several minor corrections

This commit is contained in:
kossoski 2022-03-09 20:20:46 +01:00
parent 76801a4272
commit 26010c69e0
94 changed files with 388 additions and 207 deletions

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@ -47,7 +47,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

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@ -48,7 +48,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

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@ -47,7 +47,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

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@ -48,7 +48,7 @@ set style line 14 dt 1 lw 2 linecolor rgb "sea-green" pt 7 ps 2
set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
set xlabel 'Number of determinants'
set ylabel "Force constant (Hartree/{\305}^{2})"
set ylabel "Force constant (Hartree/a_{0})"
###################################################################################
###################################################################################

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@ -49,7 +49,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

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@ -48,7 +48,7 @@ set style line 14 dt 1 lw 2 linecolor rgb "sea-green" pt 7 ps 2
set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
set xlabel 'Number of determinants'
set ylabel "Force constant (Hartree/{\305}^{2})"
set ylabel "Force constant (Hartree/a_{0})"
###################################################################################
###################################################################################

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@ -47,7 +47,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

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@ -75,7 +75,7 @@ set label 2 'CISD' at 5.0,-99.941 rotate by r(a) center tc ls 3 #font 'Verdana,2
#fit [2.5:3.5] [*:*] f(x) 'pes_CISDT.dat' u 1:($2) via a,b
#set label 3 'CISDT' at 3.0,-100.010 rotate by r(a) center tc ls 3 #font 'Verdana,20'
fit [4.0:6.0] [*:*] f(x) 'pes_CISDT.dat' u 1:($2) via a,b
set label 3 'CISDT' at 5.0,-99.989 rotate by r(a) center tc ls 3 #font 'Verdana,20'
set label 3 'CISDT' at 5.0,-99.989 rotate by r(a) center tc ls 3 #font 'Helvetica,20'
#fit [2.5:3.5] [*:*] f(x) 'pes_CISDTQ.dat' u 1:($2) via a,b
#set label 4 'CISDTQ' at 3.0,-100.040 rotate by r(a) center tc ls 3 #font 'Verdana,20'
fit [4.0:6.0] [*:*] f(x) 'pes_CIo1.dat' u 1:($2) via a,b

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@ -47,7 +47,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

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@ -47,7 +47,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

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@ -47,7 +47,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

