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\cal { cal}
\DeclareSIUnit \kcal { \kilo \cal }
\newcommand { \kcalmol } { \si { \kcal \per \mole } }
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%geometries
\newcommand { \Dtwo } { $ D _ { 2 h } $ }
\newcommand { \Dfour } { $ D _ { 4 h } $ }
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\sisetup { range-phrase=--}
\sisetup { range-units=single}
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%states
%D2h states
\newcommand { \oneAg } { $ 1 { } ^ 1 A _ g $ }
\newcommand { \tBoneg } { $ 1 { } ^ 3 B _ { 1 g } $ }
\newcommand { \sBoneg } { $ 1 { } ^ 1 B _ { 1 g } $ }
\newcommand { \twoAg } { $ 2 { } ^ 1 A _ g $ }
%D4h states
%\newcommand{\oneBoneg}{$1{}^1B_{1g}$} same label as the D2h state
\newcommand { \Atwog } { $ 1 { } ^ 3 A _ { 2 g } $ }
\newcommand { \Aoneg } { $ 1 { } ^ 1 A _ { 1 g } $ }
\newcommand { \Btwog } { $ 1 { } ^ 1 B _ { 2 g } $ }
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% addresses
\newcommand { \LCPQ } { Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\' e de Toulouse, CNRS, UPS, France}
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\newcommand { \CEISAM } { 4Nantes Universit\' e, CNRS, CEISAM UMR-6230, Nantes F-44000, France.}
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\begin { document}
\title { Supporting Information for ``Reference Energies for Cyclobutadiene: Autoisomerization and Excited States''}
\author { Enzo \surname { Monino} }
\email { emonino@irsamc.ups-tlse.fr}
\affiliation { \LCPQ }
\author { Martial \surname { Boggio-Pasqua} }
\affiliation { \LCPQ }
\author { Anthony \surname { Scemama} }
\affiliation { \LCPQ }
\author { Denis \surname { Jacquemin} }
\affiliation { \CEISAM }
\author { Pierre-Fran\c { c} ois \surname { Loos} }
\email { loos@irsamc.ups-tlse.fr}
\affiliation { \LCPQ }
%\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%
\section { Geometries}
%%%%%%%%%%%%%%%%%%%%%%%%
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Below, we provide the Cartesian coordinates (in \si { \angstrom } ) of the geometries that are employed in this work.
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\begin { itemize}
\item { \Dtwo } rectangular equilibrium geometry of the { \oneAg } ground state computed at the CASPT2(12,12)/aug-cc-pVTZ level:
\begin { verbatim}
C 0.0000000000 -0.6769380253 -0.7827569236
C 0.0000000000 -0.6769380253 0.7827569236
C 0.0000000000 0.6769380253 0.7827569236
C 0.0000000000 0.6769380253 -0.7827569236
H 0.0000000000 -1.4379809006 -1.5441628360
H 0.0000000000 -1.4379809006 1.5441628360
H 0.0000000000 1.4379809006 1.5441628360
H 0.0000000000 1.4379809006 -1.5441628360
\end { verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
\item { \Dfour } square planar equilibrium geometry of the { \sBoneg } ground state computed at the CASPT2(12,12)/aug-cc-pVTZ level:
\begin { verbatim}
C 1.0248323754 0.0000000000 0.0000000000
C 0.0000000000 -1.0248323754 0.0000000000
C -1.0248323754 0.0000000000 0.0000000000
C 0.0000000000 1.0248323754 0.0000000000
H 2.1005277359 0.0000000000 0.0000000000
H 0.0000000000 -2.1005277359 0.0000000000
H -2.1005277359 0.0000000000 0.0000000000
H 0.0000000000 2.1005277359 0.0000000000
\end { verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
\item { \Dtwo } rectangular equilibrium geometry of the { \oneAg } ground state computed at the CC3/aug-cc-pVTZ level:
\begin { verbatim}
C -0.78248546 -0.67208001 0.00000000
C 0.78248546 -0.67208001 0.00000000
C -0.78248546 0.67208001 0.00000000
C 0.78248546 0.67208001 0.00000000
H -1.54227765 -1.43404123 -0.00000000
H 1.54227765 -1.43404123 0.00000000
H -1.54227765 1.43404123 0.00000000
H 1.54227765 1.43404123 -0.00000000
\end { verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%
\item { \Dfour } square planar equilibrium geometry of the { \Atwog } state computed at the (RO)-CCSD(T)/aug-cc-pVTZ level:
\begin { verbatim}
C 0.000000 1.017702 0.000000
C 1.017702 -0.000000 0.000000
C -1.017702 0.000000 0.000000
C -0.000000 -1.017702 0.000000
H 0.000000 2.092429 0.000000
H 2.092429 -0.000000 0.000000
H -0.000000 -2.092429 0.000000
H -2.092429 0.000000 0.000000
\end { verbatim}
%%%%%%%%%%%%%%%%%%%%%%%%
\end { itemize}
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\begin { squeezetable}
\begin { table*}
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\caption { Energy differences between the states computed with various methods and the reference TBE values.
