diff --git a/Manuscript/CBD.tex b/Manuscript/CBD.tex index 0644dca..c462bbf 100644 --- a/Manuscript/CBD.tex +++ b/Manuscript/CBD.tex @@ -247,7 +247,7 @@ In the present work we investigate ${}^1A_g$, $1{}^3B_{1g}$, $1{}^1B_{1g}$, $2{} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Computational Details} \label{sec:compmet} -The system under investigation in this work is the cyclobutadiene (CBD) molecule, rectangular ($D_{2h}$) and square ($D_{4h}$) geometries are considered. The ($D_{2h}$) geometry is obtained at the CC3 level without frozen core using the aug-cc-pVTZ and the ($D_{4h}$) geometry is obtained at the RO-CCSD(T) level using aug-cc-pVTZ again without frozen core. All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X$=$D, T, Q. In the following we will use the notation AVXZ for the aug-cc-pVXZ basis, again with X$=$D, T, Q. The $\%T_1$ metric that gives the percentage of single excitation calculated at the CC3 level in \textcolor{red}{DALTON} allows to characterize the various states.Throughout all this work, spin-flip and spin-conserved calculations are performed with a UHF reference. +%The system under investigation in this work is the cyclobutadiene (CBD) molecule, rectangular ($D_{2h}$) and square ($D_{4h}$) geometries are considered. The ($D_{2h}$) geometry is obtained at the CC3 level without frozen core using the aug-cc-pVTZ and the ($D_{4h}$) geometry is obtained at the RO-CCSD(T) level using aug-cc-pVTZ again without frozen core. All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X$=$D, T, Q. In the following we will use the notation AVXZ for the aug-cc-pVXZ basis, again with X$=$D, T, Q. The $\%T_1$ metric that gives the percentage of single excitation calculated at the CC3 level in \textcolor{red}{DALTON} allows to characterize the various states.Throughout all this work, spin-flip and spin-conserved calculations are performed with a UHF reference. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -282,14 +282,42 @@ In both structures the CBD has a singlet ground state, for the spin-flip calcula %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Results and discussion} \label{sec:res} - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%================================================ +\subsection{Geometries} +\label{sec:geometries} +Two different sets of geometries obtained with different level of theory are considered for the ground state property and for the excited states of the CBD molecule. First, for the autoisomerization barrier because we consider an energy difference between two geometries it is needed to obtain these geometries at the same level of theory. Due to the fact that the square CBD is an open-shell molecule it is difficult to optimize the geometry so the most accurate method that we can use for both structures is the CASPT2(12,12) with the aug-cc-pVTZ (AVTZ) basis without frozen core. Then, for the excited states because we look at vertical energy transitions in one particular geometry we can use different methods for the different structures and use the most accurate method for each geometry. So in the case of the excited states of the CBD molecule we use CC3 without frozen core with the aug-cc-pVTZ basis for the rectangular ($D_{2h}$) geometry and we use RO-CCSD(T) with the aug-cc-pVTZ (AVTZ) basis again without frozen core for the square ($D_{4h}$) geometry. Table \ref{tab:geometries} shows the results on the geometry parameters obtained with the different methods. + +%%% TABLE I %%% +\begin{squeezetable} +\begin{table} + \caption{Optimized geometries of the $D_{2h}$ ground state $\text{X}\,{}^1 A_{g}$ of CBD. Bond lenghts are in angstr\"om and angles are in degree.} + + \label{tab:geometries} + \begin{ruledtabular} + \begin{tabular}{llrrr} + Method & C=C & C-C & C-H & H-C=C\fnm[1] \\ + \hline + CASPT2(12,12)/AVTZ & 1.355 & 1.566 & 1.077 & 134.99 \\ + CC3/AVTZ & 1.344 & 1.565 & 1.076 & 135.08 \\ + CCSD(T)/cc-pVTZ & 1.343 & 1.566 & 1.074 & 135.09 \fnm[2] +\end{tabular} + \end{ruledtabular} + \fnt[1]{Angle between the C-H bond and the C=C bond.