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| Author | SHA1 | Date |
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 Pierre-Francois Loos
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3e99514b7b | |
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Pierre-Francois Loos
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2c3d87cb1e | |
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Pierre-Francois Loos
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123d0b8e63 | |
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Pierre-Francois Loos
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cb43a246af | |
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Pierre-Francois Loos
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94653f3c8d | |
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Pierre-Francois Loos
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4b2b705d8b | |
 Anthony Scemama
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12786a98f2 | |
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Anthony Scemama
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9701f96199 |
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Data/QUESTDB.nb
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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2020-11-23 11:06:10 +0100
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%% Created for Pierre-Francois Loos at 2020-11-25 13:44:50 +0100
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%% Saved with string encoding Unicode (UTF-8)
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@article{Lee_2020,
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author = {Joonho Lee and Fionn D. Malone and David R. Reichman},
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date-added = {2020-11-25 13:44:34 +0100},
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date-modified = {2020-11-25 13:44:34 +0100},
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doi = {10.1063/5.0024835},
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journal = {J. Chem. Phys.},
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pages = {126101},
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title = {The performance of phaseless auxiliary-field quantum Monte Carlo on the ground state electronic energy of benzene},
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volume = {153},
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year = {2020},
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Bdsk-Url-1 = {https://doi.org/10.1063/5.0024835}}
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@article{Loos_2019d,
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author = {P. F. Loos and B. Pradines and A. Scemama and J. Toulouse and E. Giner},
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date-added = {2020-11-23 11:06:04 +0100},
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@ -115,7 +115,7 @@ The reasons behind this are (at least) threefold: i) one might lack a proper var
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ground-state ``bias'', ii) accurately modeling the electronic structure of excited states usually requires larger one-electron basis sets (including diffuse functions most of the times) than their
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ground-state counterpart, and iii) excited states can be governed by different amounts of dynamic/static correlations, present very different physical natures ($\pi \to \pis$, $n \to \pis$, charge
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transfer, double excitation, valence, Rydberg, singlet, doublet, triplet, etc), yet be very close in energy from one another. Hence, designing excited-state methods able to tackle simultaneously
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and on an equal footing all these types of excited states at an affordable cost remain an open challenge in theoretical computational chemistry as evidenced by the large number of review
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and on an equal footing all these types of excited states at an affordable cost remains an open challenge in theoretical computational chemistry as evidenced by the large number of review
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articles on this particular subject \cite{Roos_1996,Piecuch_2002,Dreuw_2005,Krylov_2006,Sneskov_2012,Gonzales_2012,Laurent_2013,Adamo_2013,Dreuw_2015,Ghosh_2018,Blase_2020,Loos_2020a}.
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@ -146,7 +146,7 @@ CASPT2 \cite{Andersson_1990,Andersson_1992,Roos,Roos_1996} calculations (with th
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transitions. These TBEs were quickly refined with the larger aug-cc-pVTZ basis set \cite{Silva-Junior_2010b,Silva-Junior_2010c}. In the same spirit, it is also worth mentioning Gordon's set of vertical transitions
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(based on experimental values) \cite{Leang_2012} used to benchmark the performance of time-dependent density-functional theory (TD-DFT) \cite{Runge_1984,Casida_1995,Casida_2012,Ulrich_2012}, as well
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as its extended version by Goerigk and coworkers who decided to replace the experimental reference values by CC3 excitation energies \cite{Schwabe_2017,Casanova-Paez_2019,Casanova_Paes_2020}.
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For comparisons with experimental values, there also exist various sets of measured 0-0 energies used in various benchmarks, notably by the Furche \cite{Furche_2002,Send_2011a}, H\"attig \cite{Winter_2013}
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For comparisons with experimental values, there also exists various sets of measured 0-0 energies used in various benchmarks, notably by the Furche \cite{Furche_2002,Send_2011a}, H\"attig \cite{Winter_2013}
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and our \cite{Loos_2018,Loos_2019a,Loos_2019b} groups for gas-phase compounds and by Grimme \cite{Dierksen_2004,Goerigk_2010a} and one of us \cite{Jacquemin_2012,Jacquemin_2015b} for solvated dyes.
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Let us also mention the new benchmark set of charge-transfer excited states recently introduced by Szalay and coworkers [based on equation-of-motion coupled cluster (EOM-CC) methods] \cite{Kozma_2020}
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as well as the Gagliardi-Truhlar set employed to compare the accuracy of multiconfiguration pair-density functional theory \cite{Ghosh_2018} against the well-established CASPT2 method \cite{Hoyer_2016}.
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@ -173,12 +173,12 @@ review the generic benchmark studies devoted to adiabatic and 0-0 energies perfo
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The QUEST dataset has the particularity to be based in a large proportion on selected configuration interaction (SCI) reference excitation energies as well as high-order linear-response (LR) CC methods such as LR-CCSDT and
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LR-CCSDTQ \cite{Noga_1987,Koch_1990,Kucharski_1991,Christiansen_1998b,Kucharski_2001,Kowalski_2001,Kallay_2003,Kallay_2004,Hirata_2000,Hirata_2004}. Recently, SCI methods have been a force to reckon with for
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the computation of highly-accurate energies in small- and medium-sized molecules as they yield near full configuration interaction (FCI) quality energies for only a fraction of the computational cost of a genuine FCI calculation \cite{Booth_2009,Booth_2010,Cleland_2010,Booth_2011,Daday_2012,Blunt_2015,Ghanem_2019,Deustua_2017,Deustua_2018,Holmes_2017,Chien_2018,Li_2018,Yao_2020,Li_2020,Eriksen_2017,Eriksen_2018,Eriksen_2019a,Eriksen_2019b,Xu_2018,Xu_2020,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c,Loos_2020a,Loos_2020e,Eriksen_2021}.
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Due to the fairly natural idea underlying these methods, the SCI family is composed by numerous members \cite{Bender_1969,Whitten_1969,Huron_1973,Abrams_2005,Bunge_2006,Bytautas_2009,Giner_2013,Caffarel_2014,Giner_2015,Garniron_2017b,Caffarel_2016a,Caffarel_2016b,Holmes_2016,Sharma_2017,Holmes_2017,Chien_2018,Scemama_2018,Scemama_2018b,Garniron_2018,Evangelista_2014,Schriber_2016,Schriber_2017,Liu_2016,Per_2017,Ohtsuka_2017,Zimmerman_2017,Li_2018,Ohtsuka_2017,Coe_2018,Loos_2019}.
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Their fundamental philosophy consists, roughly speaking, in retaining only the most energetically relevant determinants of the FCI space following a given criterion to slow down the exponential increase of the size of the CI expansion.
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Due to the fairly natural idea underlying these methods, the SCI family is composed by numerous members \cite{Bender_1969,Whitten_1969,Huron_1973,Abrams_2005,Bunge_2006,Bytautas_2009,Giner_2013,Caffarel_2014,Giner_2015,Garniron_2017b,Caffarel_2016a,Caffarel_2016b,Holmes_2016,Sharma_2017,Holmes_2017,Chien_2018,Scemama_2018,Scemama_2018b,Garniron_2018,Evangelista_2014,Tubman_2016,Tubman_2020,Schriber_2016,Schriber_2017,Liu_2016,Per_2017,Ohtsuka_2017,Zimmerman_2017,Li_2018,Ohtsuka_2017,Coe_2018,Loos_2019}.
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Their fundamental philosophy consists, roughly speaking, in retaining only the most \alert{\textst{energetically}} relevant determinants of the FCI space following a given criterion to slow down the exponential increase of the size of the CI expansion.
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Originally developed in the late 1960's by Bender and Davidson \cite{Bender_1969} as well as Whitten and Hackmeyer \cite{Whitten_1969}, new efficient SCI algorithms have resurfaced recently.
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Four examples are adaptive sampling CI (ASCI) \cite{Tubman_2016,Tubman_2018,Tubman_2020}, iCI \cite{Liu_2014,Liu_2016,Lei_2017,Zhang_2020}, semistochastic heat-bath CI (SHCI) \cite{Holmes_2016,Holmes_2017,Sharma_2017,Li_2018,Li_2020,Yao_2020}), and \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2019}.
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These four flavors of SCI include a second-order perturbative (PT2) correction which is key to estimate the ``distance'' to the FCI solution (see below).
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The SCI calculations performed for the QUEST set of excitation energies relies on the CIPSI algorithm, which is, from a historical point of view, one of the oldest SCI algorithm.
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Three examples are \alert{\textst{adaptive sampling CI (ASCI)}, }iCI \cite{Liu_2014,Liu_2016,Lei_2017,Zhang_2020}, semistochastic heat-bath CI (SHCI) \cite{Holmes_2016,Holmes_2017,Sharma_2017,Li_2018,Li_2020,Yao_2020}, and \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2019}.
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These flavors of SCI include a second-order perturbative (PT2) correction which is key to estimate the ``distance'' to the FCI solution (see below).
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The SCI calculations performed for the QUEST set of excitation energies relies on the CIPSI algorithm, which is, from a historical point of view, one of the oldest SCI algorithms.
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It was developed in 1973 by Huron, Rancurel, and Malrieu \cite{Huron_1973} (see also Refs.~\cite{Evangelisti_1983,Cimiraglia_1985,Cimiraglia_1987,Illas_1988,Povill_1992}).
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Recently, the determinant-driven CIPSI algorithm has been efficiently implemented \cite{Garniron_2019} in the open-source programming environment QUANTUM PACKAGE by the Toulouse group enabling to perform massively
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parallel computations \cite{Garniron_2017,Garniron_2018,Garniron_2019,Loos_2020e}. CIPSI is also frequently employed to provide accurate trial wave functions for quantum Monte Carlo calculations in molecules \cite{Caffarel_2014,Caffarel_2016a,Caffarel_2016b,Giner_2013,Giner_2015,Scemama_2015,Scemama_2016,Scemama_2018,Scemama_2018b,Scemama_2019,Dash_2018,Dash_2019,Scemama_2020} and more recently
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@ -223,7 +223,7 @@ These basis sets are available from the \href{https://www.basissetexchange.org}{
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In order to compute reference vertical energies, we have designed different strategies depending on the actual nature of the transition and the size of the system.
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For small molecules (typically 1--3 non-hydrogen atoms), we mainly resort to SCI methods which can provide near-FCI excitation energies for compact basis sets.
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Obviously, the smaller the molecule, the larger the basis we can afford.
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For larger systems (\ie, 4--6 non-hydrogen atom), one cannot afford SCI calculations anymore expect in a few special occasions, and we then rely on LR-CC theory (LR-CCSDT and LR-CCSDTQ typically \cite{Kucharski_1991,Kallay_2003,Kallay_2004,Hirata_2000,Hirata_2004}) to obtain accurate transition energies.
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For larger systems (\ie, 4--6 non-hydrogen atom), one cannot afford SCI calculations anymore except in a few special occasions, and we then rely on LR-CC theory (LR-CCSDT and LR-CCSDTQ typically \cite{Kucharski_1991,Kallay_2003,Kallay_2004,Hirata_2000,Hirata_2004}) to obtain accurate transition energies.
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In the following, we will omit the prefix LR for the sake of clarity, as equivalent values would be obtained with the equation-of-motion (EOM) formalism \cite{Rowe_1968,Stanton_1993}.
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The CC calculations are performed with several codes.
