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Manuscript/Ec.bib
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@ -1,13 +1,54 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2021-07-25 21:27:51 +0200
%% Created for Pierre-Francois Loos at 2021-07-26 11:11:15 +0200
%% Saved with string encoding Unicode (UTF-8)
@article{Chilkuri_2021,
abstract = {Selected configuration interaction (SCI) methods, when complemented with a second-order perturbative correction, provide near full configuration interaction (FCI) quality energies with only a small fraction of the Slater determinants of the FCI space. However, a selection criterion based on determinants alone does not ensure a spin-pure wave function. In other words, such SCI wave functions are not eigenfunctions of the {\^S}2 operator. In many situations (bond breaking, magnetic system, excited state, etc.), having a spin-adapted wave function is essential for a quantitatively correct description of the system. Here, we propose an efficient algorithm which, given an arbitrary determinant space, generates all the missing Slater determinants allowing one to obtain spin-adapted wave functions while avoiding manipulations involving configuration state functions. For example, generating all the possible determinants with 6 spin-up and 6 spin-down electrons in 12 open shells takes 21 CPU cycles per generated Slater determinant. The selection is still done with individual determinants, and one can take advantage of the basis of configuration state functions in the diagonalization of the Hamiltonian to reduce the memory footprint significantly.},
author = {Vijay Gopal Chilkuri and Thomas Applencourt and Kevin Gasperich and Pierre-Fran{\c c}ois Loos and Anthony Scemama},
date-added = {2021-07-26 11:06:54 +0200},
date-modified = {2021-07-26 11:09:39 +0200},
doi = {https://doi.org/10.1016/bs.aiq.2021.04.001},
journal = {Adv. Quantum Chem.},
pages = {in press},
publisher = {Academic Press},
title = {Spin-adapted selected configuration interaction in a determinant basis},
year = {2021},
Bdsk-Url-1 = {https://www.sciencedirect.com/science/article/pii/S0065327621000022},
Bdsk-Url-2 = {https://doi.org/10.1016/bs.aiq.2021.04.001}}
@article{Scemama_2020,
author = {Scemama,Anthony and Giner,Emmanuel and Benali,Anouar and Loos,Pierre-Fran{\c c}ois},
date-added = {2021-07-26 10:59:53 +0200},
date-modified = {2021-07-26 11:01:13 +0200},
doi = {10.1063/5.0026324},
journal = {J. Chem. Phys.},
number = {17},
pages = {174107},
title = {Taming the fixed-node error in diffusion Monte Carlo via range separation},
url = {https://doi.org/10.1063/5.0026324},
volume = {153},
year = {2020},
Bdsk-Url-1 = {https://doi.org/10.1063/5.0026324}}
@article{Dash_2021,
author = {Dash, Monika and Moroni, Saverio and Filippi, Claudia and Scemama, Anthony},
date-added = {2021-07-26 10:58:37 +0200},
date-modified = {2021-07-26 10:58:52 +0200},
doi = {10.1021/acs.jctc.1c00212},
journal = {J. Chem. Theory Comput.},
number = {6},
pages = {3426-3434},
title = {Tailoring CIPSI Expansions for QMC Calculations of Electronic Excitations: The Case Study of Thiophene},
volume = {17},
year = {2021},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.1c00212}}
@article{Kreplin_2020,
author = {Kreplin,David A. and Knowles,Peter J. and Werner,Hans-Joachim},
date-added = {2021-07-21 13:06:31 +0200},
@ -187,16 +228,6 @@
Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.19273892002},
Bdsk-Url-2 = {https://doi.org/10.1002/andp.19273892002}}
@misc{Chilkuri_2021,
archiveprefix = {arXiv},
author = {Vijay Gopal Chilkuri and Thomas Applencourt and Kevin Gasperich and Pierre-Fran{\c c}ois Loos and Anthony Scemama},
date-added = {2021-06-18 13:22:26 +0200},
date-modified = {2021-06-18 13:22:35 +0200},
eprint = {1812.06902},
primaryclass = {physics.chem-ph},
title = {Spin-adapted selected configuration interaction in a determinant basis},
