From 7ff64cf671390e0f31af2f15140643b30cba6b6d Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Fri, 29 May 2020 11:00:21 +0200 Subject: [PATCH] boosting seriously the intro --- BSEdyn.bib | 31 ++++++++++++++++++++++--------- BSEdyn.tex | 17 +++++++---------- 2 files changed, 29 insertions(+), 19 deletions(-) diff --git a/BSEdyn.bib b/BSEdyn.bib index 01f1df6..b571b29 100644 --- a/BSEdyn.bib +++ b/BSEdyn.bib @@ -1,13 +1,25 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2020-05-29 10:22:08 +0200 +%% Created for Pierre-Francois Loos at 2020-05-29 10:38:59 +0200 %% Saved with string encoding Unicode (UTF-8) +@article{Loos_2020b, + Author = {P. F. Loos and F. Lipparini and M. Boggio-Pasqua and A. Scemama and D. Jacquemin}, + Date-Added = {2020-05-29 10:29:27 +0200}, + Date-Modified = {2020-05-29 10:29:27 +0200}, + Doi = {10.1021/acs.jctc.9b01216}, + Journal = {J. Chem. Theory Comput.}, + Pages = {1711}, + Title = {A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Medium Size Molecules,}, + Volume = {16}, + Year = {2020}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b01216}} + @article{Casida_2005, Author = {M. E. Casida}, Date-Added = {2020-05-29 10:21:26 +0200}, @@ -17,7 +29,8 @@ Pages = {054111}, Title = {Propagator corrections to adiabatic time- dependent density-functional theory linear response theory}, Volume = {122}, - Year = {2005}} + Year = {2005}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1836757}} @article{Casida_2016, Author = {M. E. Casida and M. {Huix-Rotllant}}, @@ -97,15 +110,15 @@ Year = {2018}, Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00406}} -@article{Loos_2020b, - Author = {P. F. Loos and F. Lipparini and M. Boggio-Pasqua and A. Scemama and D. Jacquemin}, +@article{Loos_2020c, + Author = {P. F. Loos and A. Scemama and M. Boggio-Pasqua and D. Jacquemin}, Date-Added = {2020-05-18 22:13:24 +0200}, - Date-Modified = {2020-05-18 22:13:54 +0200}, - Doi = {10.1021/acs.jctc.9b01216}, + Date-Modified = {2020-05-29 10:31:08 +0200}, + Doi = {10.1021/acs.jctc.0c00227}, Journal = {J. Chem. Theory Comput.}, - Pages = {1711}, - Title = {A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Medium Size Molecules,}, - Volume = {16}, + Pages = {XXXX}, + Title = {A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Exotic Molecules and Radicals}, + Volume = {XX}, Year = {2020}, Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b01216}} diff --git a/BSEdyn.tex b/BSEdyn.tex index 2da65cd..8fd8210 100644 --- a/BSEdyn.tex +++ b/BSEdyn.tex @@ -242,15 +242,12 @@ Here, $E_s^{N}$ is the total energy of the $s$th excited state of the $N$-electr Because the excitonic effect corresponds physically to the stabilization implied by the attraction of the excited electron and its hole left behind, we have $\EgOpt < \EgFun$. Most of BSE implementations rely on the so-called static approximation, which approximates the dynamical (\ie, frequency-dependent) BSE kernel by its static limit. -In complete analogy with the ubiquitous adiabatic approximation in TD-DFT, one key consequence of the static approximation is that double (and higher) excitations are completely absent from the BSE spectrum. -Although these double excitations are usually experimentally dark (which means that they usually cannot be observed in photo-absorption spectroscopy), these states play, indirectly, a key role in many photochemistry mechanisms. \cite{Boggio-Pasqua_2007} -They are, moreover, a real challenge for high-level computational methods. \cite{Loos_2018a,Loos_2019,Loos_2020b} -% double excitations are important as well for open-shell ground state cf Pina and Miquel -%There are also important in the lowest lying excited states of polyenes (such as butadiene) because they strongly mix with the -%for example, the lowest-lying singlet state of polyenes is not a simple highest occupied molecular orbital?lowest unoccupied molecular orbital ??HOMO-LUMO?? one-electron excitation but has a HOMO^2-LUMO^2 double excitation character -%A frequency-dependent xc kernel could create extra poles in the response function, which would describe states with a multiple-excitation character -%The poles of the true response function give the excitation energies of the interacting system, where the excited states can be a mixture of single, double, and higher-multiple ex- citations, whereas the poles of the KS response function are just at single KS excitation energies -%Therefore ??s has fewer poles than ??. +In complete analogy with the ubiquitous adiabatic approximation in TD-DFT where the exchange-correlation (xc) kernel is made static, one key consequence of the static approximation within BSE is that double (and higher) excitations are completely absent from the BSE spectrum. +Indeed, a frequency-dependent kernel has the ability to create additional poles in the response function, which describe states with a multiple-excitation character, and, in particular, double excitations. +Although these double excitations are usually experimentally dark (which means that they usually cannot be observed in photo-absorption spectroscopy), these states play, indirectly, a key role in many photochemistry mechanisms, \cite{Boggio-Pasqua_2007} and are particularly important in the faithful description of the ground state of open-shell molecules. \cite{Casida_2005,Romaniello_2009a,Huix-Rotllant_2011,Loos_2020c} +They are, moreover, a real challenge for high-level computational methods. \cite{Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c} +Double excitations play also a significant role in the correct location of the excited states of polyenes that are closely related to rhodopsin which is involved in the visual transduction. \cite{Olivucci_2010,Robb_2007,Manathunga_2016} +In butadiene, for example, while the bright $1 ^1B_u$ state has a clear ($\HOMO \ra \LUMO$) single-excitation character, the dark $2 ^1A_g$ state includes a substantial fraction of doubly-excited character from the $\HOMO^2 \ra \LUMO^2$ double excitation (roughly $30\%$), yet dominant contributions from the $\HOMO-1 \ra \LUMO$ and $\HOMO \ra \LUMO+1$ single excitations. \cite{Maitra_2004,Cave_2004,Saha_2006,Watson_2012,Shu_2017,Barca_2018a,Barca_2018b,Loos_2019} Going beyond the static approximation is tricky and very few groups have dared to take the plunge. \cite{Strinati_1988,Rohlfing_2000,Sottile_2003,Ma_2009a,Ma_2009b,Romaniello_2009b,Sangalli_2011,Huix-Rotllant_2011,Zhang_2013,Rebolini_2016,Olevano_2019,Lettmann_2019} Nonetheless, it is worth mentioning the seminal work of Strinati, \cite{Strinati_1988} who \titou{bla bla bla.} @@ -272,7 +269,7 @@ The appearance of these spurious excitations was attributed to the self-screenin This was fixed in a follow-up paper by Sangalli \textit{et al.} \cite{Sangalli_2011} thanks to the design of a number-conserving approach based on the second RPA. Finally, let us mention efforts to borrow ingredients from BSE in order to go beyond the adiabatic approximation of TD-DFT. -For example, Huix-Rotllant and Casida \cite{Casida_2005,Huix-Rotllant_2011} proposed a nonadiabatic correction to the exchange-correlation (xc) kernel by using the formalism of superoperators, which includes as a special case the dressed TD-DFT method of Maitra and coworkers. \cite{Maitra_2004,Cave_2004,Elliott_2011,Maitra_2012} +For example, Huix-Rotllant and Casida \cite{Casida_2005,Huix-Rotllant_2011} proposed a nonadiabatic correction to the xc kernel by using the formalism of superoperators, which includes as a special case the dressed TD-DFT method of Maitra and coworkers. \cite{Maitra_2004,Cave_2004,Elliott_2011,Maitra_2012} Following a similar strategy, Romaniello \textit{et al.} \cite{Romaniello_2009b} took advantages of the dynamically-screened Coulomb potential from BSE to obtain a dynamic TD-DFT kernel. In this regard, MBPT provides key insights about what is missing in adiabatic TD-DFT, as discussed at length by Casida and Huix-Rotllant in Ref.~\onlinecite{Casida_2016}.