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@ -290,7 +290,7 @@ The definition of the active space considered for each system as well as the num
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%------------------------------------------------
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In this section, we present our scheme to estimate the extrapolation error in SCI calculations.
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This new protocol is then applied to five- and six-membered ring molecules for which SCI calculations are particularly challenging even for small basis sets.
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Note that the present method does only applied to ``state-averaged'' SCI calculations where ground- and excited-state energies are produced during the same calculation with the same set of molecular orbitals, not to ``state-specific'' calculations where one computes solely the energy of a single state (like conventional ground-state calculations).
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Note that the present method does only apply to ``state-averaged'' SCI calculations where ground- and excited-state energies are produced during the same calculation with the same set of molecular orbitals, not to ``state-specific'' calculations where one computes solely the energy of a single state (like conventional ground-state calculations).
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For the $m$th excited state (where $m = 0$ corresponds to the ground state), we usually estimate its FCI energy $E_{\text{FCI}}^{(m)}$ by performing a linear extrapolation of its variational energy $E_\text{var}^{(m)}$ as a function of its rPT2 correction $E_{\text{rPT2}}^{(m)}$ as follows
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\begin{equation}
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@ -330,7 +330,7 @@ This choice ensures that the statistical uncertainty vanishes at the FCI limit.
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We then search for a confidence interval $\mathcal{I}$ such that the true value of the excitation energy $\Delta E_{\text{FCI}}^{(m)}$ lies within one standard deviation of $\Delta E_\text{CIPSI}^{(m)}$, i.e., $P( \Delta E_{\text{FCI}}^{(m)} \in [ \Delta E_\text{CIPSI}^{(m)} \pm \sigma ] \; | \; \mathcal{G}) = 0.6827$.
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The probability that $\Delta E_{\text{FCI}}^{(m)}$ is in an interval $\mathcal{I}$ is
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\begin{equation}
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P( \Delta E_{\text{FCI}}^{(m)} \in \mathcal{I} ) = P( \Delta E_{\text{FCI}}^{(m)} \in I | \mathcal{G}) \times P(\mathcal{G})
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P\qty( \Delta E_{\text{FCI}}^{(m)} \in \mathcal{I} ) = P\qty( \Delta E_{\text{FCI}}^{(m)} \in I \Big| \mathcal{G}) \times P(\mathcal{G})
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\end{equation}
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where the probability $P(\mathcal{G})$ that the random variables are normally distributed can be deduced from the Jarque-Bera test $J$ as
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\begin{equation}
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@ -343,24 +343,24 @@ The inverse of the cumulative distribution function of the $t$-distribution, $t_
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\beta = t_{\text{CDF}}^{-1} \qty[
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\frac{1}{2} \qty( 1 + \frac{0.6827}{P(\mathcal{G})}), M ]
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\end{equation}
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such that $P( \Delta E_{\text{FCI}}^{(m)} \in [ \Delta E_{\text{CIPSI}}^{(m)} \pm \beta \sigma ] ) = p = 0.6827$.
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such that $P\qty( \Delta E_{\text{FCI}}^{(m)} \in \qty[ \Delta E_{\text{CIPSI}}^{(m)} \pm \beta \sigma ] ) = p = 0.6827$.
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Only the last $M>2$ computed energy differences are considered. $M$ is chosen such that $P(\mathcal{G})>0.8$ and such that the error bar is minimal.
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If all the values of $P(\mathcal{G})$ are below $0.8$, $M$ is chosen such that $P(\mathcal{G})$ is maximal.
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A Python code associated with this procedure is provided in the {\SupInf}.
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The singlet and triplet FCI/6-31+G(d) excitation energies and their corresponding error bars estimated with the method presented above based on Gaussian random variables are reported in Table \ref{tab:cycles}.
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For the sake of comparison, we also report the CC3 and CCSDT vertical energies from Ref.~\cite{Loos_2020b} computed in the same basis. We note that there is for the vas majority of considered
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For the sake of comparison, we also report the CC3 and CCSDT vertical energies from Ref.~\cite{Loos_2020b} computed in the same basis. We note that there is for the vast majority of considered
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states a very good agreement between the CC3 and CCSDT values, indicating that the CC values can be trusted.
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The estimated values of the excitation energies obtained via a three-point linear extrapolation considering the three largest CIPSI wave functions are also gathered in Table \ref{tab:cycles}.
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In this case, the error bar is estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function.
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This strategy has been considered in some of our previous works \cite{Loos_2020b,Loos_2020c,Loos_2020e}.
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The deviation from the CCSDT excitation energies for the same set of excitations are depicted in Fig.~\ref{fig:errors}, where the red dots correspond to the excitation energies and error bars estimated via the present method, and the blue dots correspond to the excitation energies obtained via a three-point linear fit and error bars estimated via the extrapolation distance.
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These results contains a good balance between well-behaved and ill-behaved cases.
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These results contain a good balance between well-behaved and ill-behaved cases.
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For example, cyclopentadiene and furan correspond to well-behaved scenarios where the two flavors of extrapolations yield nearly identical estimates and the error bars associated with these two methods nicely overlap.
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In these cases, one can observe that our method based on Gaussian random variables provides almost systematically smaller error bars.
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Even in less idealistic situations (like in imidazole, pyrrole, and thiophene), the results are very satisfactory and stable.
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The six-membered rings represent much more challenging cases for SCI methods, and even for these systems the newly-developed method provides realistic error bars, and allows to easily detect problematic events (like pyridine for instance).
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The present scheme has also been tested on smaller systems when one can tightly converged the CIPSI calculations.
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The present scheme has also been tested on smaller systems when one can tightly converge the CIPSI calculations.
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In such cases, the agreement is nearly perfect in every scenario that we have encountered.
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A selection of these results can be found in the {\SupInf}.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% A template for Wiley article submissions.
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% Developed by Overleaf.
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%
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% Please note that whilst this template provides a
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% preview of the typeset manuscript for submission, it
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% will not necessarily be the final publication layout.
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%
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% Usage notes:
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% The "blind" option will make anonymous all author, affiliation, correspondence and funding information.
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% Use "num-refs" option for numerical citation and references style.
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% Use "alpha-refs" option for author-year citation and references style.
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\documentclass[num-refs,sort&compress]{../wiley-article}
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% \documentclass[blind,alpha-refs]{wiley-article}
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\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,longtable,mhchem,siunitx,rotating,lscape}
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\usepackage[
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colorlinks=true,
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citecolor=blue,
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breaklinks=true
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]{hyperref}
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\urlstyle{same}
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% macros
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\newcommand{\ra}{\rightarrow}
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\newcommand{\pis}{\pi^*}
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\newcommand{\double}{\text{double}}
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\newcommand{\ie}{\textit{i.e.}}
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\newcommand{\eg}{\textit{e.g.}}
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\newcommand{\QP}{\textsc{quantum package}}
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\newcommand{\SupInf}{supporting information}
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%
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\newcommand{\Pop}{6-31+G(d)}
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\newcommand{\AVDZ}{aug-cc-pVDZ}
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\newcommand{\AVTZ}{aug-cc-pVTZ}
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\newcommand{\DAVTZ}{d-aug-cc-pVTZ}
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\newcommand{\AVQZ}{aug-cc-pVQZ}
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\newcommand{\DAVQZ}{d-aug-cc-pVQZ}
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\newcommand{\TAVQZ}{t-aug-cc-pVQZ}
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\newcommand{\AVPZ}{aug-cc-pV5Z}
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% Update article type if known
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% Include section in journal if known, otherwise delete
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\paperfield{Journal Section}
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\title{Supplementary Information for ``QUESTDB: a database of highly-accurate excitation energies for the electronic structure community''}
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% List abbreviations here, if any. Please note that it is preferred that abbreviations be defined at the first instance they appear in the text, rather than creating an abbreviations list.
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%\abbrevs{ABC, a black cat; DEF, doesn't ever fret; GHI, goes home immediately.}
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% Include full author names and degrees, when required by the journal.
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% Use the \authfn to add symbols for additional footnotes and present addresses, if any. Usually start with 1 for notes about author contributions; then continuing with 2 etc if any author has a different present address.
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\author[1]{Mickael V\'eril}
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\author[1]{Anthony Scemama}
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\author[1]{Michel Caffarel}
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\author[2]{Filippo Lipparini}
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\author[1]{Martial Boggio-Pasqua}
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\author[3]{Denis Jacquemin}
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\author[1]{Pierre-Fran\c{c}ois Loos}
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%\contrib[\authfn{1}]{Equally contributing authors.}
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% Include full affiliation details for all authors
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\affil[1]{Laboratoire de Chimie et Physique Quantiques, Universit\'e de Toulouse, CNRS, UPS, France}
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\affil[2]{Dipartimento di Chimica e Chimica Industriale, University of Pisa, Via Moruzzi 3, 56124 Pisa, Italy}
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\affil[3]{Universit\'e de Nantes, CNRS, CEISAM UMR 6230, F-44000 Nantes, France}
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\corraddress{Denis Jacquemin and Pierre-Fran\c{c}ois Loos}
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\corremail{denis.jacquemin@univ-nantes.fr; loos@irsamc-ups-tlse.fr}
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%\presentadd[\authfn{2}]{Department, Institution, City, State or Province, Postal Code, Country}
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\fundinginfo{European Research Council (ERC), European Union's Horizon 2020 research and innovation programme, Grant agreement No.~863481}
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% Include the name of the author that should appear in the running header
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\runningauthor{V\'eril et al.}
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\clearpage
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\begin{document}
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\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{QUEST\#5: Additional molecules}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Aza-naphthalene}
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In contrast to naphthalene (see below), its tetraaza counterpart (1,4,5,8-tetraazanaphthalene) has not been much investigated although it also has a $D_{2h}$ symmetry.
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The vibronic couplings of one low-lying state were nevertheless well characterized theoretically by Dierksen and Grimme with TD-DFT \cite{Dierksen_2004b} and compared to the experimental spectrum \cite{Hurst_1999}. The latter work also contains some CIS and CNDO calculations and a few assignments for higher-lying states.
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Our CC results collected in Table \ref{tab:azanaph} are therefore clearly the most advanced to date. For the singlet transitions, no \%$T_1$ is
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smaller than 80\%, and we have obtained consistent CC3 and CCSDT values with the Pople basis set.
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Indeed, the two models yield values within $\pm 0.03$ eV of each other, the two exceptions (the second $B_{1u}$
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and the $^1B_{3u}$ states) being considered as ``unsafe'' in the database.
|
||||
Comparisons to experimental 0-0 energies in condensed medium and CNDO calculations can be found in the Table, but are not very helpful to assess our TBEs.
|
||||
To the best of our knowledge, the present work is the first to report triplet excited states, and we list in Table \ref{tab:azanaph} eight valence transitions obtained at the CC3/{\AVTZ} level. As we were not able to
|
||||
perform CCSDT calculations for the triplets, all these transition energies are labeled ``unsafe'' in the QUEST database.
|
||||
Nevertheless, given the large \%$T_1$ values, one can likely consider them accurate (for a given basis set at least).
|
||||
|
||||
%
|
||||
%%% TABLE %%%
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in aza-naphthalene (1,4,5,8-tetraazanaphthalene).