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@ -150,7 +150,7 @@ at the same time as static correlation, by moving down (increasing the seniority
The second justification is computational.
In the hCI class of methods, each level of theory accommodates additional determinants from different excitation-seniority sectors (each block of same color tone in Fig.~\ref{fig:allCI}).
The key insight behind hCI is that the number of additional determinants presents the same scaling with respect to $\Nbas$, for all excitation-seniority sectors entering at a given hierarchy $h$.
This further justifies the parameter $h$ as being the simple average between $e$ and $s/2$.
This justifies the numerator in the definition of $h$ [Eq.~\eqref{eq:h}].
Finally, the third justification for our hCI method is empirical and closely related to the computational motivation.
There are many possible ways to populate the Hilbert space starting from a given reference determinant,
@ -170,7 +170,8 @@ In comparison to previous approaches, our hybrid hCI scheme has two key advantag
First, it is defined by a single parameter that unifies excitation degree and seniority number [see Eq.~\eqref{eq:h}].
Second and most importantly, each next level includes all classes of determinants whose number share the same scaling with system size, as discussed before, thus preserving the polynomial cost of the method.
Each level of excitation-based CI has a hCI counterpart with the same scaling of $\Ndet$ with respect to $\Nbas$.
Each level of excitation-based CI has a hCI counterpart with the same scaling of $\Ndet$ with respect to $\Nbas$,
justifying the denominator in the definition of $h$ [Eq.~\eqref{eq:h}].
For example, $\Ndet = \order*{\Nbas^4}$ in both hCI2 and CISD, whereas $\Ndet = \order*{\Nbas^6}$ in hCI3 and CISDT, 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, CISDT, then one could probably afford hCI3, due to the same scaling of $\Ndet$.
@ -200,7 +201,7 @@ Its equilibrium geometry was taken from Ref.~\onlinecite{Loos_2018} and is repro
Due to the (multiple) bond breaking, these are challenging systems for electronic structure methods,
being often considered when assessing novel methodologies.
More precisely, we have evaluated the convergence of four observables: the non-parallelity error (NPE), the distance error, the vibrational frequencies, and the equilibrium geometries.
The NPE is defined as the maximum minus the minimum differences between the PECs obtained at given CI level and the exact FCI result.
The NPE is defined as the maximum minus the minimum differences between the PECs obtained at a given CI level and the exact FCI result.
We define the distance error as the maximum plus the minimum differences between a given PEC and the FCI result.
Thus, while the NPE probes the similarity regarding the shape of the PECs, the distance error provides a measure of how their overall magnitudes compare.
From the PECs, we have also extracted the vibrational frequencies and equilibrium geometries (details can be found in the \SupInf).
@ -231,10 +232,10 @@ In order to avoid converging to a saddle point solution, we employed a similar s
Namely, whenever the eigenvalue of the orbital rotation Hessian is negative and the corresponding gradient component $g_i$ lies below a given threshold $g_0$,
then this gradient component is replaced by $g_0 \abs{g_i}/g_i$.
Here we took $g_0 = $ \SI{1}{\micro\hartree}, and considered the orbitals to be converged when the maximum orbital rotation gradient lies below \SI{0.1}{\milli\hartree}.
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
While we cannot ensure that the obtained solutions are global minima in the orbital parameter space, we verified that all stationary solutions surveyed here
correspond to real minima (rather than maxima or saddle points).
All CI calculations were performed with the cc-pVDZ basis set and within the frozen core approximation.
For the \ce{HF} molecule we have also tested basis set effects, by considered the larger cc-pVTZ and cc-pVQZ basis sets.
For the \ce{HF} molecule we have also tested basis set effects, by considering the larger cc-pVTZ and cc-pVQZ basis sets.
It is worth mentioning that obtaining smooth PECs for the orbital optimized calculations proved to be far from trivial.
First, the orbital optimization was started from the HF orbitals of each geometry.
@ -256,6 +257,7 @@ We recall that saddle point solutions were purposely avoided in our orbital opti
%\subsection{Non-parallelity errors and dissociation energies}
%\subsection{Non-parallelity errors}
We first discuss the results for HF orbitals.
In Fig.~\ref{fig:plot_stat}, we present the NPEs for the six systems studied, and for the three classes of CI methods,
as functions of $\Ndet$.
The corresponding PECs and the energy differences with respect to FCI can be found in the \SupInf.
@ -263,7 +265,7 @@ The main result contained in Fig.~\ref{fig:plot_stat} concerns the overall faste
This is observed for single bond breaking (\ce{HF} and \ce{F2}) as well as the more challenging double (ethylene), triple (\ce{N2}), and quadruple (\ce{H4}) bond breaking.
For \ce{H8}, hCI and excitation-based CI perform similarly.
The convergence with respect to $\Ndet$ is slower in the latter, more challenging cases, irrespective of the class of CI methods, as expected. \cite{Motta_2017,Motta_2020}
But more importantly, the superiority of hCI appears to be highlighted in the multiple bond break systems (compare ethylene and \ce{N2} with \ce{HF} and \ce{F2} in Fig.~\ref{fig:plot_stat}).
But more importantly, the superiority of hCI appears to be highlighted in the one-site multiple bond break systems (compare ethylene and \ce{N2} with \ce{HF} and \ce{F2} in Fig.~\ref{fig:plot_stat}).
%%% FIG 2 %%%
\begin{figure}[h!]
@ -282,10 +284,10 @@ which are accounted for in hCI but not in excitation-based CI (for a given scali
These determinants are responsible for alleviating the size-consistency problem when going from excitation-based CI to hCI.
Meanwhile, the first level of seniority-based CI (sCI0, which is the same as DOCI)
tends to offer a rather low NPE when compared to the other CI methods with a similar $\Ndet$ scaling (hCI2.5 and CISDT).
tends to offer a rather low NPE when compared to the other CI methods with a similar $\Ndet$ (hCI2.5 and CISDT).
However, convergence is clearly slower for the next levels (sCI2 and sCI4), whereas excitation-based CI and specially hCI converge faster.
Furthermore, seniority-based CI becomes less attractive for larger basis set in view of its exponential scaling.
This can be seen in Fig.~Sx of the \SupInf, which shows that augmenting the basis set leads to a much steeper increase of $\Ndet$ for seniority-based CI.
This can be seen in Figs.~S2 and S3 of the \SupInf, which shows that augmenting the basis set leads to a much steeper increase of $\Ndet$ for seniority-based CI.
It is worth mentioning the surprisingly good performance of hCI1 and hCI1.5.
For \ce{HF}, \ce{F2}, and ethylene, they yield lower NPEs than the much more expensive CISDT method, and only slightly higher in the case of \ce{N2}.
@ -297,9 +299,9 @@ become less apparent as progressively more bonds are being broken (compare, for
This reflects the fact that higher-order excitations are needed to properly describe multiple bond breaking,
and also hints at some cancelation of errors in low-order hCI methods for single bond breaking.
In Fig.~Sx of the \SupInf, we present the distance error, which is also found to decrease faster with hCI.
In Fig.~S4 of the \SupInf, we present the distance error, which is also found to decrease faster with hCI.
Most of the observations discussed for the NPE also hold for the distance error, with two main differences.
The convergence is always monotonic for the latter observable (which is expected from the definition of the observable),
The convergence is always monotonic for the latter observable (which is expected from its definition),
and the performance of seniority-based CI is much poorer (due to the slow recovery of dynamic correlation).
%\subsection{Equilibrium geometries and vibrational frequencies}
@ -318,7 +320,8 @@ are rather accurate when evaluated at the hCI1.5 level, bearing in mind its rela
%%% FIG 3 %%%
\begin{figure}[h!]
\includegraphics[width=\linewidth]{xe}
\caption{Equilibrium geometries as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green).
\caption{Equilibrium geometries as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green),
and according to the exact FCI result (black horizontal line).
}
\label{fig:xe}
\end{figure}
@ -327,13 +330,14 @@ are rather accurate when evaluated at the hCI1.5 level, bearing in mind its rela
%%% FIG 4 %%%
\begin{figure}[h!]
\includegraphics[width=\linewidth]{freq}
\caption{Vibrational frequencies (or force constants) as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green).
\caption{Vibrational frequencies (or force constants) as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green),
and according to the exact FCI result (black horizontal line).
}
\label{fig:freq}
\end{figure}
%%% %%% %%%
For the \ce{HF} molecule we have also evaluated how the convergence is affected by increasing the size of the basis set, going from cc-pVDZ to cc-pVTZ and cc-pVQZ (see Fig.~Sx and Fig.~Sy in the \SupInf).
For the \ce{HF} molecule we have also evaluated how the convergence is affected by increasing the size of the basis set, going from cc-pVDZ to cc-pVTZ and cc-pVQZ (see Figs.~S2 and S3 in the \SupInf).
While a larger $\Ndet$ is required to achieve the same level of convergence, as expected,
the convergence profiles remain very similar for all basis sets.
Vibrational frequency and equilibrium geometry present less oscillations for hCI.
@ -370,18 +374,18 @@ due to the larger energy lowering in the Franck-Condon region than at dissociati
These results suggest that, when bond breaking involves one site, orbital optimization at the DOCI level does not have such an important role,
at least in the sense of decreasing the NPE.
Optimizing the orbitals at the CI level also tends to benefit the convergence of vibrational frequencies and equilibrium geometries (shown in Fig.~Sx of the \SupInf).
Optimizing the orbitals at the CI level also tends to benefit the convergence of vibrational frequencies and equilibrium geometries.
The impact is often somewhat larger for hCI than for excitation-based CI, by a small margin.
The large oscillations observed in the hCI convergence with HF orbitals (for \ce{HF} and \ce{F2}) are significantly suppressed upon orbital optimization.
We come back to the surprisingly good performance of oo-CIS, which is interesting due to its low computational cost.
The PECs are compared with those of HF and FCI in Fig.~Sx of the \SupInf.
The PECs are compared with those of HF and FCI in Fig.~S9 of the \SupInf.
At this level, the orbital rotations provide an optimized reference (different from the HF determinant), from which only single excitations are performed.
Since the reference is not the HF determinant, Brillouin's theorem no longer holds, and single excitations actually connect with the reference.
Thus, with only single excitations (and a reference that is optimized in the presence of these excitations), one obtains a minimally correlated model.
Surprisingly, oo-CIS recovers a non-negligible fraction (15\%-40\%) of the correlation energy around the equilibrium geometries.
For all systems, significantly more correlation energy (25\%-65\% of the total) is recovered at dissociation.
In fact, the larger account of correlation at dissociation is responsible of the relatively small NPEs encountered at the oo-CIS level.
In fact, the larger account of correlation at dissociation is responsible for the relatively small NPEs encountered at the oo-CIS level.
We also found that the NPE drops more significantly (with respect to the HF one) for the single bond breaking cases (\ce{HF} and \ce{F2}),
followed by the double (ethylene) and triple (\ce{N2}) bond breaking, then \ce{H4}, and finally \ce{H8}.
@ -418,13 +422,13 @@ while the favorable polynomial scaling and encouraging performance of hCI is an
We found surprisingly good results for the first level of hCI (hCI1) and the orbital optimized version of CIS (oo-CIS), two methods with very favorable computational scaling.
In particular, oo-CIS correctly describes single bond breaking.
We hope to report on generalizations to excited states in the future.
In contrast, an important conclusion is that orbital optimization at higher CI levels is not necessarily a recommended strategy,
In contrast, orbital optimization at higher CI levels is not necessarily a recommended strategy,
given the overall modest improvement in convergence when compared to results with canonical HF orbitals.
One should bear in mind that optimizing the orbitals is always accompanied with well-known challenges (several solutions, convergence issues, etc)
and may imply a significant computational burden (associated with the calculations of the orbital gradient and Hessian, and the many iterations that are often required),
specially for larger CI spaces.
In this sense, stepping up in the CI hierarchy might be a more straightforward and possibly a cheaper alternative than optimizing the orbitals.
One interesting possibility to explore is to first optimize the orbitals at a lower level of CI, and then to employ this set of orbitals at a higher level of CI.
One possibility to explore is to first optimize the orbitals at a lower level of CI, and then to employ this set of orbitals at a higher level of CI.
The hCI pathway presented here offers several interesting possibilities to pursue.
One could generalize and adapt hCI for excited states \cite{Veril_2021} and open-shell systems, \cite{Loos_2020}