} + \fnt[2]{From reference \cite{manohar_2008}} +\end{table} +\end{squeezetable} +%%% %%% %%% %%% + +%================================================ + + %================================================ \subsection{Autoisomerization barrier} \label{sec:auto} The results for the calculation of the automerization barrier energy with and without spin-flip methods are shown in Table \ref{tab:auto_standard}. Two types of methods are used with spin-flip, SF-TD-DFT with several functionals and SF-ADC with the variants SF-ADC(2)-s, SF-ADC(2)-x and SF-ADC(3). First, one can see that there is large variations of the energy between the different functionals. Indeed if we look at the hybrid functionals B3LYP and BH\&HLYP we can see that there is a difference of around 7 \kcalmol throught all the bases, the difference in energy between the B3LYP and PBE0 functionals is much smaller with around 1.5 \kcalmol throught all the bases. We find a similar behaviour regarding the RSH functionals, we find a difference of about 8.5-9 \kcalmol between the M06-2X and the CAM-B3LYP functionals for all bases. The results between the CAM-B3LYP and the $\omega$B97X-V are very close in energy with a difference of around 0.15-0.25 \kcalmol . The energy difference between the M11 and the M06-2X functionals is larger with 0.7-0.8 \kcalmol for the AVXZ bases and with 1.79 \kcalmol for the 6-31+G(d) basis. For the SF-ADC methods the energy differences are smaller with 1.76-2 \kcalmol between the ADC(2)-s and the ADC(2)-x schemes, 0.94-1.61 \kcalmol between the ADC(2)-s and the ADC(3) schemes and 0.39-0.82 \kcalmol between the ADC(2)-x and the ADC(3) schemes. -Then we compare results for multireference methods, we can see a difference of about 2.91-3.22 \kcalmol through all the bases between the CASSCF(12,12) and the CASPT2(12,12) methods. These differences can be explained by the well known lack of dynamical correlation for the CASSCF method that is typically important for close-shell molecules which is the case for the ground states of the rectangular and square geometries of the CBD molecule. The results between the CASPT2(12,12) and the NEVPT2(12,12) are much closer with an energy difference of around 0.12-0.23 \kcalmol for all the bases. Finally the last results shown in Table \ref{tab:auto_standard} are the CC ones, for the autoisomerization barrier energy we considered the CCSD, CCSDT, CCSDTQ methods and the approximations of CCDT and of CCSDTQ, the CC3 and the CC4 methods, respectively. We can see that when we go to a larger basis the energy barrier increase meaning that the energy differen +Then we compare results for multireference methods, we can see a difference of about 2.91-3.22 \kcalmol through all the bases between the CASSCF(12,12) and the CASPT2(12,12) methods. These differences can be explained by the well known lack of dynamical correlation for the CASSCF method that is typically important for close-shell molecules which is the case for the ground states of the rectangular and square geometries of the CBD molecule. The results between the CASPT2(12,12) and the NEVPT2(12,12) are much closer with an energy difference of around 0.12-0.23 \kcalmol for all the bases. Finally the last results shown in Table \ref{tab:auto_standard} are the CC ones, for the autoisomerization barrier energy we consider the CCSD, CCSDT, CCSDTQ methods and the approximations of CCDT and of CCSDTQ, the CC3 and the CC4 methods, respectively. We can see that the CCSD values are higher than the other CC methods with an energy difference of around 1.05-1.24 \kcalmol between the CCSD and the CCSDT methods. The CCSDT and CCSDTQ autoisomerization barrier energies are closer with 0.25 \kcalmol of energy difference. The energy difference between the CCSDT and its approximation CC3 is about 0.67-0.8 \kcalmol for all the bases whereas the energy difference between the CCSDTQ and its approximate version CC4 is 0.11 \kcalmol. %%% TABLE I %%% \begin{squeezetable} @@ -370,6 +398,7 @@ CCSDTQ & $7.51$ & $\left[ 7.89\right]$\fnm[4]& $\left[ 8.93\right]$\fnm[5]& $\le %================================================ \subsection{Excited States} \label{sec:states} +All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X$=$D, T, Q. In the following we will use the notation AVXZ for the aug-cc-pVXZ basis, again with X$=$D, T, Q. \subsubsection{D2h geometry} @@ -491,7 +520,7 @@ SF-EOM-CC(2,3) & 6-31+G(d) & $1.490$ & $3.333$ & $4.061$ \\ \label{tab:D2h}} \begin{ruledtabular} \begin{tabular}{llrrr} - & \mc{4}{r}{Excitation energies (eV)} \hspace{0.5cm}\\ + & \mc{4}{c}{Excitation energies (eV)} \\ \cline{3-5} Method & Basis & $1\,{}^3B_{1g}$ & $1\,{}^1B_{1g}$ & $2\,{}^1A_{g}$ \\ \hline diff --git a/References/Casanova_2020.pdf b/References/Casanova_2020.pdf index 0a928ba..cdcc16f 100644 Binary files a/References/Casanova_2020.pdf and b/References/Casanova_2020.pdf differ