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Pierre-Francois Loos 2020-08-27 20:43:07 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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@ -116,7 +116,7 @@ to a loss of size consistency. \cite{Evangelisti_1983,Cleland_2010,Tenno_2017,Gh
Another route to solve the Schr\"odinger equation is density-functional theory (DFT). \cite{Hohenberg_1964,Kohn_1999}
Present-day DFT calculations are almost exclusively done within the so-called Kohn-Sham (KS) formalism, \cite{Kohn_1965} which
transfers the complexity of the many-body problem to the universal and yet unknown exchange-correlation (xc) functional thanks to a judicious mapping between a non-interacting reference system and its interacting analog which both have exactly the same one-electron density.
transfers the complexity of the many-body problem to the universal and yet unknown exchange-correlation (xc) functional thanks to a judicious mapping between a non-interacting reference system and its interacting analog which both have the same one-electron density.
KS-DFT \cite{Hohenberg_1964,Kohn_1965} is now the workhorse of electronic structure calculations for atoms, molecules and solids thanks to its very favorable accuracy/cost ratio. \cite{ParrBook}
As compared to WFT, DFT has the indisputable advantage of converging much faster with respect to the size of the basis set. \cite{FraMusLupTou-JCP-15,Giner_2018,Loos_2019d,Giner_2020}
However, unlike WFT where, for example, many-body perturbation theory provides a precious tool to go toward the exact wave function, there is no systematic way to improve approximate xc functionals toward the exact functional.
@ -270,7 +270,7 @@ Unless otherwise stated, atomic units are used.
%====================
Beyond the single-determinant representation, the best
multi-determinant wave function one can wish for --- in a given basis set --- is the FCI wave function.
FCI is the ultimate goal of post-HF methods, and there exists several systematic
FCI is the ultimate goal of post-HF methods, and there exist several systematic
improvements on the path from HF to FCI:
i) increasing the maximum degree of excitation of CI methods (CISD, CISDT,
CISDTQ,~\ldots), or ii) expanding the size of a complete active space
@ -845,7 +845,7 @@ In this benchmark, the great majority of the systems are weakly correlated and a
described by a single determinant. Therefore, the atomization energies
calculated at the KS-DFT level are relatively accurate, even when
the basis set is small. The introduction of exact exchange (B3LYP and
PBE) make the results more sensitive to the basis set, and reduce the
PBE) makes the results more sensitive to the basis set, and reduce the
accuracy. Note that, due to the approximate nature of the xc functionals,
the statistical quantities associated with KS-DFT atomization energies do not converge towards zero and remain altered even in the CBS limit.
Thanks to the single-reference character of these systems,