diff --git a/Manuscript/rsdft-cipsi-qmc.tex b/Manuscript/rsdft-cipsi-qmc.tex index 5b2be55..1de59ae 100644 --- a/Manuscript/rsdft-cipsi-qmc.tex +++ b/Manuscript/rsdft-cipsi-qmc.tex @@ -269,35 +269,31 @@ 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 improvements on the path from HF to FCI: -increasing the maximum degree of excitation of CI methods (CISD, CISDT, -CISDTQ, \ldots), or increasing the complete active space -(CAS) wave functions until all the orbitals are in the active space. +i) increasing the maximum degree of excitation of CI methods (CISD, CISDT, +CISDTQ, \ldots), or ii) expanding the size of a complete active space +(CAS) wave function until all the orbitals are in the active space. Selected CI methods take a shortcut between the HF determinant and the FCI wave function by increasing iteratively the number of determinants on which the wave function is expanded, selecting the determinants which are expected to contribute the most -to the FCI eigenvector. At every iteration, the lowest eigenpair is +to the FCI wave function. At each iteration, the lowest eigenpair is extracted from the CI matrix expressed in the determinant subspace, -and the FCI energy can be estimated by computing a second-order -perturbative correction (PT2) to the variational energy, $\EPT$. +and the FCI energy can be estimated by adding up to the variational energy +a second-order perturbative correction (PT2), $\EPT$. The magnitude of $\EPT$ is a -measure of the distance to the exact eigenvalue, and is an adjustable -parameter controlling the quality of the wave function. -Within the \emph{Configuration interaction using a perturbative -selection made iteratively} (CIPSI)\cite{Huron_1973} method, the PT2 +measure of the distance to the FCI energy and a diagnostic of the the quality of the wave function. +\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 correction is computed along with the determinant selection. So the magnitude of $\EPT$ can be made the only parameter of the algorithm, and we choose this parameter as the convergence criterion of the CIPSI -algorithm. +algorithm.} -Considering that the perturbatively corrected energy is a reliable +\titou{Considering that the perturbatively corrected energy is a reliable estimate of the FCI energy, using a fixed value of the PT2 correction as a stopping criterion enforces a constant distance of all the calculations to the FCI energy. In this work, we target the chemical accuracy so all the CIPSI selections were made such that $\abs{\EPT} < -1$ m\hartree{}. - - +1$ m\hartree{}.} %================================= \subsection{Range-separated DFT}