Table CBD D2h
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@ -254,20 +254,111 @@ Despite the fact that excited states are involved in ubiquitious processes such
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\section{Computational Details}
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\label{sec:compdet}
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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. In both structures the CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. Spin-flip techniques are broadly accessible and here, among them, we explore equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), configuration interaction singles (CIS), algebraic-diagrammatic construction (ADC) scheme and TD-DFT. The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1. Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1. The BLYP, B3LYP, PBE0 and BH\&HLYP functionals are considered, they contain 0\%, 20\%, 25$\%$, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. We also have done spin-flip TD-DFT calculations using RSH functionals as: CAM-B3LYP, LC-$\omega$PBE08 and $\omega$B97X-V. The main difference here between these RSHs functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V. To complete the use of spin-flip TD-DFT we also considered GH meta-GGA functional M06-2X, RSH meta-GGA functional M11 and DH functionals B2PLYP and B2GPPLYP. EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1. Throughout all this work, spin-flip and spin-conserved calculations are performed with a UHF reference.
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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. In both structures the CBD has a singlet ground state, for the spin-flip calculations we consider the lowest triplet state as reference. Spin-flip techniques are broadly accessible and here, among them, we explore equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), configuration interaction singles (CIS), algebraic-diagrammatic construction (ADC) scheme and TD-DFT. The standard and extended spin-flip ADC(2) (SF-ADC(2)-s and SF-ADC(2)-x respectively) and SF-ADC(3) are performed using Q-CHEM 5.2.1. Spin-flip TD-DFT calculations are also performed using Q-CHEM 5.2.1. The BLYP, B3LYP, PBE0 and BH\&HLYP functionals are considered, they contain 0\%, 20\%, 25$\%$, 50\% of exact exchange and are labeled, respectively, as SF-BLYP, SF-B3LYP, SF-PBE0, SF-BH\&HLYP. We also have done spin-flip TD-DFT calculations using RSH functionals as: CAM-B3LYP, LC-$\omega$PBE08 and $\omega$B97X-V. The main difference here between these RSHs functionals is the amount of exact-exchange at long-range: 75$\%$ for CAM-B3LYP and 100$\%$ for LC-$\omega$PBE08 and $\omega$B97X-V. To complete the use of spin-flip TD-DFT we also considered GH meta-GGA functional M06-2X, RSH meta-GGA functional M11 and DH functionals B2PLYP and B2GPPLYP. EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1. Throughout all this work, spin-flip and spin-conserved calculations are performed with a UHF reference.
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\section{Results and discussion}
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\label{sec:res}
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As said in \ref{sec:intro} we study both excited states and automerization barrier. Excited states under investigation are represented in Fig. \ref{fig:CBD} but not only, we also study higher excited states.
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%================================================
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\subsection{Excited States}
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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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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_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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& aug-cc-pVDZ & $1.487$ & $3.721$ & $5.348$ \\
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& aug-cc-pVTZ & $1.472$ & $3.701$ & $5.342$ \\
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& aug-cc-pVQZ & $1.471$ & $3.702$ & $5.342$ \\[0.1cm]
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SF-TD-B3LYP & 6-31+G(d) & $1.706$ & $2.211$ & $3.993$ \\
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& aug-cc-pVDZ & $1.706$ & $2.204$ & $3.992$ \\
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& aug-cc-pVTZ & $1.703$ & $2.199$ & $3.988$ \\
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& aug-cc-pVQZ & $1.703$ & $2.199$ & $3.989$\\[0.1cm]
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SF-TD-PBE0 & 6-31+G(d) & $1.687$ & $2.314$ & $4.089$ \\
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& aug-cc-pVDZ & $1.684$ & $2.301$ & $4.085$ \\
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& aug-cc-pVTZ & $1.682$ & $2.296$ & $4.081$ \\
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& aug-cc-pVQZ & $1.682$ & $2.296$ & $4.079$\\[0.1cm]
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SF-TD-BHHLYP & 6-31+G(d) & $1.552$ & $2.779$ & $4.428$ \\
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& aug-cc-pVDZ & $1.546$ & $2.744$ & $4.422$ \\
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& aug-cc-pVTZ & $1.540$ & $2.732$ & $4.492$ \\
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& aug-cc-pVQZ & $1.540$ & $2.732$ & $4.415$ \\[0.1cm]
