TBE table
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@ -327,7 +327,7 @@ Two different sets of geometries obtained with different level of theory are con
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\subsection{Autoisomerization barrier}
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\subsection{Autoisomerization barrier}
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\label{sec:auto}
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\label{sec:auto}
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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.
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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 8-9 \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 0.1-0.2 \kcalmol . The energy difference between the M11 and the M06-2X functionals is larger with 0.6-0.9 \kcalmol for the AVXZ bases and with 1.7 \kcalmol for the 6-31+G(d) basis. For the SF-ADC methods the energy differences are smaller with 1.7-2.0 \kcalmol between the ADC(2)-s and the ADC(2)-x schemes, 0.9-1.6 \kcalmol between the ADC(2)-s and the ADC(3) schemes and 0.4-0.8 \kcalmol between the ADC(2)-x and the ADC(3) schemes.
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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.
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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.
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%%% TABLE I %%%
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%%% TABLE I %%%
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@ -342,16 +342,17 @@ Then we compare results for multireference methods, we can see a difference of a
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\hline
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\hline
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%SF-CIS & $2.64$ & $2.82$ & $3.43$ & $3.43$ \\
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%SF-CIS & $2.64$ & $2.82$ & $3.43$ & $3.43$ \\
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%SF-TD-BLYP & $23.57$ & $23.62$ & $24.23$ & $24.22$ \\
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%SF-TD-BLYP & $23.57$ & $23.62$ & $24.23$ & $24.22$ \\
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SF-TD-B3LYP & $18.84$ & $18.93$ & $19.57$ & $19.57$ \\
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SF-TD-B3LYP & $18.59$ & $18.64$ & $19.34$ & $19.34$ \\
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SF-TD-PBE0 & $17.31$ & $17.36$ & $18.01$ & $18.00$ \\
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SF-TD-PBE0& $17.18$ & $17.19$ & $17.88$ & $17.88$ \\
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SF-TD-BH\&HLYP & $11.90$ & $12.07$ & $12.73$ & $12.73$ \\
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SF-TD-BHHLYP & $11.90$ & $12.02$ & $12.72$ & $12.73$ \\
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SF-TD-M06-2X & $9.34$ & $9.68$ & $10.39$ & $10.40$ \\
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SF-TD-M06-2X & $9.32$ & $9.62$ & $10.35$ & $10.37$ \\
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SF-TD-CAM-B3LYP & $18.21$ & $18.30$ & $18.98$ & $18.97$ \\
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SF-TD-CAM-B3LYP& $18.05$ & $18.10$ & $18.83$ & $18.83$ \\
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SF-TD-$\omega$B97X-V & $18.46$ & $18.48$ & $19.14$ & $19.12$ \\
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SF-TD-$\omega$B97X-V & $18.26$ & $18.24$ & $18.94$ & $18.92$ \\
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SF-TD-M11 & $11.13$ & $10.38$ & $11.28$ & $11.19$ \\
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SF-TD-M11 & $11.03$ & $10.25$ & $11.22$ & $11.12$ \\
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SF-ADC(2)-s & $6.69$ & $7.15$ & $8.64$ & $8.85$ \\
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SF-TD-LC-$\omega$PBE08 & $19.05$ & $18.98$ & $19.74$ & $19.71$ \\
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SF-ADC(2)-x & $8.66$ & $9.15$ & $10.40$ & \\
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SF-ADC2-s & $6.69$ & $6.98$ & $8.63$ & \\
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SF-ADC(3) & $8.06$ & $8.76$ & $9.58$ & \\
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SF-ADC2-x & $8.63$ & $8.96$ &$10.37$ & \\
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SF-ADC3 & $8.03$ & $8.54$ & $9.58$ \\
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CASSCF(12,12) & $10.19$ & $10.75$ & $11.59$ & $11.62$ \\
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CASSCF(12,12) & $10.19$ & $10.75$ & $11.59$ & $11.62$ \\
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CASPT2(12,12) & $7.24$ & $7.53$ & $8.51$ & $8.71$ \\