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Note that AB stands for the automerization barrier and is reported in \si { \kcalmol } .
The numbers reported in parenthesis are the percentage of single excitations involved in the transition ($ \% T _ 1 $ ) calculated at the CC3/aug-cc-pVTZ level.
The values between square brackets have been obtained by extrapolation via the procedure described in the corresponding footnote.}
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%\hl{On which geoms ? You give 2 pairs on previous page, but we are not sure which one are used here}}
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\label { tab:TBE}
\begin { ruledtabular}
\begin { tabular} { lrrrrrrr}
%\begin{tabular}{*{1}{*{8}{l}}}
& & \mc { 3} { c} { { \Dtwo } excitation energies (eV)} & \mc { 3} { c} { { \Dfour } excitation energies (eV)} \\
\cline { 3-5} \cline { 6-8}
Method & AB & { \tBoneg } (99\% ) & { \sBoneg } (95\% )& { \twoAg } (1\% ) & { \Atwog } & { \Aoneg } & { \Btwog } \\
\hline
SF-TD-B3LYP & $ 10 . 41 $ & $ 0 . 241 $ & $ - 0 . 926 $ & $ - 0 . 161 $ & $ - 0 . 164 $ & $ - 1 . 028 $ & $ - 1 . 501 $ \\
SF-TD-PBE0 & $ 8 . 95 $ & $ 0 . 220 $ & $ - 0 . 829 $ & $ - 0 . 068 $ & $ - 0 . 163 $ & $ - 0 . 903 $ & $ - 1 . 357 $ \\
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SF-TD-BH\& HLYP & $ 3 . 79 $ & $ 0 . 078 $ & $ - 0 . 393 $ & $ 0 . 343 $ & $ - 0 . 099 $ & $ - 0 . 251 $ & $ - 0 . 603 $ \\
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SF-TD-M06-2X & $ 1 . 42 $ & $ 0 . 000 $ & $ - 0 . 354 $ & $ 0 . 208 $ & $ - 0 . 066 $ & $ - 0 . 097 $ & $ - 0 . 432 $ \\
SF-TD-CAM-B3LYP & $ 9 . 90 $ & $ 0 . 280 $ & $ - 0 . 807 $ & $ - 0 . 011 $ & $ - 0 . 134 $ & $ - 0 . 920 $ & $ - 1 . 370 $ \\
SF-TD-$ \omega $ B97X-V & $ 10 . 01 $ & $ 0 . 335 $ & $ - 0 . 774 $ & $ 0 . 064 $ & $ - 0 . 118 $ & $ - 0 . 928 $ & $ - 1 . 372 $ \\
SF-TD-LC-$ \omega $ PBE08 & $ 10 . 81 $ & $ 0 . 435 $ & $ - 0 . 710 $ & $ 0 . 199 $ & $ - 0 . 086 $ & $ - 0 . 939 $ & $ - 1 . 376 $ \\
SF-TD-M11 & $ 2 . 29 $ & $ 0 . 097 $ & $ - 0 . 474 $ & $ 0 . 151 $ & $ - 0 . 063 $ & $ - 0 . 312 $ & $ - 0 . 675 $ \\ [0.1cm]
SF-ADC(2)-s & $ - 0 . 30 $ & $ 0 . 069 $ & $ - 0 . 026 $ & $ - 0 . 018 $ & $ 0 . 112 $ & $ 0 . 112 $ & $ - 0 . 190 $ \\
SF-ADC(2)-x & $ 1 . 44 $ & $ 0 . 077 $ & $ - 0 . 094 $ & $ - 0 . 446 $ & $ 0 . 068 $ & $ - 0 . 409 $ & $ - 0 . 303 $ \\
SF-ADC(2.5) & $ 0 . 18 $ & $ 0 . 013 $ & $ 0 . 006 $ & $ 0 . 029 $ & $ 0 . 024 $ & $ 0 . 094 $ & $ - 0 . 185 $ \\
SF-ADC(3) & $ 0 . 65 $ & $ - 0 . 043 $ & $ 0 . 037 $ & $ 0 . 075 $ & $ - 0 . 065 $ & $ 0 . 075 $ & $ - 0 . 181 $ \\ [0.1cm]