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@ -111,18 +111,29 @@ The following intervals have been considered for the fitting:
\caption{Potential energy curves (top) and energy differences with respect to FCI (bottom), for dissociation of \ce{HF},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals,
and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.
for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.
}
\label{fig:plot_pes_HF}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{freq_HF}
\caption{Non-parallelity error (left), vibrational frequencies (center), and equilibrium geometries (right) of \ce{HF},
\includegraphics[width=0.8\linewidth]{plot_stat_HF}
\caption{Non-parallelity error (left) and distance error (right) of \ce{HF},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals,
and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.}
for the cc-pVDZ (top), cc-pVTZ (center), and cc-pVQZ (bottom) basis sets.}
\label{fig:plot_stat_HF}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{freq_HF}
\caption{Vibrational frequencies (left) and equilibrium geometries (right) of \ce{HF},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals,
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ (top), cc-pVTZ (center), and cc-pVQZ (bottom) basis sets.}
\label{fig:freq_HF}
\end{figure}
@ -163,7 +174,8 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{xe_opt}
\caption{Equilibrium geometries as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with orbitals optimized at each CI level.
with orbitals optimized at each CI level,
and according to the exact FCI result (black horizontal line).
}
\label{fig:xe_opt}
\end{figure}
@ -171,7 +183,8 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{freq_opt}
\caption{Vibrational frequencies (or force constants) as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with orbitals optimized at each CI level.
with orbitals optimized at each CI level,
and according to the exact FCI result (black horizontal line).
}
\label{fig:freq_opt}
\end{figure}
@ -183,7 +196,7 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{plot_pes}
\caption{Potential energy curves for dissociation of six molecular systems (see main text for details), according to RHF (gray), oo-CIS (red), and FCI (black) calculations.
\caption{Potential energy curves for dissociation of six molecular systems (see main text for details), according to RHF (gray), oo-CIS (red), and FCI (black).
}
\label{fig:plot_pes}
\end{figure}
@ -196,7 +209,7 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_pes}
\caption{Potential energy curves for \ce{HF},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
@ -239,7 +252,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:HF_freq}
\end{figure}
@ -249,7 +263,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:HF_xe}
\end{figure}
@ -261,7 +276,7 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=\linewidth]{F2_pes}
\caption{Potential energy curves for \ce{F2},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
@ -304,7 +319,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:F2_freq}
\end{figure}
@ -314,7 +330,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:F2_xe}
\end{figure}
@ -326,7 +343,7 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=\linewidth]{ethylene_pes}
\caption{Potential energy curves for \ce{ethylene},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
@ -369,7 +386,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:ethylene_freq}
\end{figure}
@ -379,7 +397,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:ethylene_xe}
\end{figure}
@ -391,7 +410,7 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_pes}
\caption{Potential energy curves for \ce{N2},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
@ -434,7 +453,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:N2_freq}
\end{figure}
@ -444,7 +464,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:N2_xe}
\end{figure}
@ -456,7 +477,7 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_pes}
\caption{Potential energy curves for \ce{H4},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
@ -499,7 +520,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:H4_force}
\end{figure}
@ -509,7 +531,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:H4_xe}
\end{figure}
@ -521,7 +544,7 @@ The following intervals have been considered for the fitting:
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_pes}
\caption{Potential energy curves for \ce{H8},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
@ -564,7 +587,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:H8_force}
\end{figure}
@ -574,7 +598,8 @@ The following intervals have been considered for the fitting:
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:H8_xe}
\end{figure}

