loos/CBD
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

Notebook updates

Browse Source
This commit is contained in:
EnzoMonino 2021-11-29 15:01:04 +01:00
parent c31007608a
commit 2a6b18b889
1 changed files with 138 additions and 108 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

234
Manuscript/CBD.tex
View File

@ -236,7 +236,7 @@ An alternative to multiconfigurational and CC methods is the use of selected CI
Finally, to describe doubly excited states, one can think of spin-flip formalism established by Krylov in 2001. To briefly introduce the spin-flip idea we can present it like: instead of taking the singlet ground state as reference, the reference configuration is taken as the lowest triplet state. So one can access the singlet ground state and the singlet doubly-excited state via a spin-flip deexcitation and excitation (respectively), the difference of these two excitation energies providing an estimate of the double excitation. Obviously spin-flip methods have their own flaws, especially the spin contamination \cite{casanova_2020} (i.e., an artificial mixing of electronic states of differents spin multiplicities) due to spin incompleteness of the spin-flip expansion and by spin contamination of the reference configuration. One can adress part of this problem by expansion of the excitation order but with an increase of the computational cost or by complementing the spin-incomplete configuration set with the missing configurations. Finally, to describe doubly excited states, one can think of spin-flip formalism established by Krylov in 2001. To briefly introduce the spin-flip idea we can present it like: instead of taking the singlet ground state as reference, the reference configuration is taken as the lowest triplet state. So one can access the singlet ground state and the singlet doubly-excited state via a spin-flip deexcitation and excitation (respectively), the difference of these two excitation energies providing an estimate of the double excitation. Obviously spin-flip methods have their own flaws, especially the spin contamination \cite{casanova_2020} (i.e., an artificial mixing of electronic states of differents spin multiplicities) due to spin incompleteness of the spin-flip expansion and by spin contamination of the reference configuration. One can adress part of this problem by expansion of the excitation order but with an increase of the computational cost or by complementing the spin-incomplete configuration set with the missing configurations.
In the present work we investigate ${}^1A_g$, $1{}^3B_{1g}$, $1{}^1B_{1g}$, $2{}^1A_{g}$ and ${}^1B_{1g}$, $1{}^3A_{2g}$, $2{}^1A_{1g}$,$1{}^1B_{2g}$ excited states for the $D_{2h}$ and $D_{4h}$, respectively, geometries. Computational details are reported in \ref{sec:compmet} for SCI (\ref{sec:SCI}), EOM-CC (\ref{sec:CC}), multiconfigurational (\ref{sec:Multi}) and spin-flip (\ref{sec:sf}) methods. Section \ref{sec:res} is devoted to the discussion of our results for excited states \ref{sec:states} and autoisomerization barrier \ref{sec:auto} of the CBD molecule. In the present work we investigate ${}^1A_g$, $1{}^3B_{1g}$, $1{}^1B_{1g}$, $2{}^1A_{g}$ and ${}^1B_{1g}$, $1{}^3A_{2g}$, $2{}^1A_{1g}$,$1{}^1B_{2g}$ excited states for the $D_{2h}$ and $D_{4h}$, respectively, geometries. Computational details are reported in Section \ref{sec:compmet} for SCI (Subsection \ref{sec:SCI}), EOM-CC (Subsection \ref{sec:CC}), multiconfigurational (Subsection \ref{sec:Multi}) and spin-flip (Subsection \ref{sec:sf}) methods. Section \ref{sec:res} is devoted to the discussion of our results, first we consider the ground state property which is the autoisomerization barrier (Subsection \ref{sec:auto}) and then we study the excited states (Subsection \ref{sec:states}) of the CBD molecule.