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CASPT2(12,12) & $7.24$ & $7.53$ & $8.51$ & $8.71$ \\
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NEVPT2(12,12) & $7.12$ & $7.33$ & $8.28$ & $8.49$ \\
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NEVPT2(12,12) & $7.12$ & $7.33$ & $8.28$ & $8.49$ \\
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@ -457,7 +458,8 @@ SF-TD-CAM-B3LYP & 6-31+G(d) & $1.750$ & $2.337$ & $4.140$ \\
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& AVQZ & $1.743$ & $2.319$ & $4.138$ \\[0.1cm]
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& AVQZ & $1.743$ & $2.319$ & $4.138$ \\[0.1cm]
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SF-TD-$\omega$B97X-V & 6-31+G(d) & $1.810$ & $2.377$ & $4.220$ \\
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SF-TD-$\omega$B97X-V & 6-31+G(d) & $1.810$ & $2.377$ & $4.220$ \\
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& AVDZ & $1.800$ & $2.356$ & $4.217$ \\
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& AVDZ & $1.800$ & $2.356$ & $4.217$ \\
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& AVTZ & $1.797$ & $2.351$ & $4.213$ \\[0.1cm]
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& AVTZ & $1.797$ & $2.351$ & $4.213$ \\
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& AVQZ & $1.797$ & $2.351$ & $4.213$ \\[0.1cm]
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SF-TD-LC-$\omega $PBE08 & 6-31+G(d) & $1.917$ & $2.445$ & $4.353$ \\
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SF-TD-LC-$\omega $PBE08 & 6-31+G(d) & $1.917$ & $2.445$ & $4.353$ \\
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& AVDZ & $1.897$ & $2.415$ & $4.346$ \\
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& AVDZ & $1.897$ & $2.415$ & $4.346$ \\
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& AVTZ & $1.897$ & $2.415$ & $4.348$ \\
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& AVTZ & $1.897$ & $2.415$ & $4.348$ \\
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@ -480,11 +482,11 @@ SF-ADC(2)-x & 6-31+G(d) & $1.557$ & $3.232$ & $3.728$ \\
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SF-ADC(3) & 6-31+G(d) & $1.435$ & $3.352$ & $4.242$ \\
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SF-ADC(3) & 6-31+G(d) & $1.435$ & $3.352$ & $4.242$ \\
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& AVDZ & $1.422$ & $3.180$ & $4.208$ \\
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& AVDZ & $1.422$ & $3.180$ & $4.208$ \\
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& AVTZ & $1.419$ & $3.162$ & $4.224$ \\[0.1cm]
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& AVTZ & $1.419$ & $3.162$ & $4.224$ \\[0.1cm]
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SF-EOM-CCSD & 6-31+G(d) & $1.663$ & $3.515$ & $4.275$ \\
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% SF-EOM-CCSD & 6-31+G(d) & $1.663$ & $3.515$ & $4.275$ \\
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& AVDZ & $1.611$ & $3.315$ & $3.856$ \\
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% & AVDZ & $1.611$ & $3.315$ & $3.856$ \\
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& AVTZ & $1.609$ & $3.293$ & $4.245$ \\[0.1cm]
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% & AVTZ & $1.609$ & $3.293$ & $4.245$ \\[0.1cm]
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SF-EOM-CC(2,3) & 6-31+G(d) & $1.490$ & $3.333$ & $4.061$ \\
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%SF-EOM-CC(2,3) & 6-31+G(d) & $1.490$ & $3.333$ & $4.061$ \\
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& AVDZ & $1.464$ & $3.156$ & $4.027$ \\
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%& AVDZ & $1.464$ & $3.156$ & $4.027$ \\
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\end{tabular}
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\end{tabular}
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\end{ruledtabular}
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\end{ruledtabular}
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@ -492,42 +494,7 @@ SF-EOM-CC(2,3) & 6-31+G(d) & $1.490$ & $3.333$ & $4.061$ \\
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\end{squeezetable}
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\end{squeezetable}
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%%% %%% %%% %%%
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%%% %%% %%% %%%
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%%% TABLE III %%%
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%\begin{squeezetable}
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%\begin{table}
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% \caption{
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% Spin-flip CIS, ADC and CC 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.