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View File

@ -47,7 +47,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

View File

@ -63,7 +63,7 @@ set ytics rotate by 90 right
# "data.dat" every ::1::2 using 1:3:xtic(2) with boxes ls 2
#set xlabel 'Computational scaling'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_rhf.dat' u ($0):($2) w boxes ls 3 notitle, \
'stat_CIo1.dat' u ($0+s):($2) w boxes ls 4 notitle

View File

@ -63,7 +63,7 @@ set ytics rotate by 90 right
# "data.dat" every ::1::2 using 1:3:xtic(2) with boxes ls 2
#set xlabel 'Computational scaling'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CISD.dat' u ($0):($2) w boxes ls 3 notitle, \
'stat_CIo2.dat' u ($0+s):($2) w boxes ls 4 notitle

View File

@ -63,7 +63,7 @@ set ytics rotate by 90 right
# "data.dat" every ::1::2 using 1:3:xtic(2) with boxes ls 2
#set xlabel 'Computational scaling'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CISDT.dat' u ($0):($2) w boxes ls 3 notitle, \
'stat_CIo3.dat' u ($0+s):($2) w boxes ls 4 notitle

View File

@ -1,10 +1,11 @@
#!/bin/bash
path='/home/fabris/ongoing_projects/seniority/Manuscript'
#path='/home/fabris/ongoing_projects/seniority/Manuscript'
path='/home/fabris/seniority/Manuscript'
#molecules=( HF F2 ethylene N2 H4 H8 )
molecules=( HF F2 ethylene N2 H4 H8 )
#molecules=( ethylene )
molecules=( H8 )
#molecules=( H8 )
for mol in "${molecules[@]}"
do

View File

@ -29,7 +29,7 @@
4.4 -78.05700643
4.6 -78.03518250
4.8 -78.01613055
5.0 -78.01664273
5.0 -77.99951075
5.2 -77.98517879
5.4 -77.98271343
5.6 -77.98729739

View File

@ -47,7 +47,7 @@ set style line 18 dt 1 lw 2 linecolor rgb "medium-blue" pt 7 ps 2
#set xlabel 'Computational scaling'
set xlabel 'Number of determinants'
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
plot 'stat_CI.dat' u ($3):($4) w lp ls 3 notitle, \
'stat_CIs.dat' u ($3):($4) w lp ls 8 notitle, \

