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minor corrections in comp details

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Pierre-Francois Loos 2022-03-07 22:27:39 +01:00
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@ -221,14 +221,15 @@ 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 $h$.
by allowing only for determinants having a given maximum hierarchy $h$ to be selected.
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 the CI energy to be converged when the second-order perturbation correction lies below \SI{0.01}{\milli\hartree}, \cite{Garniron_2018}
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).
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}
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,
which are not related to the particular algorithmic choices of the CIPSI calculations.
All CI calculations were performed for the cc-pVDZ basis set and with frozen core orbitals.
For the \ce{HF} molecule we have also tested basis set effects, by considered the cc-pVTZ and cc-pVQZ basis sets.
\titou{T2: I think it might be worth mentioning that the determinant-driven framework of {\QP} allows to include any arbitrary set of determinants.
This would also justify why we are focusing on the number of determinants instead of the actual scaling of the method.
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.
@ -238,10 +239,10 @@ This shows that the determinant-driven algorithm is definitely not optimal.
However, the selected nature of the CIPSI algorithm means that the actual number of determinants is quite small and therefore calculations are technically feasable.}
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 an orbital-optimized CI (oo-CI) method.
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.
We employed the algorithm described elsewhere \cite{Damour_2021} and also implemented in {\QP} for optimizing the orbitals within a CI wave function.
In order to avoid converging to a saddle point solution, we employed a similar strategy as recently described in Ref.~\onlinecite{Elayan_2022}.
Namely, whenever the eigenvalue of the orbital rotation Hessian is negative and the corresponding gradient component $g_i$ lies below a given threshold $g_0$,
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 ?)},
then this gradient component is replaced by $g_0 \abs{g_i}/g_i$.
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
correspond to real minima (rather than maxima or saddle points).