From 2da59d658e056430f3764f498ec8ef74e68296fe Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Sun, 10 Jan 2021 16:30:46 +0100 Subject: [PATCH] tables for Enzo --- Manuscript/sfBSE.tex | 68 +++++++++++++++++++++++++++++++++++++++++--- 1 file changed, 64 insertions(+), 4 deletions(-) diff --git a/Manuscript/sfBSE.tex b/Manuscript/sfBSE.tex index 04cb167..15257de 100644 --- a/Manuscript/sfBSE.tex +++ b/Manuscript/sfBSE.tex @@ -595,7 +595,7 @@ The TD-DFT calculations have been performed with Q-CHEM 5.2.1 \cite{qchem4} and \begin{table*} \caption{ Spin-flip excitations (in eV) of \ce{Be} obtained for various methods with the 6-31G basis. - The $GW$ calculations are performed with a HF starting point. + The $GW$ calculations are performed with an UHF starting point. \label{tab:Be}} \begin{ruledtabular} \begin{tabular}{lcccccccccccc} @@ -729,13 +729,73 @@ The TD-DFT calculations have been performed with Q-CHEM 5.2.1 \cite{qchem4} and \label{sec:CBD} %=============================== -Cyclobutadiene (CBD) is an interesting example as its electronic character of its ground state can be tune via geometrical deformation. \cite{Balkova_1994,Manohar_2008,Lefrancois_2015} +Cyclobutadiene (CBD) is an interesting example as its electronic character of its ground state can be tune via geometrical deformation. \cite{Balkova_1994,Manohar_2008,Lefrancois_2015,Casanova_2020} %with potential large spin contamination. -In its $D_{2h}$ rectangular $^1 A_g$ ground-state equilibrium geometry, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are non-degenerate, and the singlet ground state can be safely labeled as single-reference with well-defined doubly-occupied orbitals -However, in its $D_{4h}$ square-planar $^3 A_{2g}$ ground-state equilibrium geometry, the HOMO and LUMO are strictly degenerate, and the electronic ground state (which is still of singlet nature with $B_{1g}$ spatial symmetry, hence violating Hund's rule) is strongly multi-reference with singly occupied orbitals. +In its $D_{2h}$ rectangular $^1 A_g$ singlet ground-state equilibrium geometry, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are non-degenerate, and the singlet ground state can be safely labeled as single-reference with well-defined doubly-occupied orbitals +However, in its $D_{4h}$ square-planar $^3 A_{2g}$ triplet round-state equilibrium geometry, the HOMO and LUMO are strictly degenerate, and the electronic ground state (which is still of singlet nature with $B_{1g}$ spatial symmetry, hence violating Hund's rule) is strongly multi-reference with singly occupied orbitals. In this case, single-reference methods notoriously fail. Nonetheless, the lowest triplet state of symmetry $^3 A_{2g}$ remains of single-reference character and is then a perfect starting point for spin-flip calculations. +The $D_{2h}$ and $D_{4h}$ optimized geometries of the $^1 A_g$ and $^3 A_{2g}$ states of CBD have been extracted from Ref.~\onlinecite{Manohar_2008} and have been obtained at the CCSD(T)/cc-pVTZ level. +EOM-CCSD and SF-ADC calculations have been taken from Refs.~\onlinecite{Manohar_2008} and Ref.~\onlinecite{Lefrancois_2015}. +All of them have been obtained with a UHF reference like the SF-BSE calculations performed here. + +%%% TABLE ?? %%% +\begin{table} + \caption{ + Vertical excitation energies (with respect to the singlet $X\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{1g}$ states at the $D_{2h}$ rectangular equilibrium geometry of the $X\,{}^1 A_{g}$ singlet ground state. + \label{tab:CBD_D2h}} + \begin{ruledtabular} + \begin{tabular}{lccc} + & \mc{3}{c}{Excitation energies (eV)} \\ + \cline{2-4} + Method & $1\,{}^3B_{1g}$ & $1\,{}^1B_{1g}$ & $2\,{}^1A_{1g}$ \\ + \hline + EOM-SF-CIS\fnm[1] & & & \\ + EOM-SF-CCSD\fnm[1] & & & \\ + EOM-SF-CCSD(fT)\fnm[1] & & & \\ + EOM-SF-CCSD(dT)\fnm[1] & & & \\ + SF-ADC(2)-s\fnm[2] & & & \\ + SF-ADC(2)-x\fnm[2] & & & \\ + SF-ADC(3)\fnm[2] & & & \\ + SF-BSE@{\GOWO}@UHF\fnm[3] & & & \\ + SF-dBSE@{\GOWO}@UHF\fnm[3] & & & \\ + \end{tabular} + \end{ruledtabular} + \fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.} + \fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015} using a UHF reference.} + \fnt[3]{This work.} +\end{table} +%%% %%% %%% %%% + +%%% TABLE ?? %%% +\begin{table} + \caption{ + Vertical excitation energies (with respect to the singlet $X\,{}^1B_{1g}$ ground state) of the $1\,{}^3A_{2g}$, $2\,{}^1A_{1g}$, and $1\,{}^1B_{2g}$ states at the $D_{4h}$ square-planar equilibrium geometry of the $X\,{}^1B_{1g}$ singlet ground state. + \label{tab:CBD_D2h}} + \begin{ruledtabular} + \begin{tabular}{lccc} + & \mc{3}{c}{Excitation energies (eV)} \\ + \cline{2-4} + Method & $1\,{}^3A_{2g}$ & $2\,{}^1A_{1g}$ & $1\,{}^1B_{2g}$ \\ + \hline + EOM-SF-CIS\fnm[1] & & & \\ + EOM-SF-CCSD\fnm[1] & & & \\ + EOM-SF-CCSD(fT)\fnm[1] & & & \\ + EOM-SF-CCSD(dT)\fnm[1] & & & \\ + SF-ADC(2)-s\fnm[2] & & & \\ + SF-ADC(2)-x\fnm[2] & & & \\ + SF-ADC(3)\fnm[2] & & & \\ + SF-BSE@{\GOWO}@UHF\fnm[3] & & & \\ + SF-dBSE@{\GOWO}@UHF\fnm[3] & & & \\ + \end{tabular} + \end{ruledtabular} + \fnt[1]{Value from Ref.~\onlinecite{Manohar_2008} using a UHF reference.} + \fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015} using a UHF reference.} + \fnt[3]{This work.} +\end{table} +%%% %%% %%% %%% + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusion} \label{sec:ccl}