year = {2021}}
@article{Loos_2021,
author = {Loos,Pierre-Fran{\c c}ois and Matthews,Devin A. and Lipparini,Filippo and Jacquemin,Denis},
date-added = {2021-06-18 11:30:08 +0200},
@ -498,14 +529,12 @@
@article{Krishnan_1980,
author = {Krishnan,R. and Frisch,M. J. and Pople,J. A.},
date-added = {2021-05-06 15:42:45 +0200},
date-modified = {2021-05-06 15:43:10 +0200},
date-modified = {2021-07-26 11:05:04 +0200},
doi = {10.1063/1.439657},
eprint = {https://doi.org/10.1063/1.439657},
journal = {J. Chem. Phys.},
number = {7},
pages = {4244-4245},
title = {Contribution of triple substitutions to the electron correlation energy in fourth order perturbation theory},
url = {https://doi.org/10.1063/1.439657},
volume = {72},
year = {1980},
Bdsk-Url-1 = {https://doi.org/10.1063/1.439657}}
@ -1660,10 +1689,10 @@
booktitle = {Recent Progress in Quantum Monte Carlo},
chapter = {2},
date-added = {2020-10-10 13:52:37 +0200},
date-modified = {2020-10-10 13:53:07 +0200},
date-modified = {2021-07-26 11:11:15 +0200},
doi = {10.1021/bk-2016-1234.ch002},
pages = {15-46},
title = {Using CIPSI Nodes in Diffusion Monte Carlo},
title = {{Using CIPSI Nodes in Diffusion Monte Carlo}},
Bdsk-Url-1 = {https://pubs.acs.org/doi/abs/10.1021/bk-2016-1234.ch002},
Bdsk-Url-2 = {https://doi.org/10.1021/bk-2016-1234.ch002}}

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Manuscript/Ec.tex
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@ -703,6 +703,18 @@ As a final remark, we would like to mention that even if the two families of CC
\section{Conclusion}
\label{sec:ccl}
%%%%%%%%%%%%%%%%%%%%%%%%%
Using the SCI algorithm named \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI), we have produced FCI-quality frozen-core correlation energies for twelve cyclic molecules (see Fig.~\ref{fig:mol}) in the correlation-consistent double-$\zeta$ Dunning basis set (cc-pVDZ).
These estimates, which are likely accurate to a few tenths of a millihartree, have been obtained by extrapolating CIPSI energies to the FCI limit based on a set of orbitals obtained by minimizing the CIPSI variational energy.
Compared to natural orbitals, we have shown that, by using energetically optimized orbitals, one can reduce the size of the variational space by one order of magnitude for the same variational energy.
Thanks to these reference FCI energies, we have then benchmarked three families of popular electronic structure methods: i) the MP perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), ii) the approximate CC series CC2, CC3, and CC4, and iii) the ``complete'' CC series CCSD, CCSDT, and CCSDTQ.
Our results have shown that, with a $\order*{N^7}$ scaling, MP4 provides an interesting accuracy/cost ratio for this particular set of weakly correlated systems, while MP5 systematically worsen the perturbative estimates of the correlation energy.
We have evidenced that CC3 (where the triples are computed iteratively) also outperforms the perturbative-triples CCSD(T) method with the same $\order*{N^7}$ scaling but also its more expensive parent, CCSDT.
A similar trend is observed for the methods including quadruple excitations, where the $\order*{N^9}$ CC4 model has been shown to be more accurate than CCSDTQ [which scales as $\order*{N^{10}}$].
As perspectives, we are currently investigating the performance of the present approach for excited states in order to expand the QUEST database of vertical excitation energies. \cite{Veril_2021}
We hope to report on this in the near future.
The compression of the variational space brought by optimized orbitals could be also beneficial in the context of quantum Monte Carlo methods to generate compact, yet accurate multi-determinant trial wave functions. \cite{Dash_2018,Dash_2019,Scemama_2020,Dash_2021}
%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{acknowledgements}