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% \label{tab:sf_adc_D2h}}
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% \begin{ruledtabular}
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% \begin{tabular}{llrrr}
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% & \mc{4}{r}{Excitation energies (eV)} \hspace{0.5cm}\\
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% \cline{3-5}
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% Method & Basis & $1\,{}^3B_{1g}$ & $1\,{}^1B_{1g}$ & $2\,{}^1A_{g}$ \\
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% \hline
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% SF-CIS & 6-31+G(d) & $1.514$ & $3.854$ & $5.379$ \\
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% & AVDZ & $1.487$ & $3.721$ & $5.348$ \\
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% & AVTZ & $1.472$ & $3.701$ & $5.342$ \\
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% & AVQZ & $1.471$ & $3.702$ & $5.342$ \\[0.1cm]
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% SF-ADC(2)-s & 6-31+G(d) & $1.577$ & $3.303$ & $4.196$ \\
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% & AVDZ & $1.513$ & $3.116$ & $4.114$ \\
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% & AVTZ & $1.531$ & $3.099$ & $4.131$ \\
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% & AVQZ & $1.544$ & $3.101$ & $4.140$ \\[0.1cm]
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%SF-ADC(2)-x & 6-31+G(d) & $1.557$ & $3.232$ & $3.728$ \\
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% & AVDZ & $1.524$ & $3.039$ & $3.681$ \\
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% & AVTZ & $1.539$ & $3.031$ & $3.703$ \\[0.1cm]
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%SF-ADC(3) & 6-31+G(d) & $1.435$ & $3.352$ & $4.242$ \\
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% & AVDZ & $1.422$ & $3.180$ & $4.208$ \\
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% & AVTZ & $1.419$ & $3.162$ & $4.224$ \\[0.1cm]
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% SF-EOM-CCSD & 6-31+G(d) & $1.663$ & $3.515$ & $4.275$ \\
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% & AVDZ & $1.611$ & $3.315$ & $3.856$ \\
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% & AVTZ & $1.609$ & $3.293$ & $4.245$ \\[0.1cm]
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%SF-EOM-CC(2,3) & 6-31+G(d) & $1.490$ & $3.333$ & $4.061$ \\
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%& AVDZ & $1.464$ & $3.156$ & $4.027$ \\
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% \end{tabular}
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% \end{ruledtabular}
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%\end{table}
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%\end{squeezetable}
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%%% %%% %%% %%%
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%%% TABLE IV %%%
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%%% TABLE IV %%%
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\begin{squeezetable}
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\begin{squeezetable}
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@ -611,54 +578,6 @@ CIPSI &6-31+G(d)& $1.486\pm 0.005$ & $3.348\pm 0.024$ & $4.084\pm 0.012$ \\
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\end{squeezetable}
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\end{squeezetable}
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%%% %%% %%% %%%
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%%% %%% %%% %%%
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%%% TABLE I %%%
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\begin{squeezetable}
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\begin{table*}
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\caption{}
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\label{tab:TBE_D2h}
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\begin{ruledtabular}
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\begin{tabular}{llrrr}
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Method & $1\,{}^3B_{1g}$ & $1\,{}^1B_{1g}$ & $2\,{}^1A_{g}$ & TBE (AVTZ) \\
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\hline
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SF-TD-B3LYP & & & & \\
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SF-TD-PBE0 & & & & \\
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SF-TD-BH\&HLYP & & & & \\
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SF-TD-M06-2X & & & & \\
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SF-TD-CAM-B3LYP & & & & \\
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SF-TD-$\omega$B97X-V & & & & \\
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SF-TD-M11 & & & & \\
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SF-ADC2-s & & & & \\
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SF-ADC2-x & & & & \\
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SF-ADC3 & & & & \\
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CCSD & & & & \\
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CC3 & & & & \\
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CCSDT & & & & \\
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CC4 & & & & \\
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CCSDTQ & & & & \\
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SA2-CASSCF(4,4) & & & & \\
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CASPT2(4,4) & & & & \\