\begin{figure} \begin{figure}
\includegraphics[width=0.6\linewidth]{figure2.png} \includegraphics[width=0.6\linewidth]{figure2.png}
@ -286,6 +286,87 @@ In both structures the CBD has a singlet ground state, for the spin-flip calcula
As said in \ref{sec:intro} we study both excited states and automerization barrier. The excited states of interest in this work are the $^1 Ag$, $1 ^3B_{1g}$, $1 ^1B_{1g}$ and $2 ^1A_{g}$ states for the rectangular ($D_{2h}$) structure and the $1 ^1B_{1g}$, $1 ^3A_{2g}$, $2 ^1A_{1g}$ and $1 ^1B_{2g}$ states for the square ($D_{4h}$) structure. For the excited states part we study vertical excitations, as mentioned in \ref{sec:intro} the study of the CBD molecule is a difficult task due to the multi-configurational character of some excited states and there are not reference methods for the description of those. Because of this it is important to define our reference in this work to be able to compare the results of differents methods. To do so we use the Theoretical Best Estimates (TBE) As said in \ref{sec:intro} we study both excited states and automerization barrier. The excited states of interest in this work are the $^1 Ag$, $1 ^3B_{1g}$, $1 ^1B_{1g}$ and $2 ^1A_{g}$ states for the rectangular ($D_{2h}$) structure and the $1 ^1B_{1g}$, $1 ^3A_{2g}$, $2 ^1A_{1g}$ and $1 ^1B_{2g}$ states for the square ($D_{4h}$) structure. For the excited states part we study vertical excitations, as mentioned in \ref{sec:intro} the study of the CBD molecule is a difficult task due to the multi-configurational character of some excited states and there are not reference methods for the description of those. Because of this it is important to define our reference in this work to be able to compare the results of differents methods. To do so we use the Theoretical Best Estimates (TBE)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%================================================
\subsection{Autoisomerization barrier}
\label{sec:auto}
The autoisomerization barrier for the CBD molecule is defined as the energy difference between the singlet ground state of the square ($D_{4h}$) structure and the singlet ground state of the rectangular ($D_{2h}$) geometry. Results for the calculation of the automerization barrier are shown in Tables \ref{tab:auto_standard} and \ref{tab:auto_spin_flip}. As said in \ref{sec:intro} the range for this barrier is quite large. So again, it is important to define our reference in this work in order to be able to compare our results. Table \ref{tab:auto_standard} gives standard methods results, we can observe a large difference for the autoisomerization barrier between the multi-configurational methods. Indeed, for the CASSCF(12,12) we have a difference of the order of 3 kcal.mol$^{-1}$ with CASPT2(12,12) and NEVPT2(12,12) for all the basis. However, the difference between CASPT2(12,12) and NEVPT2(12,12) is much smaller, of the order of 0.2 kcal.mol$^{-1}$ for all the basis.
%%% TABLE VI %%%
\begin{squeezetable}
\begin{table*}
\caption{Autoisomerization barrier in \kcalmol.}
\label{tab:auto_standard}
\begin{ruledtabular}
\begin{tabular}{llrrrr}
Method & 6-31+G(d) & AVDZ& AVTZ & AVQZ\\
\hline
SF-CIS & $2.64$ & $2.82$ & $3.43$ & $3.43$ \\
SF-TD-BLYP & $23.57$ & $23.62$ & $24.23$ & $24.22$ \\
SF-TD-B3LYP & $18.84$ & $18.93$ & $19.57$ & $19.57$ \\
SF-TD-PBE0 & $17.31$ & $17.36$ & $18.01$ & $18.00$ \\
SF-TD-BH\&HLYP & $11.90$ & $12.07$ & $12.73$ & $12.73$ \\
SF-TD-M06-2X & $9.34$ & $9.68$ & $10.39$ & $10.40$ \\
SF-TD-CAM-B3LYP & $18.21$ & $18.30$ & $18.98$ & $18.97$ \\
