saving work in Sec II
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@ -269,35 +269,31 @@ Beyond the single-determinant representation, the best
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multi-determinant wave function one can wish for --- in a given basis set --- is the FCI wave function.
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multi-determinant wave function one can wish for --- in a given basis set --- is the FCI wave function.
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FCI is the ultimate goal of post-HF methods, and there exists several systematic
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FCI is the ultimate goal of post-HF methods, and there exists several systematic
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improvements on the path from HF to FCI:
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improvements on the path from HF to FCI:
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increasing the maximum degree of excitation of CI methods (CISD, CISDT,
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i) increasing the maximum degree of excitation of CI methods (CISD, CISDT,
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CISDTQ, \ldots), or increasing the complete active space
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CISDTQ, \ldots), or ii) expanding the size of a complete active space
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(CAS) wave functions until all the orbitals are in the active space.
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(CAS) wave function until all the orbitals are in the active space.
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Selected CI methods take a shortcut between the HF
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Selected CI methods take a shortcut between the HF
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determinant and the FCI wave function by increasing iteratively the
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determinant and the FCI wave function by increasing iteratively the
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number of determinants on which the wave function is expanded,
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number of determinants on which the wave function is expanded,
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selecting the determinants which are expected to contribute the most
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selecting the determinants which are expected to contribute the most
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to the FCI eigenvector. At every iteration, the lowest eigenpair is
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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 computing a second-order
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and the FCI energy can be estimated by adding up to the variational energy
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perturbative correction (PT2) to the variational energy, $\EPT$.
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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
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measure of the distance to the exact eigenvalue, and is an adjustable
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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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parameter controlling 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 \emph{Configuration interaction using a perturbative
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selection made iteratively} (CIPSI)\cite{Huron_1973} method, the PT2
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correction is computed along with the determinant selection. So the
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correction is computed along with the determinant selection. So the
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magnitude of $\EPT$ can be made the only parameter of the algorithm,
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magnitude of $\EPT$ can be made the only parameter of the algorithm,
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and we choose this parameter as the convergence criterion of the CIPSI
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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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algorithm.}
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Considering that the perturbatively corrected energy is a reliable
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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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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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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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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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accuracy so all the CIPSI selections were made such that $\abs{\EPT} <
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1$ m\hartree{}.
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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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