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XMS-CASPT2(4,4) & & & & \\
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SC-NEVPT2(4,4) & & & & \\
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PC-NEVPT2(4,4) & & & & \\
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MRCI(4,4) & & & & \\
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SA2-CASSCF(12,12) & & & & \\
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CASPT2(12,12) & & & & \\
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XMS-CASPT2(12,12) & & & & \\
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SC-NEVPT2(12,12) & & & & \\
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PC-NEVPT2(12,12) & & & & \\
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MRCI(12,12) & & & & \\
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CIPSI & & & & \\
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\end{tabular}
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\end{ruledtabular}
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\end{table*}
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\end{squeezetable}
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%%% %%% %%% %%%
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\subsubsection{D4h geometry}
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\subsubsection{D4h geometry}
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Table \ref{tab:sf_D4h} shows vertical energies obtained with spin-flip methods and Table \ref{tab:D4h} vertical energies obtained with standard methods. As for the previous geometry we start with the SF-TD-DFT results with hybrid functionals. We can first notice that for the B3LYP and the PBE0 functionals we have a wrong ordering of the first triplet state $1\,{}^3A_{2g}$ and the ground state $\text{X}\,{}^1B_{1g}$. We retrieve the good ordering with the BH\&HLYP functional, so adding exact exchange to the functional allows us to have the right ordering between these two states. For the B3LYP and the PBE0 functionals we have that the energy differences for each states and for all bases are small with 0.004-0.007 eV for the triplet state $1\,{}^3A_{2g}$. We have 0.015-0.021 eV of energy difference for the $2\,{}^1A_{1g}$ state through all bases, we can notice that this state is around 0.13 eV (considering all bases) higher with the PBE0 functional. We can make the same observation for the $1\,{}^1B_{2g}$ state for the B3LYP and the PBE0 functionals, indeed we have small energy differences for all bases and the state is around 0.14-0.15 eV for the PBE0 functional. For the BH\&HLYP functional the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states are higher in energy than for the two other hybrid functionals with about 0.65-0.69 eV higher for the $2\,{}^1A_{1g}$ state and 0.75-0.77 eV for the $1\,{}^1B_{2g}$ state compared to the PBE0 functional. Then, we have the RSH functionals CAM-B3LYP, $\omega$B97X-V and LC-$\omega$PBE08. For these functionals the vertical energies are similar for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states with a maximum energy difference of 0.01-0.02 eV for the $2\,{}^1A_{1g}$ state and 0.005-0.009 eV for the $1\,{}^1B_{2g}$ state considering all bases. The maximum energy difference for the triplet state is larger with 0.047-0.057 eV for all bases. Note that the vertical energies obtained with the RSH functionals are close to the PBE0 ones except that we have the right ordering between the triplet state $1\,{}^3A_{2g}$ and the ground state $\text{X}\,{}^1B_{1g}$. The M06-2X results are closer to the BH\&HLYP ones but the M06-2X vertical energies are always higher than the BH\&HLYP ones. We can notice that the M06-2X energies for the $2\,{}^1A_{1g}$ state are close to the BH\&HLYP energies for the $1\,{}^1B_{2g}$ state. For these two states, when we compared the results obtained with the M06-2X and the BH\&HLYP functionals, we have an energy difference of 0.16-0.17 eV for the $2\,{}^1A_{1g}$ state and 0.17-0.18 eV for the $1\,{}^1B_{2g}$ state considering all bases. For the triplet state $1\,{}^3A_{2g}$ the energy differences are smaller with 0.03-0.04 eV for all bases. The M11 vertical energies are very close to the M06-2X ones for the triplet state with a maximum energy difference of 0.003 eV considering all bases, and are closer to the BH\&HLYP results for the two other states with 0.06-0.07 eV and 0.07-0.08 eV of energy difference for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, respectively. Then we discuss the various ADC scheme results, note that we were not able to obtain the vertical energies with the AVQZ basis due to computational resources. For the ADC(2)-s scheme we can see that the energy difference for the triplet state are smaller than for the two other states, indeed we have an energy difference of 0.09 eV for the triplet state whereas we have 0.15 eV and 0.25 eV for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, again when considering all bases. The energy difference for each state and through the bases are similar for the two other ADC schemes. We can notice a large variation of the vertical energies for the $2\,{}^1A_{1g}$ state between ADC(2)-s and ADC(2)-x with around 0.52-0.58 eV through all bases. The ADC(3) vertical energies are very similar to the ADC(2) ones for the $1\,{}^1B_{2g}$ state with an energy difference of 0.01-0.02 eV for all bases, whereas we have an energy difference of 0.04-0.11 eV and 0.17-0.22 eV for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, respectively.