SF-TD-$\omega$B97X-V & $18.46$ & $18.48$ & $19.14$ & $19.12$ \\
SF-TD-M11 & $11.13$ & $10.38$ & $11.28$ & $11.19$ \\
SF-ADC2-s & $6.69$ & $7.15$ & $8.64$ & $8.85$ \\
SF-ADC2-x & $8.66$ & $9.15$ & $10.40$ & \\
SF-ADC3 & $8.06$ & $8.76$ & $9.58$ & \\
CASSCF(12,12) & $10.19$ & $10.75$ & $11.59$ & $11.62$ \\
CASPT2(12,12) & $7.24$ & $7.53$ & $8.51$ & $8.71$ \\
NEVPT2(12,12) & $7.12$ & $7.33$ & $8.28$ & $8.49$ \\
CCSD & $8.31$ & $8.80$ & $9.88$ & $10.10$ \\
CC3 & $6.59$ & $6.89$ & $7.88$ & $8.06$ \\
CCSDT & $7.26$ & $7.64$ & $8.68$ &$\left[ 8.86\right]$\fnm[1] \\
CC4 & $7.40$ & $7.78$ & $\left[ 8.82\right]$\fnm[2] & $\left[ 9.00\right]$\fnm[3]\\
CCSDTQ & $7.51$ & $\left[ 7.89\right]$\fnm[4]& $\left[ 8.93\right]$\fnm[5]& $\left[ 9.11\right]$\fnm[6]\\
%CIPSI & $7.91\pm 0.21$ & $8.58\pm 0.14$ & & \\
\end{tabular}
\end{ruledtabular}
\fnt[1]{Value of CCSDT/AVQZ obtained using CCSDT/AVTZ corrected by the difference between CC3/AVQZ and CC3/AVTZ.}
\fnt[2]{Value of CC4/AVTZ obtained using CC4/AVDZ corrected by the difference between CCSDT/AVTZ and CCSDT/AVDZ.}
\fnt[3]{Value of CC4/AVQZ obtained using CC4/AVTZ corrected by the difference between CCSDT/AVQZ and CCSDT/AVTZ.}
\fnt[4]{Value of CCSDTQ/AVDZ obtained using CCSDTQ/6-31+G(d) corrected by the difference between CC4/AVDZ basis and CC4/6-31+G(d).}
\fnt[5]{Value of CCSDTQ/AVTZ obtained using CCSDTQ/AVDZ corrected by the difference between CC4/AVTZ and CC4/AVDZ.}
\fnt[6]{Value of CCSDTQ/AVQZ obtained using CCSDTQ/AVTZ corrected by the difference between CC4/AVQZ and CC4/AVTZ.}
\end{table*}
\end{squeezetable}
%%% %%% %%% %%%
%%% TABLE VII %%%
%\begin{squeezetable}
%\begin{table}
% \caption{Autoisomerization barrier for spin-flip methods in \kcalmol.}
%
% \label{tab:auto_spin_flip}
% \begin{ruledtabular}
% \begin{tabular}{llrrrr}
% Method & 6-31+G(d) & AVDZ& AVTZ & AVQZ\\
% \hline
%SF-CIS & $2.64$ & $2.82$ & $3.43$ & $3.43$ \\
%SF-TD-BLYP & $23.57$ & $23.62$ & $24.23$ & $24.22$ \\
%SF-TD-B3LYP & $18.84$ & $18.93$ & $19.57$ & $19.57$ \\
%SF-TD-PBE0 & $17.31$ & $17.36$ & $18.01$ & $18.00$ \\
%SF-TD-BH\&HLYP & $11.90$ & $12.07$ & $12.73$ & $12.73$ \\
%SF-TD-M06-2X & $9.34$ & $9.68$ & $10.39$ & $10.40$ \\
%SF-TD-CAM-B3LYP & $18.21$ & $18.30$ & $18.98$ & $18.97$ \\
%SF-TD-$\omega$B97X-V & $18.46$ & $18.48$ & $19.14$ & $19.12$ \\
%SF-TD-M11 & $11.13$ & $10.38$ & $11.28$ & $11.19$ \\
%SF-ADC2-s & $6.69$ & $7.15$ & $8.64$ & $8.85$ \\
%SF-ADC2-x & $8.66$ & $9.15$ & $10.40$ & \\
%SF-ADC3 & $8.06$ & $8.76$ & $9.58$ & \\
%
% \end{tabular}
% \end{ruledtabular}
%
%\end{table}
%\end{squeezetable}
%%% %%% %%% %%%
%================================================
%================================================ %================================================
\subsection{Excited States} \subsection{Excited States}
\label{sec:states} \label{sec:states}
@ -383,7 +464,7 @@ SF-EOM-CC(2,3) & 6-31+G(d) & $1.490$ & $3.333$ & $4.061$ \\
%%% TABLE III %%% %%% TABLE III %%%
\begin{squeezetable} \begin{squeezetable}
\begin{table} \begin{table*}
\caption{ \caption{
Standard vertical excitation energies (with respect to the singlet $\text{X}\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{g}$ states of CBD at the $D_{2h}$ rectangular equilibrium geometry of the $\text{X}\,{}^1 A_{g}$ ground state. Standard vertical excitation energies (with respect to the singlet $\text{X}\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{g}$ states of CBD at the $D_{2h}$ rectangular equilibrium geometry of the $\text{X}\,{}^1 A_{g}$ ground state.