View File

@ -3,14 +3,12 @@
#path='/home/fabris/ongoing_projects/seniority/Manuscript'
path='/home/fabris/seniority/Manuscript'
cp plot_pes.pdf $path/
cp plot_stat.pdf $path/
cp plot_stat_opt.pdf $path/
cp plot_distance.pdf $path/
cp plot_distance_opt.pdf $path/
cp freq.pdf $path/
cp freq_opt.pdf $path/
cp xe.pdf $path/
cp xe_opt.pdf $path/
cp plot_pes_HF.pdf $path/
cp freq_HF.pdf $path/
plots=( plot_pes plot_stat plot_stat_opt plot_distance plot_distance_opt freq freq_opt xe xe_opt plot_pes_HF plot_stat_HF freq_HF )
for plot in "${plots[@]}"
do
cp ${plot}.pdf $path/
done

View File

@ -37,13 +37,13 @@ if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 rowsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 13 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 13 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 13 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
set label 2 'Vibrational frequency (cm^{-1})' at screen 0.03,0.71 rotate by 90 tc ls 2 #font 'Verdana,20'
@ -84,7 +84,7 @@ unset label
set xrange[1:1e10]
set yrange[600:1200]
set ytics 100
set ytics 200
nel=14
nel=1
mass1=18.9984032
@ -127,7 +127,7 @@ plot '../N2_cc-pvdz/det_aD_FCI.dat' u 2:(sqrt(2*$5)*$3*fac) w l ls 2 notit
set xrange[1:1e5]
#set xtics 10**2
set yrange[0.58:0.68]
set yrange[0.60:0.68]
set format y "%.2f"
set ytics 0.02
nel=4
@ -139,7 +139,7 @@ plot '../H4_cc-pvdz/det_aD_FCI.dat' u 2:(2*$3*$3*$5) w l ls 2 notitle, \
set xrange[1:1e9]
#set xtics 10**3
set yrange[1.14:1.30]
set yrange[1.15:1.30]
set format y "%.2f"
set ytics 0.05
nel=8

View File

@ -2,7 +2,7 @@
#set terminal pngcairo size 600,600 enhanced font 'Verdana,10'
#set output 'plot_pes.png'
set terminal postscript eps size 7.3,7.3 enhanced color \
set terminal postscript eps size 5.5,7.3 enhanced color \
font 'Helvetica,22' linewidth 2
set output 'freq_HF.eps'
set encoding iso_8859_1
@ -34,35 +34,32 @@ set mxtics 1
#if (!exists("MP_xGAP")) MP_xGAP = 0.15
#if (!exists("MP_yGAP")) MP_yGAP = 0.07
if (!exists("MP_LEFT")) MP_LEFT = 0.10
if (!exists("MP_LEFT")) MP_LEFT = 0.13
if (!exists("MP_RIGHT")) MP_RIGHT = 0.98
if (!exists("MP_BOTTOM")) MP_BOTTOM = 0.09
if (!exists("MP_TOP")) MP_TOP = 0.97
if (!exists("MP_xGAP")) MP_xGAP = 0.11
if (!exists("MP_xGAP")) MP_xGAP = 0.16
if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,3 columnsfirst \
set multiplot layout 3,2 columnsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 13 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 13 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 13 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
#set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
set label 11 'cc-pVDZ' at screen 0.20,0.94 tc ls 2 font 'Helvetica,26'
set label 12 'cc-pVTZ' at screen 0.20,0.62 tc ls 2 font 'Helvetica,26'
set label 13 'cc-pVQZ' at screen 0.20,0.31 tc ls 2 font 'Helvetica,26'
set label 21 'cc-pVDZ' at screen 0.53,0.94 tc ls 2 font 'Helvetica,26'
set label 22 'cc-pVTZ' at screen 0.53,0.62 tc ls 2 font 'Helvetica,26'
set label 23 'cc-pVQZ' at screen 0.53,0.31 tc ls 2 font 'Helvetica,26'
set label 31 'cc-pVDZ' at screen 0.86,0.94 tc ls 2 font 'Helvetica,26'
set label 32 'cc-pVTZ' at screen 0.86,0.62 tc ls 2 font 'Helvetica,26'
set label 33 'cc-pVQZ' at screen 0.86,0.31 tc ls 2 font 'Helvetica,26'
set label 11 'cc-pVDZ' at screen 0.32,0.94 tc ls 2 font 'Helvetica,26'
set label 12 'cc-pVTZ' at screen 0.32,0.62 tc ls 2 font 'Helvetica,26'
set label 13 'cc-pVQZ' at screen 0.32,0.31 tc ls 2 font 'Helvetica,26'
set label 21 'cc-pVDZ' at screen 0.82,0.94 tc ls 2 font 'Helvetica,26'
set label 22 'cc-pVTZ' at screen 0.82,0.62 tc ls 2 font 'Helvetica,26'
set label 23 'cc-pVQZ' at screen 0.82,0.31 tc ls 2 font 'Helvetica,26'
hartree = 4.3597447222071e-18 # joules
bohr = 1./18897161646.321 # m
@ -71,46 +68,6 @@ c = 299792458.0 # m/s
mole = 6.02214076e23
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.30]
set ytics 0.1
nel=8
nel=1
plot '../HF_cc-pvdz/stat_CI.dat' u ($3):($4/nel) w lp ls 3 notitle, \
'../HF_cc-pvdz/stat_CIs.dat' u ($3):($4/nel) w lp ls 8 notitle, \
'../HF_cc-pvdz/stat_CIo.dat' u ($3):($4/nel) w lp ls 4 notitle
unset ylabel
unset label
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.30]
set ytics 0.1
set ylabel 'Nonparallelity error (Hartree)'
nel=8
nel=1
plot '../HF_cc-pvtz/stat_CI.dat' u ($3):($4/nel) w lp ls 3 notitle, \
'../HF_cc-pvtz/stat_CIs.dat' u ($3):($4/nel) w lp ls 8 notitle, \
'../HF_cc-pvtz/stat_CIo.dat' u ($3):($4/nel) w lp ls 4 notitle
unset ylabel
unset label
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.30]
set ytics 0.1
nel=8
nel=1
plot '../HF_cc-pvqz/stat_CI.dat' u ($3):($4/nel) w lp ls 3 notitle, \
'../HF_cc-pvqz/stat_CIs.dat' u ($3):($4/nel) w lp ls 8 notitle, \
'../HF_cc-pvqz/stat_CIo.dat' u ($3):($4/nel) w lp ls 4 notitle
unset ylabel
unset label
set format y "%.0f"
set xrange[1:1e9]
@ -180,6 +137,7 @@ plot '../HF_cc-pvtz/det_xe_FCI.dat' u 2:3 w l ls 2 notitle, \
'../HF_cc-pvtz/det_xe_CIo.dat' u 1:3 w lp ls 4 notitle
unset ylabel
set xlabel 'Number of determinants'
plot '../HF_cc-pvqz/det_xe_FCI.dat' u 2:3 w l ls 2 notitle, \
'../HF_cc-pvqz/det_xe_CI.dat' u 1:3 w lp ls 3 notitle, \
'../HF_cc-pvqz/det_xe_CIs.dat' u 1:3 w lp ls 8 notitle, \

