as we aim for the lowest energy of a single state. We have found that $\expval*{\Hat{S}^2}$ is, nonetheless, very close to zero \toto{($\sim 5 \times 10^{-3}$ a.u.)}.
Note that, unlike excited-state calculations where it is important to enforce that the wave functions are `eigenfunctions of the $\Hat{S}^2$ spin operator, \cite{Applencourt_2018} the present wave functions do not fulfil this property as we aim for the lowest energy of a single state. We have found that $\expval*{\Hat{S}^2}$ is, nonetheless, very close to zero ($\sim 5 \times 10^{-3}$ a.u.).
The corresponding energies are reported in Table \ref{tab:NOvsLO} as functions of the number of determinants in the variational space $N_\text{det}$.
A second run has been performed with localized orbitals.
Starting from the same natural orbitals, a Boys-Foster localization procedure \cite{Boys_1960} was performed in several orbital windows: i) core, ii) valence $\sigma$, iii) valence $\pi$, iv) valence $\pi^*$, v) valence $\sigma^*$, vi) the higher-lying $\sigma$ orbitals, and vii) the higher-lying $\pi$ orbitals. Like Pipek-Mezey, \cite{Pipek_1989} this choice of orbital windows allows to preserve a strict $\sigma$-$\pi$ separation in planar systems like benzene. \toto{T2: add MO indices (see comments in tex file).}
Starting from the same natural orbitals, a Boys-Foster localization procedure \cite{Boys_1960} was performed in several orbital windows: i) core, ii) valence $\sigma$, iii) valence $\pi$, iv) valence $\pi^*$, v) valence $\sigma^*$, vi) the higher-lying $\sigma$ orbitals, and vii) the higher-lying $\pi$ orbitals. Like Pipek-Mezey, \cite{Pipek_1989} this choice of orbital windows allows to preserve a strict $\sigma$-$\pi$ separation in planar systems like benzene.
% MO Indices:
%[1-6] # Core
%[7,8,9,10,11,12,13,14,15,16,17,18] # Sigma occ
@ -154,7 +154,7 @@ The three flavours of SCI fall into an interval ranging from $-860.0$ m$E_h$ (AS
The present calculations have been performed on the AMD partition of GENCI's Irene supercomputer.
Each Irene's AMD node is a dual-socket AMD Rome (Epyc) CPU@2.60 GHz with 256GiB of RAM, with a total of 64 physical CPU cores per socket.
These nodes are connected via Infiniband HDR100.
The first step of the calculation, \ie, performing a CIPSI calculation up to $N_\text{det} \sim 10^7$ with Hartree-Fock orbitals in order to produce natural orbitals, takes roughly 24 hours \toto{on a single node}, and reaching the same number of determinants with natural orbitals or localized orbitals takes roughly the same amount of time. \toto{A second 24-hour run on 10 distributed nodes was performed to push the selection to 80M determinants, and a third distributed run using 40 nodes was used to reach 160M determinants.}
The first step of the calculation, \ie, performing a CIPSI calculation up to $N_\text{det} \sim 10^7$ with Hartree-Fock orbitals in order to produce natural orbitals, takes roughly 24 hours on a single node, and reaching the same number of determinants with natural orbitals or localized orbitals takes roughly the same amount of time. A second 24-hour run on 10 distributed nodes was performed to push the selection to $8 \times 10^7$ determinants, and a third distributed run using 40 nodes was used to reach 160M determinants.
%%$ FIG. 1 %%%
\begin{figure*}
@ -209,6 +209,7 @@ The statistical error on $E_\text{PT2}$, corresponding to one standard deviation
20\,971\,520 & $-231.474\,019$ & $-231.561\,315(430)$ & $-231.560\,063(424)$ & $-231.508\,714$ & $-231.564\,707(275)$ & $-231.564\,223(273)$ \\
41\,943\,040 & $-231.487\,978$ & $-231.564\,529(382)$ & $-231.563\,593(377)$ & $-231.519\,122$ & $-231.567\,419(240)$ & $-231.567\,069(238)$ \\
83\,886\,080 & $-231.501\,334$ & $-231.566\,994(317)$ & $-231.566\,325(314)$ & $-231.528\,568$ & $-231.570\,084(199)$ & $-231.569\,832(198)$ \\
167\,772\,160 & \\
\end{tabular}
\end{ruledtabular}
\end{table*}
@ -239,7 +240,7 @@ The statistical error on $E_\text{PT2}$, corresponding to one standard deviation
% Acknowledgements
This work was performed using HPC resources from GENCI-TGCC (2020-gen1738) and from CALMIP (Toulouse) under allocation 2020-18005.\toto{L'allocation Grand-Challenge est finie!}
This work was performed using HPC resources from GENCI-TGCC (2020-gen1738) and from CALMIP (Toulouse) under allocation 2020-18005.
\bibliography{benzene}