\label{tab:D2h}} \label{tab:D2h}}
@ -393,7 +474,7 @@ SF-EOM-CC(2,3) & 6-31+G(d) & $1.490$ & $3.333$ & $4.061$ \\
\cline{3-5} \cline{3-5}
Method & Basis & $1\,{}^3B_{1g}$ & $1\,{}^1B_{1g}$ & $2\,{}^1A_{g}$ \\ Method & Basis & $1\,{}^3B_{1g}$ & $1\,{}^1B_{1g}$ & $2\,{}^1A_{g}$ \\
\hline \hline
CC3 &6-31+G(d)& $1.42$ & $3.341$ & $4.658$ \\ CC3 &6-31+G(d)& $1.420$ & $3.341$ & $4.658$ \\
& AVDZ & $1.396$ & $3.158$ & $4.711$ \\ & AVDZ & $1.396$ & $3.158$ & $4.711$ \\
& AVTZ & $1.402$ & $3.119$ & $4.777$ \\ & AVTZ & $1.402$ & $3.119$ & $4.777$ \\
& AVQZ & $1.409$ & $3.113$ & $4.774$ \\[0.1cm] & AVQZ & $1.409$ & $3.113$ & $4.774$ \\[0.1cm]
@ -401,13 +482,16 @@ CCSDT &6-31+G(d)& $1.442$ & $3.357$ & $4.311$ \\
& AVDZ & $1.411$ & $3.175$ & $4.327$ \\ & AVDZ & $1.411$ & $3.175$ & $4.327$ \\
& AVTZ & $1.411$ & $3.139$ & $4.429$ \\[0.1cm] & AVTZ & $1.411$ & $3.139$ & $4.429$ \\[0.1cm]
CC4 &6-31+G(d)& & $3.343$ & $4.067$ \\ CC4 &6-31+G(d)& & $3.343$ & $4.067$ \\
& AVDZ & & $3.164$ & $4.041$ \\[0.1cm] & AVDZ & & $3.164$ & $4.041$ \\
CCSDTQ &6-31+G(d)& & $3.34$ & $4.073$ \\[0.1cm] & AVTZ & & $\left[3.128\right]$\fnm[1] & $\left[4.143\right]$\fnm[1]\\[0.1cm]
CCSDTQ &6-31+G(d)& & $3.340$ & $4.073$ \\
& AVDZ & & $\left[3.161\right]$\fnm[2]& $\left[4.047\right]$\fnm[2] \\
& AVTZ & & $\left[3.125\right]$\fnm[3]& $\left[4.149\right]$\fnm[3]\\[0.1cm]
SA2-CASSCF(4,4) &6-31+G(d)& $1.662$ & $4.657$ & $4.439$ \\ SA2-CASSCF(4,4) &6-31+G(d)& $1.662$ & $4.657$ & $4.439$ \\
& AVDZ & $1.672$ & $4.563$ & $4.448$ \\ & AVDZ & $1.672$ & $4.563$ & $4.448$ \\
& AVTZ & $1.67$ & $4.546$ & $4.441$ \\ & AVTZ & $1.670$ & $4.546$ & $4.441$ \\
& AVQZ & $1.671$ & $4.549$ & $4.44$ \\[0.1cm] & AVQZ & $1.671$ & $4.549$ & $4.440$ \\[0.1cm]
CASPT2(4,4) &6-31+G(d)& $1.44$ & $3.162$ & $4.115$ \\ CASPT2(4,4) &6-31+G(d)& $1.440$ & $3.162$ & $4.115$ \\
& AVDZ & $1.414$ & $2.971$ & $4.068$ \\ & AVDZ & $1.414$ & $2.971$ & $4.068$ \\
& AVTZ & $1.412$ & $2.923$ & $4.072$ \\ & AVTZ & $1.412$ & $2.923$ & $4.072$ \\
& AVQZ & $1.417$ & $2.911$ & $4.081$ \\[0.1cm] & AVQZ & $1.417$ & $2.911$ & $4.081$ \\[0.1cm]
@ -419,27 +503,27 @@ SC-NEVPT2(4,4) &6-31+G(d)& $1.407$ & $2.707$ & $4.145$ \\
& AVDZ & $1.381$ & $2.479$ & $4.109$ \\ & AVDZ & $1.381$ & $2.479$ & $4.109$ \\
& AVTZ & $1.379$ & $2.422$ & $4.108$ \\ & AVTZ & $1.379$ & $2.422$ & $4.108$ \\
& AVQZ & $1.384$ & $2.408$ & $4.125$ \\[0.1cm] & AVQZ & $1.384$ & $2.408$ & $4.125$ \\[0.1cm]
PC-NEVPT2(4,4) &6-31+G(d)& $1.409$ & $2.652$ & $4.12$ \\ PC-NEVPT2(4,4) &6-31+G(d)& $1.409$ & $2.652$ & $4.120$ \\
& AVDZ & $1.384$ & $2.424$ & $4.084$ \\ & AVDZ & $1.384$ & $2.424$ & $4.084$ \\
& AVTZ & $1.382$ & $2.368$ & $4.083$ \\ & AVTZ & $1.382$ & $2.368$ & $4.083$ \\
& AVQZ & $1.387$ & $2.353$ & $4.091$ \\[0.1cm] & AVQZ & $1.387$ & $2.353$ & $4.091$ \\[0.1cm]
MRCI(4,4) &6-31+G(d)& $1.564$ & $3.802$ & $4.265$ \\ MRCI(4,4) &6-31+G(d)& $1.564$ & $3.802$ & $4.265$ \\
