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Manuscript update D2h excited states

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EnzoMonino 2021-12-23 18:39:12 +01:00
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Manuscript/CBD.tex
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@ -272,7 +272,7 @@ State-averaged complete-active-space self-consistent field (SA-CASSCF) calculati
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Spin-Flip}
\label{sec:sf}
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. EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1.
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 B3LYP, PBE0 and BH\&HLYP Hybrid GGA functionals are considered, they contain 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 Range-Separated Hybrid (RSH) functionals as: CAM-B3LYP, LC-$\omega$PBE08 and $\omega$B97X-V. The main difference here between these RSH 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 the Hybrid meta-GGA functional M06-2X and the RSH meta-GGA functional M11. EOM-SF-CCSD and EOM-SF-CC(2,3) are also performed with Q-CHEM 5.2.1.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -292,16 +292,27 @@ Two different sets of geometries obtained with different level of theory are con
%%% 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.}
\caption{Optimized geometries of the CBD molecule. 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
$D_{2h}$\\
\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]
CCSD(T)/cc-pVTZ & 1.343 & 1.566 & 1.074 & 135.09 \fnm[2]\\
\hline
$D_{4h} ({}^1 B_{1g})$ \\
\hline
CASPT2(12,12)/AVTZ & 1.449 & 1.449 & 1.076 & 135.00 \\
\hline
$D_{4h} ({}^3 A_{2g})$ \\
\hline
CASPT2(12,12)/AVTZ & 1.445 & 1.445 & 1.076 & 135.00 \\
RO-CCSD(T)/AVTZ & 1.439 & 1.439 & 1.075 & 135.00
\end{tabular}
\end{ruledtabular}
\fnt[1]{Angle between the C-H bond and the C=C bond.}
@ -349,7 +360,7 @@ 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 & $7.91\pm 0.21$ & $8.58\pm 0.14$ & & \\
CIPSI & $7.91\pm 0.21$ & $8.58\pm 0.14$ & & \\
\end{tabular}
@ -401,6 +412,10 @@ CCSDTQ & $7.51$ & $\left[ 7.89\right]$\fnm[4]& $\left[ 8.93\right]$\fnm[5]& $\le
All the calculations are performed using four basis set, the 6-31+G(d) basis and the aug-cc-pVXZ with X$=$D, T, Q. In the following we will use the notation AVXZ for the aug-cc-pVXZ basis, again with X$=$D, T, Q.
\subsubsection{D2h geometry}
Table \ref{tab:sf_tddft_D2h} shows the results obtained for the vertical transition energies using spin-flip methods and Table \ref{tab:D2h} shows the results obtained with the standard methods. We discuss first the SF-TD-DFT values with hybrid functionals. For the B3LYP functional we can see that the energy differences for each state and throughout all bases are small with the largest one for the $1\,{}^3B_{1g}$ state with 0.012 eV. The same observation can be done for the PBE0 and BH\&HLYP functionals, we can also oberve that adding exact exchange to the functional (20\% of exact exchange for B3LYP, 25\% for PBE0 and 50\% for BH\&HLYP increase the energy difference between the $1\,{}^1B_{1g}$ and the $1\,{}^3B_{1g}$ states. Put another way, increasing the amount of exact exchange in the functional reduces the energy difference between the $1\,{}^3B_{1g}$ and the $\text{X}\,{}^1A_{g}$ states. We can also notice that the vertical energies of the different states do not vary in the same way when adding exact exchange, for instance the energy variation for the $1\,{}^3B_{1g}$ state from PBE0 to BH\&HLYP is around 0.1 eV whereas for the $1\,{}^1B_{1g}$ and the $1\,{}^1A_{1g}$ states this energy variation is about 0.4-0.5 eV and 0.34 eV respectively. For the RSH functionals we can not make the same observation, indeed we can see that for the CAM-B3LYP functional we have that the energy difference between the $1\,{}^1B_{1g}$ and the $1\,{}^3B_{1g}$ states is larger than for the $\omega$B97X-V and LC-$\omega $PBE08 functionals despite the fact that the latter ones have a bigger amount of exact exchange. However we can observe that we have a small energy difference for each state throughout the bases and for each RSH functional. The M06-2X functional is an Hybrid meta-GGA functional and contains 54\% of Hartree-Fock exchange, we can compare the energies with the BH\&HLYP functional and we can see that the energy differences are small with around 0.03-0.08 eV. We can notice that the upper bound of 0.08 eV in the energy differences is due to the $1\,{}^3B_{1g}$ state.