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SF-TD-M06-2X & 6-31+G(d) & $1.477$ & $2.835$ & $4.378$ \\
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& aug-cc-pVDZ & $1.467$ & $2.785$ & $4.360$ \\
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& aug-cc-pVTZ & $1.462$ & $2.771$ & $4.357$ \\
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& aug-cc-pVQZ & $1.458$ & $2.771$ & $4.352$ \\[0.1cm]
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SF-TD-CAM-B3LYP & 6-31+G(d) & $1.750$ & $2.337$ & $3.315$ \\
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& aug-cc-pVDZ & $1.745$ & $2.323$ & $4.140$ \\
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& aug-cc-pVTZ & $1.742$ & $2.318$ & $4.138$ \\
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& aug-cc-pVQZ & $1.743$ & $2.319$ & $4.138$ \\[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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& aug-cc-pVDZ & $1.800$ & $2.356$ & $4.217$ \\
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& aug-cc-pVTZ & $1.797$ & $2.351$ & $4.213$ \\[0.1cm]
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SF-TD-M11 & 6-31+G(d) & $1.566$ & $2.687$ & $4.292$ \\
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& aug-cc-pVDZ & $1.546$ & $2.640$ & $4.267$ \\
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& aug-cc-pVTZ & $1.559$ & $2.651$ & $4.300$ \\
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& aug-cc-pVQZ & $1.557$ & $2.650$ & $4.299$ \\[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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& aug-cc-pVDZ & $1.897$ & $2.415$ & $4.346$ \\
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& aug-cc-pVTZ & $1.897$ & $2.415$ & $4.348$ \\
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& aug-cc-pVQZ & $1.897$ & $2.415$ & $4.348$ \\[0.1cm]
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SF-TD-B2PLYP & 6-31+G(d) & $1.538$ & $2.827$ & $4.462$ \\
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& aug-cc-pVDZ & $1.531$ & $2.788$ & $4.455$ \\
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& aug-cc-pVTZ & $1.525$ & $2.776$ & $4.448$ \\[0.1cm]
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SF-ADC(2)-s & 6-31+G(d) & $1.577$ & $3.303$ & $4.196$ \\
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& aug-cc-pVDZ & $1.513$ & $3.116$ & $4.114$ \\
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& aug-cc-pVTZ & $1.531$ & $3.099$ & $4.131$ \\
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& aug-cc-pVQZ & $1.544$ & $3.101$ & $4.140$ \\[0.1cm]
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SF-ADC(2)-x & 6-31+G(d) & $1.557$ & $3.232$ & $3.728$ \\
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& aug-cc-pVDZ & $1.524$ & $3.039$ & $3.681$ \\
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& aug-cc-pVTZ & $1.539$ & $3.031$ & $3.703$ \\[0.1cm]
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SF-ADC(3) & 6-31+G(d) & $1.435$ & $3.352$ & $4.242$ \\
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& aug-cc-pVDZ & $1.422$ & $3.180$ & $4.208$ \\
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& aug-cc-pVTZ & $1.419$ & $3.162$ & $4.224$ \\[0.1cm]
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SF-EOM-CCSD & 6-31+G(d) & $1.663$ & $3.515$ & $4.275$ \\
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& aug-cc-pVDZ & $1.611$ & $3.315$ & $3.856$ \\
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& aug-cc-pVTZ & $1.609$ & $3.293$ & $4.245$ \\[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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& aug-cc-pVDZ & $1.464$ & $3.156$ & $4.027$ \\
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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 II %%%
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\begin{table}
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\caption{
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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.
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\label{tab:sf_D4h}}
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\begin{ruledtabular}
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\begin{tabular}{lrrr}
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& \mc{3}{c}{Excitation energies (eV)} \\
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\cline{2-4}
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Method & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ \\
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\hline
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\end{tabular}
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\end{ruledtabular}
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\end{table}
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%%% %%% %%% %%%
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%================================================
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%================================================
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\subsection{Automerization}
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\subsection{Automerization Barrier}
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%================================================
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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