& AVDZ & $1.558$ & $3.67$ & $4.254$ \\ & AVDZ & $1.558$ & $3.670$ & $4.254$ \\
& AVTZ & $1.568$ & $3.678$ & $4.27$ \\ & AVTZ & $1.568$ & $3.678$ & $4.270$ \\
& AVQZ & $1.574$ & $3.681$ & $4.28$ \\[0.1cm] & AVQZ & $1.574$ & $3.681$ & $4.280$ \\[0.1cm]
SA2-CASSCF(12,12) &6-31+G(d)& $1.675$ & $3.924$ & $4.22$ \\ SA2-CASSCF(12,12) &6-31+G(d)& $1.675$ & $3.924$ & $4.220$ \\
& AVDZ & $1.685$ & $3.856$ & $4.221$ \\ & AVDZ & $1.685$ & $3.856$ & $4.221$ \\
& AVTZ & $1.686$ & $3.844$ & $4.217$ \\ & AVTZ & $1.686$ & $3.844$ & $4.217$ \\
& AVQZ & $1.687$ & $3.846$ & $4.216$ \\[0.1cm] & AVQZ & $1.687$ & $3.846$ & $4.216$ \\[0.1cm]
CASPT2(12,12) &6-31+G(d)& $1.508$ & $3.407$ & $4.099$ \\ CASPT2(12,12) &6-31+G(d)& $1.508$ & $3.407$ & $4.099$ \\
& AVDZ & $1.489$ & $3.256$ & $4.044$ \\ & AVDZ & $1.489$ & $3.256$ & $4.044$ \\
& AVTZ & $1.48$ & $3.183$ & $4.043$ \\ & AVTZ & $1.480$ & $3.183$ & $4.043$ \\
& AVQZ & $1.482$ & $3.163$ & $4.047$ \\[0.1cm] & AVQZ & $1.482$ & $3.163$ & $4.047$ \\[0.1cm]
XMS-CASPT2(12,12) &6-31+G(d)& && $4.111$ \\ XMS-CASPT2(12,12) &6-31+G(d)& && $4.111$ \\
& AVDZ & & & $4.056$ \\ & AVDZ & & & $4.056$ \\
& AVTZ & & & $4.059$ \\ & AVTZ & & & $4.059$ \\
& AVQZ & & & $4.065$ \\[0.1cm] & AVQZ & & & $4.065$ \\[0.1cm]
SC-NEVPT2(12,12) &6-31+G(d)& $1.522$ & $3.409$ & $4.13$ \\ SC-NEVPT2(12,12) &6-31+G(d)& $1.522$ & $3.409$ & $4.130$ \\
& AVDZ & $1.511$ & $3.266$ & $4.093$ \\ & AVDZ & $1.511$ & $3.266$ & $4.093$ \\
& AVTZ & $1.501$ & $3.188$ & $4.086$ \\ & AVTZ & $1.501$ & $3.188$ & $4.086$ \\
& AVQZ & $1.503$ & $3.167$ & $4.088$ \\[0.1cm] & AVQZ & $1.503$ & $3.167$ & $4.088$ \\[0.1cm]
@ -453,49 +537,55 @@ CIPSI &6-31+G(d)& $1.486\pm 0.005$ & $3.348\pm 0.024$ & $4.084\pm 0.012$ \\
& AVTZ & $1.461\pm 0.030$ & $3.142\pm 0.035$ & $4.03\pm 0.09$ \\ & AVTZ & $1.461\pm 0.030$ & $3.142\pm 0.035$ & $4.03\pm 0.09$ \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\end{table} \fnt[1]{Value of CC4/AVTZ obtained using CC4/AVDZ corrected by the difference between CCSDT/AVTZ and CCSDT/AVDZ.}
\fnt[2]{Value of CCSDTQ/AVDZ obtained using CCSDTQ/6-31+G(d) corrected by the difference between CC4/AVDZ and CC4/6-31+G(d).}
\fnt[3]{Value of CCSDTQ/AVTZ obtained using CCSDTQ/AVDZ corrected by the difference between CC4/AVTZ and CC4/AVDZ.}
\end{table*}
\end{squeezetable} \end{squeezetable}
%%% %%% %%% %%% %%% %%% %%% %%%
%%% TABLE IV %%% %%% TABLE IV %%%
\begin{squeezetable} \begin{squeezetable}
\begin{table} \begin{table*}
\caption{ \caption{
Standard vertical excitation energies (with respect to the singlet $\text{X}\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states of CBD at the $D_{4h}$ square-planar equilibrium geometry of the $1\,{}^3A_{2g}$ state. Standard vertical excitation energies (with respect to the singlet $\text{X}\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states of CBD at the $D_{4h}$ square-planar equilibrium geometry of the $1\,{}^3A_{2g}$ state.
