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minor corrections in intro

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Pierre-Francois Loos 2020-08-17 11:49:25 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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@ -89,7 +89,7 @@ Having low energies does not mean that they are good for chemical properties.
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}
In order to achieve this formidable endeavour, various strategies have been carefully designed and efficiently implemented in various quantum chemistry software packages.
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.
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.
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.
The FB-FCI wave function and its corresponding energy form the eigenpair of an approximate Hamiltonian defined as
the projection of the exact Hamiltonian onto the finite many-electron basis of
@ -113,8 +113,8 @@ Present-day DFT calculations are almost exclusively done within the so-called Ko
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.
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,Loos_2019d,Giner_2020}
However, \manu{there is no systematic way of refining the approximation of the unknown exact xc functional, and therefore in practice }
one faces the unsettling choice of the \emph{approximate} xc functional\cite{Becke_2014}. \sout{ which makes inexorably KS-DFT hard to systematically improve. }
\titou{However, there is no systematic way of refining the approximation of the unknown exact xc functional, and therefore in practice
one faces the unsettling choice of the \emph{approximate} xc functional. \cite{Becke_2014}}
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.
Diffusion Monte Carlo (DMC), which belongs to the family of stochastic methods, is yet another numerical scheme to obtain
@ -142,7 +142,7 @@ approximation.
However, because it is not possible to minimize directly the FN-DMC energy with respect
to the linear and non-linear parameters of the trial wave function, the
fixed-node approximation is much more difficult to control than the
finite-basis approximation\manu{, especially to compute energy differences}.
finite-basis approximation, especially to compute energy differences.
The conventional approach consists in multiplying the trial wave
function by a positive function, the \emph{Jastrow factor}, taking
account of the bulk of the dynamical correlation.