|
Table \ref{tab:sf_D4h} shows vertical energies obtained with spin-flip methods and Table \ref{tab:D4h} vertical energies obtained with standard methods. As for the previous geometry we start with the SF-TD-DFT results with hybrid functionals. We can first notice that for the B3LYP and the PBE0 functionals we have a wrong ordering of the first triplet state $1\,{}^3A_{2g}$ and the ground state $\text{X}\,{}^1B_{1g}$. We retrieve the good ordering with the BH\&HLYP functional, so adding exact exchange to the functional allows us to have the right ordering between these two states. For the B3LYP and the PBE0 functionals we have that the energy differences for each states and for all bases are small with 0.004-0.007 eV for the triplet state $1\,{}^3A_{2g}$. We have 0.015-0.021 eV of energy difference for the $2\,{}^1A_{1g}$ state through all bases, we can notice that this state is around 0.13 eV (considering all bases) higher with the PBE0 functional. We can make the same observation for the $1\,{}^1B_{2g}$ state for the B3LYP and the PBE0 functionals, indeed we have small energy differences for all bases and the state is around 0.14-0.15 eV for the PBE0 functional. For the BH\&HLYP functional the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states are higher in energy than for the two other hybrid functionals with about 0.65-0.69 eV higher for the $2\,{}^1A_{1g}$ state and 0.75-0.77 eV for the $1\,{}^1B_{2g}$ state compared to the PBE0 functional. Then, we have the RSH functionals CAM-B3LYP, $\omega$B97X-V and LC-$\omega$PBE08. For these functionals the vertical energies are similar for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states with a maximum energy difference of 0.01-0.02 eV for the $2\,{}^1A_{1g}$ state and 0.005-0.009 eV for the $1\,{}^1B_{2g}$ state considering all bases. The maximum energy difference for the triplet state is larger with 0.047-0.057 eV for all bases. Note that the vertical energies obtained with the RSH functionals are close to the PBE0 ones except that we have the right ordering between the triplet state $1\,{}^3A_{2g}$ and the ground state $\text{X}\,{}^1B_{1g}$. The M06-2X results are closer to the BH\&HLYP ones but the M06-2X vertical energies are always higher than the BH\&HLYP ones. We can notice that the M06-2X energies for the $2\,{}^1A_{1g}$ state are close to the BH\&HLYP energies for the $1\,{}^1B_{2g}$ state. For these two states, when we compared the results obtained with the M06-2X and the BH\&HLYP functionals, we have an energy difference of 0.16-0.17 eV for the $2\,{}^1A_{1g}$ state and 0.17-0.18 eV for the $1\,{}^1B_{2g}$ state considering all bases. For the triplet state $1\,{}^3A_{2g}$ the energy differences are smaller with 0.03-0.04 eV for all bases. The M11 vertical energies are very close to the M06-2X ones for the triplet state with a maximum energy difference of 0.003 eV considering all bases, and are closer to the BH\&HLYP results for the two other states with 0.06-0.07 eV and 0.07-0.08 eV of energy difference for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, respectively. Then we discuss the various ADC scheme results, note that we were not able to obtain the vertical energies with the AVQZ basis due to computational resources. For the ADC(2)-s scheme we can see that the energy difference for the triplet state are smaller than for the two other states, indeed we have an energy difference of 0.09 eV for the triplet state whereas we have 0.15 eV and 0.25 eV for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, again when considering all bases. The energy difference for each state and through the bases are similar for the two other ADC schemes. We can notice a large variation of the vertical energies for the $2\,{}^1A_{1g}$ state between ADC(2)-s and ADC(2)-x with around 0.52-0.58 eV through all bases. The ADC(3) vertical energies are very similar to the ADC(2) ones for the $1\,{}^1B_{2g}$ state with an energy difference of 0.01-0.02 eV for all bases, whereas we have an energy difference of 0.04-0.11 eV and 0.17-0.22 eV for the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states, respectively.
