From c7d03c369a2b52914a97f5cdd85a033e73e833b8 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 13 Jan 2021 09:43:24 +0100 Subject: [PATCH] modifications in computational details --- Manuscript/sfBSE.bib | 52 +++++++++++++++++++++++++++++++++++++++----- Manuscript/sfBSE.tex | 38 +++++++++++++++++--------------- 2 files changed, 68 insertions(+), 22 deletions(-) diff --git a/Manuscript/sfBSE.bib b/Manuscript/sfBSE.bib index 86990cd..0aa2945 100644 --- a/Manuscript/sfBSE.bib +++ b/Manuscript/sfBSE.bib @@ -1,13 +1,55 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2021-01-11 09:47:39 +0100 +%% Created for Pierre-Francois Loos at 2021-01-13 09:41:10 +0100 %% Saved with string encoding Unicode (UTF-8) +@article{Becke_1993b, + author = {Becke,Axel D.}, + date-added = {2021-01-13 09:37:07 +0100}, + date-modified = {2021-01-13 09:40:17 +0100}, + doi = {10.1063/1.464304}, + journal = {J. Chem. Phys.}, + number = {2}, + pages = {1372-1377}, + title = {A new mixing of Hartree--Fock and local density‐functional theories}, + volume = {98}, + year = {1993}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.464304}} + +@article{Lee_1988, + author = {C. Lee and W. Yang and R. G. Parr}, + date-added = {2021-01-13 09:35:39 +0100}, + date-modified = {2021-01-13 09:35:47 +0100}, + doi = {10.1103/PhysRevB.37.785}, + issue = {2}, + journal = {Phys. Rev. B}, + month = {Jan}, + pages = {785}, + publisher = {American Physical Society}, + title = {Development of the Colle--Salvetti correlation-energy formula into a functional of the electron density}, + url = {http://link.aps.org/doi/10.1103/PhysRevB.37.785}, + volume = {37}, + year = {1988}, + Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.37.785}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.37.785}} + +@article{Becke_1988, + author = {A. D. Becke}, + date-added = {2021-01-13 09:34:25 +0100}, + date-modified = {2021-01-13 09:34:25 +0100}, + doi = {10.1103/PhysRevA.38.3098}, + journal = {Phys. Rev. A}, + pages = {3098}, + title = {Density-functional exchange-energy approximation with correct asymptotic behavior}, + volume = {38}, + year = {1988}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.38.3098}} + @article{Koch_1994, author = {Koch,Henrik and Kobayashi,Rika and Sanchez de Mer{\'a}s,Alfredo and Jorgensen, Poul}, date-added = {2021-01-11 09:32:50 +0100}, @@ -8699,9 +8741,9 @@ Bdsk-Url-1 = {http://dx.doi.org/10.1080/00268976.2014.1003621}} @article{Koch_1990, - author = {Koch, Henrik and Jensen, Hans Jo/rgen Aa. and Jo/rgensen, Poul and Helgaker, Trygve}, + author = {Koch, Henrik and Jensen, Hans Jorgen Aa. and Jorgensen, Poul and Helgaker, Trygve}, date-added = {2020-01-01 21:36:51 +0100}, - date-modified = {2021-01-11 09:32:58 +0100}, + date-modified = {2021-01-13 09:40:51 +0100}, doi = {10.1063/1.458815}, journal = {J. Chem. Phys.}, number = {5}, @@ -13435,10 +13477,10 @@ year = {2016}, Bdsk-Url-1 = {https://doi.org/10.1063/1.4963749}} -@article{Becke_1993, +@article{Becke_1993a, author = {A. D. Becke}, date-added = {2018-07-04 21:18:18 +0000}, - date-modified = {2018-07-18 13:08:55 +0000}, + date-modified = {2021-01-13 09:37:24 +0100}, doi = {10.1063/1.464913}, journal = {J. Chem. Phys.}, pages = {5648--5652}, diff --git a/Manuscript/sfBSE.tex b/Manuscript/sfBSE.tex index be02867..21918de 100644 --- a/Manuscript/sfBSE.tex +++ b/Manuscript/sfBSE.tex @@ -577,10 +577,12 @@ In the following, all linear response calculations are performed within the TDA %\titou{As one-electron basis sets, we employ Pople's 6-31G basis or the Dunning families cc-pVXZ and aug-cc-pVXZ (X = D, T, and Q) defined with cartesian Gaussian functions.