diff --git a/Manuscript/Benzene_EvsNdet.pdf b/Manuscript/Benzene_EvsNdet.pdf index f217e69..64dafcb 100644 Binary files a/Manuscript/Benzene_EvsNdet.pdf and b/Manuscript/Benzene_EvsNdet.pdf differ diff --git a/Manuscript/Benzene_EvsPT2.pdf b/Manuscript/Benzene_EvsPT2.pdf index 9bc544d..51f0d0b 100644 Binary files a/Manuscript/Benzene_EvsPT2.pdf and b/Manuscript/Benzene_EvsPT2.pdf differ diff --git a/Manuscript/Cyclopentadiene_EvsNdet.pdf b/Manuscript/Cyclopentadiene_EvsNdet.pdf index d9482f1..126c390 100644 Binary files a/Manuscript/Cyclopentadiene_EvsNdet.pdf and b/Manuscript/Cyclopentadiene_EvsNdet.pdf differ diff --git a/Manuscript/Cyclopentadiene_EvsPT2.pdf b/Manuscript/Cyclopentadiene_EvsPT2.pdf index a1d1f5e..9c6435a 100644 Binary files a/Manuscript/Cyclopentadiene_EvsPT2.pdf and b/Manuscript/Cyclopentadiene_EvsPT2.pdf differ diff --git a/Manuscript/Ec.tex b/Manuscript/Ec.tex index 7523ee1..b0cffc0 100644 --- a/Manuscript/Ec.tex +++ b/Manuscript/Ec.tex @@ -365,8 +365,10 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}. \label{fig:vsEPT2}} \end{figure*} +\begin{squeezetable} \begin{table*} \caption{Total energy $E$ (in \SI{}{\hartree}) and correlation energy $\Delta E$ (in \SI{}{\milli\hartree}) for the frozen-core ground state of five-membered rings in the cc-pVDZ basis set. + For the CIPSI estimates of the correlation energy, the fitting error associated with the 4-point linear fit is reported in parenthesis. \label{tab:Tab5-VDZ}} \begin{ruledtabular} \begin{tabular}{lcccccccccc} @@ -392,14 +394,16 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}. CCSD(T) & $-193.5439$ & $-735.6$ & $-229.4073$ & $-764.0$ & $-225.6099$ & $-774.5$ & $-209.5836$ & $-754.9$ & $-552.0458$ & $-724.8$ \\ \hline - CIPSI & & $-739.3$ & & $-768.1$ & & $-778.3$ & & $-758.4$ & & $-729.1$\\ + CIPSI & & $-739.3(1)$ & & $-768.1(2)$ & & $-778.3(1)$ & & $-758.4(2)$ & & $-729.1(3)$\\ \end{tabular} \end{ruledtabular} \end{table*} +\end{squeezetable} \begin{squeezetable} \begin{table*} \caption{Total energy $E$ (in \SI{}{\hartree}) and correlation energy $\Delta E$ (in \SI{}{\milli\hartree}) for the frozen-core ground state of six-membered rings in the cc-pVDZ basis set. + For the CIPSI estimates of the correlation energy, the fitting error associated with the 4-point linear fit is reported in parenthesis. \label{tab:Tab6-VDZ}} \begin{ruledtabular} \begin{tabular}{lcccccccccccccc} @@ -425,18 +429,127 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}. \hline CCSD(T) & $-231.5798$ & $-857.5$ & $-263.6024$ & $-899.4$ & $-263.5740$ & $-904.1$ & $-247.5929$ & $-877.7$ & $-263.6099$ & $-896.2$ & $-295.5680$ & $-952.2$ & $-279.6305$ & $-913.1$ \\ \hline - CIPSI & & $-863.0$ & & $-904.6$ & & $-908.8$ & & $-883.4$ & & $-900.4$ & & $-957.3$ & & $-918.5$\\ + CIPSI & & $-863.0(4)$ & & $-904.6(6)$ & & $-908.8(2)$ & & $-883.4(0)$ & & $-900.4(4)$ & & $-957.3(2)$ & & $-918.5(5)$\\ \end{tabular} \end{ruledtabular} \end{table*} \end{squeezetable} + +\begin{squeezetable} +\begin{table} + \caption{ + \label{tab:fit}} + \begin{ruledtabular} + \begin{tabular}{lccc} + Molecule & Number & \mc{2}{c}{Fitting parameter} \\ + \cline{3-4} + & of points & $\Delta \Evar$ & Standard error \\ + \hline + Cyclopentadiene & 3 & $-739.295$ & $0.199$ \\ + & 4 & $-739.309$ & $0.088$ \\ + & 5 & $-739.230$ & $0.074$ \\ + & 6 & $-739.304$ & $0.072$ \\ + & 7 & $-739.292$ & $0.055$ \\ + & 8 & $-739.119$ & $0.131$ \\ + \hline + Furan & 3 & $-767.790$ & $0.064$ \\ + & 4 & $-768.104$ & $0.196$ \\ + & 5 & $-768.194$ & $0.135$ \\ + & 6 & $-768.060$ & $0.131$ \\ + & 7 & $-768.086$ & $0.101$ \\ + & 8 & $-767.904$ & $0.154$ \\ + \hline + Imidazole & 3 & $-778.295$ & $0.356$ \\ + & 4 & $-778.270$ & $0.150$ \\ + & 5 & $-778.178$ & $0.105$ \\ + & 6 & $-778.174$ & $0.072$ \\ + & 7 & $-778.051$ & $0.099$ \\ + & 8 & $-777.992$ & $0.089$ \\ + \hline + Pyrrole & 3 & $-758.650$ & $0.321$ \\ + & 4 & $-758.389$ & $0.174$ \\ + & 5 & $-758.460$ & $0.110$ \\ + & 6 & $-758.352$ & $0.100$ \\ + & 7 & $-758.347$ & $0.075$ \\ + & 8 & $-758.357$ & $0.059$ \\ + \hline + Thiophene & 3 & $-728.744$ & $0.691$ \\ + & 4 & $-729.052$ & $0.331$ \\ + & 5 & $-728.948$ & $0.203$ \\ + & 6 & $-728.987$ & $0.140$ \\ + & 7 & $-729.067$ & $0.117$ \\ + & 8 & $-728.876$ & $0.162$ \\ + \hline + Benzene & 3 & $-862.325$ & $0.279$ \\ + & 4 & $-863.024$ & $0.424$ \\ + & 5 & $-862.890$ & $0.266$ \\ + & 6 & $-862.360$ & $0.383$ \\ + & 7 & $-862.083$ & $0.339$ \\ + & 8 & $-861.711$ & $0.370$ \\ + \hline + Pyrazine & 3 & $-904.867$ & $1.420$ \\ + & 4 & $-904.588$ & $0.650$ \\ + & 5 & $-904.550$ & $0.385$ \\ + & 6 & $-903.982$ & $0.439$ \\ + & 7 & $-903.746$ & $0.359$ \\ + & 8 & $-903.549$ & $0.311$ \\ + \hline + Pyridazine & 3 & $-909.292$ & $0.024$ \\ + & 4 & $-908.808$ & $0.230$ \\ + & 5 & $-908.820$ & $0.133$ \\ + & 6 & $-908.342$ & $0.303$ \\ + & 7 & $-908.368$ & $0.224$ \\ + & 8 & $-908.229$ & $0.198$ \\ + \hline + Pyridine & 3 & $-883.363$ & $0.047$ \\ + & 4 & $-883.413$ & $0.029$ \\ + & 5 & $-882.700$ & $0.405$ \\ + & 6 & $-882.361$ & $0.341$ \\ + & 7 & $-882.023$ & $0.330$ \\ + & 8 & $-881.732$ & $0.322$ \\ + \hline + Pyrimidine & 3 & $-900.817$ & $0.726$ \\ + & 4 & $-900.383$ & $0.356$ \\ + & 5 & $-900.496$ & $0.214$ \\ + & 6 & $-900.698$ & $0.190$ \\ + & 7 & $-900.464$ & $0.206$ \\ + & 8 & $-900.226$ & $0.227$ \\ + \hline + Tetrazine & 3 & $-957.559$ & $0.246$ \\ + & 4 & $-957.299$ & $0.160$ \\ + & 5 & $-957.869$ & $0.349$ \\ + & 6 & $-957.744$ & $0.247$ \\ + & 7 & $-957.709$ & $0.183$ \\ + & 8 & $-957.558$ & $0.176$ \\ + \hline + Triazine & 3 & $-919.596$ & $0.105$ \\ + & 4 & $-918.457$ & $0.538$ \\ + & 5 & $-918.355$ & $0.312$ \\ + & 6 & $-918.206$ & $0.226$ \\ + & 7 & $-917.876$ & $0.267$ \\ + & 8 & $-917.533$ & $0.308$ \\ + \end{tabular} + \end{ruledtabular} +\end{table} +\end{squeezetable} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{CIPSI estimates} +\label{sec:cipsi_res} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + We first study the convergence of the variational energy as a function of the number of determinants. For the natural and optimized orbital sets we report, in Fig.