Then we discuss the various ADC scheme (ADC(2)-s, ADC(2)-x and ADC(3)) results. For ADC(2) we have vertical energy differencies of about 0.03 eV for the $1\,{}^3B_{1g}$ state and around 0.06 eV for $1\,{}^1A_{1g}$ state throughout all bases. However for the $1\,{}^1B_{1g}$ state we have an energy difference of about 0.2 eV. For the ADC(2)-x and ADC(3) schemes the calculations with the AVQZ basis are not feasible with our resources. With ADC(2)-x we have similar vertical energies for the triplet and the $1\,{}^1B_{1g}$ states but for the $1\,{}^1A_{1g}$ state the energy difference between the ADC(2) and ADC(2)-x schemes is about 0.4-0.5 eV.
%%% TABLE II %%%
\begin{squeezetable}
@ -414,10 +429,10 @@ All the calculations are performed using four basis set, the 6-31+G(d) basis and
\cline{3-5}
Method & Basis & $1\,{}^3B_{1g}$ & $1\,{}^1B_{1g}$ & $2\,{}^1A_{g}$ \\
\hline
SF-TD-BLYP & 6-31+G(d) & $1.829$ & $1.926$ & $3.755$ \\
& AVDZ & $1.828$ & $1.927$ & $3.586$ \\
& AVTZ & $1.825$ & $1.927$ & $3.546$ \\
& AVQZ & $1.825$ & $1.927$ & $3.528$ \\[0.1cm]
% SF-TD-BLYP & 6-31+G(d) & $1.829$ & $1.926$ & $3.755$ \\
% & AVDZ & $1.828$ & $1.927$ & $3.586$ \\
% & AVTZ & $1.825$ & $1.927$ & $3.546$ \\
% & AVQZ & $1.825$ & $1.927$ & $3.528$ \\[0.1cm]
SF-TD-B3LYP & 6-31+G(d) & $1.706$ & $2.211$ & $3.993$ \\
& AVDZ & $1.706$ & $2.204$ & $3.992$ \\
& AVTZ & $1.703$ & $2.199$ & $3.988$ \\
@ -430,7 +445,7 @@ SF-TD-BH\&HLYP & 6-31+G(d) & $1.552$ & $2.779$ & $4.428$ \\
& AVDZ & $1.546$ & $2.744$ & $4.422$ \\
& AVTZ & $1.540$ & $2.732$ & $4.492$ \\
& AVQZ & $1.540$ & $2.732$ & $4.415$ \\[0.1cm]
SF-TD-M06-2X & 6-31+G(d) & $1.477$ & $2.835$ & $4.378$ \\
SF-TD-M06-2X & 6-31+G(d) & $1.477$ & $2.835$ & $4.378$ \\
& AVDZ & $1.467$ & $2.785$ & $4.360$ \\
& AVTZ & $1.462$ & $2.771$ & $4.357$ \\
& AVQZ & $1.458$ & $2.771$ & $4.352$ \\[0.1cm]
@ -441,14 +456,14 @@ SF-TD-CAM-B3LYP & 6-31+G(d) & $1.750$ & $2.337$ & $4.140$ \\
SF-TD-$\omega$B97X-V & 6-31+G(d) & $1.810$ & $2.377$ & $4.220$ \\
& AVDZ & $1.800$ & $2.356$ & $4.217$ \\
& AVTZ & $1.797$ & $2.351$ & $4.213$ \\[0.1cm]
SF-TD-LC-$\omega $PBE08 & 6-31+G(d) & $1.917$ & $2.445$ & $4.353$ \\
& AVDZ & $1.897$ & $2.415$ & $4.346$ \\
& AVTZ & $1.897$ & $2.415$ & $4.348$ \\
& AVQZ & $1.897$ & $2.415$ & $4.348$ \\[0.1cm]
SF-TD-M11 & 6-31+G(d) & $1.566$ & $2.687$ & $4.292$ \\
& AVDZ & $1.546$ & $2.640$ & $4.267$ \\
& AVTZ & $1.559$ & $2.651$ & $4.300$ \\
& AVQZ & $1.557$ & $2.650$ & $4.299$ \\[0.1cm]
SF-TD-LC-$\omega $PBE08 & 6-31+G(d) & $1.917$ & $2.445$ & $4.353$ \\
& AVDZ & $1.897$ & $2.415$ & $4.346$ \\
& AVTZ & $1.897$ & $2.415$ & $4.348$ \\
& AVQZ & $1.897$ & $2.415$ & $4.348$ \\[0.1cm]
%SF-CIS & 6-31+G(d) & $1.514$ & $3.854$ & $5.379$ \\
%& AVDZ & $1.487$ & $3.721$ & $5.348$ \\
%& AVTZ & $1.472$ & $3.701$ & $5.342$ \\