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% range-separated density functional theory and selected configuration interaction}
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\author{Anthony Scemama}
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\email{scemama@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\author{Emmanuel Giner}
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\email{emmanuel.giner@lct.jussieu.fr}
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@ -68,40 +69,43 @@ exact solution is recovered.
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Hence, the accuracy of a FCI calculation can be systematically improved by increasing the size of the one-electron basis set.
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Nevertheless, its exponential scaling with the number of electrons and with the size of the basis is prohibitive for most chemical systems.
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In recent years, the introduction of new algorithms \cite{Booth_2009} and the
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revival \cite{Abrams_2005,Bytautas_2009,Roth_2009,Giner_2013,Knowles_2015,Holmes_2016,Liu_2016}
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revival \cite{Abrams_2005,Bytautas_2009,Roth_2009,Giner_2013,Knowles_2015,Holmes_2016,Liu_2016,Garniron_2018}
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of selected configuration interaction (sCI)
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methods \cite{Bender_1969,Huron_1973,Buenker_1974} pushed the limits of
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the sizes of the systems that could be computed at the FCI level.
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the sizes of the systems that could be computed at the FCI level. \cite{Booth_2010,Cleland_2010,Daday_2012,Chien_2018,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c}
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However, the scaling remains exponential unless some bias is introduced leading
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to a loss of size consistency. % CITE CIPSI 3-CLASS AND INITIATOR APPROXIMATION.
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to a loss of size consistency. \cite{Evangelisti_1983,Cleland_2010,Tenno_2017}
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Diffusion Monte Carlo (DMC) is a numerical scheme to obtain
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the exact solution of the Schr\"odinger equation with a different
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constraint, imposing the solution to have the same nodal hypersurface
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as a given trial wave function.
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constraint. In DMC, the solution is imposed to have the same nodes (or zeroes)
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as a given trial (approximate) wave function.
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Within this so-called \emph{fixed-node} (FN) approximation,
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the FN-DMC energy associated with a given trial wave function is an upper
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bound to the exact energy, and the latter is recovered only when the
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nodes of the trial wave function coincide with the nodes of the exact
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wave function.
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The polynomial scaling with the number of electrons and with the size
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of the trial wave function makes the FN-DMC method attractive.
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of the trial wave function makes the FN-DMC method particularly attractive.
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In addition, the total energies obtained are usually far below
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those obtained with the FCI method in computationally tractable basis
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sets because the constraints imposed by the fixed-node approximation
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sets because the constraints imposed by the FN approximation
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are less severe than the constraints imposed by the finite-basis
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approximation.
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\alert{However, it is usually harder to control the FN error in DMC, and this might affect energy differences such as atomization energies.
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Moreover, improving systematically the nodal surface of the trial wave function can be a tricky job as there is no variational principle for the nodes.}
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The qualitative picture of the electronic structure of weakly
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correlated systems, such as organic molecules near their equilibrium
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geometry, is usually well represented with a single Slater
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determinant. This feature is in part responsible for the success of
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density functional theory (DFT) and coupled cluster.
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density-functional theory (DFT) and coupled cluster.
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DMC with a single-determinant trial wave function can be used as a
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single-reference post-Hatree-Fock method, with an accuracy comparable
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to coupled cluster.\cite{Dubecky_2014,Grossman_2002}
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The favorable scaling of QMC, its very low memory requirements and
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its adequation with massively parallel architectures make it a
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its adequacy with massively parallel architectures make it a
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serious alternative for high-accuracy simulations on large systems.
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As it is not possible to minimize directly the FN-DMC energy with respect
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