first iteration of Sec II done
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@ -121,8 +121,8 @@ 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, 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}
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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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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@ -280,20 +280,11 @@ to the FCI wave function. At each iteration, the lowest eigenpair is
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extracted from the CI matrix expressed in the determinant subspace,
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extracted from the CI matrix expressed in the determinant subspace,
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and the FCI energy can be estimated by adding up to the variational energy
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and the FCI energy can be estimated by adding up to the variational energy
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a second-order perturbative correction (PT2), $\EPT$.
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a second-order perturbative correction (PT2), $\EPT$.
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The magnitude of $\EPT$ is a
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The magnitude of $\EPT$ is a measure of the distance to the FCI energy
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measure of the distance to the FCI energy and a diagnostic of the the quality of the wave function.
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and a diagnostic of the the quality of the wave function.
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\titou{Within the CIPSI algorithm originally developed by Huron \textit{et al.} in Ref.~\onlinecite{Huron_1973} and efficiently implemented as described in Ref.~\onlinecite{Garniron_2019}, the PT2
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Within the CIPSI algorithm originally developed by Huron \textit{et al.} in Ref.~\onlinecite{Huron_1973} and efficiently implemented as described in Ref.~\onlinecite{Garniron_2019}, the PT2
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correction is computed along with the determinant selection. So the
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correction is computed simultaneously to the determinant selection at no extra cost.
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magnitude of $\EPT$ can be made the only parameter of the algorithm,
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$\EPT$ is then the sole parameter of the CIPSI algorithm and is chosen to be its convergence criterion.
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and we choose this parameter as the convergence criterion of the CIPSI
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algorithm.}
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\titou{Considering that the perturbatively corrected energy is a reliable
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estimate of the FCI energy, using a fixed value of the PT2 correction
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as a stopping criterion enforces a constant distance of all the
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calculations to the FCI energy. In this work, we target the chemical
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accuracy so all the CIPSI selections were made such that $\abs{\EPT} <
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1$ m\hartree{}.}
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%=================================
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%=================================
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\subsection{Range-separated DFT}
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\subsection{Range-separated DFT}
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@ -444,7 +435,8 @@ of the local-density approximation (LDA)\cite{Sav-INC-96a,TouSavFla-IJQC-04} and
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and correlation functionals defined in
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and correlation functionals defined in
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Ref.~\onlinecite{GolWerStoLeiGorSav-CP-06} (see also
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Ref.~\onlinecite{GolWerStoLeiGorSav-CP-06} (see also
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Refs.~\onlinecite{TouColSav-JCP-05,GolWerSto-PCCP-05}).
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Refs.~\onlinecite{TouColSav-JCP-05,GolWerSto-PCCP-05}).
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The convergence criterion for stopping the CIPSI calculations
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In this work, we target chemical accuracy, so
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the convergence criterion for stopping the CIPSI calculations
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has been set to $\EPT < 10^{-3}$ \hartree{} or $ \Ndet > 10^7$.
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has been set to $\EPT < 10^{-3}$ \hartree{} or $ \Ndet > 10^7$.
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All the wave functions are eigenfunctions of the $\Hat{S}^2$ spin operator, as
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All the wave functions are eigenfunctions of the $\Hat{S}^2$ spin operator, as
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described in Ref.~\onlinecite{Applencourt_2018}.
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described in Ref.~\onlinecite{Applencourt_2018}.
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