CASSCF(4,4) & $ - 1 . 55 $ & $ 0 . 208 $ & $ 1 . 421 $ & $ 0 . 292 $ & $ 0 . 290 $ & $ 0 . 734 $ & $ 1 . 390 $ \\
CASPT2(4,4) & $ - 1 . 16 $ & $ - 0 . 050 $ & $ - 0 . 202 $ & $ - 0 . 077 $ & $ - 0 . 016 $ & $ 0 . 006 $ & $ - 0 . 399 $ \\
%XMS-CASPT2(4,4) & & & & $-0.035$ & & & \\
SC-NEVPT2(4,4) & $ 0 . 30 $ & $ - 0 . 083 $ & $ - 0 . 703 $ & $ - 0 . 041 $ & $ - 0 . 120 $ & $ - 0 . 072 $ & $ - 0 . 979 $ \\
PC-NEVPT2(4,4) & $ 0 . 31 $ & $ - 0 . 080 $ & $ - 0 . 757 $ & $ - 0 . 066 $ & $ - 0 . 118 $ & $ - 0 . 097 $ & $ - 1 . 031 $ \\
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%MRCI(4,4) & & $0.106$ & $0.553$ & $0.121$ & $0.127$ & $0.324$ & $0.381$ \\[0.1cm]
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CASSCF(12,12) & $ 2 . 66 $ & $ 0 . 224 $ & $ 0 . 719 $ & $ 0 . 068 $ & $ 0 . 226 $ & $ 0 . 443 $ & $ 0 . 600 $ \\
CASPT2(12,12) & $ - 0 . 42 $ & $ 0 . 018 $ & $ 0 . 058 $ & $ - 0 . 106 $ & $ 0 . 039 $ & $ 0 . 038 $ & $ - 0 . 108 $ \\
%XMS-CASPT2(12,12) & & & & $-0.090$ & & & \\
SC-NEVPT2(12,12) & $ - 0 . 64 $ & $ 0 . 039 $ & $ 0 . 063 $ & $ - 0 . 063 $ & $ 0 . 021 $ & $ 0 . 046 $ & $ - 0 . 142 $ \\
PC-NEVPT2(12,12) & $ - 0 . 65 $ & $ 0 . 000 $ & $ - 0 . 062 $ & $ - 0 . 093 $ & $ - 0 . 013 $ & $ - 0 . 024 $ & $ - 0 . 278 $ \\ [0.1cm]
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CCSD & $ 0 . 95 $ & $ - 0 . 145 $ & $ 0 . 067 $ & & $ - 0 . 059 $ & $ 0 . 100 $ & \\
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CC3 & $ - 1 . 05 $ & $ - 0 . 060 $ & $ - 0 . 006 $ & $ 0 . 628 $ & & $ 0 . 162 $ & $ 0 . 686 $ \\
CCSDT & $ - 0 . 25 $ & $ - 0 . 051 $ & $ 0 . 014 $ & $ 0 . 280 $ & $ 0 . 005 $ & $ 0 . 131 $ & $ 0 . 503 $ \\
CC4 & $ - 0 . 11 $ & & $ 0 . 003 $ & $ - 0 . 006 $ & & $ 0 . 011 $ & $ - 0 . 013 $ \\
CCSDTQ & $ 0 . 00 $ & & $ 0 . 000 $ & $ 0 . 000 $ & $ 0 . 000 $ & $ 0 . 000 $ & $ 0 . 000 $ \\ [0.1cm]
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%CIPSI & & $-0.001\pm 0.030$ & $0.017\pm 0.035$ & $-0.120\pm 0.090$ & $0.025\pm 0.029$ & $0.130\pm 0.050$ & \\
\bf { TBE} & $ [ \bf { 8 . 93 } ] $ \fnm [1] & $ [ \bf { 1 . 462 } ] $ \fnm [2] & $ [ \bf { 3 . 125 } ] $ \fnm [3] & $ [ \bf { 4 . 149 } ] $ \fnm [3] & $ [ \bf { 0 . 144 } ] $ \fnm [4] & $ [ \bf { 1 . 500 } ] $ \fnm [3] & $ [ \bf { 2 . 034 } ] $ \fnm [3] \\ [0.1cm]
Literature & $ 8 . 53 $ \fnm [5] & $ 1 . 573 $ \fnm [5] & $ 3 . 208 $ \fnm [5] & $ 4 . 247 $ \fnm [5] & $ 0 . 266 $ \fnm [5] & $ 1 . 664 $ \fnm [5] & $ 1 . 910 $ \fnm [5] \\