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:azanaph}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llcccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & \thead{CCSDT} &\thead{Litt.} & \\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ}& {\Pop} &Th.$^a$ &Exp.$^b$ \\
|
||||
Aza-naphthalene &$^1B_{3g} (n \ra \pis)$ & &88.5 &3.26 &3.15 &3.11 &3.29 &2.64 &2.61 \\
|
||||
&$^1B_{2u} (\pi \ra \pis)$ &0.190 &86.5 &4.37 &4.32 &4.28 &4.37 &4.05 &3.86 \\
|
||||
&$^1B_{1u} (n \ra \pis)$ &n.d. &88.5 &4.47 &4.39 &4.34 &4.47 &3.32 & \\
|
||||
&$^1B_{2g} (n \ra \pis)$ & &87.3 &4.62 &4.55 &4.53 &4.64 &4.48 & \\
|
||||
&$^1B_{2g} (n \ra \pis)$ & &84.1 &5.00 &4.91 &4.86 &5.03 &4.76 & \\
|
||||
&$^1B_{1u} (n \ra \pis)$ &n.d. &82.6 &5.31 &5.17 &5.13 &5.42 & & \\
|
||||
&$^1A_u (n \ra \pis)$ & &83.1 &5.47 &5.40 &5.34 &5.47 &4.51 & \\
|
||||
&$^1B_{3u} (\pi \ra \pis)$ &0.028 &88.5 &5.86 &5.69 &5.63 &5.91 &5.26 &5.03 \\
|
||||
&$^1A_g (\pi \ra \pis)$ & &85.3 &5.96 &5.87 &5.81 &5.95 & & \\
|
||||
&$^1A_u (n \ra \pis)$ & &84.8 &5.97 &5.90 &5.89 &6.00 & & \\
|
||||
&$^1A_g (n \ra 3s)$ & &90.5 &6.56 &6.39 &6.49 &6.57 & & \\
|
||||
&$^3B_{3g} (n \ra \pis)$ & &96.5 &2.93 &2.84 &2.82 & & & \\
|
||||
&$^3B_{2u} (\pi \ra \pis)$ & &97.2 &3.86 &3.73 &3.67 & & & \\
|
||||
&$^3B_{3u} (\pi \ra \pis)$ & &97.7 &3.78 &3.76 &3.75 & & & \\
|
||||
&$^3B_{1u} (n \ra \pis)$ & &97.1 &3.85 &3.79 &3.77 & & & \\
|
||||
&$^3B_{2g} (n \ra \pis)$ & &96.2 &4.43 &4.37 &4.34 & & & \\
|
||||
&$^3B_{2g} (n \ra \pis)$ & &95.3 &4.71 &4.63 &4.61 & & & \\
|
||||
&$^3B_{3u} (\pi \ra \pis)$ & &96.6 &4.82 &4.78 &4.75 & & & \\
|
||||
&$^3A_u (n \ra \pis)$ & &96.6 &4.96 &4.91 &4.87 & & & \\
|
||||
|
||||
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
\begin{tablenotes}
|
||||
\item $^a$ CNDO/S values from Ref.~\cite{Hurst_1999}.
|
||||
\item $^b$ 0-0 energy in solution estimated in Ref.~\cite{Hurst_1999}. There are other tentative assignments in that work.
|
||||
\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
|
||||
\subsection{Benzoquinone}
|
||||
|
||||
Benzoquinone, the simplest quinoidic dye, has been treated at several levels of theory previously, e.g., CASPT2 \cite{Pou-Amerigo_1999,Weber_2001,Schreiber_2008,Silva-Junior_2010}, SAC-CI \cite{Honda_2002,Bousquet_2013,Bousquet_2014} and various CC levels up to CC3 \cite{Schreiber_2008,Silva-Junior_2010b}, ADC(2) and ADC(3) \cite{Harbach_2014,Loos_2020d} as well as TD-DFT \cite{Silva-Junior_2008,Jacquemin_2009,Bousquet_2013,Bousquet_2014,Jones_2017,daCosta_2018}.
|
||||
Our results and comparisons with a selection of the existing literature can be found in Table \ref{tab:bq}.
|
||||
|
||||
For the singlet transitions, we could obtain CCSDT/{\AVDZ} values for the 10 considered excited states.
|
||||
For the two lowest transitions of $n \ra \pis$ character, these agree well with the corresponding CC3 values and we can define safe TBE/{\AVTZ} of 2.82 and 2.96 eV.
|
||||
These values are within 0.10 eV of the most recent estimates of Thiel \cite{Silva-Junior_2010b} and are clearly larger than older CASPT2 estimates \cite{Pou-Amerigo_1999,Weber_2001}, which appear too low.
|
||||
The experimentally available data return 0-0 energies of roughtly 2.5 eV for both transitions \cite{Trommsdorff_1972,Goodman_1978}.
|
||||
These values are located 0.3--0.4 eV below our vertical estimates which is a quite reasonable difference between vertical and 0-0 energies.
|
||||
The next transition of $A_g$ symmetry has a pure double excitation character so that unsurprisingly both CC3 and CCSDT yield values that are much too large.
|
||||
Indeed, at the NEVPT2/{\AVTZ} level, we obtain a transition energy of 4.57 eV for this excitation, more than 1 eV below the CC3 estimate, yet again slightly above earlier CASPT2 estimates.
|
||||
Although one cannot consider this 4.57 eV estimate as chemically accurate (the error bar of NEVPT2 is typically $\pm 0.10$ eV for transitions of pure double character \cite{Loos_2019}), it is likely the most accurate value available at this stage.
|
||||
The next transition of $^1B_{3g}$ symmetry is the first of $\pi \ra \pis$ character.
|
||||
Although its associated \%$T_1$ value is rather large, there is substantial difference between CC3 and CCSDT, making our TBE of 4.58 eV falling in the ``unsafe'' category, though it is obviously more accurate than previous CASPT2 values that are too close from the experimental 0-0 energies to be trustworthy.
|
||||
For the next strongly-allowed transition ($^1B_{1u}$), one also notices small yet non-negligible differences between CC3 and CCSDT.
|
||||
Our TBE of 5.62 eV is slightly larger than Thiel's one (5.47 eV obtained using CC3) \cite{Silva-Junior_2010},
|
||||
It is objectively hard to determined which one is the most accurate, and if the difference in the ground-state geometries (CC3 here \emph{vs} MP2 in Thiel's work) also plays a significant role in this discrepancy.
|
||||
The situation is similar for the $B_{3u}$ transition, although in that case the present TBE of 5.79 eV is close to Thiel's CC3 value of 5.71 eV.
|
||||
Note that Thiel selected a CASPT2 value of 5.55 eV as TBE due to the rather small \%$T_1$ value for that state.
|
||||
However, this value is likely slightly too low as the agreement between CC3 and CCSDT is rather good.
|
||||
For the higher-lying singlet transitions, we note that: i) we could produce ``safe'' TBEs for the two $B_{2g}$ excited states that both show minimal changes between CC3 and CCSDT, although \%$T_1$ is small for the lowest transition of that symmetry; ii) for the (second) $^1A_u$ transition, the differences are too large between
|
||||
CC3 and CCSDT to provide trustworthy estimates; iii) for the (second) $^1B_{1g}$ excitation, these differences are less marked and although we rated our TBE (6.38 eV) as ``unsafe'', it is likely the best estimate proposed to date in the literature.
|
||||
|
||||
For the triplets, we considered the four lowest transitions, two of $n \ra \pis$ character ($^3B_{1g}$ and $^3A_u$) and two of $\pi \ra \pis$ character ($^3B_{1u}$ and $^3B_{3g}$), see Table \ref{tab:bq}.
|
||||
For all fours excited states, there is a very nice match between the CC3 and CCSDT transition energies obtained with Pople's basis set, and the single-excitation characters are very large, so that we are confident that our TBEs are trustworthy.
|
||||
For the $^3B_{1g}$ and $^3A_u$ transitions, our energies are very slightly larger than Thiel's extrapolated CC3 ones, and again ca.~0.3--0.4 eV above the experimental 0-0 energies.
|
||||
As for the singlet transitions, the early CASPT2 values are too low.
|
||||
For the two $\pi \ra \pis$ excitations, exactly the same trends are found, but no experimental measurements exist to our knowledge.
|
||||
|
||||
%%% TABLE %%%
|
||||
\begin{landscape}
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in $p$-benzoquinone.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:bq}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llcccccccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & \thead{CCSDT}& &\thead{Litt.} & & & & & &\\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ}& {\Pop} & {\AVDZ} &Th.$^a$ &Th.$^b$ &Th.$^c$ &Exp.$^d$ &Exp.$^e$&Exp.$^f$ &Exp.$^g$\\
|
||||
Benzoquinone &$^1B_{1g} (n \ra \pis)$ & &85.3 &2.85 &2.81 &2.79 &2.87 &2.84 &2.50 &2.39 &2.74 & & &2.52 &2.49 \\
|
||||
&$^1A_u (n \ra \pis)$ & &84.1 &2.99 &2.95 &2.94 &3.01 &2.97 &2.50 &2.43 &2.86 & & &2.49 &2.48 \\
|
||||
&$^1A_g (n,n \ra \pis,\pis)$ & &0.0 &5.92 &5.94 &6.02 &5.79 &5.84 &4.41 &4.36 & & & & &\\
|
||||
&$^1B_{3g} (\pi \ra \pis)$ & &88.6 &4.66 &4.58 &4.53 &4.71 &4.63 &4.19 &4.01 &4.44 &4.3 &4.09 &4.07 &\\
|
||||
&$^1B_{1u} (\pi \ra \pis)$ &0.471 &88.4 &5.71 &5.63 &5.58 &5.75 &5.67 &5.15 &5.09 &5.47 &5.38--5.70 &5.08 &5.12 &\\
|
||||
&$^1B_{3u} (n \ra \pis)$ &0.001 &79.8 &5.95 &5.77 &5.75 &5.96 &5.81 &5.15 &4.91 &5.71 & & & &\\
|
||||
&$^1B_{2g} (n \ra \pis)$ & &76.2 &6.11 &5.96 &5.94 &6.10 &5.97 &4.80 &4.99 & & & & &\\
|
||||
&$^1A_u (n \ra \pis)$ & &74.8 &6.41 &6.29 &6.27 &6.46 &6.37 &5.79 &5.47 & & & & &\\
|
||||
&$^1B_{1g} (n \ra \pis)$ & &83.5 &6.48 &6.37 &6.34 &6.51 &6.41 &5.76 &5.68 & & & & &\\
|
||||
&$^1B_{2g} (n \ra \pis)$ & &86.6 &7.33 &7.28 &7.20 &7.33 &7.30 &5.49 &5.62 & & & & &\\
|
||||
&$^3B_{1g} (n \ra \pis)$ & &96.0 &2.61 &2.56 &2.56 &2.63 & &2.17 &2.16 &2.50 & & &2.31 &2.31\\
|
||||
&$^3A_u (n \ra \pis)$ & &95.6 &2.76 &2.71 &2.71 &2.77 & &2.27 &2.22 &2.61 & & &2.35 &2.31\\
|
||||
&$^3B_{1u} (\pi \ra \pis)$ & &97.7 &3.13 &3.16 &3.14 &3.11 & &2.91 &2.57 &3.02 & & & &\\
|
||||
&$^3B_{3g} (\pi \ra \pis)$ & &97.9 &3.46 &3.46 &3.44 &3.48 & &3.19 &3.09 &3.37 & & & &\\
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
\begin{tablenotes}
|
||||
\item $^a$ CASPT2 values from Ref.~\cite{Pou-Amerigo_1999}.