\label{tab:D4h}} \label{tab:D4h}}
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{llrrr} \begin{tabular}{llrrr}
& \mc{4}{r}{Excitation energies (eV)} \hspace{0.5cm}\\ & \mc{3}{r}{Excitation energies (eV)} \hspace{0.1cm}\\
\cline{3-5} \cline{3-5}
Method & Basis & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ \\ Method & Basis & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ \\
\hline \hline
CCSD & 6-31+G(d) & $0.148$ & $1.788$ & \\ CCSD & 6-31+G(d) & $0.148$ & $1.788$ & \\
& AVDZ & $0.1$ & $1.65$ & \\ & AVDZ & $0.100$ & $1.650$ & \\
& AVTZ & $0.085$ & $1.6$ & \\ & AVTZ & $0.085$ & $1.600$ & \\
& AVQZ & $0.084$ & $1.588$ & \\[0.1cm] & AVQZ & $0.084$ & $1.588$ & \\[0.1cm]
CC3 & 6-31+G(d) & & $1.809$ & $2.836$ \\ CC3 & 6-31+G(d) & & $1.809$ & $2.836$ \\
& AVDZ & & $1.695$ & $2.646$ \\ & AVDZ & & $1.695$ & $2.646$ \\
& AVTZ & & $1.662$ & $2.72$ \\[0.1cm] & AVTZ & & $1.662$ & $2.720$ \\[0.1cm]
CCSDT & 6-31+G(d) & $0.21$ & $1.751$ & $2.565$ \\ CCSDT & 6-31+G(d) & $0.210$ & $1.751$ & $2.565$ \\
& AVDZ & $0.165$ & $1.659$ & $2.45$ \\ & AVDZ & $0.165$ & $1.659$ & $2.450$ \\
& AVTZ & $0.149$ & $1.631$ & $2.537$ \\[0.1cm] & AVTZ & $0.149$ & $1.631$ & $2.537$ \\[0.1cm]
CC4 & 6-31+G(d) & & $1.604$ & $2.121$ \\ CC4 & 6-31+G(d) & & $1.604$ & $2.121$ \\
& AVDZ & & $1.539$ & $1.934$ \\[0.1cm] & AVDZ & & $1.539$ & $1.934$ \\
CCSDTQ & 6-31+G(d) & $0.205$ & $1.593$ & $2.134$ \\[0.1cm] & AVTZ & & $\left[1.511 \right]$\fnm[1] &$\left[2.021 \right]$\fnm[1] \\[0.1cm]
CCSDTQ & 6-31+G(d) & $0.205$ & $1.593$ & $2.134$ \\
& AVDZ & & $\left[1.528 \right]$\fnm[2]&$\left[1.947\right]$\fnm[2] \\
& AVTZ & & $\left[1.500 \right]$\fnm[3]&$\left[2.034\right]$\fnm[3] \\ [0.1cm]
SA2-CASSCF(4,4) & 6-31+G(d) & $0.447$ & $2.257$ & $3.549$ \\ SA2-CASSCF(4,4) & 6-31+G(d) & $0.447$ & $2.257$ & $3.549$ \\
& AVDZ & $0.438$ & $2.24$ & $3.443$ \\ & AVDZ & $0.438$ & $2.240$ & $3.443$ \\
& AVTZ & $0.434$ & $2.234$ & $3.424$ \\ & AVTZ & $0.434$ & $2.234$ & $3.424$ \\
& AVQZ & $0.435$ & $2.235$ & $3.427$ \\[0.1cm] & AVQZ & $0.435$ & $2.235$ & $3.427$ \\[0.1cm]
CASPT2(4,4) & 6-31+G(d) & $0.176$ & $1.588$ & $1.899$ \\ CASPT2(4,4) & 6-31+G(d) & $0.176$ & $1.588$ & $1.899$ \\
& AVDZ & $0.137$ & $1.54$ & $1.708$ \\ & AVDZ & $0.137$ & $1.540$ & $1.708$ \\
& AVTZ & $0.128$ & $1.506$ & $1.635$ \\ & AVTZ & $0.128$ & $1.506$ & $1.635$ \\
& AVQZ & $0.128$ & $1.498$ & $1.612$ \\[0.1cm] & AVQZ & $0.128$ & $1.498$ & $1.612$ \\[0.1cm]
SC-NEVPT2(4,4) & 6-31+G(d) & $0.083$ & $1.52$ & $1.38$ \\ SC-NEVPT2(4,4) & 6-31+G(d) & $0.083$ & $1.520$ & $1.380$ \\
& AVDZ & $0.037$ & $1.465$ & $1.14$ \\ & AVDZ & $0.037$ & $1.465$ & $1.140$ \\
& AVTZ & $0.024$ & $1.428$ & $1.055$ \\ & AVTZ & $0.024$ & $1.428$ & $1.055$ \\
& AVQZ & $0.024$ & $1.42$ & $1.03$ \\[0.1cm] & AVQZ & $0.024$ & $1.420$ & $1.030$ \\[0.1cm]
PC-NEVPT2(4,4) & 6-31+G(d) & $0.085$ & $1.496$ & $1.329$ \\ PC-NEVPT2(4,4) & 6-31+G(d) & $0.085$ & $1.496$ & $1.329$ \\
& AVDZ & $0.039$ & $1.44$ & $1.088$ \\ & AVDZ & $0.039$ & $1.440$ & $1.088$ \\
