From ad4581524ce857e1bcecc0064fccea8473d76286 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Fri, 17 Apr 2020 20:05:55 +0200 Subject: [PATCH] clean up --- Manuscript/BSE_JPCL.tex | 73 ++++-- Manuscript/xbbib.bib | 482 +++++++++++++++++++++------------------- 2 files changed, 311 insertions(+), 244 deletions(-) diff --git a/Manuscript/BSE_JPCL.tex b/Manuscript/BSE_JPCL.tex index 1f7b294..9da56d9 100644 --- a/Manuscript/BSE_JPCL.tex +++ b/Manuscript/BSE_JPCL.tex @@ -67,8 +67,11 @@ %matrices \newcommand{\bO}{\boldsymbol{0}} +\newcommand{\bI}{\boldsymbol{I}} +\newcommand{\bA}{\boldsymbol{A}} \newcommand{\bH}{\boldsymbol{H}} -\newcommand{\bh}{\boldsymbol{h}} +\newcommand{\bx}{\boldsymbol{x}} +\newcommand{\bb}{\boldsymbol{b}} \newcommand{\bc}{\boldsymbol{c}} \renewcommand{\tr}[1]{{#1}^{\dag}} @@ -395,28 +398,70 @@ diabatization and conical intersections \cite{Kaczmarski_2010} \noindent {\textbf{The Concept of dynamical properties.}} As a chemist, it is maybe difficult to understand the concept of dynamical properties, the motivation behind their introduction, and their actual usefulness. -Here, we will try to give a pedagogical example showing the importance of dynamical quantities and their main purposes. -To do so, let us consider we want to solve a hard problem given by the Schr{\"o}dinger-like equation of the form $\bH \bc = \omega \bc$. -If we assume that the Hamiltonian $\bH$ is of size $N \times N$, this \textit{linear} set of equations yields $K$ solutions. -However, in practice, $K$ can be very large. -Therefore, it is usually convenient to recast it as +Here, we will try to give a pedagogical example showing the importance of dynamical quantities and their main purposes. \cite{Romaniello_2009,Sangalli_2011,ReiningBook} +To do so, let us consider the usual chemical scenario where one wants to get the neutral excitations of a given system. +In most cases, this can be done by solving a set of linear equations of the form \begin{equation} + \label{eq:lin_sys} + \bA \bx = \omega \bx, +\end{equation} +where $\omega$ is one of the neutral excitation energies of the system associated with the transition vector $\bx$. +If we assume that the operator $\bA$ has a matrix representation of size $K \times K$, this \textit{linear} set of equations yields $K$ excitation energies. +However, in practice, $K$ might be very large, and it might therefore be practically useful to recast this system as two smaller coupled systems, such that +\begin{equation} + \label{eq:lin_sys_split} \begin{pmatrix} - \bH_0 & \tr{\bh} \\ - \bh & \bH_1 \\ + \bA_1 & \tr{\bb} \\ + \bb & \bA_2 \\ \end{pmatrix} \begin{pmatrix} - \bc_0\\ - \bc_1 \\ + \bx_1 \\ + \bx_2 \\ \end{pmatrix} = \omega \begin{pmatrix} - \bc_0 \\ - \bc_1 \\ - \end{pmatrix} + \bx_1 \\ + \bx_2 \\ + \end{pmatrix}, \end{equation} +where the blocks $\bA_1$ and $\bA_2$, of sizes $K_1 \times K_1$ and $K_2 \times K_2$ (with $K_1 + K_2 = K$), can be associated with, for example, the single and double excitations of the system. +Note that this \textit{exact} decomposition does not alter, in any case, the values of the excitation energies, not their eigenvectors. -This system of equation has exactly the same number of solutions. +Solving separately each row of the system \eqref{eq:lin_sys_split} yields +\begin{subequations} +\begin{gather} + \label{eq:row1} + \bA_1 \bx_1 + \tr{\bb} \bx_2 = \omega \bx_1, + \\ + \label{eq:row2} + \bx_2 = (\omega \bI - \bA_2)^{-1} \bb \bx_1. +\end{gather} +\end{subequations} +Substituting Eq.~\eqref{eq:row2} into Eq.