saving work

HF_cc-pvdz/pes_ooCIs2.dat

@@ -18,3 +18,8 @@
 1.35        -100.08718412
 1.4         -100.07631643
 1.45        -100.06598555
+1.5         -100.05621453
+1.6         -100.03671856
+1.7         -100.02411561
+1.8         -100.01205708
+1.9         -100.00243938

Manuscript/seniority.tex

@@ -148,7 +148,7 @@ Fig.~\ref{fig:allCI} shows how the Hilbert space is populated in excitation-base
 %    \hfill
 \begin{subfigure}[b]{0.48\linewidth}
 \includegraphics[width=\linewidth]{table_hCI}
-        \caption{Hybrid excitation-seniority CI.}
+        \caption{Hierarchy-based CI.}
         \label{fig:hCI}
 \end{subfigure}
 	\caption{Partionining of the full Hilbert space into blocks of specific excitation degree $e$ (with respect to a closed-shell determinant) and seniority number $s$.
@@ -170,10 +170,10 @@ at the same time as static correlation, by moving down (increasing the seniority
 The second justification is computational.
 %Fig.~\ref{fig:scaling} also illustrates how the number of determinants within each block scales with the number of occupied orbitals $O$ and the number of virtual orbitals $V$.
 In the hCI class of methods, each next level of theory accomodates additional determinants from different excitation-seniority sectors (each block of Fig.~\ref{fig:allCI}).
-The key realization behind hCI is that the number of additional determinants presents the same scaling with respect to $N$, for all excitation-seniority sectors entering at a given order $o$.
-%to $O$ and $V$, for all excitation-seniority sectors of a given order $o$.
+The key realization behind hCI is that the number of additional determinants presents the same scaling with respect to $N$, for all excitation-seniority sectors entering at a given hierarchy $h$.
+%to $O$ and $V$, for all excitation-seniority sectors of a given hierarchy $h$.
 %This computational realization represents the second justification for the introduction of the hCI method.
-This further justifies the parameter $o$ as being the simple average between $e$ and $s/2$.
+This further justifies the parameter $h$ as being the simple average between $e$ and $s/2$.
 
 Each level of excitation-based CI has a hCI counterpart with the same scaling of $N_{det}$ with respect to $N$.
 %However, hCI counts with additional half-integer levels of theory, with no parallel in excitation-based CI.
@@ -181,7 +181,7 @@ For example, in both hCI2 and CISD we have $N_{det} \sim N^4$, whereas in hCI3 a
 %the number of determinants of hCI2 and CISD scale as $O^2V^2$, those of hCI3 and CISDT scale as $O^3V^3$, and so on.
 From this computational perspective, hCI can be seen as a more natural choice than the traditional excitation-based CI,
 because if one can afford for, say, the $N_{det} \sim N^6$ cost of a CISDT calculation, than one can probably afford a hCI3 calculation, which has the same computational scaling.
-Of course, in practice an integer-$o$ hCI method will have more determinants than its excitation-based counterpart (though the same scaling),
+Of course, in practice an integer-$h$ hCI method will have more determinants than its excitation-based counterpart (though the same scaling),
 and thus one should first ensure whether including the lower-triangular blocks (going from CISDT to hCI3 in our example)
 is a better strategy than adding the next column (going from CISDT to CISDTQ).
 Therefore, here we decided to discuss the results in terms of the number of determinants, rather than the computational scaling,
@@ -194,7 +194,7 @@ Therefore, while the HF-based lowest level of excitation-based CI (CIS) does not
 the hCI1 counterpart already represents a minimally correlated model, with the very favourable $N_{det} \sim N^2$ scaling.
 %number of determinants scaling only as $OV$.
 %
-In addition, hCI allows for half-integer orders $o$, with no parallel in excitation-based CI.
+In addition, hCI allows for half-integer values of $h$, with no parallel in excitation-based CI.
 This gives extra flexibility in terms of choice of method.
 %when evaluating the computational cost and desired accuracy of a calculation.
 For a particular application with excitation-based CI, CISD might be too inaccurate, for example, while the price for the improved accuracy of CISDT might be too high.
@@ -224,8 +224,8 @@ And second, each next level includes all classes of determinants sharing the sam
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 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},
-by allowing only for determinants at a given order $o$.
-In practice, the CI energy is converged (within a chosen threshold of) with considerably fewer determinants than the formal number of determinants at a given $o$.
+by allowing only for determinants at a given hierarchy $h$.
+In practice, the CI energy is converged (within a chosen threshold of) with considerably fewer determinants than the formal number of determinants at a given $h$.
 The traditional excitation-based CI and the FCI calculations presented here were also performed with the CIPSI algorithm implemented in {\QP}. \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2019}
 The CI calculations were performed with both canonical Hartree-Fock (HF) orbitals and optimized orbitals (oo).
 In the latter case, the energy is obtained variationally in both the CI space and in the orbital parameter space, given rise to what may be called an orbital-optimized CI (ooCI) method.
@@ -238,7 +238,7 @@ then this gradient component is replaced by $g_0 |g_i|/g_i$.
 While we can never ensure that the obtained solutions are global minima in the orbital parameter space, we verified that in all cases surveyed here, the stationary solutions are real minima (rather than maxima or stationary points).
 
 Here we assess the performance of the hCI methods against its excitation-based and seniority-based counterparts.
-To do so, we calculated the potential energy curves (PECs) for a total of 8 systems:
+To do so, we calculated the potential energy curves (PECs) for a total of 6 systems:
 \ce{HF}, \ce{F2}, \ce{N2}, 
 %\ce{Be2}, \ce{H2O}, 
 ethylene, \ce{H4}, and \ce{H8}.
@@ -249,7 +249,7 @@ For ethylene, we considered the C$=$C double bond stretching, while freezing the
 All CI calculations were performed for the cc-pVDZ basis set and with frozen core orbitals.
 From the PECs, we have also extrated the equilibrium geometries and vibrational frequencies (details can be found in the SI).
 
-It is worth mentioning that obtaining smooth PECs for the orbital optimized calculations was far from trivial.
+It is worth mentioning that obtaining smooth PECs for the orbital optimized calculations proved to be far from trivial.
 First, the orbital optimization started from the HF orbitals of each geometry.
 This usually lead to discontinuous PECs, meaning that distinct solutions of the orbital optimization have been found with our algorithm.
 Then, at some geometry or geometries that seem to present the lowest lying solution,

ethylene_cc-pvdz/pes_ooCIo2.dat

@@ -29,3 +29,7 @@
 4.4          -78.05700643
 4.6          -78.03518250
 4.8          -78.01613055
+5.0          -78.01664273
+5.2          -77.98517879
+5.4          -77.97289399
+5.6          -77.96242176