} Finally, the infinitesimal $\eta$ is set to $100$ meV for all calculations. -All the static and dynamic BSE calculations have been performed with the software \texttt{QuAcK}, \cite{QuAcK} developed in our group and freely available on \texttt{github}. -The SF-ADC, EOM-SF-CC and SF-TD-DFT calculations have been performed with Q-CHEM 5.2.1 \cite{qchem4} and the EOM-CCSD calculation with Gaussian 09. \cite{g09} -As a consistency check, we systematically perform the SF-CIS calculations with both \texttt{QuAcK} and Q-CHEM, and make sure that they yield identical excitation energies. -Throughout this work, all spin-flip calculations have been performed with a UHF reference. +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. +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 the 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 calculations are performed with a UHF reference. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Results} @@ -625,9 +627,9 @@ The excitation energies corresponding to the first singlet and triplet single ex FCI\fnm[3] & 2.862 & 6.577 & 7.669 & 8.624 \\ \end{tabular} \end{ruledtabular} - \fnt[1]{Excitation energies extracted from Ref.~\onlinecite{Casanova_2020}.} + \fnt[1]{Values from Ref.~\onlinecite{Casanova_2020}.} \fnt[2]{This work.} - \fnt[3]{Excitation energies taken from Ref.~\onlinecite{Krylov_2001a}.} + \fnt[3]{Values from Ref.~\onlinecite{Krylov_2001a}.} \end{table} \end{squeezetable} %%% %%% %%% %%% @@ -637,7 +639,7 @@ The excitation energies corresponding to the first singlet and triplet single ex \includegraphics[width=\linewidth]{Be} \caption{ Excitation energies [with respect to the $^1S(1s^2 2s^2)$ singlet ground state] of \ce{Be} obtained with the 6-31G basis for various levels of theory: - SD-TD-DFT \cite{Casanova_2020} (red), SF-BSE (blue), SF-CIS \cite{Krylov_2001a} and SF-ADC (orange), and FCI \cite{Krylov_2001a} (black). + SF-TD-DFT \cite{Casanova_2020} (red), SF-BSE (blue), SF-CIS \cite{Krylov_2001a} and SF-ADC (orange), and FCI \cite{Krylov_2001a} (black). All the spin-flip calculations have been performed with a UHF reference. \label{fig:Be}} \end{figure} @@ -797,7 +799,8 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations %%% 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. + Vertical excitation energies (with respect to the singlet $\text{X}\,{}^1A_{g}$ ground state) of the $1\,{}^3B_{1g}$, $1\,{}^1B_{1g}$, and $2\,{}^1A_{1g}$ states at the $D_{2h}$ rectangular equilibrium geometry of the $X\,{}^1 A_{g}$ singlet ground state. + All the spin-flip calculations have been performed with a UHF reference. \label{tab:CBD_D2h}} \begin{ruledtabular} \begin{tabular}{lccc} @@ -812,12 +815,12 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations SF-ADC(2)-s\fnm[2] & 1.572& 3.201& 4.241\\ SF-ADC(2)-x\fnm[2] &1.576 &3.134 &3.792 \\ SF-ADC(3)\fnm[2] & 1.455&3.276 &4.328 \\ - SF-BSE@{\GOWO}@UHF\fnm[3] & 1.438 & 2.704 &4.540 \\ - SF-dBSE@{\GOWO}@UHF\fnm[3] & 1.403 &2.883 &4.621 \\ + SF-BSE@{\GOWO}\fnm[3] & 1.438 & 2.704 &4.540 \\ + SF-dBSE@{\GOWO}\fnm[3] & 1.403 &2.883 &4.621 \\ \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[1]{Spin-flip EOM-CC values from Ref.~\onlinecite{Manohar_2008}.} + \fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015}.} \fnt[3]{This work.} \end{table} %%% %%% %%% %%% @@ -825,7 +828,8 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations %%% 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. + 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 at the $D_{4h}$ square-planar equilibrium geometry of the $X\,{}^1B_{1g}$ singlet ground state. + All the spin-flip calculations have been performed with a UHF reference. \label{tab:CBD_D2h}} \begin{ruledtabular} \begin{tabular}{lccc} @@ -840,12 +844,12 @@ All of them have been obtained with a UHF reference like the SF-BSE calculations SF-ADC(2)-s\fnm[2] & & & \\ SF-ADC(2)-x\fnm[2] & & & \\ SF-ADC(3)\fnm[2] & & & \\ - SF-BSE@{\GOWO}@UHF\fnm[3] & -0.049 & 1.189 & 1.480 \\ - SF-dBSE@{\GOWO}@UHF\fnm[3] & 0.012 & 1.507 & 1.841 \\ + SF-BSE@{\GOWO}\fnm[3] & -0.049 & 1.189 & 1.480 \\ + SF-dBSE@{\GOWO}\fnm[3] & 0.012 & 1.507 & 1.841 \\ \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[1]{Spin-flip EOM-CC values from Ref.~\onlinecite{Manohar_2008}.} + \fnt[2]{Value from Ref.~\onlinecite{Lefrancois_2015}.} \fnt[3]{This work.} \end{table} %%% %%% %%% %%%