~\eqref{eq:row1} yields the following effective \textit{non-linear}, frequency-dependent operator +\begin{equation} + \label{eq:non_lin_sys} + \Tilde{\bA}_1(\omega) \bx_1 = \omega \bx_1 +\end{equation} +with +\begin{equation} + \Tilde{\bA}_1(\omega) = \bA_1 + \tr{\bb} (\omega \bI - \bA_2)^{-1} \bb +\end{equation} +which has, by construction, exactly the same solutions than the linear system \eqref{eq:lin_sys} but a smaller dimension. +For example, an operator $\Tilde{\bA}_1(\omega)$ built in the basis of single excitations can potentially provide excitation energies for double excitations thanks to its frequency-dependent nature, the information from the double excitations being ``folded'' into $\Tilde{\bA}_1(\omega)$ via Eq.~\eqref{eq:row2}. \cite{Romaniello_2009,Sangalli_2011,ReiningBook} + +How have we been able to reduce the dimension of the problem while keeping the same number of solutions? +To do so, we have transformed a linear operator $\bA$ into a non-linear operator $\Tilde{\bA}_1(\omega)$ by making it frequency dependent. +In other words, we have sacrificed the linearity of the system in order to obtain a new, non-linear systems of equations of smaller dimension. +This procedure converting degrees of freedom into frequency or energy dependence is very general and can be applied in various contexts. \cite{Gatti_2007,Garniron_2018} +Thanks to its non-linearity, Eq.~\eqref{eq:non_lin_sys} can produce more solutions than its actual dimension. +However, because there is no free lunch, this non-linear system is obviously harder to solve than its corresponding linear analogue given by Eq.~\eqref{eq:lin_sys}. +Nonetheless, approximations can be now applied to Eq.~\eqref{eq:non_lin_sys} in order to solve it efficiently. + +One of these approximations is the so-called \textit{static} approximation, which corresponds to fix the frequency to a particular value. +For example, as commonly done within the Bethe-Salpeter formalism, $\Tilde{\bA}_1(\omega) = \Tilde{\bA}_1 \equiv \Tilde{\bA}_1(\omega = 0)$. +In such a way, the operator $\Tilde{\bA}_1$ is made linear again by removing its frequency-dependent nature. +This approximation comes with a heavy price as the number of solutions provided by the system of equations \eqref{eq:non_lin_sys} has now been reduced from $K$ to $K_1$. +Coming back to our example, in the static approximation, the operator $\Tilde{\bA}_1$ built in the basis of single excitations cannot provide double excitations anymore, and the only $K_1$ excitation energies are associated with single excitations. %%%%%%%%%%%%%%%%%% %%% CONCLUSION %%% diff --git a/Manuscript/xbbib.bib b/Manuscript/xbbib.bib index 0d0edf5..73e529a 100644 --- a/Manuscript/xbbib.bib +++ b/Manuscript/xbbib.bib @@ -1,13 +1,43 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2020-04-16 22:33:55 +0200 +%% Created for Pierre-Francois Loos at 2020-04-17 20:05:26 +0200 %% Saved with string encoding Unicode (UTF-8) +@article{Gatti_2007, + Author = {M. Gatti and V. Olevano and L. Reining,and I. V. Tokatly}, + Date-Added = {2020-04-17 10:10:16 +0200}, + Date-Modified = {2020-04-17 10:11:34 +0200}, + Doi = {10.1103/PhysRevLett.99.057401}, + Journal = {Phys. Rev. Lett.}, + Pages = {057401}, + Title = {Transforming Nonlocality into a Frequency Dependence: A Shortcut to Spectroscopy}, + Volume = {99}, + Year = {2007}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.99.057401}} + +@article{Sangalli_2011, + Author = {Sangalli, Davide and Romaniello, Pina and Onida, Giovanni and Marini, Andrea}, + Date-Added = {2020-04-17 10:04:29 +0200}, + Date-Modified = {2020-04-17 10:04:29 +0200}, + Doi = {10.1063/1.3518705}, + File = {/Users/loos/Zotero/storage/9S3XW2FJ/Sangalli et al. - 2011 - Double excitations in correlated systems A many--b.