& AVTZ & $0.026$ & $1.403$ & $1.003$ \\ & AVTZ & $0.026$ & $1.403$ & $1.003$ \\
& AVQZ & $0.026$ & $1.395$ & $0.977$ \\[0.1cm] & AVQZ & $0.026$ & $1.395$ & $0.977$ \\[0.1cm]
MRCI(4,4) & 6-31+G(d) & $0.297$ & $1.861$ & $2.571$ \\ MRCI(4,4) & 6-31+G(d) & $0.297$ & $1.861$ & $2.571$ \\
@ -504,27 +594,29 @@ MRCI(4,4) & 6-31+G(d) & $0.297$ & $1.861$ & $2.571$ \\
& AVQZ & $0.273$ & $1.825$ & $2.413$ \\[0.1cm] & AVQZ & $0.273$ & $1.825$ & $2.413$ \\[0.1cm]
SA2-CASSCF(12,12) & 6-31+G(d) & $0.386$ & $1.974$ & $2.736$ \\ SA2-CASSCF(12,12) & 6-31+G(d) & $0.386$ & $1.974$ & $2.736$ \\
& AVDZ & $0.374$ & $1.947$ & $2.649$ \\ & AVDZ & $0.374$ & $1.947$ & $2.649$ \\
& AVTZ & $0.37$ & $1.943$ & $2.634$ \\ & AVTZ & $0.370$ & $1.943$ & $2.634$ \\
& AVQZ & $0.371$ & $1.945$ & $2.637$ \\[0.1cm] & AVQZ & $0.371$ & $1.945$ & $2.637$ \\[0.1cm]
CASPT2(12,12) & 6-31+G(d) & $0.235$ & $1.635$ & $2.17$ \\ CASPT2(12,12) & 6-31+G(d) & $0.235$ & $1.635$ & $2.170$ \\
& AVDZ & $0.203$ & $1.588$ & $2.015$ \\ & AVDZ & $0.203$ & $1.588$ & $2.015$ \\
& AVTZ & $0.183$ & $1.538$ & $1.926$ \\ & AVTZ & $0.183$ & $1.538$ & $1.926$ \\
& AVQZ & $0.179$ & $1.522$ & $1.898$ \\[0.1cm] & AVQZ & $0.179$ & $1.522$ & $1.898$ \\[0.1cm]
SC-NEVPT2(12,12) & 6-31+G(d) & $0.218$ & $1.644$ & $2.143$ \\ SC-NEVPT2(12,12) & 6-31+G(d) & $0.218$ & $1.644$ & $2.143$ \\
& AVDZ & $0.189$ & $1.6$ & $1.991$ \\ & AVDZ & $0.189$ & $1.600$ & $1.991$ \\
& AVTZ & $0.165$ & $1.546$ & $1.892$ \\ & AVTZ & $0.165$ & $1.546$ & $1.892$ \\
& AVQZ & $0.16$ & $1.529$ & $1.862$ \\[0.1cm] & AVQZ & $0.160$ & $1.529$ & $1.862$ \\[0.1cm]
PC-NEVPT2(12,12) & 6-31+G(d) & $0.189$ & $1.579$ & $2.02$ \\ PC-NEVPT2(12,12) & 6-31+G(d) & $0.189$ & $1.579$ & $2.020$ \\
& AVDZ & $0.156$ & $1.53$ & $1.854$ \\ & AVDZ & $0.156$ & $1.530$ & $1.854$ \\
& AVTZ & $0.131$ & $1.476$ & $1.756$ \\ & AVTZ & $0.131$ & $1.476$ & $1.756$ \\
& AVQZ & $0.126$ & $1.46$ & $1.727$ \\[0.1cm] & AVQZ & $0.126$ & $1.460$ & $1.727$ \\[0.1cm]
CIPSI & 6-31+G(d) & $0.2010\pm 0.0030$ & $1.602\pm 0.007$ & $2.13\pm 0.04$ \\ CIPSI & 6-31+G(d) & $0.2010\pm 0.0030$ & $1.602\pm 0.007$ & $2.13\pm 0.04$ \\
& AVDZ & $0.1570\pm 0.0030$ & $1.587\pm 0.005$ & $2.102\pm 0.027$ \\ & AVDZ & $0.1570\pm 0.0030$ & $1.587\pm 0.005$ & $2.102\pm 0.027$ \\
& AVTZ & $0.169\pm 0.029$ & $1.63\pm 0.05$ & \\ & AVTZ & $0.169\pm 0.029$ & $1.63\pm 0.05$ & \\
\end{tabular} \end{tabular}
\end{ruledtabular} \end{ruledtabular}
\fnt[1]{Value of CC4/AVTZ obtained using CC4/AVDZ corrected by the difference between CCSDT/AVTZ and CCSDT/AVDZ.}
\end{table} \fnt[2]{Value of CCSDTQ/AVDZ obtained using CCSDTQ/6-31+G(d) corrected by the difference between CCSDT/AVDZ and CCSDT/6-31+G(d).}
\fnt[3]{Value of CCSDTQ/AVTZ obtained using CCSDTQ/AVDZ corrected by the difference between CCSDT/AVTZ and CCSDT/AVDZ.}
\end{table*}
\end{squeezetable} \end{squeezetable}
%%% %%% %%% %%% %%% %%% %%% %%%
@ -597,69 +689,7 @@ SF-ADC(3) & 6-31+G(d) & $0.123$ & $1.650$ & $2.078$ \\
