diff --git a/Manuscript/sfBSE.bib b/Manuscript/sfBSE.bib index 576ac13..54ffc70 100644 --- a/Manuscript/sfBSE.bib +++ b/Manuscript/sfBSE.bib @@ -1,13 +1,25 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2021-01-17 20:15:25 +0100 +%% Created for Pierre-Francois Loos at 2021-01-17 21:22:19 +0100 %% Saved with string encoding Unicode (UTF-8) +@article{Kannar_2014, + author = {K{\'a}nn{\'a}r, D{\'a}niel and Szalay, P{\'e}ter G.}, + date-added = {2021-01-17 21:18:03 +0100}, + date-modified = {2021-01-17 21:18:03 +0100}, + doi = {10.1021/ct500495n}, + journal = {J. Chem. Theory Comput.}, + pages = {3757-3765}, + title = {Benchmarking Coupled Cluster Methods on Valence Singlet Excited States}, + volume = {10}, + year = {2014}, + Bdsk-Url-1 = {http://dx.doi.org/10.1021/ct500495n}} + @article{Cohen_2008c, abstract = {Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, for many predicted properties, there are spectacular failures that can be traced to the delocalization error and static correlation error of commonly used approximations. These errors can be characterized and understood through the perspective of fractional charges and fractional spins introduced recently. Reducing these errors will open new frontiers for applications of density functional theory.}, author = {Cohen, Aron J. and Mori-S{\'a}nchez, Paula and Yang, Weitao}, @@ -117,10 +129,10 @@ @article{Sarkar_2021, author = {R. Sarkar and M. Boggio-Pasqua and P. F. Loos and D. Jacquemin}, date-added = {2021-01-10 18:27:30 +0100}, - date-modified = {2021-01-10 18:27:30 +0100}, + date-modified = {2021-01-17 21:22:19 +0100}, journal = {J. Chem. Theory Comput.}, title = {Benchmark of TD-DFT and Wavefunction Methods for Oscillator Strengths and Excited-State Dipoles}, - year = {submitted}} + year = {in press}} @article{Krylov_2000b, author = {Krylov,Anna I.}, diff --git a/Manuscript/sfBSE.tex b/Manuscript/sfBSE.tex index 12fd2e1..b0d8a84 100644 --- a/Manuscript/sfBSE.tex +++ b/Manuscript/sfBSE.tex @@ -517,6 +517,8 @@ In most cases, the value of $\zeta_{m}$ is close to unity which indicates that t \subsection{Oscillator strengths} \label{sec:os} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +Oscillator strengths, \ie, transition dipole moments from the ground to the corresponding excited state, are key quantities that are linked to experimental intensities and are usually used to probe the quality of excited-state calculations. \cite{Harbach_2014,Kannar_2014,Chrayteh_2021,Sarkar_2021} + For the spin-conserved transitions, the $x$ component of the transition dipole moment is \begin{equation} \mu_{x,m}^{\spc} = \sum_{ia\sig} (i_\sig|x|a_\sig)(\bX{m}{\spc}+\bY{m}{\spc})_{i_\sig a_\sig} @@ -526,7 +528,7 @@ where (p_\sig|x|q_\sigp) = \int \MO{p_\sig}(\br) \, x \, \MO{q_\sigp}(\br) d\br \end{equation} are one-electron integrals in the orbital basis. -The total oscillator strength in the so-called length gauge \cite{Chrayteh_2021,Sarkar_2021} is given by +The total oscillator strength in the so-called length gauge \cite{Sarkar_2021} is given by \begin{equation} f_{m}^{\spc} = \frac{2}{3} \Om{m}{\spc} \qty[ \qty(\mu_{x,m}^{\spc})^2 + \qty(\mu_{x,m}^{\spc})^2 + \qty(\mu_{x,m}^{\spc})^2 ] \end{equation}