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Pierre-Francois Loos 2021-01-18 13:59:36 +01:00
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Manuscript/Be.pdf
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Manuscript/sfBSE.tex
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@ -632,7 +632,7 @@ Finally, both SF-ADC(2)-x and SF-ADC(3) yield excitation energies very close to
\label{tab:Be}} \label{tab:Be}}
\begin{ruledtabular} \begin{ruledtabular}
\begin{tabular}{lcccccccccc} \begin{tabular}{lcccccccccc}
& \mc{5}{c}{States} \\ & \mc{5}{c}{Excitation energies (eV)} \\
% & \mc{5}{c}{6-31G} & \mc{5}{c}{aug-cc-pVQZ} \\ % & \mc{5}{c}{6-31G} & \mc{5}{c}{aug-cc-pVQZ} \\
\cline{2-6} %\cline{7-11} \cline{2-6} %\cline{7-11}
Method & $^1S(1s^2 2s^2)$ & $^3P(1s^2 2s^1 2p^1)$ & $^1P(1s^2 2s^1 2p^1)$ Method & $^1S(1s^2 2s^2)$ & $^3P(1s^2 2s^1 2p^1)$ & $^1P(1s^2 2s^1 2p^1)$
@ -645,7 +645,7 @@ Finally, both SF-ADC(2)-x and SF-ADC(3) yield excitation energies very close to
SF-TD-BH\&HLYP\fnm[1] & (0.000) & 2.874(1.981) & 4.922(0.023) & 7.112(1.000) & 8.188(0.002) \\ SF-TD-BH\&HLYP\fnm[1] & (0.000) & 2.874(1.981) & 4.922(0.023) & 7.112(1.000) & 8.188(0.002) \\
SF-CIS\fnm[2] & (0.002) & 2.111(2.000) & 6.036(0.014) & 7.480(1.000) & 8.945(0.006) \\ SF-CIS\fnm[2] & (0.002) & 2.111(2.000) & 6.036(0.014) & 7.480(1.000) & 8.945(0.006) \\
SF-BSE@{\GOWO} & (0.004) & 2.399(1.999) & 6.191(0.023) & 7.792(1.000) & 9.373(0.013) \\ SF-BSE@{\GOWO} & (0.004) & 2.399(1.999) & 6.191(0.023) & 7.792(1.000) & 9.373(0.013) \\
SF-BSE@{\evGW} & (0.004) & 2.407(1.999) & 6.199(0.023) & 7.788(1.000) & 9.388(0.013) \\ % SF-BSE@{\evGW} & (0.004) & 2.407(1.999) & 6.199(0.023) & 7.788(1.000) & 9.388(0.013) \\
SF-dBSE@{\GOWO} & & 2.363 & 6.263 & 7.824 & 9.424 \\ SF-dBSE@{\GOWO} & & 2.363 & 6.263 & 7.824 & 9.424 \\
% SF-dBSE@{\evGW} & & 2.369 & 6.273 & 7.820 & 9.441 \\ % SF-dBSE@{\evGW} & & 2.369 & 6.273 & 7.820 & 9.441 \\
SF-ADC(2)-s & & 2.433 & 6.255 & 7.745 & 9.047 \\ SF-ADC(2)-s & & 2.433 & 6.255 & 7.745 & 9.047 \\
@ -682,7 +682,7 @@ The $\text{X}\,{}^1 \Sigma_g^+$ ground state of \ce{H2} has an electronic config
The variation of the excitation energies associated with the three lowest singlet excited states with respect to the elongation of the \ce{H-H} bond are of particular interest here. The variation of the excitation energies associated with the three lowest singlet excited states with respect to the elongation of the \ce{H-H} bond are of particular interest here.
The lowest singly excited state $\text{B}\,{}^1 \Sigma_u^+$ has a $(1\sigma_g )(1\sigma_u)$ configuration, while the singly excited state $\text{E}\,{}^1 \Sigma_g^+$ and the doubly excited state $\text{F}\,{}^1 \Sigma_g^+$ have $(1\sigma_g ) (2\sigma_g)$ and $(1\sigma_u )(1\sigma_u)$ configurations, respectively. The lowest singly excited state $\text{B}\,{}^1 \Sigma_u^+$ has a $(1\sigma_g )(1\sigma_u)$ configuration, while the singly excited state $\text{E}\,{}^1 \Sigma_g^+$ and the doubly excited state $\text{F}\,{}^1 \Sigma_g^+$ have $(1\sigma_g ) (2\sigma_g)$ and $(1\sigma_u )(1\sigma_u)$ configurations, respectively.
Because these latter two excited states interact strongly and form an avoided crossing around $R(\ce{H-H}) = 1.4$ \AA, they are usually labeled as the $\text{EF}\,{}^1 \Sigma_g^+$ state. Because these latter two excited states interact strongly and form an avoided crossing around $R(\ce{H-H}) = 1.4$ \AA, they are usually labeled as the $\text{EF}\,{}^1 \Sigma_g^+$ state.
Note that this avoided crossing is not visible with non-spin-flip methods, such as CIS, TD-DFT, and BSE, as these are ``blind'' to double excitations. Note that this avoided crossing is not visible with non-spin-flip methods restricted to single excitations (such as CIS, TD-DFT, and BSE) as these are ``blind'' to double excitations.
Three methods, in their standard and spin-flip versions, are studied here (CIS, TD-BH\&HLYP and BSE) and are compared to the reference EOM-CCSD excitation energies (that is equivalent to FCI in the case of \ce{H2}). Three methods, in their standard and spin-flip versions, are studied here (CIS, TD-BH\&HLYP and BSE) and are compared to the reference EOM-CCSD excitation energies (that is equivalent to FCI in the case of \ce{H2}).
All these calculations are performed in the cc-pVQZ basis, and both the spin-conserved and spin-flip calculations are performed with an unrestricted reference. All these calculations are performed in the cc-pVQZ basis, and both the spin-conserved and spin-flip calculations are performed with an unrestricted reference.
@ -846,9 +846,9 @@ This project has received funding from the European Research Council (ERC) under
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\section*{Data availability statement} %\section*{Data availability statement}
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The data that supports the findings of this study are available within the article and its supplementary material. %The data that supports the findings of this study are available within the article and its supplementary material.
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\bibliography{sfBSE} \bibliography{sfBSE}