|
||||
\item $^b$ CASPT2 values from Ref.~\cite{Weber_2001}.
|
||||
\item $^c$ CC3 (extrapolated to {\AVTZ}) values from Ref.~\cite{Silva-Junior_2010}.
|
||||
\item $^d$ EELS from Ref.~\cite{daCosta_2018}.
|
||||
\item $^e$ Absorption spectroscopy (0-0 energies) from Ref.~\cite{Brint_1986}.
|
||||
\item $^f$ Absorption spectroscopy (0-0 energies) from Ref.~\cite{Trommsdorff_1972} (gas-phase and pure crystals).
|
||||
\item $^g$ Absorption spectroscopy (0-0 energies) from Ref.~\cite{Goodman_1978}.
|
||||
\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
\end{landscape}
|
||||
|
||||
\subsection{Cyclopentadienone and cyclopentadienethione}
|
||||
|
||||
This two five-membered rings with an external (thio)ketone moiety have been investigated theoretically by Serrano-Andr\'es and coworkers in 2002 \cite{Serrano-Andres_2002} who used the best method available at the time, namely CASPT2 (without IPEA).
|
||||
Our results are compared to these earlier estimates in Table \ref{tab:cyclops}.
|
||||
For both structures and both spin symmetries, the two lowest singlet transitions are of $A_2 (n \ra \pis)$ and $B_2 (\pi \ra \pis)$ spatial symmetries.
|
||||
There is a good to excellent agreement between the CC3 and CCSDT values for both the {\Pop} and the {\AVDZ} basis sets for these eight excited states, consistent with the large single excitation character.
|
||||
Thus, one can likely trust the obtained TBEs as these transitions are unproblematic.
|
||||
Experimentally, a $t$Bu substituted cyclopentadienone
|
||||
shows a weakly-allowed band peaking at 3.22 eV in vapour \cite{Garbisch_1966}, which is likely the $^1B_2$ state.
|
||||
For the lowest triplet state of cyclopentadienone, the experimental triplet energy was (indirectly) estimated experimentally to be $1.50 \pm 0.02$ eV \cite{Khuseynov_2014}, but this value corresponds to the triplet lowest-energy geometry, so that direct comparisons with our data is unreasonable.
|
||||
This 2014 work also contains CCSD(T) estimates of the adiabatic electron affinities for the two lowest triplet states.
|
||||
|
||||
In the singlet manifold of this molecule, one next finds one dark transition of purely double $(n,\pi) \ra (\pis,\pis)$ character, for which CC theory is not well suited, as clearly illustrated by the huge difference between CC3 and CCSDT.
|
||||
Using a minimal active space ($\pi$ space and lone pairs), we obtained with NEVPT2 value of 5.02 eV, i.e., 0.7 eV below the CCSDT estimate and roughly half an eV higher than the earlier CASPT2 values. This 5.02 eV estimate although not chemically accurate is likely the best available today.
|
||||
The fourth singlet state is an interesting yet challenging $(pi,\pi) \ra (\pis,\pis)$ showing a \%$T_1$ of 49.9 \%.
|
||||
For this particular state, the NEVPT2 value is 6.02 eV, which is likely again the most realistic value available.
|
||||
The fifth transition shows a butadiene-$A_g$-like character, that is a totally-symmetric $\pi \ra \pis$ transition with a significant double excitation character around 25\%.
|
||||
For this transition, we based our TBE on the CCSDT estimate, but it might be too large by roughly 0.10 eV.
|
||||
The experimental spectrum of the related compounds shows a strong peak at 5.93 eV \cite{Garbisch_1966}, likely corresponding to the overlap between these two $^1A_1$ transitions.
|
||||
In cyclopentadienone, the third triplet is an unproblematic $\pi \ra \pis$ transition, for which there is a remarkable consistency between our CC estimates, again significantly above the previous CASPT2 data \cite{Serrano-Andres_2002}.
|
||||
Finally, the highest triplet considered has originally a highly dominant multi-excitation character and our best estimate of 4.91 eV was obtained with NEVPT2, the CC values being too large.
|
||||
|
||||
For the singlet manifold of cyclopentadienethione, on finds again a $^1B_1 (n,\pi \ra \pis,\pis)$ purely double transition and a 50/50 single/double $^1A_1 (\pi,\pi) \ra (\pis,\pis)$ transition.
|
||||
The methodological trends are similar to those noted for the oxygen-derivatives, and the TBE listed in the QUEST database are obtained with NEVPT2: 3.16 eV and 5.43 eV.
|
||||
For the latter, it should be noted that there are several transitions of mixed character close in energy, so that definitive attribution is challenging.
|
||||
In contrast to cyclopentadienone, the $^1A_1 (\pi \ra \pis)$ transition shows a very large \%$T_1$ value and small differences between CC3 and CCSDT, so that we have been able to define a ``safe'' TBE of 4.96 eV.
|
||||
For the records, our NEVPT2 estimate for that state is consistent, 4.90 eV.
|
||||
For the triplets of cyclopentadienethione, the trends are totally similar to those of the oxygen structure.
|
||||
For the fourth triplet of double character, our TBE is 3.13 eV, a value again obtained with NEVPT2.
|
||||
|
||||
%%% TABLE %%%
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in cyclopentadienone and cyclopentadienethione.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:cyclops}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & & \thead{CCSDT}& &\thead{Litt.}\\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ}& {\AVQZ}& {\Pop} & {\AVDZ} &Th.$^a$ \\
|
||||
Cyclopentadienone &$^1A_2 (n \ra \pis)$ & &88.5 &3.03 &2.95 &2.94 &2.95 &3.03 &2.95 &2.48\\
|
||||
&$^1B_2 (\pi \ra \pis)$ &0.004 &91.2 &3.69 &3.57 &3.54 &3.53 &3.72 &3.61 &3.00\\
|
||||
&$^1B_1 (n,\pi \ra \pis,\pis)$ &0.000 &3.1 &6.06 &6.07 &6.12 &6.12 &5.67 &5.69 &4.49\\
|
||||
&$^1A_1 (\pi,\pi \ra \pis,\pis)$ &0.131 &49.9 &7.20 &7.12 &7.10 &7.08 &7.07 &6.95 &5.42\\
|
||||
&$^1A_1 (\pi \ra \pis)$ &0.090 &73.6 &6.26 &6.23 &6.21 &6.20 &6.12 &6.11 &5.98\\
|
||||
&$^3B_2 (\pi \ra \pis)$ & &98.0 &2.30 &2.29 &2.28 &2.28 &2.32 &2.30 &1.97\\
|
||||
&$^3A_2 (n \ra \pis)$ & &96.9 &2.72 &2.63 &2.64 &2.65 &2.72 &2.64 &2.51\\
|
||||
&$^3A_1 (\pi \ra \pis)$ & &98.2 &4.21 &4.20 &4.19 &4.20 &4.20 &4.20 &3.78\\
|
||||
&$^3B_1 (n,\pi \ra \pis,\pis)$ & &10.0 &5.98 &5.99 &6.05 &6.04 &5.55 & &4.46\\
|
||||
Cyclopentadienethione&$^1A_2 (n \ra \pis)$ & &87.2 &1.76 &1.74 &1.71 &1.72 &1.74 &1.73 &1.43\\
|
||||
&$^1B_2 (\pi \ra \pis)$ &0.000 &85.3 &2.71 &2.66 &2.62 &2.61 &2.71 &2.67 &1.99\\
|
||||
&$^1B_1 (n,\pi \ra \pis,\pis)$ &0.000 &1.1 &4.27 &4.35 &4.40 &4.39 &3.84 &3.93 &2.89\\
|
||||
&$^1A_1 (\pi \ra \pis)$ &0.378 &89.2 &5.13 &5.01 &4.94 &4.93 &5.14 &5.03 &4.42\\
|
||||
&$^1A_1 (\pi,\pi \ra \pis,\pis)$ &0.003 &51.7 &5.86 &5.90 &5.89 &5.88 &5.68 & &4.84\\
|
||||
&$^3A_2 (n \ra \pis)$ & &97.0 &1.50 &1.47 &1.47 &1.48 &1.49 &1.47 &1.26\\
|
||||
&$^3B_2 (\pi \ra \pis)$ & &97.1 &1.91 &1.90 &1.88 &1.88 &1.91 &1.90 &1.61\\
|
||||
&$^3A_1 (\pi \ra \pis)$ & &98.1 &2.51 &2.55 &2.52 &2.53 &2.50 &2.54 &2.41\\
|
||||
&$^3B_1 (n,\pi \ra \pis,\pis)$ & &4.2 &4.25 &4.34 &4.39 &4.37 &3.81 &3.90 &2.88\\
|
||||
%\hiderowcolors
|
||||
|
||||
|
||||
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
\begin{tablenotes}
|
||||
\item $^a$ CASPT2 values from Ref.~\cite{Serrano-Andres_2002}.
|
||||
\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
|
||||
\subsection{Diazirine}
|
||||
|
||||
This compact molecule is the diazo equivalent of cycloproprene, and it has been introduced in our latest work \cite{Sarkar_2021}.
|
||||
It is a rather elusive compound experimentally so that the most complete study of its transitions energies are theoretical and have been performed at the MCQDPT2 \cite{Han_1999} and EOM-CCSD \cite{Fedorov_2009} levels.
|
||||
For the eight considered transitions (Table \ref{tab:diazirine}), the \%$T_1$ values are larger than 90\%\ and the differences between the CC3, CCSDT, and CCSDTQ values are at most 0.02 eV.
|
||||
In addition, except possibly for the $^1B_2$ transition, the basis set effects are rather limited.
|
||||
In short, one can be very confident that the TBEs/{\AVTZ} given in the database are chemically accurate at least for the selected geometry and basis set.
|
||||
If we compare to the previously published values, one notes that the MCQDPT2 results are likely slightly off target, whereas there is quite a good agreement with the EOM-CCSD values of Krylov and coworkers \cite{Fedorov_2009}.
|
||||
This latter work used a very diffuse basis set, so that one cannot be definitive that the remaining differences are purely related to the level of theory.
|
||||
Finally, we are aware of only one experimental data: the 0-0 energy of the lowest singlet state at 3.87 eV \cite{Robertson_1966}, a value slightly smaller than the computed vertical transition energy, as it should.