& $ 10 . 35 $ \fnm [6] & $ 1 . 576 $ \fnm [6] & $ 3 . 141 $ \fnm [6] & $ 3 . 796 $ \fnm [6] & $ 0 . 217 $ \fnm [6] & $ 1 . 123 $ \fnm [6] & $ 1 . 799 $ \fnm [6] \\
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& $ 9 . 58 $ \fnm [7] & $ 1 . 456 $ \fnm [7] & $ 3 . 285 $ \fnm [7] & $ 4 . 334 $ \fnm [7] & $ 0 . 083 $ \fnm [7] & $ 1 . 621 $ \fnm [7] & $ 1 . 930 $ \fnm [7] \\
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& $ 7 . 48 $ \fnm [8] & $ 1 . 654 $ \fnm [8] & $ 3 . 416 $ \fnm [8] & $ 4 . 360 $ \fnm [8] & $ 0 . 369 $ \fnm [8] & $ 1 . 824 $ \fnm [8] & $ 2 . 143 $ \fnm [8] \\
\end { tabular}
\end { ruledtabular}
\fnt [1] { Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
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\fnt [2] { Value obtained using NEVPT2(12,12).}
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\fnt [3] { Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CC4/aug-cc-pVTZ and CC4/aug-cc-pVDZ.}
\fnt [4] { Value obtained using CCSDTQ/aug-cc-pVDZ corrected by the difference between CCSDT/aug-cc-pVTZ and CCSDT/aug-cc-pVDZ.}
\fnt [5] { Value obtained from Ref.~\onlinecite { Lefrancois_ 2015} at the SF-ADC(2)-s/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
\fnt [6] { Value obtained from Ref.~\onlinecite { Lefrancois_ 2015} at the SF-ADC(2)-x/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
\fnt [7] { Value obtained from Ref.~\onlinecite { Lefrancois_ 2015} at the SF-ADC(3)/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
\fnt [8] { Value obtained from Ref.~\onlinecite { Manohar_ 2008} at the EOM-SF-CCSD/cc-pVTZ level with the geometry obtained at the CCSD(T)/cc-pVTZ level.}
\end { table*}
\end { squeezetable}
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%%% %%% %%% %%%
\begin { table}
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\caption { Automerization energy (in \si { \kcalmol } ) of CBD computed at various levels of theory.}
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% \label{}
\begin { ruledtabular}
\begin { tabular} { lcr}
% & \mc{4}{c}{Basis sets} \\
% \cline{2-5}
Level of theory & Automerization barrier & Reference \\
& (\kcalmol ) & \\
\hline
CCSDTQ/aug-cc-pVTZ & $ 8 . 93 $ & This work \\
ic-MRCISD+Q/cc-pVTZ & $ 8 . 93 $ & Ref.~\onlinecite { Zhang_ 2019} \\
Mk-MRCCSD/cc-pVTZ & $ 10 . 09 $ & Ref.~\onlinecite { Zhang_ 2019} \\
Mk-MRCCSD(T)/cc-pVTZ & $ 8 . 56 $ & Ref.~\onlinecite { Zhang_ 2019} \\
SUCCSD/cc-pVTZ & $ 8 . 7 $ & Ref.~\onlinecite { Li_ 2009} \\
MkCCSD/cc-pVTZ & $ 9 . 6 $ & Ref.~\onlinecite { Li_ 2009} \\
RMRCCSD(T)/cc-pVTZ & $ 9 . 5 $ & Ref.~\onlinecite { Li_ 2009} \\
