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StochasticTriples
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Updated curves

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Anthony Scemama 2024-04-18 19:23:40 +02:00
parent d29f74984b
commit 5792b0f3ce
11 changed files with 2143 additions and 2965 deletions
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5041
Data/benzene.dat
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File diff suppressed because it is too large Load Diff

4
Data/benzene_qz.plt
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@ -14,13 +14,13 @@ set style fill transparent solid 0.50 border
#set yrange [-231.8075:-231.8040]
data='benzene.dat'
tmax=2812.08030200005 * 0.01
tmax=2070.63480687141 * 0.01
set xrange [0:tmax*100.]
set yrange [-231.8724:-231.8712]
plot data i 1 u ($3*tmax):($1+$2):($1-$2) w filledcurves ls 1 notitle, \
data i 1 u ($3*tmax):($1) w l ls 1 notitle , \
-231.871740549698 notitle ls 3
-231.87174565 notitle ls 3

9
Data/benzene_tz.plt
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@ -7,19 +7,20 @@ set ylabel "Energy (au)"
set format y "%10.4f"
set xrange [0:240]
set term pdfcairo enhanced font "Times,14" linewidth 2 rounded size 5.0in, 3.0in
set output 'benzene_tz.pdf'
set style fill transparent solid 0.50 border
set yrange [-231.8072:-231.8046]
set yrange [-231.8068:-231.8042]
data='benzene.dat'
tmax=239.890999078751 * 0.01
tmax=102.592093944550 * 0.01
set xrange [0:tmax*100]
plot data i 0 u ($3*tmax):($1+$2):($1-$2) w filledcurves ls 1 notitle, \
data i 0 u ($3*tmax):($1) w l ls 1 notitle , \
-231.805729365546 notitle ls 3
-231.805731383683 notitle ls 3

24
Data/cucl.dat
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@ -1,15 +1,15 @@
# R CCSD(T) Stochastic CCSD(T)
#---------------------------------------------------------
1.55 -2099.590506349950 -2099.58890791 1.3630E-03
1.65 -2099.671184187604 -2099.67175286 1.5710E-03
1.75 -2099.720045862965 -2099.71877319 1.3199E-03
1.85 -2099.747811193906 -2099.74897746 1.4668E-03
1.95 -2099.761752030920 -2099.76232971 1.6105E-03
2.05 -2099.766727898670 -2099.76565267 1.5202E-03
2.15 -2099.765956694308 -2099.76485609 1.7470E-03
2.25 -2099.761562105614 -2099.76237391 1.7474E-03
2.35 -2099.754944906474 -2099.75681975 1.9951E-03
2.45 -2099.747028328725 -2099.74813718 2.4288E-03
2.55 -2099.738443175793 -2099.74031232 2.4057E-03
2.65 -2099.729597826175 -2099.72866832 1.6894E-03
1.55 -2099.590506349950 -2099.58900041 1.2867E-03
1.65 -2099.671184187604 -2099.67111214 1.4130E-03
1.75 -2099.720045862965 -2099.72247666 1.8605E-03
1.85 -2099.747811193906 -2099.74783889 1.7384E-03
1.95 -2099.761752030920 -2099.76294620 1.5644E-03
2.05 -2099.766727898670 -2099.76607775 1.6396E-03
2.15 -2099.765956694308 -2099.76889281 2.0352E-03
2.25 -2099.761562105614 -2099.76003424 1.4932E-03
2.35 -2099.754944906474 -2099.75495657 1.8955E-03
2.45 -2099.747028328725 -2099.74878665 1.8202E-03
2.55 -2099.738451107727 -2099.73743548 1.6473E-03
2.65 -2099.729597826175 -2099.73119406 1.7203E-03

6
Data/cucl.plt
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@ -22,9 +22,9 @@ set term pdfcairo enhanced font "Times,14" linewidth 2 rounded size 5.0in, 3.0in
set output 'cucl.pdf'
set pointsize 0.5
plot \
'cucl.dat' using ($1*a0):2 pointtype 7 lt 4 title "Full (T)", \
E(x) title "" lt 3, \
'cucl.dat' using ($1*a0):3:4 w err pt 0 lt 1 title "1% (T)"
'cucl.dat' using ($1*a0):2 pointtype 3 lc rgb "red" title "Full (T)", \
E(x) title "" lt 3 lc rgb "grey", \
'cucl.dat' using ($1*a0):3:4 w err pt 0 lc rgb "blue" title "1% (T)"