|
||||
|
||||
%%% TABLE %%%
|
||||
\begin{landscape}
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in diazirine with CC3, CCSDT, and CCSDTQ.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:diazirine}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llccccccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & & \thead{CCSDT}& & & \thead{CCSDTQ}& &\thead{Litt.} &\\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ} & {\AVQZ} & {\Pop} & {\AVDZ} & {\AVTZ} & {\Pop} & {\AVDZ} &Th.$^a$ &Th.$^b$ \\
|
||||
Diazirine &$^1B_1 (n \ra \pis)$ & 0.002 &92.5 &4.20 &4.16 &4.11 &4.11 &4.18 &4.15 &4.10 &4.17 &4.14 &4.01 &4.27\\
|
||||
&$^1A_2 (\sigma \ra \pis)$& &90.9 &7.43 &7.40 &7.31 &7.29 &7.40 &7.37 &7.28 &7.39 &7.36 &7.79 &7.61\\
|
||||
&$^1B_2 (n \ra 3s)$ &0.000 &93.5 &7.62 &7.36 &7.45 &7.48 &7.62 &7.35 &7.44 & &7.35 &7.16 &7.32\\
|
||||
&$^1A_1 (n \ra 3p)$ &0.132 &93.8 &8.05 &7.97 &8.04 &8.05 &8.03 &7.95 &8.03 &8.02 &7.95 &9.91 &7.86\\
|
||||
&$^3B_1 (n \ra \pis)$ & &98.2 &3.56 &3.53 &3.51 &3.51 &3.55 &3.53 &3.50 &3.54 & &3.37 &\\
|
||||
&$^3B_2 (\pi \ra \pis)$ & &98.8 &5.08 &5.06 &5.05 &5.05 &5.08 &5.06 &5.05 &5.09 & &5.46 &\\
|
||||
&$^3A_2 (n \ra \pis)$ & &98.3 &6.20 &6.15 &6.13 &6.13 &6.18 &6.14 &6.12 &6.18 & &5.97 &\\
|
||||
&$^3A_1 (n \ra 3p)$ & &98.4 &6.87 &6.82 &6.83 &6.85 &6.85 &6.80 &6.81 &6.85 & &6.57 &\\
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
\begin{tablenotes}
|
||||
\item $^a$ MCQDPT2 values from Ref.~\cite{Han_1999}.
|
||||
\item $^b$ EOM-CCSD energies from Ref.~\cite{Fedorov_2009}.
|
||||
\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
\end{landscape}
|
||||
|
||||
\subsection{Hexatriene and octatetraene}
|
||||
|
||||
Ethylene and butadiene, the two shortest members of the polyenes, have been treated in QUEST\#1 and QUEST\#3, respectively \cite{Loos_2018a,Loos_2020b}.
|
||||
The evolution of excited state energies in longer polyenic chains is obviously of interest and this is why we considered hexatriene and octatetraene here.
|
||||
It should be noted that the transition energies are rather sensitive to the bond length alternation in polyenes, so that we trust that our choice of CC3 geometries is an asset as compared to previous estimates.
|
||||
Our results are collected in Table \ref{tab:hexaocta}.
|
||||
Let us start by the famous singlet $B_u$ and $A_g$ valence states.
|
||||
The transition to $B_u$ is bright and has a strong single-excitation character, so that one expects CC to be an adequate methodology, and one indeed finds small differences between CC3 and CCSDT values (ca.~0.03 eV).
|
||||
Our TBE/{\AVTZ} are 5.37 and 4.78 eV for hexatriene and octatetraene, respectively.
|
||||
These values are compared to selected previous theoretical estimates in Table \ref{tab:hexaocta} and one clearly notices quite a large spread.
|
||||
Experimentally, the 0-0 transition has been measured to be 4.95 eV by electron impact \cite{Flicker_1977} and 4.93 eV by optical spectroscopy \cite{Leopold_1984} for hexatriene, and 4.41 eV with the latter technique for the longer oligomer \cite{Leopold_1984b}, values logically smaller than our vertical estimates.
|
||||
However, one clearly notices a decrease of 0.53 eV when increasing the chain length, as compared to 0.59 eV with our TBE/{\AVTZ} highlighting the consistency of quantum and
|
||||
measured trends.
|
||||
The $A_g$ transitions are known to be much more challenging: the states are dark in one-photon absorption, and it has a very significant multi-excitation character (\%$T_1$ of roughly 65\%\ for both compounds).
|
||||
On a positive note, the basis set effects are very limited for the $A_g$ state, {\Pop} being apparently sufficient.
|
||||
In contrast, as expected for such transition, there is a significant drop of the theoretical estimate in going from CC3 to CCSDT.
|
||||
From the analysis performed for double excitations in Ref.~\cite{Loos_2019}, it is unclear if NEVPT2 or CASPT2 would in fact outperform CCSDT for such ``mixed-character'' state, so that we cannot define a trustworthy TBE on this basis.
|
||||
However, based on our experience for butadiene \cite{Loos_2020b}, one can widely estimate the transition energies to be in the range 5.55--5.60 eV for hexatriene and in the range 4.80--4.85 eV for octratetraene.
|
||||
Interestingly the FCI value of Chien \textit{et al.}~with a small basis set for hexatriene (5.59 eV) is compatible with such an estimate.
|
||||
Experimentally, for hexatriene, multiphoton experiments estimate the $A_g$ state to be slightly above the $B_u$ transition \cite{Fujii_1985}, an outcome that theory reproduces.
|
||||
|
||||
For the two Rydberg transitions of hexatriene, the differences between CC3 and CCSDT estimates are very small, \%$T_1$ values are large, so that CC estimates can likely be trusted.
|
||||
However, the basis set effects are rather large, and {\AVTZ} might be insufficient to reach basis set convergence.
|
||||
Our values are reasonably similar to those obtained with CASPT2 almost thirty years ago \cite{Serrano-Andres_1993}.
|
||||
The experimental 0-0 energies are 5.68 eV and 6.06 eV \cite{Sabljic_1985}, but the assignments of Rydberg transitions is a matter of discussion \cite{Serrano-Andres_1993}, so that we prefer again not to use measured data as reference.
|
||||
|
||||
For the triplet excited states, given their very large \%$T_1$ values, we logically trust the CC estimates.
|
||||
We note that, to the best of our knowledge, this work is the first to report true CC3/{\AVTZ} values for these two systems.
|
||||
Indeed, the previous CC3 estimates provided by Thiel \cite{Silva-Junior_2010,Silva-Junior_2010b} were obtained by correcting CC3/TZVP values thanks to CC2 calculations using a larger basis set.
|
||||
These authors nevertheless provided very close estimates to ours: 2.71, 4.33, 2.32, and 3.69 eV (going down the list of triplet excited states in Table \ref{tab:hexaocta}).
|
||||
These data are within 0.04 eV of the current values.
|
||||
Comparatively, the previous MRMP and CASPT2 results \cite{Serrano-Andres_1993,Nakayama_1998,Silva-Junior_2010} are therefore slightly too low for the triplet transition energies.
|
||||
For hexatriene (octatetraene), electron impact studies return maxima at 2.61 (2.10) and 4.11 (3.55) eV for the two lowest transitions \cite{Flicker_1977} (\cite{Allan_1984}), in reasonable agreement with the values listed in the QUEST database.
|
||||
|
||||
%%% TABLE %%%
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in hexatriene and octatetraene.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:hexaocta}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llccccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & \thead{CCSDT}& &\thead{Litt.} & & &\\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ}& {\Pop} & {\AVDZ} &Th.$^a$ &Th.$^b$ &Th.$^c$ &Th.$^d$\\
|
||||
Hexatriene &$^1 B_u (\pi \ra \pis)$ &1.115 &92.2 &5.54 &5.37 &5.34 &5.56 &5.40 &5.01 &5.37 &5.74 &5.59\\
|
||||
&$^1 A_g (\pi \ra \pis)$ & &65.3 &5.76 &5.76 &5.75 &5.62 &5.63 &5.19 &5.34 &5.73 &5.58\\
|
||||
&$^1 A_u (\pi \ra 3s)$ &0.009 &93.6 &6.04 &5.71 &5.78 &6.05 &5.72 &5.84 & & &\\
|
||||
&$^1 B_g (\pi \ra 3p)$ & &93.5 &6.05 &5.84 &5.92 &6.07 &5.86 &6.12 & & &\\
|
||||
&$^3 B_u (\pi \ra \pis)$ & &97.9 &2.73 &2.73 &2.73 &2.73 & &2.55 &2.40 & &\\
|
||||
&$^3 A_g (\pi \ra \pis)$ & &98.3 &4.37 &4.37 &4.36 &4.37 & &4.12 &4.15 & &\\
|
||||
Octatetraene &$^1 B_u (\pi \ra \pis)$ &n.d. &91.5 &4.95 &4.78 &4.75 &4.98 & &4.35 &4.66 & &\\
|
||||
&$^1 A_g (\pi \ra \pis)$ & &63.7 &5.05 &5.05 &5.04 &4.91 & &4.53 &4.47 & &\\
|
||||
&$^3 B_u (\pi \ra \pis)$ & &97.5 &2.35 &2.36 &2.36 & & &2.27 &2.20 & &\\
|
||||
&$^3 A_g (\pi \ra \pis)$ & &98.0 &3.73 &3.73 &3.73 & & &3.61 &3.55 & &\\
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
\begin{tablenotes}
|
||||
\item $^a$ CASPT2 values from Ref.~\cite{Serrano-Andres_1993} (hexatriene) and Ref.~\cite{Silva-Junior_2010} (octatetraene).
|
||||
\item $^b$ MRMP values from Ref.~\cite{Nakayama_1998}.
|
||||
\item $^c$ Cumulant values from Ref.~\cite{Copan_2018}.
|
||||
\item $^d$ FCI/double-$\zeta$ values from Ref.~\cite{Chien_2018}.
|
||||
\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
|
||||
\subsection{Maleimide}
|
||||
|
||||
Maleimide was quite surprisingly much less studied theoretically than other similar compounds.
|
||||
We are only aware of the 2003 CASPT2 analysis of Climent and coworkers \cite{Climent_2003}, a refined 2020 joint theory/experiment study using CASPT2, ADC(3), and EOM-CCSD \cite{Lehr_2020}, as well as two quite recent investigations focussed on the geometries of specific states \cite{Tuna_2016,Budzak_2017} rather than on the transition energies.
|
||||
Our results are listed in Table \ref{tab:malei}.
|
||||
For all considered singlet (triplet) transitions, we obtained \%$T_1$ values larger than 85\%\ (95\%), and one indeed notices very consistent estimates with CC3 and CCSDT, the largest difference being 0.03 eV.
|
||||
All transitions can therefore be considered as rather ``safe''.
|
||||
Comparing the 2003 and 2020 CASPT2 values (see Table \ref{tab:malei}), one notices large differences between the two, and our present estimates are (much) closer from the
|
||||
most recent values.
|
||||
Nevertheless, even the 2020 CASPT2 results seem rather too low as compared to the values provided here.
|
||||
The experimental data are limited.
|
||||
Interestingly, Climent and coworkers attributed the experimental 0-0 absorption at 3.33 eV (see footnotes in Table \ref{tab:malei}) to the second transition, but given our data, we believe that it is more likely the $B_1$ transition, an assignment consistent with the fact that this band shows non-zero experimental intensities.
|
||||
The $A_2$ transition seems indeed significantly too high with CCSDT to be attributed to the 3.33 eV measurement.
|
||||
For this assignment, we therefore agree with the analysis of Ref.~\citenum{Lehr_2020}.
|
||||
Globally, our CCSDT values are typically bracketed by the EOM-CCSD and CASPT2 values of this recent study, which we consider a good hint of accuracy.