View File

@ -37,13 +37,13 @@ if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 rowsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
set label 2 'Vibrational frequency (cm^{-1})' at screen 0.03,0.71 rotate by 90 tc ls 2 #font 'Verdana,20'
@ -83,7 +83,7 @@ unset ylabel
unset label
set xrange[1:1e10]
set yrange[600:1200]
set yrange[700:1200]
set ytics 100
nel=14
nel=1
@ -139,7 +139,7 @@ plot '../H4_cc-pvdz/det_aD_FCI.dat' u 2:(2*$3*$3*$5) w l ls 2 notitle, \
set xrange[1:1e9]
#set xtics 10**3
set yrange[1.14:1.30]
set yrange[1.10:1.30]
set format y "%.2f"
set ytics 0.05
nel=8

View File

@ -36,13 +36,13 @@ if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 rowsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 13 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 13 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 13 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Distance error (Hartree)' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'

View File

@ -36,13 +36,13 @@ if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 rowsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Distance error (Hartree)' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'

View File

@ -28,7 +28,6 @@ set style line 7 dt 2 lw 2 linecolor rgb "orange"
set style line 8 dt 1 lw 2 linecolor rgb "medium-blue"
set label 1 'Distance (a_{0})' at screen 0.46,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Nonparallelity error (Hartree)' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'
set label 11 'HF' at screen 0.34,0.75 tc ls 2 font 'Helvetica,26'
set label 12 'F_2' at screen 0.79,0.75 tc ls 2 font 'Helvetica,26'
set label 13 'ethylene' at screen 0.34,0.43 tc ls 2 font 'Helvetica,26'

View File

@ -28,9 +28,6 @@ set style line 6 dt 1 lw 2 linecolor rgb "orange"
set style line 7 dt 2 lw 2 linecolor rgb "orange"
set style line 8 dt 1 lw 2 linecolor rgb "medium-blue"
#set label 1 'Distance (a_{0})' at screen 0.46,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Nonparallelity error (Hartree)' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'
set format y "%.1f"
set xrange[0.5:6.0]
set yrange[-100.40:-99.80]

View File

@ -28,7 +28,7 @@ set style line 7 dt 2 lw 2 linecolor rgb "orange"
set style line 8 dt 1 lw 2 linecolor rgb "medium-blue"
set label 1 'Distance (a_{0})' at screen 0.46,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Nonparallelity error (Hartree)' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'
#set label 2 'Non-parallelity error (Hartree)' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'
set label 11 'HF' at screen 0.34,0.75 tc ls 2 font 'Helvetica,26'
set label 12 'F_2' at screen 0.79,0.75 tc ls 2 font 'Helvetica,26'
set label 13 'ethylene' at screen 0.34,0.43 tc ls 2 font 'Helvetica,26'

View File

@ -36,16 +36,15 @@ if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 rowsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 13 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 13 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 13 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Nonparallelity error (Hartree)' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'
set label 11 'HF' at screen 0.34,0.93 tc ls 2 font 'Helvetica,26'
set label 12 'F_2' at screen 0.79,0.93 tc ls 2 font 'Helvetica,26'
set label 13 'ethylene' at screen 0.34,0.62 tc ls 2 font 'Helvetica,26'
@ -81,7 +80,7 @@ set xrange[1:1e11]
#set xtics 10**3
set yrange[0:0.50]
set ytics 0.1
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
nel=12
nel=1
plot '../ethylene_cc-pvdz/stat_CI.dat' u ($3):($4/nel) w lp ls 3 notitle, \

