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boosting seriously the intro

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Pierre-Francois Loos 2020-05-29 11:00:21 +02:00
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31
BSEdyn.bib
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@ -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}}

17
BSEdyn.tex
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@ -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}.