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jan, + Number = {3}, + Pages = {034115}, + Shorttitle = {Double Excitations in Correlated Systems}, + Title = {Double Excitations in Correlated Systems: {{A}} Many\textendash{}Body Approach}, + Volume = {134}, + Year = {2011}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.3518705}} + @article{Dreuw_2015, Author = {Dreuw, Andreas and Wormit, Michael}, Date-Added = {2020-04-16 22:30:10 +0200}, @@ -185,34 +215,36 @@ Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.45.290}} @article{Perdew_1983, - title = {Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities}, - author = {Perdew, John P. and Levy, Mel}, - journal = {Phys. Rev. Lett.}, - volume = {51}, - issue = {20}, - pages = {1884--1887}, - numpages = {0}, - year = {1983}, - month = {Nov}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.51.1884}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1884} -} + Author = {Perdew, John P. and Levy, Mel}, + Doi = {10.1103/PhysRevLett.51.1884}, + Issue = {20}, + Journal = {Phys. Rev. Lett.}, + Month = {Nov}, + Numpages = {0}, + Pages = {1884--1887}, + Publisher = {American Physical Society}, + Title = {Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities}, + Url = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1884}, + Volume = {51}, + Year = {1983}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1884}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.51.1884}} @article{Sham_1983, - title = {Density-Functional Theory of the Energy Gap}, - author = {Sham, L. J. and Schl\"uter, M.}, - journal = {Phys. Rev. Lett.}, - volume = {51}, - issue = {20}, - pages = {1888--1891}, - numpages = {0}, - year = {1983}, - month = {Nov}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.51.1888}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1888} -} + Author = {Sham, L. J. and Schl\"uter, M.}, + Doi = {10.1103/PhysRevLett.51.1888}, + Issue = {20}, + Journal = {Phys. Rev. Lett.}, + Month = {Nov}, + Numpages = {0}, + Pages = {1888--1891}, + Publisher = {American Physical Society}, + Title = {Density-Functional Theory of the Energy Gap}, + Url = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1888}, + Volume = {51}, + Year = {1983}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1888}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.51.1888}} @article{Hybertsen_1986, Author = {Hybertsen, Mark S. and Louie, Steven G.}, @@ -278,93 +310,100 @@ Bdsk-Url-2 = {https://doi.org/10.1088/0034-4885/61/3/002}} @article{Northrup_1991, - title = {Many-body Calculation of the Surface-State Energies for Si(111)2\ifmmode\times\else\texttimes\fi{}1}, - author = {Northrup, John E. and Hybertsen, Mark S. and Louie, Steven G.}, - journal = {Phys. Rev. Lett.}, - volume = {66}, - issue = {4}, - pages = {500--503}, - numpages = {0}, - year = {1991}, - month = {Jan}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.66.500}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.66.500} -} + Author = {Northrup, John E. and Hybertsen, Mark S. and Louie, Steven G.}, + Doi = {10.1103/PhysRevLett.66.500}, + Issue = {4}, + Journal = {Phys. Rev. Lett.}, + Month = {Jan}, + Numpages = {0}, + Pages = {500--503}, + Publisher = {American Physical Society}, + Title = {Many-body Calculation of the Surface-State Energies for Si(111)2\ifmmode\times\else\texttimes\fi{}1}, + Url = {https://link.aps.org/doi/10.1103/PhysRevLett.66.500}, + Volume = {66}, + Year = {1991}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.66.500}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.66.500}} @article{Blase_1994, - title = {Self-Energy Effects on the Surface-State Energies of H-Si(111)1\ifmmode\times\else\texttimes\fi{}1}, - author = {Blase, X. and Zhu, Xuejun and Louie, Steven G.