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36
Manuscript/rsdft-cipsi-qmc.bib
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@ -1,13 +1,47 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Pierre-Francois Loos at 2020-08-17 09:17:11 +0200
%% Created for Pierre-Francois Loos at 2020-08-17 10:19:43 +0200
%% Saved with string encoding Unicode (UTF-8)
@article{Scemama_2016,
Author = {Scemama, Anthony and Applencourt, Thomas and Giner, Emmanuel and Caffarel, Michel},
Date-Added = {2020-08-17 10:18:21 +0200},
Date-Modified = {2020-08-17 10:18:21 +0200},
Doi = {10.1002/jcc.24382},
Issn = {0192-8651},
Journal = {J. Comput. Chem.},
Month = {Jun},
Number = {20},
Pages = {1866--1875},
Publisher = {Wiley-Blackwell},
Title = {Quantum Monte Carlo with very large multideterminant wavefunctions},
Url = {http://dx.doi.org/10.1002/jcc.24382},
Volume = {37},
Year = {2016},
Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.24382}}
@article{Scemama_2014,
Author = {Scemama, A. and Applencourt, T. and Giner, E. and Caffarel, M.},
Date-Added = {2020-08-17 10:18:00 +0200},
Date-Modified = {2020-08-17 10:18:00 +0200},
Doi = {10.1063/1.4903985},
Issn = {1089-7690},
Journal = {J. Chem. Phys.},
Month = {Dec},
Number = {24},
Pages = {244110},
Publisher = {AIP Publishing},
Title = {Accurate nonrelativistic ground-state energies of 3d transition metal atoms},
Url = {http://dx.doi.org/10.1063/1.4903985},
Volume = {141},
Year = {2014},
Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4903985}}
@article{Scemama_2019,
Author = {A. Scemama and M. Caffarel and A. Benali and D. Jacquemin and P. F. Loos.},
Date-Added = {2020-08-17 09:16:18 +0200},

17
Manuscript/rsdft-cipsi-qmc.tex
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@ -174,13 +174,16 @@ In such cases or when very high accuracy is required, a viable alternative is to
``post-FCI'' method. A multi-determinant trial wave function is then produced by
approaching FCI with a SCI method such as the \emph{configuration interaction using a perturbative
selection made iteratively} (CIPSI) method.\cite{Giner_2013,Giner_2015,Caffarel_2016_2}
\titou{When the basis set is enlarged, the trial wave function gets closer to
When the basis set is enlarged, the trial wave function gets closer to
the exact wave function, so we expect the nodal surface to be
improved.\cite{Caffarel_2016}}
This technique has the advantage of using the FCI nodes in a given basis
set, which is perfectly well defined and therefore makes the calculations reproducible in a
improved.\cite{Caffarel_2016}
Note that, as discussed in Ref.~\onlinecite{Caffarel_2016_2}, there is no mathematical guarantee that increasing the size of the one-electron basis lowers the FN-DMC energy, because the variational principle does not explicitly optimize the nodal surface, nor the FN-DMC energy.
However, in all applications performed so far, \cite{Giner_2013,Scemama_2014,Scemama_2016,Giner_2015,Caffarel_2016,Scemama_2018,Scemama_2018b,Scemama_2019} a systematic decrease of the FN-DMC energy has been observed whenever the SCI trial wave function is improved variationally upon enlargement of the basis set.
The technique relying on SCI multi-determinant trial wave functions described above has the advantage of using near-FCI quality nodes in a given basis
set, which is perfectly well defined and therefore makes the calculations systematically improvable and reproducible in a
black-box way without needing any QMC expertise.
Nevertheless, this technique cannot be applied to large systems because of the
Nevertheless, this procedure cannot be applied to large systems because of the
exponential growth of the number of Slater determinants in the trial wave function.
Extrapolation techniques have been used to estimate the FN-DMC energies
obtained with FCI wave functions,\cite{Scemama_2018,Scemama_2018b,Scemama_2019} and other authors
@ -190,13 +193,13 @@ of a Jastrow factor to keep the number of determinants
small,\cite{Giner_2016} and where the consistency between the
different wave functions is kept by imposing a constant energy
difference between the estimated FCI energy and the variational energy
of the CI wave function.\cite{Dash_2018,Dash_2019}
of the SCI wave function.\cite{Dash_2018,Dash_2019}
Nevertheless, finding a robust protocol to obtain high accuracy
calculations which can be reproduced systematically and
applicable to large systems with a multi-configurational character is
still an active field of research. The present paper falls
within this context.
The central idea of the present work, and the launch-pad for the remainder of this study, is that one can combine the various strengths of WFT, DFT, and DMC in order to create a new hybrid method with more attractive properties.
In particular, we show here that one can combine CIPSI and KS-DFT via the range separation (RS) of the interelectronic Coulomb operator \cite{Sav-INC-96a,Toulouse_2004} to obtain accurate FN-DMC energies with compact multi-determinant trial wave functions.