|
||||||
@ -745,10 +664,10 @@ SF-ADC(3) & 6-31+G(d) & $0.123$ & $1.650$ & $2.078$ \\
|
|||||||
\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 & $0.100$ & $1.650$ & \\
|
& AVDZ & $0.100$ & $1.650$ & \\
|
||||||
% & AVTZ & $0.085$ & $1.600$ & \\
|
& 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 & & $1.662$ & $2.720$ \\[0.1cm]
|
& AVTZ & & $1.662$ & $2.720$ \\[0.1cm]
|
||||||
@ -809,56 +728,57 @@ CIPSI & 6-31+G(d) & $0.2010\pm 0.0030$ & $1.602\pm 0.007$ & $2.13\pm 0.04$ \\
|
|||||||
\end{squeezetable}
|
\end{squeezetable}
|
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%%% %%% %%% %%%
|
%%% %%% %%% %%%
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||||||
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|
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|
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|
|
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%%% TABLE I %%%
|
%%% TABLE I %%%
|
||||||
\begin{squeezetable}
|
\begin{squeezetable}
|
||||||
\begin{table*}
|
\begin{table*}
|
||||||
\caption{}
|
\caption{}
|
||||||
|
|
||||||
\label{tab:TBE_D4h}
|
\label{tab:TBE}
|
||||||
\begin{ruledtabular}
|
\begin{ruledtabular}
|
||||||
\begin{tabular}{llrrr}
|
|
||||||
Method & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ & TBE (AVTZ) \\
|
\begin{tabular}{*{1}{*{7}{l}}}
|
||||||
\hline
|
Method & $1\,{}^3B_{1g} (D_{2h})$ & $1\,{}^1B_{1g} (D_{2h})$ & $2\,{}^1A_{g} (D_{2h})$ & $1\,{}^3A_{2g} (D_{4h})$ & $2\,{}^1A_{1g} (D_{4h})$ & $1\,{}^1B_{2g} (D_{4h})$ \\
|
||||||
|
\hline
|
||||||
SF-TD-B3LYP & & & & \\
|
SF-TD-B3LYP & $1.703$ & $0.926$ & $0.161$ & $0.164$ & $1.028$ & $1.501$ \\
|
||||||
SF-TD-PBE0 & & & & \\
|
SF-TD-PBE0 & $1.682$ & $0.829$ & $0.068$ & $0.163$ & $0.903$ & $1.357$ \\
|
||||||
SF-TD-BH\&HLYP & & & & \\
|
SF-TD-BHHLYP & $1.540$ & $0.393$ & $0.343$ & $0.099$ & $0.251$ & $0.603$ \\
|
||||||
SF-TD-M06-2X & & & & \\
|
SF-TD-M06-2X & $1.462$ & $0.354$ & $0.208$ & $0.066$ & $0.096$ & $0.432$ \\
|
||||||
SF-TD-CAM-B3LYP & & & & \\
|
SF-TD-CAM-B3LYP & $1.742$ & $0.807$ & $0.011$ & $0.134$ & $0.920$ & $1.370$ \\
|
||||||
SF-TD-$\omega$B97X-V & & & & \\
|
SF-TD-$\omega $B97X-V & $1.797$ & $0.774$ & $0.064$ & $0.117$ & $0.928$ & $1.372$ \\
|
||||||
SF-TD-M11 & & & & \\
|
SF-TD-M11 & $1.559$ & $0.474$ & $0.151$ & $0.063$ & $0.312$ & $0.675$ \\
|
||||||
SF-ADC2-s & & & & \\
|
SF-TD-LC-$\omega $PBE08 & $1.897$ & $0.710$ & $0.199$ & $0.086$ & $0.939$ & $1.376$ \\
|
||||||
SF-ADC2-x & & & & \\
|
SF-ADC(2)-s & $1.531$ & $0.026$ & $0.018$ & $0.112$ & $0.112$ & $0.190$ \\
|
||||||
SF-ADC3 & & & & \\
|