}, - journal = {Phys. Rev. B}, - volume = {49}, - issue = {7}, - pages = {4973--4980}, - numpages = {0}, - year = {1994}, - month = {Feb}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevB.49.4973}, - url = {https://link.aps.org/doi/10.1103/PhysRevB.49.4973} -} + Author = {Blase, X. and Zhu, Xuejun and Louie, Steven G.}, + Doi = {10.1103/PhysRevB.49.4973}, + Issue = {7}, + Journal = {Phys. Rev. B}, + Month = {Feb}, + Numpages = {0}, + Pages = {4973--4980}, + Publisher = {American Physical Society}, + Title = {Self-Energy Effects on the Surface-State Energies of H-Si(111)1\ifmmode\times\else\texttimes\fi{}1}, + Url = {https://link.aps.org/doi/10.1103/PhysRevB.49.4973}, + Volume = {49}, + Year = {1994}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.49.4973}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.49.4973}} @article{Blase_1995, - title = {Quasiparticle Band Structure of Bulk Hexagonal Boron Nitride and Related Systems}, - author = {Blase, X. and Rubio, Angel and Louie, Steven G. and Cohen, Marvin L.}, - journal = {Phys. Rev. B}, - volume = {51}, - issue = {11}, - pages = {6868--6875}, - numpages = {0}, - year = {1995}, - month = {Mar}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevB.51.6868}, - url = {https://link.aps.org/doi/10.1103/PhysRevB.51.6868} -} + Author = {Blase, X. and Rubio, Angel and Louie, Steven G. and Cohen, Marvin L.}, + Doi = {10.1103/PhysRevB.51.6868}, + Issue = {11}, + Journal = {Phys. Rev. B}, + Month = {Mar}, + Numpages = {0}, + Pages = {6868--6875}, + Publisher = {American Physical Society}, + Title = {Quasiparticle Band Structure of Bulk Hexagonal Boron Nitride and Related Systems}, + Url = {https://link.aps.org/doi/10.1103/PhysRevB.51.6868}, + Volume = {51}, + Year = {1995}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.51.6868}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.51.6868}} @article{Rohlfing_1995, - title = {Efficient Scheme for GW Quasiparticle Band-Structure Calculations with Aapplications to Bulk Si and to the Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) Surface}, - author = {Rohlfing, Michael and Kr{\"u}ger, Peter and Pollmann, Johannes}, - journal = {Phys. Rev. B}, - volume = {52}, - issue = {3}, - pages = {1905--1917}, - numpages = {0}, - year = {1995}, - month = {Jul}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevB.52.1905}, - url = {https://link.aps.org/doi/10.1103/PhysRevB.52.1905} -} + Author = {Rohlfing, Michael and Kr{\"u}ger, Peter and Pollmann, Johannes}, + Doi = {10.1103/PhysRevB.52.1905}, + Issue = {3}, + Journal = {Phys. Rev. B}, + Month = {Jul}, + Numpages = {0}, + Pages = {1905--1917}, + Publisher = {American Physical Society}, + Title = {Efficient Scheme for GW Quasiparticle Band-Structure Calculations with Aapplications to Bulk Si and to the Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) Surface}, + Url = {https://link.aps.org/doi/10.1103/PhysRevB.52.1905}, + Volume = {52}, + Year = {1995}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.52.1905}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.52.1905}} @article{Verdozzi_1995, - title = {Evaluation of $\mathit{GW}$ Approximations for the Self-Energy of a Hubbard Cluster}, - author = {Verdozzi, C. and Godby, R. W. and Holloway, S.}, - journal = {Phys. Rev. Lett.}, - volume = {74}, - issue = {12}, - pages = {2327--2330}, - numpages = {0}, - year = {1995}, - month = {Mar}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.74.2327}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.74.2327} -} + Author = {Verdozzi, C. and Godby, R. W. and Holloway, S.}, + Doi = {10.1103/PhysRevLett.74.2327}, + Issue = {12}, + Journal = {Phys. Rev. Lett.