|
||||
|
||||
%%% TABLE %%%
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in maleimide.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:malei}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llccccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & \thead{CCSDT}& &\thead{Litt.} &&& \\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ}& {\Pop} & {\AVDZ} &Th.$^a$ &Th.$^b$ &Exp$^c$ & Exp$^d$\\
|
||||
Maleimide &$^1B_1 (n \ra \pis)$ &0.000 &87.6 &3.86 &3.80 &3.78 &3.87 &3.82 &2.48 &3.37 &3.33 &\\
|
||||
&$^1A_2 (n \ra \pis)$ & &85.9 &4.58 &4.54 &4.51 &4.59 &4.55 &3.29 &3.96 & &\\
|
||||
&$^1B_2 (\pi \ra \pis)$ &0.025 &88.2 &4.93 &4.87 &4.86 &4.96 &4.90 &4.44 &4.62 &$\sim$4.4&4.72\\
|
||||
&$^1B_2 (\pi \ra \pis)$ &0.373 &89.1 &6.32 &6.23 &6.18 &6.35 &6.26 &5.59 &5.80 &5.53 &4.95\\
|
||||
&$^1B_2 (n \ra 3s)$ &0.034 & 89.1 &7.25 &7.08 &7.19 &7.27 &7.09 &5.98 & & &\\
|
||||
&$^3B_1 (n \ra \pis)$ & &96.3 &3.63 &3.57 &3.56 &3.64 & &2.31 &3.61 & &\\
|
||||
&$^3B_2 (\pi \ra \pis)$ & &98.4 &3.72 &3.75 &3.73 &3.73 & &3.49 &3.32 & &\\
|
||||
&$^3B_2 (\pi \ra \pis)$ & &96.9 &4.28 &4.25 &4.25 &4.27 & &3.84 &3.83 & &\\
|
||||
&$^3A_2 (n \ra \pis)$ & &96.1 &4.37 &4.33 &4.31 &4.38 & &3.14 &4.32 & &\\
|
||||
|
||||
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
\begin{tablenotes}
|
||||
\item $^a$ CASPT2 values from Ref.~\cite{Climent_2003}.
|
||||
\item $^a$ CASPT2 (singlet) or ADC(3) (triplet) values from Ref.~\cite{Lehr_2020}.
|
||||
\item $^c$ From Ref.~\citenum{Seliskar_1971}: the 3.33 eV value is a 0-0 energy at low temperature in (frozen) EPA, the 4.4 eV value is the lowest (close from 0-0) peak
|
||||
observed in vapour for $N$-Me-maleimide, and the 5.53 eV value is a 0-0 energy in vapour for the N-Me-maleimide.
|
||||
\item $^d$ Vapour measurements at 315 K from Ref.~\cite{Lehr_2020}.
|
||||
\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
|
||||
\subsection{Naphthalene}
|
||||
|
||||
Naphthalene, due to its high-symmetry and significance for organic electronics, is also a popular benchmark molecule \cite{Rubio_1994,Packer_1996,Schreiber_2008,Silva-Junior_2010,Silva-Junior_2010b,Sauri_2011,Harbach_2014,Fliegl_2014}, although some studies are focussed on the lowest-energy states ``only'' \cite{Prlj_2016,Bettanin_2017}.
|
||||
Our results are listed in Table \ref{tab:naphth}.
|
||||
We believe that the convincing work of Fliegl and Sundholm remains the most complete analysis to date \cite{Fliegl_2014}.
|
||||
|
||||
For the singlet transitions, we could obtain CCSDT, albeit only with Pople's basis set.
|
||||
However, these remain quite significant as none of the considered excited state (even those with Rydberg character) seems to be strongly affected by the basis set.
|
||||
Indeed, the mean absolute deviation between CC3/{\Pop} and CC3/{\AVTZ} is 0.16 eV, the maximal discrepancy being 0.23 eV.
|
||||
When one compares the CCSDT and CC3 values, we note that there are only two transitions (the lowest $^1A_g$ and the second $^1B_{3u}$) for which changes exceeding 0.03 eV can be found between the two bases.
|
||||
It is also striking that for the higher-lying $A_g$ state, both CC3 and CCSDT transition energies are the same despite \%$T_1$ being 72\%\ only.
|
||||
It therefore appears that naphthalene provides a series of well-behaved transitions for which CC theory is well suited.
|
||||
For the valence transition, the TBEs that we obtained are very close from the previous Thiel's CC3 values.
|
||||
Let us now discuss the valence transitions in more details.
|
||||
For the lowest $^1B_{3u}$ and $^1B_{2u}$ transitions, our TBEs{\AVTZ} are 4.27 eV and 4.90 eV.
|
||||
On the theoretical side, these can be compared to Thiel's 4.25 eV and 4.82 eV values \cite{Silva-Junior_2010}, or Fliegl and Sundholm 4.16 and 4.80 eV estimates (obtained with larger basis sets) \cite{Fliegl_2014}.
|
||||
On the experimental side, we are aware of vapour phase energy loss values of 4.0 and 4.45 eV \cite{Huebner_1972} and (optical) 0-0 energies of 3.97 and 4.45 eV \cite{George_1968}, as well as a 3.93 and 4.35 eV 0-0 energy measurement in cyclohexane \cite{Mikami_1975}.
|
||||
The next transition is the lowest Rydberg state [$^1A_u (\pi \ra 3s)$], and our TBE/{\AVTZ} is 5.65 eV, which fits very well the old CASPT2 estimates of Rubio and coworkers (5.54 eV \cite{Rubio_1994}), the more recent CC-derived value (5.56 eV \cite{Fliegl_2014}) and the only experimental value we are aware off (5.60 eV by energy loss \cite{Huebner_1972}).
|
||||
It is also likely that the use of even large basis set than {\AVTZ} would decrease a bit our estimate.
|
||||
Next come the valence $^1B_{1g}$ and $A_g$ states for which our TBE/{\AVTZ} are 5.84 and 5.89 eV (we recall that we labeled the second one as ``unsafe'').
|
||||
On the theoretical side, previous calculations led 5.75 and 5.90 eV with exCC3 \cite{Silva-Junior_2010}, 5.87 and 6.00 eV with RASPT2 \cite{Sauri_2011}, 5.64 and 5.77 eV with exCC3 \cite{Fliegl_2014}.
|
||||
On the experimental side, the measured 0-0 energies are 5.22 and 5.52 eV \cite{Dick_1981} and 5.28 and 5.50 eV, both in solution \cite{Mikami_1975}.
|
||||
All these estimates are rather consistent with one another.
|
||||
Next come two $\pi \ra 3p$ Rydberg transitions, for which our TBE of 6.07 and 6.09 eV are slightly larger than the CASPT2 values of Ref.~\cite{Rubio_1994} and the extrapolated CC2 estimates of 5.94 and 5.96 eV.
|
||||
To our knowledge, no experimental measurement exists for these two transitions.
|
||||
We estimate the next valence $^1B_{3u}$ excited state to be close to 6.19 eV with the {\AVTZ} basis set.
|
||||
This value is consistent with recent estimates of 6.11 \cite{Silva-Junior_2010},
|
||||
6.20 \cite{Sauri_2011} and 6.06 eV \cite{Fliegl_2014}.
|
||||
For this bright state, there are several available experimental values: 5.55 eV (crystal) \cite{Bree_1962}, 5.62/5.63 eV (solution)
|
||||
\cite{Klevens_1949,Bree_1962} and 5.89 (vapour) eV \cite{George_1968}, the latter value being also found by energy loss \cite{Huebner_1972}.
|
||||
The last of the four Rydberg states considered herein, $^1B_{1u} (\pi \ra 3s)$, is located by us at 6.33 eV, a value 0.3 eV above the CASPT2 value \cite{Rubio_1994} but consistent with a recent CC2 estimate (6.26 eV \cite{Fliegl_2014}).
|
||||
For the second $^1B_{2u} (\pi \ra \pis)$ transition, our vertical best estimate is 6.42 eV, fitting Thiel's (6.36 eV) \cite{Silva-Junior_2010} and Sundholm's (6.30 eV) results \cite{Fliegl_2014}.
|
||||
The experimental values are around 6.0 eV (energy loss \cite{Huebner_1972}) and 6.14 eV (optical spectroscopy) \cite{George_1968}.
|
||||
Finally, for the higher-lying $^1B_{1g} (\pi \ra \pis)$ and $^1A_g (\pi \ra \pis)$ states, our TBE/{\AVTZ} values of 6.48 and 6.87 eV appear too high as compared to the estimates of Ref.~\cite{Fliegl_2014} (6.19 and 6.40 eV), which is likely due to the strong basis set effects for these two excited states.
|
||||
The $^1A_g$ transition was estimated at 6.05 eV \cite{Dick_1981} by two-photon spectroscopy.
|
||||
|
||||
For the triplet transitions, we have investigated almost the same valence transitions as in Thiel's set \cite{Schreiber_2008,Silva-Junior_2010,Silva-Junior_2010b}.
|
||||
Let us note that for all states, CC3 returns very large \%$T_1$, and that the differences between {\AVDZ} and {\AVTZ} estimates is at most 0.04 eV.
|
||||
This clearly hints that the present estimates are trustworthy, but as we have been unable to perform CCSDT calculations, we nevertheless rate all of them as ``unsafe'' in the QUEST database, which is a conservative choice.
|
||||
The present values are also very similar to those obtained by basis set extrapolation thanks to the work of Thiel \cite{Silva-Junior_2010}, except for the highest triplet transition considered here in which a significant difference of 0.2 eV is found.
|
||||
For most transitions, one also find a good consistency with earlier RASPT2 calculations \cite{Sauri_2011}.
|
||||
Experimentally, the available data are typically T-T absorption, and this includes values of +2.25 eV, +2.93 eV for the two $^3A_g$ states \cite{Hunziker_1972} and 3.12 eV for the intermediate $^3B_{1g}$ transition \cite{Hunziker_1969}, that we can compare to our +2.32, +3.22, and +3.00 eV values, respectively.
|
||||
|
||||
%
|
||||
%%% TABLE %%%
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in naphthalene.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:naphth}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llcccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & \thead{CCSDT} &\thead{Litt.} & & \\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ}& {\Pop} &Th.$^a$ &Th.$^b$ &Th.$^c$ \\
|
||||
Naphthalene &$^1B_{3u} (\pi \ra \pis)$ &0.000 &85.8 &4.36 &4.33 &4.30 &4.33 &4.03 &4.25 &4.23\\
|
||||
&$^1B_{2u} (\pi \ra \pis)$ &0.067 &90.3 &5.10 &4.91 &4.87 &5.13 &4.56 &4.82 &4.61\\
|
||||
&$^1A_u (\pi \ra 3s)$ & &92.7 &5.85 &5.57 &5.63 &5.87 &5.54 & & \\
|
||||
&$^1B_{1g} (\pi \ra \pis)$ & &84.7 &5.99 &5.85 &5.83 &6.00 &5.53 &5.75 &5.87\\
|
||||
&$^1A_g (\pi \ra \pis)$ & &83.8 &6.03 &5.97 &5.94 &5.98 &5.39 &5.90 &6.00\\
|
||||
&$^1B_{3g} (\pi \ra 3p)$ & &92.8 &6.12 &5.98 &6.04 &6.15 &5.98 & & \\
|
||||
&$^1B_{2g} (\pi \ra 3p)$ & &92.5 &6.24 &6.00 &6.07 &6.26 &5.94 & & \\
|
||||
&$^1B_{3u} (\pi \ra \pis)$ &n.d. &90.6 &6.30 &6.19 &6.15 &6.34 &5.54 &6.11 &6.20\\
|
||||
&$^1B_{1u} (\pi \ra 3s)$ &n.d. &91.9 &6.55 &6.27 &6.32 &6.56 &6.03 & & \\
|
||||
&$^1B_{2u} (\pi \ra \pis)$ &n.d. &90.2 &6.61 &6.45 &6.39 &6.64 &5.93 &6.36 &6.12\\
|
||||
&$^1B_{1g} (\pi \ra \pis)$ & &87.5 &6.64 &6.52 &6.46 &6.66 &5.87 &6.46 &6.35\\
|
||||
&$^1A_g (\pi \ra \pis)$ & &71.5 &6.99 &6.91 &6.87 &6.99 &6.04 &6.87 &6.66\\
|
||||
&$^3B_{2u} (\pi \ra \pis)$ & &97.7 &3.19 &3.18 &3.17 & & &3.09 &3.21 \\
|
||||
&$^3B_{3u} (\pi \ra \pis)$ & &96.6 &4.25 &4.19 &4.16 & & &4.09 &4.11 \\
|
||||
&$^3B_{1g} (\pi \ra \pis)$ & &97.8 &4.53 &4.49 &4.48 & & &4.42 &4.44 \\
|
||||
&$^3B_{2u} (\pi \ra \pis)$ & &96.8 &4.71 &4.67 &4.64 & & &4.56 &4.62 \\
|
||||
&$^3B_{3u} (\pi \ra \pis)$ & &97.5 &5.17 &4.99 &4.95 & & &4.92 &4.66 \\
|
||||
&$^3A_g (\pi \ra \pis)$ & &97.3 &5.56 &5.52 &5.49 & & &5.42 &5.46 \\
|
||||
&$^3B_{1g} (\pi \ra \pis)$ & &95.6 &6.37 &6.21 &6.17 & & &6.12 &5.95 \\
|
||||
&$^3A_g (\pi \ra \pis)$ & &95.2 &6.52 &6.42 &6.39 & & &6.17 &6.25 \\
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
\begin{tablenotes}
|
||||
\item $^a$CASPT2 values from Ref.~\cite{Rubio_1994}.