151
plot_all/plot_stat_HF.gnu Normal file
View File

@ -0,0 +1,151 @@
#!/bin/gnuplot
#set terminal pngcairo size 600,600 enhanced font 'Verdana,10'
#set output 'plot_pes.png'
set terminal postscript eps size 5.5,7.3 enhanced color \
font 'Helvetica,22' linewidth 2
set output 'plot_stat_HF.eps'
set encoding iso_8859_1
###################################################################################
###################################################################################
# SYSTEM DEPENDENT PART:
#set yrange[1e-2:1]
#set logscale y
#set format y "10^{%T}"
#set yrange[0:1]
set xrange[1:1e9]
set logscale x
set format x "10^{%T}"
###################################################################################
###################################################################################
set xtics 10**3
set mxtics 1
#set grid xtics ytics mxtics mytics #lc rgb 'blue' lt 1, lc rgb 'red' lt 1
#if (!exists("MP_LEFT")) MP_LEFT = 0.14
#if (!exists("MP_RIGHT")) MP_RIGHT = 0.97
#if (!exists("MP_BOTTOM")) MP_BOTTOM = 0.09
#if (!exists("MP_TOP")) MP_TOP = 0.97
#if (!exists("MP_xGAP")) MP_xGAP = 0.15
#if (!exists("MP_yGAP")) MP_yGAP = 0.07
if (!exists("MP_LEFT")) MP_LEFT = 0.13
if (!exists("MP_RIGHT")) MP_RIGHT = 0.98
if (!exists("MP_BOTTOM")) MP_BOTTOM = 0.09
if (!exists("MP_TOP")) MP_TOP = 0.97
if (!exists("MP_xGAP")) MP_xGAP = 0.16
if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 columnsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 13 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 13 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 13 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
#set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
set label 11 'cc-pVDZ' at screen 0.32,0.94 tc ls 2 font 'Helvetica,26'
set label 12 'cc-pVTZ' at screen 0.32,0.62 tc ls 2 font 'Helvetica,26'
set label 13 'cc-pVQZ' at screen 0.32,0.31 tc ls 2 font 'Helvetica,26'
set label 21 'cc-pVDZ' at screen 0.82,0.94 tc ls 2 font 'Helvetica,26'
set label 22 'cc-pVTZ' at screen 0.82,0.62 tc ls 2 font 'Helvetica,26'
set label 23 'cc-pVQZ' at screen 0.82,0.31 tc ls 2 font 'Helvetica,26'
hartree = 4.3597447222071e-18 # joules
bohr = 1./18897161646.321 # m
amu = 1.6605402e-27 # kg
c = 299792458.0 # m/s
mole = 6.02214076e23
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.30]
set ytics 0.1
nel=8
nel=1
plot '../HF_cc-pvdz/stat_CI.dat' u ($3):($4/nel) w lp ls 3 notitle, \
'../HF_cc-pvdz/stat_CIs.dat' u ($3):($4/nel) w lp ls 8 notitle, \
'../HF_cc-pvdz/stat_CIo.dat' u ($3):($4/nel) w lp ls 4 notitle
unset ylabel
unset label
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.30]
set ytics 0.1
set ylabel 'Non-parallelity error (Hartree)'
nel=8
nel=1
plot '../HF_cc-pvtz/stat_CI.dat' u ($3):($4/nel) w lp ls 3 notitle, \
'../HF_cc-pvtz/stat_CIs.dat' u ($3):($4/nel) w lp ls 8 notitle, \
'../HF_cc-pvtz/stat_CIo.dat' u ($3):($4/nel) w lp ls 4 notitle
unset ylabel
unset label
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.30]
set ytics 0.1
nel=8
nel=1
set xlabel 'Number of determinants'
plot '../HF_cc-pvqz/stat_CI.dat' u ($3):($4/nel) w lp ls 3 notitle, \
'../HF_cc-pvqz/stat_CIs.dat' u ($3):($4/nel) w lp ls 8 notitle, \
'../HF_cc-pvqz/stat_CIo.dat' u ($3):($4/nel) w lp ls 4 notitle
unset xlabel
unset ylabel
unset label
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.90]
set ytics 0.2
nel=8
nel=1
plot '../HF_cc-pvdz/stat_CI.dat' u ($3):($5/nel) w lp ls 3 notitle, \
'../HF_cc-pvdz/stat_CIs.dat' u ($3):($5/nel) w lp ls 8 notitle, \
'../HF_cc-pvdz/stat_CIo.dat' u ($3):($5/nel) w lp ls 4 notitle
unset ylabel
unset label
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.90]
set ytics 0.2
set ylabel 'Distance error (Hartree)'
nel=8
nel=1
plot '../HF_cc-pvtz/stat_CI.dat' u ($3):($5/nel) w lp ls 3 notitle, \
'../HF_cc-pvtz/stat_CIs.dat' u ($3):($5/nel) w lp ls 8 notitle, \
'../HF_cc-pvtz/stat_CIo.dat' u ($3):($5/nel) w lp ls 4 notitle
unset ylabel
unset label
set xrange[1:1e9]
set xtics 10**2
set yrange[0:0.90]
set ytics 0.2
nel=8
nel=1
set xlabel 'Number of determinants'
plot '../HF_cc-pvqz/stat_CI.dat' u ($3):($5/nel) w lp ls 3 notitle, \
'../HF_cc-pvqz/stat_CIs.dat' u ($3):($5/nel) w lp ls 8 notitle, \
'../HF_cc-pvqz/stat_CIo.dat' u ($3):($5/nel) w lp ls 4 notitle
unset ylabel
unset label