}, + Month = {Mar}, + Numpages = {0}, + Pages = {2327--2330}, + Publisher = {American Physical Society}, + Title = {Evaluation of $\mathit{GW}$ Approximations for the Self-Energy of a Hubbard Cluster}, + Url = {https://link.aps.org/doi/10.1103/PhysRevLett.74.2327}, + Volume = {74}, + Year = {1995}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.74.2327}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.74.2327}} + @article{Campillo_1999, - title = {Inelastic Lifetimes of Hot Electrons in Real Metals}, - author = {Campillo, I. and Pitarke, J. M. and Rubio, A. and Zarate, E. and Echenique, P. M.}, - journal = {Phys. Rev. Lett.}, - volume = {83}, - issue = {11}, - pages = {2230--2233}, - numpages = {0}, - year = {1999}, - month = {Sep}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.83.2230}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.2230} -} + Author = {Campillo, I. and Pitarke, J. M. and Rubio, A. and Zarate, E. and Echenique, P. M.}, + Doi = {10.1103/PhysRevLett.83.2230}, + Issue = {11}, + Journal = {Phys. Rev. Lett.}, + Month = {Sep}, + Numpages = {0}, + Pages = {2230--2233}, + Publisher = {American Physical Society}, + Title = {Inelastic Lifetimes of Hot Electrons in Real Metals}, + Url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.2230}, + Volume = {83}, + Year = {1999}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.2230}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.83.2230}} @article{Onida_2002, Author = {Onida, Giovanni and Reining, Lucia and Rubio, Angel}, @@ -708,13 +747,14 @@ @article{Dreuw_2004, Author = {Dreuw, Andreas and Head-Gordon, Martin}, + Date-Modified = {2020-04-17 20:05:23 +0200}, Doi = {10.1021/ja039556n}, Eprint = {https://doi.org/10.1021/ja039556n}, Journal = {Journal of the American Chemical Society}, Note = {PMID: 15038755}, Number = {12}, Pages = {4007-4016}, - Title = {Failure of Time-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States:  The Zincbacteriochlorin−Bacteriochlorin and Bacteriochlorophyll−Spheroidene Complexes}, + Title = {Failure of Time-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States: The Zincbacteriochlorin-Bacteriochlorin and Bacteriochlorophyll-Spheroidene Complexes}, Url = {https://doi.org/10.1021/ja039556n}, Volume = {126}, Year = {2004}, @@ -1248,143 +1288,125 @@ Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.115433}, Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.81.115433}} - @article{Rangel_2016, -author = {Rangel, Tonatiuh and Hamed, Samia M. and Bruneval, Fabien and Neaton, Jeffrey B.}, -title = {Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes}, -journal = {J. Chem. Theory Comput. }, -volume = {12}, -number = {6}, -pages = {2834-2842}, -year = {2016}, -doi = {10.1021/acs.jctc.6b00163}, - note ={PMID: 27123935}, -URL = { https://doi.org/10.1021/acs.jctc.6b00163}, -eprint = { https://doi.org/10.1021/acs.jctc.6b00163} -} - + Author = {Rangel, Tonatiuh and Hamed, Samia M. and Bruneval, Fabien and Neaton, Jeffrey B.}, + Doi = {10.1021/acs.jctc.6b00163}, + Eprint = {https://doi.org/10.1021/acs.jctc.6b00163}, + Journal = {J. Chem. Theory Comput.}, + Note = {PMID: 27123935}, + Number = {6}, + Pages = {2834-2842}, + Title = {Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes}, + Url = {https://doi.org/10.1021/acs.jctc.6b00163}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00163}} @article{Bruneval_2013, -author = {Bruneval, Fabien and Marques, Miguel A. L.}, -title = {Benchmarking the Starting Points of the GW Approximation for Molecules}, -journal = {J. Chem. Theory Comput. }, -volume = {9}, -number = {1}, -pages = {324-329}, -year = {2013}, -doi = {10.1021/ct300835h}, - note ={PMID: 26589035}, -URL = { https://doi.org/10.1021/ct300835h}, -eprint = { https://doi.org/10.1021/ct300835h} -} - + Author = {Bruneval, Fabien and Marques, Miguel A. L.