|
||||
\item $^b$exCC3 values from Ref.~\cite{Silva-Junior_2010}.
|
||||
\item $^c$RASPT2 values from Ref.~\cite{Sauri_2011}.
|
||||
\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
|
||||
\subsection{Nitroxyl (HNO)}
|
||||
|
||||
In QUEST\#2\ \cite{Loos_2019}, we treated only one excited state, of pure double-excitation character, of this compact molecule.
|
||||
We have used a large panel of high-level methods here, considering five excited states (see Table \ref{tab:hno}).
|
||||
For all transitions (except the Rydberg one), we could nicely converge FCI/{\AVTZ} values that can be used a solid references.
|
||||
For the Rydberg transition, which is naturally more sensitive to the basis set effect, the CCSDTQ/{\AVDZ} and FCI{\AVDZ} also perfectly match.
|
||||
A previous CASPT2 work \cite{Luna_1995}, reported transition energies to the lowest singlet and triplet of 0.67 eV and 1.53 eV, two
|
||||
values that now appear rather too low, a usual trend for CASPT2 when no IPEA shift is applied.
|
||||
|
||||
%%% TABLE %%%
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in nitroxyl with CC3, CCSDT, CCSDTQ and FCI.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:hno}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & \thead{CCSDT}& & \thead{CCSDTQ} & \thead{FCI} & \\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\AVDZ} & {\AVTZ} & {\AVDZ} & {\AVTZ} & {\AVDZ} & {\AVDZ} & {\AVTZ}\\
|
||||
HNO & $^1 A'' (n \ra \pis)$ &0.000 &93.2 &1.78 & 1.75 &1.77 &1.74 &1.77 &1.78(1) &1.74(2) \\
|
||||
& $^1 A' (n,n \ra \pis,\pis)$ &0.000 &0.3 &5.25 & 5.26 &4.76 &4.79 &4.42 &4.41(1) &4.33(0) \\
|
||||
& $^1 A' (\mathrm{Ryd})$ &0.038 &92.4 &6.12 & 6.26 &6.12 &6.25 &6.14 &6.15(1) & \\
|
||||
& $^3 A'' (n \ra \pis)$ & &99.2 &0.87 & 0.88 &0.87 &0.88 &0.87 &0.87(1) &0.88(2) \\
|
||||
& $^3 A' (\pi \ra \pis)$ & &98.5 &5.62 & 5.59 &5.62 &5.59 &5.64 & &5.61 (1) \\
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
%\begin{tablenotes}
|
||||
%\item $^a$ Excitation energies and error bars estimated via the present method (see Sec.~\ref{sec:error}).
|
||||
%\item $^b$ Excitation energies obtained via a three-point linear fit using the three largest CIPSI variational wave functions, and error bars estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function.
|
||||
%\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
|
||||
\subsection{Streptocyanines}
|
||||
|
||||
In addition to the smallest streptocyanine treated in our earliest work \cite{Loos_2018a}, we have investigated here the properties of the two next members of the cationic series which contain 3 and 5 carbon atoms respectively bracketed by NH$_2$ groups (Table \ref{tab:cyanine}).
|
||||
These systems are of specific interest because it is well-known that there are challenging for TD-DFT \cite{LeGuennic_2015}.
|
||||
We report in Table \ref{tab:cyanine} the transition energies to the lowest excited states of both spin symmetries with (valence) $\pi \ra \pis$ character.
|
||||
For the smallest of the two compounds treated here, we have been able to converge a CIPSI calculation with the 6-31+G(d) basis set, and it clearly gives us confidence that both CC3 and CCSDT values are accurate, the former method being actually even closer to the FCI extrapolation for that specific molecules.
|
||||
The detailed investigation of these compounds likely remains the one of Send, Valsson, and Filippi \cite{Send_2011b}.
|
||||
These authors reported for the singlet states of these two cyanines: i) exCC3 values of 4.84 and 3.65 eV; ii) DMC values of 5.03(2) and 3.83(2) eV; and iii) CASPT2 estimates of 4.69 and 3.53 eV.
|
||||
The present estimates better match the previous CC estimates, the DMC (CASPT2) transition energies appearing sightly too large (too low).
|
||||
Once more, given the results in Table \ref{tab:cyanine}, we believe that our TBEs are the most accurate to date, at least for the considered geometries.
|
||||
|
||||
%%% TABLE %%%
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in two cyanines with CC3, CCSDT and FCI.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:cyanine}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & & \thead{CCSDT} & & \thead{FCI} \\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ}& {\AVQZ} & {\Pop} & {\AVDZ} &{\Pop} \\
|
||||
Streptocyanine-3 & $^1 B_2 (\pi \ra \pis)$&0.755 &87.2 &4.83 &4.83 &4.82 &4.82 &4.80 &4.81 &4.83(1)\\
|
||||
& $^3 B_2 (\pi \ra \pis)$& &98.0 &3.45 &3.45 &3.44 &3.44 &3.44 & &3.45(1)\\
|
||||
Streptocyanine-5 & $^1 B_2 (\pi \ra \pis)$&1.182 &85.8 &3.63 &3.66 &3.66 & &3.60 &3.64 &\\
|
||||
& $^3 B_2 (\pi \ra \pis)$& &97.7 &2.49 &2.49 &2.48 & &2.48 & &\\
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
%\begin{tablenotes}
|
||||
%\item $^a$ Excitation energies and error bars estimated via the present method (see Sec.~\ref{sec:error}).
|
||||
%\item $^b$ Excitation energies obtained via a three-point linear fit using the three largest CIPSI variational wave functions, and error bars estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function.
|
||||
%\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
|
||||
\subsection{Thioacrolein}
|
||||
|
||||
This heavier analog of acrolein was not much studied theoretically before, except for calculations of its 0-0 energies \cite{Loos_2018} and rather old TD-DFT calculations \cite{Fabian_2001}.
|
||||
We report in Table \ref{tab:thioacrolein} the transition energies to the lowest excited states of both spin symmetries, of clear valence $n \ra \pis$ character.
|
||||
As one can see, there is for both excited states, a remarkable insensibility to the basis set size, and also very similar CC3 and CCSDT estimates.
|
||||
The experimental 0-0 energies are 1.88 eV (singlet) and 1.74 eV (triplet) \cite{Judge_1984}, both slightly below our vertical estimates as it should.
|
||||
|
||||
%%% TABLE %%%
|
||||
\begin{table}[htp]
|
||||
\centering
|
||||
\scriptsize
|
||||
\caption{Transition energies (in eV) determined in thioacrolein with CC3 and CCSDT.
|
||||
For all transitions, we provide the single-excitation character \%$T_1$ obtained at LR-CC3/{\AVTZ} level.
|
||||
For the dipole-allowed transitions, we provide the corresponding values of the oscillator strength at the same level of theory.}
|
||||
\label{tab:thioacrolein}
|
||||
\begin{threeparttable}
|
||||
\begin{tabular}{llccccccccc}
|
||||
\headrow
|
||||
& \thead{Transition} & & & \thead{CC3} & & & & \thead{CCSDT} &&\\
|
||||
\headrow & Nature & $f$ & \%$T_1$& {\Pop} & {\AVDZ} & {\AVTZ}& {\AVQZ} & {\Pop} & {\AVDZ} & {\AVTZ}\\
|
||||
Thioacrolein & $^1 A'' (n \ra \pis)$ &0.000 &86.4 &2.17 &2.17 &2.14 &2.15 &2.14 &2.15 &2.11\\
|
||||
& $^3 A'' (n \ra \pis)$ & &96.9 &1.96 &1.95 &1.93 &1.94 &1.94 &1.93 \\
|
||||
|
||||
%\hiderowcolors
|
||||
\hline % Please only put a hline at the end of the table
|
||||
\end{tabular}
|
||||
%\begin{tablenotes}
|
||||
%\item $^a$ Excitation energies and error bars estimated via the present method (see Sec.~\ref{sec:error}).
|
||||
%\item $^b$ Excitation energies obtained via a three-point linear fit using the three largest CIPSI variational wave functions, and error bars estimated via the extrapolation distance, \ie, the difference in excitation energies obtained with the three-point linear extrapolation and the largest CIPSI wave function.
|
||||
%\end{tablenotes}
|
||||
\end{threeparttable}
|
||||
\end{table}
|
||||
\clearpage
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histograms13}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the molecules of the QUEST database containing from one to three non-hydrogen atoms (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histograms4}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the molecules of the QUEST database containing four non-hydrogen atoms (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histograms56}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the molecules of the QUEST database containing five or six non-hydrogen atoms (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histograms710}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the molecules of the QUEST database containing from 7 and 10 non-hydrogen atoms (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histogramsnpi}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the $n \ra \pis$ excitations of the QUEST database (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histogramsppi}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the $\pi \ra \pis$ excitations of the QUEST database (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histogramsR}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the Rydberg excitations of the QUEST database (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histogramsV}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the valence excitations of the QUEST database (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histogramsS}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the singlet excitations of the QUEST database (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.9\textwidth]{histogramsT}
|
||||
\caption{Distribution of the error (in eV) in excitation energies (with respect to the TBE/aug-cc-pVTZ values) for various methods for the triplet excitations of the QUEST database (closed-shell compounds only).
|
||||
Only the ``safe'' TBEs are considered (see Table \ref{tab:TBE}).
|
||||
See Table in the main text for the values of the corresponding statistical quantities.
|
||||
QC and TM indicate that Q-CHEM and TURBOMOLE scaling factors are considered, respectively.
