minor corrections in intro
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@ -89,7 +89,7 @@ Having low energies does not mean that they are good for chemical properties.
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Solving the Schr\"odinger equation for the ground state of atoms and molecules is a complex task that has kept theoretical and computational chemists busy for almost hundred years now. \cite{Schrodinger_1926}
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Solving the Schr\"odinger equation for the ground state of atoms and molecules is a complex task that has kept theoretical and computational chemists busy for almost hundred years now. \cite{Schrodinger_1926}
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In order to achieve this formidable endeavour, various strategies have been carefully designed and efficiently implemented in various quantum chemistry software packages.
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In order to achieve this formidable endeavour, various strategies have been carefully designed and efficiently implemented in various quantum chemistry software packages.
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One of \manu{these} strategies consists in relying on wave function theory \cite{Pople_1999} (WFT) and, in particular, on the full configuration interaction (FCI) method.
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One of these strategies consists in relying on wave function theory \cite{Pople_1999} (WFT) and, in particular, on the full configuration interaction (FCI) method.
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However, FCI delivers only an approximate solution of the Schr\"odinger equation within a finite basis (FB) of one-electron basis functions, the FB-FCI energy being an upper bound to the exact energy in accordance with the variational principle.
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However, FCI delivers only an approximate solution of the Schr\"odinger equation within a finite basis (FB) of one-electron basis functions, the FB-FCI energy being an upper bound to the exact energy in accordance with the variational principle.
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The FB-FCI wave function and its corresponding energy form the eigenpair of an approximate Hamiltonian defined as
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The FB-FCI wave function and its corresponding energy form the eigenpair of an approximate Hamiltonian defined as
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the projection of the exact Hamiltonian onto the finite many-electron basis of
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the projection of the exact Hamiltonian onto the finite many-electron basis of
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@ -113,8 +113,8 @@ Present-day DFT calculations are almost exclusively done within the so-called Ko
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transfers the complexity of the many-body problem to the 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.
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transfers the complexity of the many-body problem to the 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.
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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}
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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}
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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,Loos_2019d,Giner_2020}
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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,Loos_2019d,Giner_2020}
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However, \manu{there is no systematic way of refining the approximation of the unknown exact xc functional, and therefore in practice }
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\titou{However, there is no systematic way of refining the approximation of the unknown exact xc functional, and therefore in practice
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one faces the unsettling choice of the \emph{approximate} xc functional\cite{Becke_2014}. \sout{ which makes inexorably KS-DFT hard to systematically improve. }
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one faces the unsettling choice of the \emph{approximate} xc functional. \cite{Becke_2014}}
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Moreover, because of the approximate nature of the xc functional, although the resolution of the KS equations is variational, the resulting KS energy does not have such property.
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Moreover, because of the approximate nature of the xc functional, although the resolution of the KS equations is variational, the resulting KS energy does not have such property.
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Diffusion Monte Carlo (DMC), which belongs to the family of stochastic methods, is yet another numerical scheme to obtain
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Diffusion Monte Carlo (DMC), which belongs to the family of stochastic methods, is yet another numerical scheme to obtain
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@ -142,7 +142,7 @@ approximation.
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However, because it is not possible to minimize directly the FN-DMC energy with respect
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However, because it is not possible to minimize directly the FN-DMC energy with respect
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to the linear and non-linear parameters of the trial wave function, the
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to the linear and non-linear parameters of the trial wave function, the
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fixed-node approximation is much more difficult to control than the
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fixed-node approximation is much more difficult to control than the
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finite-basis approximation\manu{, especially to compute energy differences}.
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finite-basis approximation, especially to compute energy differences.
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The conventional approach consists in multiplying the trial wave
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The conventional approach consists in multiplying the trial wave
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function by a positive function, the \emph{Jastrow factor}, taking
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function by a positive function, the \emph{Jastrow factor}, taking
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account of the bulk of the dynamical correlation.
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account of the bulk of the dynamical correlation.
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