MRCISD/cc-pVTZ & $ 8 . 4 $ & Ref.~\onlinecite { Eckert-Maksic_ 2006} \\
MRCISD + Q/cc-pVTZ & $ 8 . 8 $ & Ref.~\onlinecite { Eckert-Maksic_ 2006} \\
MRAQCC/cc-pVTZ & $ 8 . 9 $ & Ref.~\onlinecite { Eckert-Maksic_ 2006} \\
CCSDt/cc-pVTZ & $ 9 . 5 $ & Ref.~\onlinecite { Shen_ 2012} \\
CCSD(T)-h/cc-pVTZ & $ 6 . 8 $ & Ref.~\onlinecite { Shen_ 2012} \\
CC(t;3)/cc-pVTZ & $ 10 . 0 $ & Ref.~\onlinecite { Shen_ 2012} \\
\end { tabular}
\end { ruledtabular}
\end { table}
%%% %%% %%% %%%
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%%%%%%%%%%%%%%%%%%%%%%%%
\begin { table}
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\caption { $ \expval * { S ^ 2 } $ values for the different excited states computed at the SF-TD-DFT/aug-cc-pVTZ level for the { \Dtwo } and { \Dfour } structures.}
%\hl{same comment as for Table I}
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% \label{tab:Ssquare}
\begin { ruledtabular}
\begin { tabular} { lrrrrrr}
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& \mc { 3} { c} { $ \expval * { S ^ 2 } $ for { \Dtwo } geometry} & \mc { 3} { c} { { $ \expval * { S ^ 2 } $ for { \Dfour } geometry} } \\
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\cline { 2-4} \cline { 5-7}
Method & { \tBoneg } & { \sBoneg } & { \twoAg } & { \Atwog } & { \Aoneg } & { \Btwog } \\
\hline
SF-TD-B3LYP
& $ 1 . 989 $ & $ 0 . 030 $ & $ 0 . 017 $ & $ 2 . 007 $ & $ 0 . 014 $ & $ 0 . 012 $ \\ [0.1cm]
SF-TD-PBE0
& $ 2 . 001 $ & $ 0 . 021 $ & $ 0 . 019 $ & $ 2 . 009 $ & $ 0 . 018 $ & $ 0 . 012 $ \\ [0.1cm]
SF-TD-BH\& HLYP
& $ 2 . 017 $ & $ 0 . 026 $ & $ 0 . 041 $ & $ 2 . 020 $ & $ 0 . 021 $ & $ 0 . 018 $ \\ [0.1cm]
SF-TD-M06-2X
& $ 2 . 014 $ & $ 0 . 017 $ & $ 0 . 040 $ & $ 2 . 014 $ & $ 0 . 015 $ & $ 0 . 012 $ \\ [0.1cm]
SF-TD-CAM-B3LYP
& $ 1 . 990 $ & $ 0 . 033 $ & $ 0 . 024 $ & $ 2 . 008 $ & $ 0 . 013 $ & $ 0 . 012 $ \\ [0.1cm]
SF-TD-$ \omega $ B97X-V
& $ 1 . 986 $ & $ 0 . 035 $ & $ 0 . 024 $ & $ 2 . 008 $ & $ 0 . 012 $ & $ 0 . 010 $ \\ [0.1cm]
SF-TD-LC-$ \omega $ PBE08
& $ 1 . 984 $ & $ 0 . 044 $ & $ 0 . 031 $ & $ 2 . 012 $ & $ 0 . 015 $ & $ 0 . 012 $ \\ [0.1cm]
SF-TD-M11
& $ 2 . 011 $ & $ 0 . 023 $ & $ 0 . 045 $ & $ 2 . 012 $ & $ 0 . 016 $ & $ 0 . 014 $ \\
\end { tabular}
\end { ruledtabular}
\end { table}
%%% %%% %%% %%%
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\clearpage
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%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\bibliography { CBD}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\end { document}