5
plot_all/plot_stat_HF.sh Executable file
View File

@ -0,0 +1,5 @@
#!/bin/bash
gnuplot plot_stat_HF.gnu
epspdf plot_stat_HF.eps
okular plot_stat_HF.pdf

View File

@ -36,16 +36,15 @@ if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 rowsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Nonparallelity error (Hartree)' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'
set label 11 'HF' at screen 0.34,0.93 tc ls 2 font 'Helvetica,26'
set label 12 'F_2' at screen 0.79,0.93 tc ls 2 font 'Helvetica,26'
set label 13 'ethylene' at screen 0.34,0.62 tc ls 2 font 'Helvetica,26'
@ -81,7 +80,7 @@ set xrange[1:1e11]
#set xtics 10**3
set yrange[0:0.50]
set ytics 0.1
set ylabel 'Nonparallelity error (Hartree)'
set ylabel 'Non-parallelity error (Hartree)'
nel=12
nel=1
plot '../ethylene_cc-pvdz/stat_ooCI.dat' u ($3):($4/nel) w lp ls 3 notitle, \

12
plot_all/run_all_figures.sh Executable file
View File

@ -0,0 +1,12 @@
#!/bin/bash
plots=( plot_pes plot_stat plot_stat_opt plot_distance plot_distance_opt freq freq_opt xe xe_opt plot_pes_HF plot_stat_HF freq_HF )
for plot in "${plots[@]}"
do
gnuplot ${plot}.gnu
epspdf ${plot}.eps
done

View File

@ -37,13 +37,13 @@ if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 rowsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 13 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 13 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 13 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Equilibrium geometry ({\305})' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'

View File

@ -37,18 +37,18 @@ if (!exists("MP_yGAP")) MP_yGAP = 0.07
set multiplot layout 3,2 rowsfirst \
margins screen MP_LEFT, MP_RIGHT, MP_BOTTOM, MP_TOP spacing screen MP_xGAP, MP_yGAP
set style line 2 dt 1 lw 1.5 linecolor rgb "black"
set style line 3 dt 1 lw 1.5 linecolor rgb "light-red" pt 13 ps 1.5
set style line 4 dt 1 lw 1.5 linecolor rgb "sea-green" pt 13 ps 1.5
set style line 8 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 13 ps 1.5
set style line 13 dt 1 lw 1.5 linecolor rgb "light-red" pt 7 ps 1.5
set style line 14 dt 1 lw 1.5 linecolor rgb "sea-green" pt 7 ps 1.5
set style line 18 dt 1 lw 1.5 linecolor rgb "medium-blue" pt 7 ps 1.5
set style line 2 dt 1 lw 2.0 linecolor rgb "black"
set style line 3 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 4 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 8 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set style line 13 dt 1 lw 2.0 linecolor rgb "light-red" pt 7 ps 2.0
set style line 14 dt 1 lw 2.0 linecolor rgb "sea-green" pt 7 ps 2.0
set style line 18 dt 1 lw 2.0 linecolor rgb "medium-blue" pt 7 ps 2.0
set label 1 'Number of determinants' at screen 0.40,0.03 tc ls 2 #font 'Verdana,20'
#set label 2 'Equilibrium geometry ({\305})' at screen 0.03,0.35 rotate by 90 tc ls 2 #font 'Verdana,20'
set label 11 'HF' at screen 0.34,0.94 tc ls 2 font 'Helvetica,26'
set label 12 'F_2' at screen 0.79,0.94 tc ls 2 font 'Helvetica,26'
set label 11 'HF' at screen 0.34,0.95 tc ls 2 font 'Helvetica,26'
set label 12 'F_2' at screen 0.79,0.95 tc ls 2 font 'Helvetica,26'
set label 13 'ethylene' at screen 0.34,0.63 tc ls 2 font 'Helvetica,26'
set label 14 'N_2' at screen 0.79,0.63 tc ls 2 font 'Helvetica,26'
set label 15 'H_4' at screen 0.34,0.310 tc ls 2 font 'Helvetica,26'
@ -125,7 +125,7 @@ unset ylabel
set xrange[1:1e9]
#set xtics 10**3
set yrange[1.77:1.81]
set yrange[1.77:1.82]
set format y "%.2f"
set ytics 0.01
nel=8

33
run_all_figures.sh Executable file
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@ -0,0 +1,33 @@
#!/bin/bash
molecules=( HF F2 ethylene N2 H4 H8 )
for mol in "${molecules[@]}"
do
cd ${mol}_cc-pvdz
gnuplot plot_pes.gnu
epspdf plot_pes.eps
gnuplot plot_error.gnu
epspdf plot_error.eps
gnuplot plot_stat.gnu
epspdf plot_stat.eps
gnuplot plot_distance.gnu
epspdf plot_distance.eps
gnuplot freq.gnu
epspdf freq.eps
gnuplot xe.gnu
epspdf xe.eps
gnuplot force.gnu
epspdf force.eps
cd ..
done