}, + Doi = {10.1021/ct300835h}, + Eprint = {https://doi.org/10.1021/ct300835h}, + Journal = {J. Chem. Theory Comput.}, + Note = {PMID: 26589035}, + Number = {1}, + Pages = {324-329}, + Title = {Benchmarking the Starting Points of the GW Approximation for Molecules}, + Url = {https://doi.org/10.1021/ct300835h}, + Volume = {9}, + Year = {2013}, + Bdsk-Url-1 = {https://doi.org/10.1021/ct300835h}} @article{Knight_2016, -author = {Knight, Joseph W. and Wang, Xiaopeng and Gallandi, Lukas and Dolgounitcheva, Olga and Ren, Xinguo and Ortiz, J. Vincent and Rinke, Patrick and Körzdörfer, Thomas and Marom, Noa}, -title = {Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules III: A Benchmark of GW Methods}, -journal = {J. Chem. Theory Comput. }, -volume = {12}, -number = {2}, -pages = {615-626}, -year = {2016}, -doi = {10.1021/acs.jctc.5b00871}, - note ={PMID: 26731609}, -URL = { https://doi.org/10.1021/acs.jctc.5b00871}, -eprint = { https://doi.org/10.1021/acs.jctc.5b00871} -} - - + Author = {Knight, Joseph W. and Wang, Xiaopeng and Gallandi, Lukas and Dolgounitcheva, Olga and Ren, Xinguo and Ortiz, J. Vincent and Rinke, Patrick and K{\"o}rzd{\"o}rfer, Thomas and Marom, Noa}, + Doi = {10.1021/acs.jctc.5b00871}, + Eprint = {https://doi.org/10.1021/acs.jctc.5b00871}, + Journal = {J. Chem. Theory Comput.}, + Note = {PMID: 26731609}, + Number = {2}, + Pages = {615-626}, + Title = {Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules III: A Benchmark of GW Methods}, + Url = {https://doi.org/10.1021/acs.jctc.5b00871}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00871}} @article{Kaplan_2016, -author = {Kaplan, F. and Harding, M. E. and Seiler, C. and Weigend, F. and Evers, F. and van Setten, M. J.}, -title = {Quasi-Particle Self-Consistent GW for Molecules}, -journal = {J. Chem. Theory Comput. }, -volume = {12}, -number = {6}, -pages = {2528-2541}, -year = {2016}, -doi = {10.1021/acs.jctc.5b01238}, - note ={PMID: 27168352}, -URL = { https://doi.org/10.1021/acs.jctc.5b01238}, -eprint = { https://doi.org/10.1021/acs.jctc.5b01238} -} - + Author = {Kaplan, F. and Harding, M. E. and Seiler, C. and Weigend, F. and Evers, F. and van Setten, M. J.}, + Doi = {10.1021/acs.jctc.5b01238}, + Eprint = {https://doi.org/10.1021/acs.jctc.5b01238}, + Journal = {J. Chem. Theory Comput.}, + Note = {PMID: 27168352}, + Number = {6}, + Pages = {2528-2541}, + Title = {Quasi-Particle Self-Consistent GW for Molecules}, + Url = {https://doi.org/10.1021/acs.jctc.5b01238}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01238}} @article{Caruso_2016, -author = {Caruso, Fabio and Dauth, Matthias and van Setten, Michiel J. and Rinke, Patrick}, -title = {Benchmark of GW Approaches for the GW100 Test Set}, -journal = {Journal of Chemical Theory and Computation}, -volume = {12}, -number = {10}, -pages = {5076-5087}, -year = {2016}, -doi = {10.1021/acs.jctc.6b00774}, - note ={PMID: 27631585}, -URL = { https://doi.org/10.1021/acs.jctc.6b00774}, -eprint = { https://doi.org/10.1021/acs.jctc.6b00774} -} - + Author = {Caruso, Fabio and Dauth, Matthias and van Setten, Michiel J. and Rinke, Patrick}, + Doi = {10.1021/acs.jctc.6b00774}, + Eprint = {https://doi.org/10.1021/acs.jctc.6b00774}, + Journal = {Journal of Chemical Theory and Computation}, + Note = {PMID: 27631585}, + Number = {10}, + Pages = {5076-5087}, + Title = {Benchmark of GW Approaches for the GW100 Test Set}, + Url = {https://doi.org/10.1021/acs.jctc.6b00774}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00774}} @article{Korbel_2014, -author = {K{\"{o}}rbel, Sabine and Boulanger, Paul and Duchemin, Ivan and Blase, Xavier and Marques, Miguel A. L. and Botti, Silvana}, -title = {Benchmark Many-Body GW and Bethe–Salpeter Calculations for Small Transition Metal Molecules}, -journal = {J. Chem. Theory Comput. }, -volume = {10}, -number = {9}, -pages = {3934-3943}, -year = {2014}, -doi = {10.1021/ct5003658}, - note ={PMID: 26588537}, -URL = { https://doi.org/10.1021/ct5003658}, -eprint = { https://doi.org/10.1021/ct5003658} -} - + Author = {K{\"{o}}rbel, Sabine and Boulanger, Paul and Duchemin, Ivan and Blase, Xavier and Marques, Miguel A. L. and Botti, Silvana}, + Doi = {10.1021/ct5003658}, + Eprint = {https://doi.org/10.1021/ct5003658}, + Journal = {J. Chem. Theory Comput.}, + Note = {PMID: 26588537}, + Number = {9}, + Pages = {3934-3943}, + Title = {Benchmark Many-Body GW and Bethe--Salpeter Calculations for Small Transition Metal Molecules}, + Url = {https://doi.org/10.1021/ct5003658}, + Volume = {10}, + Year = {2014}, + Bdsk-Url-1 = {https://doi.org/10.1021/ct5003658}} @article{Blase_2011b, -author = {Blase,X. and Attaccalite,C. }, -title = {Charge-Transfer Excitations in Molecular Donor-Acceptor Complexes within the Many-Body Bethe-Salpeter Approach}, -journal = {Appl. Phys. Lett. }, -volume = {99}, -number = {17}, -pages = {171909}, -year = {2011}, -doi = {10.1063/1.3655352}, -URL = { https://doi.org/10.1063/1.3655352}, -eprint = { https://doi.org/10.1063/1.3655352} -} - - -@article{Duchemin_2012, - title = {Short-Range to Long-Range Charge-Transfer Excitations in the Zincbacteriochlorin-Bacteriochlorin Complex: A Bethe-Salpeter Study}, - author = {Duchemin, I. and Deutsch, T. and Blase, X.}, - journal = {Phys. Rev. Lett.}, - volume = {109}, - issue = {16}, - pages = {167801}, - numpages = {6}, - year = {2012}, - month = {Oct}, - publisher = {American Physical Society}, - doi = {10.1103/PhysRevLett.109.167801}, - url = {https://link.aps.org/doi/10.1103/PhysRevLett.109.167801} -} - - + Author = {Blase,X. and Attaccalite,C.}, + Doi = {10.1063/1.3655352}, + Eprint = {https://doi.org/10.1063/1.3655352}, + Journal = {Appl. Phys. Lett.}, + Number = {17}, + Pages = {171909}, + Title = {Charge-Transfer Excitations in Molecular Donor-Acceptor Complexes within the Many-Body Bethe-Salpeter Approach}, + Url = {https://doi.org/10.1063/1.3655352}, + Volume = {99}, + Year = {2011}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.3655352}} @article{Stein_2009, -author = {Stein, Tamar and Kronik, Leeor and Baer, Roi}, -title = {Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory}, -journal = {J. Am. Chem. Soc.}, -volume = {131}, -number = {8}, -pages = {2818-2820}, -year = {2009}, -doi = {10.1021/ja8087482}, - note ={PMID: 19239266}, -URL = { https://doi.org/10.1021/ja8087482}, -eprint = { https://doi.org/10.1021/ja8087482} -} - - - + Author = {Stein, Tamar and Kronik, Leeor and Baer, Roi}, + Doi = {10.1021/ja8087482}, + Eprint = {https://doi.org/10.1021/ja8087482}, + Journal = {J. Am. Chem. Soc.}, + Note = {PMID: 19239266}, + Number = {8}, + Pages = {2818-2820}, + Title = {Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory}, + Url = {https://doi.org/10.1021/ja8087482}, + Volume = {131}, + Year = {2009}, + Bdsk-Url-1 = {https://doi.org/10.1021/ja8087482}} +@article{Garniron_2018, + Author = {Y. Garniron and A. Scemama and E. Giner and M. Caffarel and P. F. Loos}, + Date-Added = {2018-11-29 14:23:11 +0100}, + Date-Modified = {2018-11-29 14:23:11 +0100}, + Doi = {10.1063/1.5044503}, + Journal = {J. Chem. Phys.}, + Pages = {064103}, + Title = {Selected Configuration Interaction Dressed by Perturbation}, + Volume = {149}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5044503}}