%================================================ %================================================
%================================================
\subsection{Autoisomerization barrier}
\label{sec:auto}
The autoisomerization barrier for the CBD molecule is defined as the energy difference between the singlet ground state of the square ($D_{4h}$) structure and the singlet ground state of the rectangular ($D_{2h}$) geometry. Results for the calculation of the automerization barrier are shown in Tables \ref{tab:auto_standard} and \ref{tab:auto_spin_flip}. As said in \ref{sec:intro} the range for this barrier is quite large. So again, it is important to define our reference in this work in order to be able to compare our results. Table \ref{tab:auto_standard} gives standard methods results, we can observe a large difference for the autoisomerization barrier between the multi-configurational methods. Indeed, for the CASSCF(12,12) we have a difference of the order of 3 kcal.mol$^{-1}$ with CASPT2(12,12) and NEVPT2(12,12) for all the basis. However, the difference between CASPT2(12,12) and NEVPT2(12,12) is much smaller, of the order of 0.2 kcal.mol$^{-1}$ for all the basis.
%%% TABLE VI %%%
\begin{squeezetable}
\begin{table}
\caption{Autoisomerization barrier for standard methods in \kcalmol.}
\label{tab:auto_standard}
\begin{ruledtabular}
\begin{tabular}{llrrrr}
Method & 6-31+G(d) & AVDZ& AVTZ & AVQZ\\
\hline
CASSCF(12,12) & $10.19$ & $10.75$ & $11.59$ & $11.62$ \\
CASPT2(12,12) & $7.24$ & $7.53$ & $8.51$ & $8.71$ \\
NEVPT2(12,12) & $7.12$ & $7.33$ & $8.28$ & $8.49$ \\
CCSD & $8.31$ & $8.8$ & $9.88$ & $10.1$ \\
CC3 & $6.59$ & $6.89$ & $7.88$ & $8.06$ \\
CCSDT & $7.26$ & $7.64$ & $8.68$ & \\
CC4 & $7.4$ & $7.78$ & & \\
CCSDTQ & $7.51$ & & & \\
CIPSI & $7.91\pm 0.21$ & $8.58\pm 0.14$ & & \\
\end{tabular}
\end{ruledtabular}
\end{table}
\end{squeezetable}
%%% %%% %%% %%%
%%% TABLE VII %%%
\begin{squeezetable}
\begin{table}
\caption{Autoisomerization barrier for spin-flip methods in \kcalmol.}
\label{tab:auto_spin_flip}
\begin{ruledtabular}
\begin{tabular}{llrrrr}
Method & 6-31+G(d) & AVDZ& AVTZ & AVQZ\\
\hline
SF-CIS & $2.64$ & $2.82$ & $3.43$ & $3.43$ \\
SF-TD-BLYP & $23.57$ & $23.62$ & $24.23$ & $24.22$ \\
SF-TD-B3LYP & $18.84$ & $18.93$ & $19.57$ & $19.57$ \\
SF-TD-PBE0 & $17.31$ & $17.36$ & $18.01$ & $18.00$ \\
SF-TD-BH\&HLYP & $11.90$ & $12.07$ & $12.73$ & $12.73$ \\
SF-TD-M06-2X & $9.34$ & $9.68$ & $10.39$ & $10.40$ \\
SF-TD-CAM-B3LYP & $18.21$ & $18.30$ & $18.98$ & $18.97$ \\
SF-TD-$\omega$B97X-V & $18.46$ & $18.48$ & $19.14$ & $19.12$ \\
SF-TD-M11 & $11.13$ & $10.38$ & $11.28$ & $11.19$ \\
SF-ADC2-s & $6.69$ & $7.15$ & $8.64$ & $8.85$ \\
SF-ADC2-x & $8.66$ & $9.15$ & $10.40$ & \\
SF-ADC3 & $8.06$ & $8.76$ & $9.58$ & \\
\end{tabular}
\end{ruledtabular}
\end{table}
\end{squeezetable}
%%% %%% %%% %%%
%================================================
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusion} \section{Conclusion}