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Pierre-Francois Loos 2022-03-09 10:12:25 +01:00
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Manuscript/seniority.bib
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@ -1,13 +1,25 @@
%% This BibTeX bibliography file was created using BibDesk.
%% https://bibdesk.sourceforge.io/
%% Created for Pierre-Francois Loos at 2022-03-07 20:27:55 +0100
%% Created for Pierre-Francois Loos at 2022-03-09 10:00:09 +0100
%% Saved with string encoding Unicode (UTF-8)
@article{Davidson_1975,
author = {E. R. Davidson},
date-added = {2022-03-09 10:00:08 +0100},
date-modified = {2022-03-09 10:00:08 +0100},
doi = {10.1016/0021-9991(75)90065-0},
journal = {J. Comput. Phys.},
pages = {87--94},
title = {The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices},
volume = {17},
year = {1975},
bdsk-url-1 = {https://doi.org/10.1016/0021-9991(75)90065-0}}
@article{Veril_2021,
author = {Micka{\"e}l V{\'e}ril and Anthony Scemama and Michel Caffarel and Filippo Lipparini and Martial Boggio-Pasqua and Denis Jacquemin and Pierre-Fran{\c c}ois Loos},
date-added = {2022-03-07 20:24:41 +0100},

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Manuscript/seniority.tex
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@ -214,16 +214,16 @@ From the PECs, we have also extracted the vibrational frequencies and equilibriu
The hCI method was implemented in {\QP} via a straightforward adaptation of the
\textit{configuration interaction using a perturbative selection made iteratively} (CIPSI) algorithm, \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2018}
by allowing only for determinants having a given maximum hierarchy $h$ to be selected.
\fk{It is worth mentioning that the determinant-driven framework of {\QP} allows the inclusion of any arbitrary set of determinants.}
The excitation-based CI, seniority-based CI, and FCI calculations presented here were also performed with the CIPSI algorithm implemented in {\QP}. \cite{Garniron_2019}
In practice, we consider, for a given CI level, the ground state energy to be converged when the second-order perturbation correction \fk{from the truncated Hilbert space} (which approximately measures the error between the selective and complete calculations) lies below \SI{0.01}{\milli\hartree}. \cite{Garniron_2018}
It is worth mentioning that the determinant-driven framework of {\QP} allows the inclusion of any arbitrary set of determinants.
In practice, we consider, for a given CI level, the ground state energy to be converged when the second-order perturbation correction computed in the truncated Hilbert space (which approximately measures the error between the selective and complete calculations) lies below \SI{0.01}{\milli\hartree}. \cite{Garniron_2018}
These selected versions of CI require considerably fewer determinants than the formal number of determinants (understood as all those that belong to a given CI level, regardless of their weight or symmetry) of their complete counterparts.
Nevertheless, we decided to present the results as functions of the formal number of determinants,
Nevertheless, we decided to present the results as functions of the formal number of determinants (see above),
which are not related to the particular algorithmic choices of the CIPSI calculations.
\fk{The ground-state CI energy is obtained with the Davidson's iterative algorithm \cite{Davidson_1975} [Titou, please add the ref.],
The ground-state CI energy is obtained with the Davidson iterative algorithm, \cite{Davidson_1975}
which in the present implementation of {\QP} means that the computation and storage cost us $\order*{\Ndet^{3/2}}$ and $\order*{\Ndet}$, respectively.
This shows that the determinant-driven algorithm is not optimal in general.
However, the selected nature of the CIPSI algorithm means that the actual number of determinants is quite small and therefore calculations are technically feasable.}
However, the selected nature of the CIPSI algorithm drastically reduces the actual number of determinants and therefore calculations are technically feasible.
The CI calculations were performed with both canonical HF orbitals and optimized orbitals.
In the latter case, the energy is obtained variationally in the CI space and in the orbital parameter space, hence defining orbital-optimized CI (oo-CI) methods.