minor corrections in comp details
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@ -221,14 +221,15 @@ From the PECs, we have also extracted the vibrational frequencies and equilibriu
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The hCI method was implemented in {\QP} via a straightforward adaptation of the
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The hCI method was implemented in {\QP} via a straightforward adaptation of the
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\textit{configuration interaction using a perturbative selection made iteratively} (CIPSI) algorithm, \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2018}
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\textit{configuration interaction using a perturbative selection made iteratively} (CIPSI) algorithm, \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2018}
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by allowing only for determinants having a given maximum hierarchy $h$.
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by allowing only for determinants having a given maximum hierarchy $h$ to be selected.
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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}
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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}
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In practice, we consider the CI energy to be converged when the second-order perturbation correction lies below \SI{0.01}{\milli\hartree}, \cite{Garniron_2018}
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In practice, we consider, for a given CI level, the CI energy to be converged when the second-order perturbation correction \titou{(which approximately measures the error between the selective and complete calculations)} lies below \SI{0.01}{\milli\hartree}. \cite{Garniron_2018}
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which requires 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).
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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.
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Nevertheless, we decided to present the results as functions of the formal number of determinants,
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Nevertheless, we decided to present the results as functions of the formal number of determinants,
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which are not related to the particular algorithmic choices of the CIPSI calculations.
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which are not related to the particular algorithmic choices of the CIPSI calculations.
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All CI calculations were performed for the cc-pVDZ basis set and with frozen core orbitals.
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All CI calculations were performed for the cc-pVDZ basis set and with frozen core orbitals.
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For the \ce{HF} molecule we have also tested basis set effects, by considered the cc-pVTZ and cc-pVQZ basis sets.
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For the \ce{HF} molecule we have also tested basis set effects, by considered the cc-pVTZ and cc-pVQZ basis sets.
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\titou{T2: I think it might be worth mentioning that the determinant-driven framework of {\QP} allows to include any arbitrary set of determinants.
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\titou{T2: I think it might be worth mentioning that the determinant-driven framework of {\QP} allows to include any arbitrary set of determinants.
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This would also justify why we are focusing on the number of determinants instead of the actual scaling of the method.
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This would also justify why we are focusing on the number of determinants instead of the actual scaling of the method.
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I think this is a important point because the CISD Hilbert space has a size proportional to $N^4$ but the cost associated with solving the CISD equations scales as $N^6$... Actually, it follows the same rules as CC: CISD scales as $N^6$, CISDT as $N^8$, CISDTQ as $N^{10}$, etc.
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I think this is a important point because the CISD Hilbert space has a size proportional to $N^4$ but the cost associated with solving the CISD equations scales as $N^6$... Actually, it follows the same rules as CC: CISD scales as $N^6$, CISDT as $N^8$, CISDTQ as $N^{10}$, etc.
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@ -238,10 +239,10 @@ This shows that the determinant-driven algorithm is definitely not optimal.
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However, the selected nature of the CIPSI algorithm means that the actual number of determinants is quite small and therefore calculations are technically feasable.}
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However, the selected nature of the CIPSI algorithm means that the actual number of determinants is quite small and therefore calculations are technically feasable.}
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The CI calculations were performed with both canonical HF orbitals and optimized orbitals.
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The CI calculations were performed with both canonical HF orbitals and optimized orbitals.
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In the latter case, the energy is obtained variationally in the CI space and in the orbital parameter space, hence an orbital-optimized CI (oo-CI) method.
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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.
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We employed the algorithm described elsewhere \cite{Damour_2021} and also implemented in {\QP} for optimizing the orbitals within a CI wave function.
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We employed the algorithm described elsewhere \cite{Damour_2021} and also implemented in {\QP} for optimizing the orbitals within a CI wave function.
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In order to avoid converging to a saddle point solution, we employed a similar strategy as recently described in Ref.~\onlinecite{Elayan_2022}.
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In order to avoid converging to a saddle point solution, we employed a similar strategy as recently described in Ref.~\onlinecite{Elayan_2022}.
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Namely, whenever the eigenvalue of the orbital rotation Hessian is negative and the corresponding gradient component $g_i$ lies below a given threshold $g_0$,
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Namely, whenever the eigenvalue of the orbital rotation Hessian is negative and the corresponding gradient component $g_i$ lies below a given threshold $g_0$ \titou{(typically equal to ?)},
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then this gradient component is replaced by $g_0 \abs{g_i}/g_i$.
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then this gradient component is replaced by $g_0 \abs{g_i}/g_i$.
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While we cannot ensure that the obtained solutions are global minima in the orbital parameter space, we verified that in all stationary solutions surveyed here
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While we cannot ensure that the obtained solutions are global minima in the orbital parameter space, we verified that in all stationary solutions surveyed here
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correspond to real minima (rather than maxima or saddle points).
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correspond to real minima (rather than maxima or saddle points).
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