SF-ADC(2)-x & $1.539$ & $0.094$ & $0.446$ & $0.067$ & $0.409$ & $0.303$ \\
|
||||||
CCSD & & & & \\
|
SF-ADC(3) & $1.419$ & $0.037$ & $0.074$ & $0.064$ & $0.075$ & $0.181$ \\
|
||||||
CC3 & & & & \\
|
CCSD & & & & $0.059$ & $0.100$ & \\
|
||||||
CCSDT & & & & \\
|
CC3 & $1.402$ & $0.006$ & $0.628$ & & $0.162$ & $0.686$ \\
|
||||||
CC4 & & & & \\
|
CCSDT & $1.411$ & $0.014$ & $0.280$ & $0.005$ & $0.131$ & $0.503$ \\
|
||||||
CCSDTQ & & & & \\
|
CC4 & & $0.003$ & $0.006$ & & $0.011$ & $0.013$ \\
|
||||||
SA2-CASSCF(4,4) & & & & \\
|
CCSDTQ & $\text{}$ & $0.$ & $0.$ & $0.$ & $0.$ & $0.$ \\
|
||||||
CASPT2(4,4) & & & & \\
|
SA2-CASSCF(4,4) & $1.670$ & $1.421$ & $0.292$ & $0.290$ & $0.734$ & $1.390$ \\
|
||||||
XMS-CASPT2(4,4) & & & & \\
|
$\text{CASPT2(4,4)}$ & $1.412$ & $0.202$ & $0.077$ & $0.016$ & $0.006$ & $0.399$ \\
|
||||||
SC-NEVPT2(4,4) & & & & \\
|
$\text{XMS-CASPT2(4,4)}$ & & & $0.035$ & & & \\
|
||||||
PC-NEVPT2(4,4) & & & & \\
|
$\text{SC-NEVPT2(4,4)}$ & $1.379$ & $0.703$ & $0.041$ & $0.120$ & $0.072$ & $0.979$ \\
|
||||||
MRCI(4,4) & & & & \\
|
$\text{PC-NEVPT2(4,4)}$ & $1.382$ & $0.757$ & $0.066$ & $0.118$ & $0.097$ & $1.031$ \\
|
||||||
SA2-CASSCF(12,12) & & & & \\
|
$\text{MRCI(4,4)}$ & $1.568$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\
|
||||||
CASPT2(12,12) & & & & \\
|
$\text{SA2-CASSCF(12,12)}$ & $1.686$ & $0.719$ & $0.068$ & $0.226$ & $0.443$ & $0.600$ \\
|
||||||
XMS-CASPT2(12,12) & & & & \\
|
$\text{CASPT2(12,12)}$ & $1.48$ & $0.058$ & $0.106$ & $0.039$ & $0.038$ & $0.108$ \\
|
||||||
SC-NEVPT2(12,12) & & & & \\
|
$\text{XMS-CASPT2(12,12)}$ & & & $0.090$ & & & \\
|
||||||
PC-NEVPT2(12,12) & & & & \\
|
$\text{SC-NEVPT2(12,12)}$ & $1.501$ & $0.063$ & $0.063$ & $0.021$ & $0.046$ & $0.142$ \\
|
||||||
MRCI(12,12) & & & & \\
|
$\text{PC-NEVPT2(12,12)}$ & $1.462$ & $0.062$ & $0.093$ & $0.013$ & $0.024$ & $0.278$ \\
|
||||||
CIPSI & & & & \\
|
MRCI(12,12) & & & & & & \\
|
||||||
|
CIPSI & $1.461\pm 0.030$ & $0.017\pm 0.035$ & $0.120\pm 0.09$ & $0.025\pm 0.029$ & $0.130\pm 0.05$ & \\
|
||||||
|
\bf{TBE} & & $3.125$ & $4.149$ & $0.144$ & $1.500$ & $2.034$ \\
|
||||||
|
\end{tabular}
|
||||||
|
|
||||||
|
|
||||||
\end{tabular}
|
|
||||||
\end{ruledtabular}
|
\end{ruledtabular}
|
||||||
|
|
||||||
\end{table*}
|
\end{table*}
|
||||||
\end{squeezetable}
|
\end{squeezetable}
|
||||||
%%% %%% %%% %%%
|
%%% %%% %%% %%%
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
%================================================
|
%================================================
|
||||||
|
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user