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Manuscript/benzene_err.pdf
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Manuscript/benzene_qz.pdf
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Manuscript/benzene_tz.pdf
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Manuscript/cucl.pdf
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12
Manuscript/stochastic_triples.tex
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@ -221,9 +221,9 @@ Consequently, employing a sufficient number of Monte Carlo samples to ensure tha
To reduce the variance, the samples are drawn using the probability
\begin{equation}
P^{abc} = \frac{1}{\mathcal{N}} \frac{1}{|\epsilon_a + \epsilon_b + \epsilon_c|}
P^{abc} = \frac{1}{\mathcal{N}} \frac{1}{\max \left(\epsilon_{\min}, \epsilon_a + \epsilon_b + \epsilon_c \right)}
\end{equation}
where $\mathcal{N}$ normalizes the sum such that $\sum_{abc} P^{abc} = 1$.
where $\mathcal{N}$ normalizes the sum such that $\sum_{abc} P^{abc} = 1$, and $\epsilon_{\min}$ is an arbitrary minimal denominator to ensure that $P^{abc}$ does not diverge. In our calculations, we have set $\epsilon_{\min}$ to 0.2~a.u.
The perturbative contribution is then evaluated as an average over $M$ samples
\begin{equation}
E_{(T)} = \left\langle \frac{E^{abc}}{P^{abc}} \right \rangle_{P^{abc}} =
@ -370,7 +370,7 @@ $t_0 \leftarrow \text{WallClockTime}()$ \;
In this section we illustrate the convergence of the statistical error of the perturbative triples correction as a function of the computational cost.
The benzene molecule serves as our reference system for conducting frozen-core CCSD(T) calculations with the cc-pVTZ and cc-pVQZ basis sets.
Essentially, this involves the correlation of 30 electrons using either 258 or 503 molecular orbitals.
The calculations were performed on an Intel Xeon Gold 6130 dual socket server (32 cores in total).
The calculations were performed on an AMD \textsc{Epyc} 7513 dual socket server (64 cores in total).
\begin{figure}
\includegraphics[width=\columnwidth]{benzene_tz.pdf}
@ -413,7 +413,7 @@ with $\mu$ denoting the reduced mass of the \ce{CuCl} molecule, and $c$ the spee
\begin{figure}
\includegraphics[width=\columnwidth]{cucl.pdf}
\caption{\label{fig:cucl} CCSD(T) energies of CuCl obtained with the exact CCSD(T) algorithm (dots), the stochastic algorithm using only 1\% of the contributions (error bars), and the Morse potential fitting the points obtained with the stochastic algorithm.}
\caption{\label{fig:cucl} CCSD(T) energies of CuCl obtained with the exact CCSD(T) algorithm (stars), the stochastic algorithm using only 1\% of the contributions (error bars), and the Morse potential fitting the points obtained with the stochastic algorithm.}
\end{figure}
The initial step involved the precise calculation of the CCSD(T) energy across various points along the potential curve.
@ -421,8 +421,8 @@ We froze the six lowest molecular orbitals, specifically the $1s$ orbital of \ce
The fitted Morse potential revealed a vibrational frequency of $\nu = \SI{414.7}{\per\centi\meter}$ and an equilibrium bond length of $r_e = \SI{3.92}{\bohr}$, aligning remarkably well with experimental values from the NIST database\cite{nist_2022} $\nu = \SI{417.6}{\per\centi\meter}$ and $r_e = \SI{3.88}{\bohr}$.
Subsequently, we applied our semi-stochastic algorithm to estimate the perturbative triples correction, utilizing merely 1\% of the total contributions.
This approach yielded a hundredfold acceleration in computational efficiency, achieving statistical uncertainty within the range of \SI{1.3} to \SI{2.5}{\milli\hartree}.
The vibrational frequency and equilibrium distance estimated using this data, $\nu = \SI{415.0}{\per\centi\meter}$ and $r_e = \SI{3.92}{\bohr}$, demonstrated comparable precision to the full computational results.
This approach yielded a hundredfold acceleration in computational efficiency, achieving statistical uncertainty within the range of \SI{1.2} to \SI{2.0}{\milli\hartree}.
The vibrational frequency and equilibrium distance estimated using this data, $\nu = \SI{415.1}{\per\centi\meter}$ and $r_e = \SI{3.91}{\bohr}$, demonstrated comparable precision to the full computational results.
Figure \ref{fig:cucl} illustrates the potential energy surface of \ce{CuCl}, displaying both the exact CCSD(T) energies and those estimated via the semi-stochastic method.

12
triples.org
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@ -7635,16 +7635,16 @@ plot E(x), data using ($1*a0):2 w p
[[file:cucl_ccsd.png]]
#+begin_example
a = 0.850836 +/- 0.005939 (0.698%)
re = 3.94582 +/- 0.001786 (0.04526%)
De = 0.0961907 +/- 0.00189 (1.965%)
E0 = -2099.73 +/- 0.0001574 (7.496e-06%)
a = 0.879992 +/- 0.02833 (3.219%)
re = 3.91095 +/- 0.009327 (0.2385%)
De = 0.0946485 +/- 0.007497 (7.92%)
E0 = -2099.77 +/- 0.0007291 (3.472e-05%)
#+end_example
#+CALL:freq(0.8637,0.0912735)
#+CALL:freq(0.879992,0.0946485)
#+RESULTS:
: 400.10303409950683
: 415.11857299491743
** CCSD(T) 1%