~\ref{fig:vsNdet}, the evolution of the variational correlation energy $\Delta \Evar$ with respect to the number of determinants for the set of twelve cyclic molecules represented in Fig.~\ref{fig:mol}. As one can see, the use of optimized orbitals greatly facilitate the convergence towards the FCI limit. This is further evidenced in Fig.~\ref{fig:vsEPT2} where we show the behavior of $\Delta \Evar$ as a function of $\EPT$ as well as its 4-point linear fit using the four largest variational wave functions. In both cases, the CCSDTQ correlation energy is also represented for comparison purposes. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Benchmark of CC and MP methods} +\label{sec:cc_mp_res} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + %%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusion} %%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/Manuscript/Furan_EvsNdet.pdf b/Manuscript/Furan_EvsNdet.pdf index 8d9bef0..3a52d44 100644 Binary files a/Manuscript/Furan_EvsNdet.pdf and b/Manuscript/Furan_EvsNdet.pdf differ diff --git a/Manuscript/Furan_EvsPT2.pdf b/Manuscript/Furan_EvsPT2.pdf index efc373a..7d737ae 100644 Binary files a/Manuscript/Furan_EvsPT2.pdf and b/Manuscript/Furan_EvsPT2.pdf differ diff --git a/Manuscript/Imidazole_EvsNdet.pdf b/Manuscript/Imidazole_EvsNdet.pdf index 6d0292f..b109207 100644 Binary files a/Manuscript/Imidazole_EvsNdet.pdf and b/Manuscript/Imidazole_EvsNdet.pdf differ diff --git a/Manuscript/Imidazole_EvsPT2.pdf b/Manuscript/Imidazole_EvsPT2.pdf index d2d2803..486761d 100644 Binary files a/Manuscript/Imidazole_EvsPT2.pdf and b/Manuscript/Imidazole_EvsPT2.pdf differ diff --git a/Manuscript/Pyridazine_EvsNdet.pdf b/Manuscript/Pyridazine_EvsNdet.pdf index 63b8800..29e8129 100644 Binary files a/Manuscript/Pyridazine_EvsNdet.pdf and b/Manuscript/Pyridazine_EvsNdet.pdf differ diff --git a/Manuscript/Pyridazine_EvsPT2.pdf b/Manuscript/Pyridazine_EvsPT2.pdf index fa2dc09..cbad70d 100644 Binary files a/Manuscript/Pyridazine_EvsPT2.pdf and b/Manuscript/Pyridazine_EvsPT2.pdf differ diff --git a/Manuscript/Pyridine_EvsNdet.pdf b/Manuscript/Pyridine_EvsNdet.pdf index 4f2fc64..dd93112 100644 Binary files a/Manuscript/Pyridine_EvsNdet.pdf and b/Manuscript/Pyridine_EvsNdet.pdf differ diff --git a/Manuscript/Pyridine_EvsPT2.pdf b/Manuscript/Pyridine_EvsPT2.pdf index b8eded8..849aa13 100644 Binary files a/Manuscript/Pyridine_EvsPT2.pdf and b/Manuscript/Pyridine_EvsPT2.pdf differ diff --git a/Manuscript/Pyrimidine_EvsNdet.pdf b/Manuscript/Pyrimidine_EvsNdet.pdf index 55288dd..25e01e7 100644 Binary files a/Manuscript/Pyrimidine_EvsNdet.pdf and b/Manuscript/Pyrimidine_EvsNdet.pdf differ diff --git a/Manuscript/Pyrimidine_EvsPT2.pdf b/Manuscript/Pyrimidine_EvsPT2.pdf index 57f7e7c..7f8371f 100644 Binary