PTEROSOR/sfBSE
10
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

RSH

Browse Source
This commit is contained in:
Pierre-Francois Loos 2021-02-25 21:05:30 +01:00
parent 50e5a6bf65
commit d06587f9d0
2 changed files with 11 additions and 5 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

9
Manuscript/sfBSE.tex
View File

@ -760,8 +760,9 @@ Finally, the infinitesimal $\eta$ is set to $100$ meV for all calculations.
All the static and dynamic BSE calculations (labeled in the following as SF-BSE and SF-dBSE respectively) are performed with the software \texttt{QuAcK}, \cite{QuAcK} developed in our group and freely available on \texttt{github}.
The standard and extended spin-flip ADC(2) calculations [SF-ADC(2)-s and SF-ADC(2)-x, respectively] as well as the SF-ADC(3) \cite{Lefrancois_2015} are performed with Q-CHEM 5.2.1. \cite{qchem4}
Spin-flip TD-DFT calculations \cite{Shao_2003} considering the BLYP, \cite{Becke_1988,Lee_1988} B3LYP, \cite{Becke_1988,Lee_1988,Becke_1993a} and BH\&HLYP \cite{Lee_1988,Becke_1993b} functionals with contains $0\%$, $20\%$, and $50\%$ of exact exchange are labeled as SF-TD-BLYP, SF-TD-B3LYP, and SF-TD-BH\&HLYP, respectively, and are also performed with Q-CHEM 5.2.1.
\alert{Additionally, we have performed spin-flip TD-DFT calculations considering the following the range-separated hybrid (RSH) functionals: CAM-B3LYP, \cite{Yanai_2004} LC-$\omega$HPBE, \cite{Henderson_2009} and $\omega$B97X-D. \cite{Chai_2008a,Chai_2008b}}
Spin-flip TD-DFT calculations \cite{Shao_2003} (also performed with Q-CHEM 5.2.1) considering the BLYP, \cite{Becke_1988,Lee_1988} B3LYP, \cite{Becke_1988,Lee_1988,Becke_1993a} and BH\&HLYP \cite{Lee_1988,Becke_1993b} functionals with contains $0\%$, $20\%$, and $50\%$ of exact exchange are labeled as SF-TD-BLYP, SF-TD-B3LYP, and SF-TD-BH\&HLYP, respectively.
\alert{Additionally, we have performed spin-flip TD-DFT calculations considering the following the range-separated hybrid (RSH) functionals: CAM-B3LYP, \cite{Yanai_2004} LC-$\omega$HPBE, \cite{Henderson_2009} and $\omega$B97X-D. \cite{Chai_2008a,Chai_2008b}
In the present context, the main difference between these RSHs is their amount of exact exchange at long range: 75\% for CAM-B3LYP and 100\% for both LC-$\omega$HPBE and $\omega$B97X-D.}
EOM-CCSD excitation energies \cite{Koch_1990,Stanton_1993,Koch_1994} are computed with Gaussian 09. \cite{g09}
As a consistency check, we systematically perform SF-CIS calculations \cite{Krylov_2001a} with both \texttt{QuAcK} and Q-CHEM, and make sure that they yield identical excitation energies.
Throughout this work, all spin-flip and spin-conserved calculations are performed with a UHF reference.
@ -787,6 +788,7 @@ Indeed, due to the lack of coupling terms in the spin-flip block of the SD-TD-DF
Including exact exchange, like in SF-TD-B3LYP and SF-TD-BH\&HLYP, lifts this degeneracy and improves the description of both states.
However, the SF-TD-BH\&HLYP excitation energy of the $^1P(1s^2 2s^1 2p^1)$ state is still off by $1.6$ eV as compared to the FCI reference.
For the other states, the agreement between SF-TD-BH\&HLYP and FCI is significantly improved.
\alert{Comments on RSHs for Be.}
The center part of Fig.~\ref{fig:Be} shows the SF-(d)BSE results (blue lines) alongside the SF-CIS excitation energies (purple lines).
All of these are computed with 100\% of exact exchange with the additional inclusion of correlation in the case of SF-BSE and SF-dBSE thanks to the introduction of static and dynamical screening, respectively.
@ -879,6 +881,7 @@ SF-TD-BH\&HLYP shows, at best, qualitative agreement with EOM-CCSD, while the TD
Note that \ce{H2} is a rather challenging system for (SF)-TD-DFT from a general point of view. \cite{Vuckovic_2017,Cohen_2008a,Cohen_2008c,Cohen_2012}
Similar graphs for (SF-)TD-BLYP and (SF-)TD-B3LYP are reported in the {\SI} from which one can draw similar conclusions.
Notably, one can see that the $\text{E}\,{}^1\Sigma_g^+$ and $\text{F}\,{}^1 \Sigma_g^+$ states crossed without interacting at the SF-TD-BLYP level due to the lack of Hartree-Fock exchange.
\alert{Comments on RSHs for H2.}
In the bottom panel of Fig.~\ref{fig:H2}, (SF-)BSE excitation energies for the same three singlet states are represented.
SF-BSE provides surprisingly accurate excitation energies for the $\text{B}\,{}^1\Sigma_u^+$ state with errors between $0.05$ and $0.3$ eV, outperforming in the process the standard BSE formalism.
@ -954,7 +957,7 @@ Nonetheless, it is pleasing to see that adding the dynamical correction in SF-dB
Then, CBD stands as an excellent example for which dynamical corrections are necessary to get the right chemistry at the SF-BSE level.
Another interesting feature is the wrong ordering of the $2\,{}^1A_{1g}$ and $1\,{}^1B_{2g}$ states at the SF-B3LYP, SF-BH\&HLYP, and SF-CIS levels which give the former higher in energy than the latter.
This issue does not appear at the SF-BSE, SF-ADC, and SF-EOM-SF-CCSD levels.
\alert{Comments on RSHs for CBD.}
%%% FIG 3 %%%
\begin{figure*}

7
Response_Letter/Response_Letter.tex
View File

@ -16,7 +16,7 @@ Please find attached a revised version of the manuscript entitled
\begin{quote}
\textit{``Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism''}.
\end{quote}
We thank the reviewers for their constructive comments.
We thank the reviewers for their constructive comments which, we believe, have improved the overall quality of the present manuscript.
Our detailed responses to their comments can be found below.
For convenience, changes are highlighted in red in the revised version of the manuscript.
@ -41,7 +41,10 @@ I recommend this manuscript for publication after the minor points addressed:}
\\
\alert{Following the excellent advice of Reviewer \#1, we have added data for the following range-separated hybrid functionals: CAM-B3LYP, LC-$\omega$HPBE, and $\omega$B97X-D.
These results have been added to the corresponding Tables and Figures.
In a nutshell, CAM-B3LYP does not really improved things and is less reliable than BH\&HLYP.}
In the case of \ce{H2}, we have chosen to add some of the graphs to the supporting information instead for the sake of clarity.
In a nutshell, CAM-B3LYP does not really improved things and is less reliable than BH\&HLYP.
Note that CAM-B3LYP only has 75\% exact exchange at long range while LC-$\omega$HPBE and $\omega$B97X-D have 100\% of HF exact exchange at longe range.
All these results are discussed in the revised version of the manuscript.}
\item
{Figure 1: The similarity between SF-dBSE and SF-ADC(2)-s is more than simply the results.