files a/Manuscript/Pyrimidine_EvsPT2.pdf and b/Manuscript/Pyrimidine_EvsPT2.pdf differ diff --git a/Manuscript/Pyrrole_EvsNdet.pdf b/Manuscript/Pyrrole_EvsNdet.pdf index d745155..afe5a7e 100644 Binary files a/Manuscript/Pyrrole_EvsNdet.pdf and b/Manuscript/Pyrrole_EvsNdet.pdf differ diff --git a/Manuscript/Pyrrole_EvsPT2.pdf b/Manuscript/Pyrrole_EvsPT2.pdf index a8c8c1a..349f581 100644 Binary files a/Manuscript/Pyrrole_EvsPT2.pdf and b/Manuscript/Pyrrole_EvsPT2.pdf differ diff --git a/Manuscript/Tetrazine_EvsNdet.pdf b/Manuscript/Tetrazine_EvsNdet.pdf index 1bfbd41..582ed99 100644 Binary files a/Manuscript/Tetrazine_EvsNdet.pdf and b/Manuscript/Tetrazine_EvsNdet.pdf differ diff --git a/Manuscript/Tetrazine_EvsPT2.pdf b/Manuscript/Tetrazine_EvsPT2.pdf index 6a469bd..f66f764 100644 Binary files a/Manuscript/Tetrazine_EvsPT2.pdf and b/Manuscript/Tetrazine_EvsPT2.pdf differ diff --git a/Manuscript/Thiophene_EvsNdet.pdf b/Manuscript/Thiophene_EvsNdet.pdf index 15805c9..31b5642 100644 Binary files a/Manuscript/Thiophene_EvsNdet.pdf and b/Manuscript/Thiophene_EvsNdet.pdf differ diff --git a/Manuscript/Thiophene_EvsPT2.pdf b/Manuscript/Thiophene_EvsPT2.pdf index 8184fcd..a5e3807 100644 Binary files a/Manuscript/Thiophene_EvsPT2.pdf and b/Manuscript/Thiophene_EvsPT2.pdf differ diff --git a/Manuscript/Triazine_EvsNdet.pdf b/Manuscript/Triazine_EvsNdet.pdf index 70db7e0..b4ac0a2 100644 Binary files a/Manuscript/Triazine_EvsNdet.pdf and b/Manuscript/Triazine_EvsNdet.pdf differ diff --git a/Manuscript/Triazine_EvsPT2.pdf b/Manuscript/Triazine_EvsPT2.pdf index 776d64d..fb1eabf 100644 Binary files a/Manuscript/Triazine_EvsPT2.pdf and b/Manuscript/Triazine_EvsPT2.pdf differ diff --git a/data_AS/benzene_opt.dat b/data_AS/benzene_opt.dat index 5f6badb..919bb1c 100644 --- a/data_AS/benzene_opt.dat +++ b/data_AS/benzene_opt.dat @@ -24,4 +24,3 @@ 20971520 -231.5252061140 -0.0406298392 0.0000791195 -0.0403887454 0.0000786500 41943040 -231.5337886859 -0.0346957844 0.0000668061 -0.0345247390 0.0000664767 83886080 -231.5413391318 -0.0256659821 0.0001461668 -0.0294457584 0.0001455696 - 167772160 diff --git a/data_AS/cyclopentadiene_opt.dat b/data_AS/cyclopentadiene_opt.dat index cd599c9..2d9d0f1 100644 --- a/data_AS/cyclopentadiene_opt.dat +++ b/data_AS/cyclopentadiene_opt.dat @@ -24,4 +24,3 @@ 20971520 -193.5126035896 -0.0246344737 0.0000479428 -0.0245465962 0.0000477718 41943040 -193.5183426226 -0.0206049053 0.0000402624 -0.0205451654 0.0000401457 83886080 -193.5232476384 -0.0170993616 0.0000813000 -0.0170594255 0.0000811101 - 167772160 diff --git a/data_AS/furan_opt.dat b/data_AS/furan_opt.dat index 3c5d523..89a27b4 100644 --- a/data_AS/furan_opt.dat +++ b/data_AS/furan_opt.dat @@ -24,4 +24,3 @@ 20971520 -229.3797442530 -0.0224998381 0.0000423186 -0.0224333245 0.0000421935 41943040 -229.3852109522 -0.0185751065 0.0000362444 -0.0185311719 0.0000361586 83886080 -229.3897820101 -0.0152739899 0.0000641000 -0.0152452221 0.0000639793 - 167772160