|
||||
The SOS-CC2 and SCS-CC2 approaches are obtained with the latter code.}
|
||||
\end{figure}
|
||||
|
||||
\clearpage
|
||||
|
||||
\bibliography{QUESTDB}
|
||||
|
||||
|
||||
\end{document}
|
||||
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|
||||
\@numrefstrue
|
||||
\@alpharefsfalse
|
||||
\@amsrefsfalse
|
||||
}
|
||||
\DeclareOption{alpha-refs}{
|
||||
\@numrefsfalse
|
||||
\@alpharefstrue
|
||||
\@amsrefsfalse
|
||||
}
|
||||
\DeclareOption{ams-refs}{
|
||||
\@numrefsfalse
|
||||
\@alpharefsfalse
|
||||
\@amsrefstrue
|
||||
}
|
||||
|
||||
%% Option for blind review
|
||||
\DeclareOption{blind}{\@blindreviewtrue}
|
||||
|
||||
\ExecuteOptions{num-refs}
|
||||
\ProcessOptions\relax
|
||||
|
||||
|
||||
\LoadClass[twoside]{article}
|
||||
|
||||
\RequirePackage[table]{xcolor}
|
||||
\RequirePackage{ifpdf}
|
||||
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|
||||
\RequirePackage{ifluatex}
|
||||
\RequirePackage{mathtools}
|
||||
\RequirePackage{bm}
|
||||
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|
||||
\RequirePackage{tabularx}
|
||||
\RequirePackage{textcase}
|
||||
\RequirePackage{dashrule}
|
||||
\RequirePackage{ragged2e}
|
||||
\RequirePackage{authblk}
|
||||
\RequirePackage[hyphens]{url}
|
||||
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|
||||
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|
||||
|
||||
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
\ifxetexorluatex
|
||||
\RequirePackage[framemethod=tikz]{mdframed}
|
||||
\else
|
||||
\ifpdf
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
|
||||
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
{geometry}
|
||||
|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
\fnsymbolmult{#1}%
|
||||
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|
||||
|
||||
\newcommand{\presentadd}[2][]{
|
||||
\ifx\empty\@presentaddress\else\appto{\@presentaddress}{\\}{}{}\fi
|
||||
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|
||||
\ifx\empty#1\else\textsuperscript{#1}\fi
|
||||
#2%
|
||||
}{}{}
|
||||
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|
||||
|
||||
|
||||
%% These will be set by the \journal{} command
|
||||
\newcommand{\jlogo}[1]{\def\@jlogo{#1}}
|
||||
\newcommand{\jname}[1]{\def\@jname{#1}}
|
||||
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|
||||
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|
||||
\newcommand{\jpages}[1]{\def\@jpages{#1}}
|
||||
\newcommand{\jwebsite}[1]{\def\@jwebsite{#1}}
|
||||
|
||||
|
||||
\newcommand{\runningauthor}[1]{\def\@runningauthor{#1}}
|
||||
\newcommand{\corraddress}[1]{\def\@corraddress{#1}}
|
||||
\newcommand{\corremail}[1]{\def\@corremail{#1}}
|
||||
|
||||
\newcommand{\fundinginfo}[1]{\def\@fundinginfo{#1}}
|
||||
|
||||
\newcommand{\paperdoi}[1]{\def\@paperdoi{#1}}
|
||||
\newcommand{\paperreceived}[1]{\def\@paperreceived{#1}}
|
||||
\newcommand{\paperrevised}[1]{\def\@paperrevised{#1}}
|
||||
\newcommand{\paperaccepted}[1]{\def\@paperaccepted{#1}}
|
||||
\newcommand{\papereditor}[1]{\def\@papereditor{#1}}
|
||||
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|
||||
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|
||||
|
||||
% normal font is 8pt/13pt
|
||||
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|
||||
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|
||||
|
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% sectional headings
|
||||
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|
||||
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|
||||
%% Fake small caps
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
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|
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|
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|
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{\fontsize{10pt}{13\p@}\bfseries}
|
||||
{\thesection}{1em}{\textmd{|}\quad\allcaps{#1}}
|
||||
|
||||
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|
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|
||||
{\fontsize{10pt}{13\p@}\bfseries}
|
||||
{}{0pt}{\allcaps{##1}}%
|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
|
||||
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|
||||
{\fontsize{10pt}{13\p@}\bfseries}
|
||||
{\thesubsubsection}{1em}{\textmd{|}\quad#1}
|
||||
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||||
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
{\normalsize\fontspec{Lato Black}\color{black!75}}
|
||||
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|
||||
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|
||||
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|
||||
{\normalsize\fontseries{eb}\selectfont\color{black!75}}
|
||||
{\thesubparagraph}{0pt}{#1}
|
||||
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|
||||
\titlespacing*{\subparagraph}{0pt}{\baselineskip}{1em}
|
||||
|
||||
|
||||
% Formatting of footer for first page
|
||||
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|
||||
\def\blfootnote{\gdef\@thefnmark{}\@footnotetext}
|
||||
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|
||||
\renewcommand{\footnoterule}{\noindent\textcolor{black!50}{\rule{\textwidth}{0.5\p@}}\vskip2\p@}
|
||||
|
||||
|
||||
%% Headers
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\arrayrulecolor{black}%
|
||||
\begin{tabularx}{\textwidth}{@{}X r | r @{}}%
|
||||
\textsc{\@runningauthor} & & \thepage\\\hline
|
||||
%& %\multicolumn{1}{r}{%
|
||||
%\raisebox{0pt}[0pt][0pt]{\includegraphics[height=2.5em]{\@jlogo}}%
|
||||
%\quad%
|
||||
%\raisebox{0.25em}[0pt][0pt]{\colorbox{white}{\includegraphics[height=2em]{Wiley_Wordmark_black}}}} & \\
|
||||
\end{tabularx}%
|
||||
}}
|
||||
|
||||
\fancyhead[LE]{{\fontsize{7\p@}{13\p@}\selectfont%
|
||||
\setlength{\arrayrulewidth}{.5\p@}%
|
||||
\arrayrulecolor{black}%
|
||||
\begin{tabularx}{\textwidth}{@{}l | l >{\raggedleft\arraybackslash}X @{}}%
|
||||
\thepage & & \textsc{\@runningauthor}\\\hline
|
||||
% \multicolumn{1}{@{}c}{} &
|
||||
% \raisebox{0.25em}[0pt][0pt]{\colorbox{white}{\includegraphics[height=2em]{Wiley_Wordmark_black}}}%
|
||||
% \quad%
|
||||
% \raisebox{0pt}[0pt][0pt]{\includegraphics[height=2.5em]{\@jlogo}}\\
|
||||
\end{tabularx}%
|
||||
}}
|
||||
|
||||
%% First page header + footer
|
||||
\fancypagestyle{firstpage}{
|
||||
% \renewcommand{\footrule}{\hdashrule{\textwidth}{0.5\p@}{2\p@}\\[-2\p@]}
|
||||
|
||||
\fancyhead[L]{\fontsize{7\p@}{13\p@}\selectfont%
|
||||
\setlength{\arrayrulewidth}{.5\p@}%
|
||||
\arrayrulecolor{black}%
|
||||
\begin{tabularx}{\textwidth}{@{}l | l | X @{}}%
|
||||
\ifdefempty{\@paperreceived}
|
||||
{\multicolumn{3}{l}{}}
|
||||
{Received: \@paperreceived &
|
||||
Revised: \@paperrevised &
|
||||
Accepted: \@paperaccepted}
|
||||
\\\hline
|
||||
\ifdefempty{\@paperdoi}{}{\multicolumn{3}{@{}l}{DOI: \@paperdoi}}
|
||||
\end{tabularx}}
|
||||
|
||||
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|
||||
% \setlength{\arrayrulewidth}{.5\p@}%
|
||||
% \arrayrulecolor{black}\raggedright%
|
||||
% This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.\\[3\p@]
|
||||
% \begingroup
|
||||
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|
||||
\begin{tabularx}{\textwidth}{@{}X >{\centering\arraybackslash}X r | r @{}}%
|
||||
\hline
|
||||
\ifdefempty{\@paperreceived}{& & & }{%
|
||||
\textit{\@jname}~\@jyear; \@jvolume: \@jpages &
|
||||
\@jwebsite &
|
||||
\textcopyright~\@jyear\space Wiley Periodicals, Inc. &
|
||||
}
|
||||
\thepage
|
||||
\end{tabularx}%
|
||||
% \endgroup
|
||||
}
|
||||
}
|
||||
|
||||
% For adding notes about author contributions
|
||||
\newcommand{\contrib}[2][]{%
|
||||
\blfootnote{\textsuperscript{#1}#2}%
|
||||
}
|
||||
|
||||
|
||||
% Author and affiliation fonts
|
||||
\setcounter{Maxaffil}{1}
|
||||
\renewcommand{\Authsep}{\quad|\quad}
|
||||
\renewcommand{\Authand}{\quad|\quad}
|
||||
\renewcommand{\Authands}{\quad|\quad}
|
||||
\renewcommand{\Authfont}{\fontsize{12\p@}{20pt}\bfseries\raggedright}
|
||||
\renewcommand{\Affilfont}{\fontsize{7\p@}{10pt}\selectfont\raggedright}
|
||||
\renewcommand\AB@authnote[1]{\textsuperscript{#1}}
|
||||
\patchcmd{\AB@affilsepx}{\\}{\\[3\p@]}{}{}
|
||||
|
||||
\patchcmd{\@author}{\AB@authlist\\[\affilsep]\AB@affillist}{\AB@authlist}{}{}
|
||||
|
||||
% % \AtBeginDocument{
|
||||
% \if@blindreview
|
||||
% \let\oldauthor\author
|
||||
% \let\oldaffil\affil
|
||||
% \renewcommand{\author}[2][]{\oldauthor{Author}}
|
||||
% \renewcommand{\affil}[2][]{\oldaffil{An affiliation}}
|
||||
% % % \def\AB@authors{Anonymous Authors}
|
||||
% % \def\AB@affillist{Anonymous Affiliations}
|
||||
% \fi
|
||||
% % }
|
||||
|
||||
% Title
|
||||
\renewcommand{\maketitle}{%
|
||||
\if@blindreview
|
||||
\def\AB@authlist{\Authfont Anonymous Authors}
|
||||
\def\AB@affillist{\Affilfont Anonymous Affiliations}
|
||||
\def\@runningauthor{Authors (Anon)}
|
||||
\def\@corraddress{Anonymous correspoundence}
|
||||
\def\@corremail{anon@example.com}
|
||||
\def\@presentaddress{Anonymous present address}
|
||||
\def\@fundinginfo{Anonymous funders}
|
||||
\fi
|
||||
\vspace*{\dimexpr 27\p@-2\baselineskip}%
|
||||
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|
||||
\setul{3\p@}{1\p@}%
|
||||
\ifxetexorluatex\fontspec{Lato Heavy}\else\fontseries{eb}\selectfont\fi
|
||||
{\fontsize{9\p@}{15\p@}\allcaps[\ifxetexorluatex 20\else 200\fi]{\ul{\@papertype}}}
|
||||
\ifdefempty{\@jlogo}{\rule{0pt}{2em}}{%
|
||||
\hfill%
|
||||
% \includegraphics[height=1.5em]{Wiley_Wordmark_black}%
|
||||
% \quad%
|
||||
\includegraphics[height=2em]{\@jlogo}}
|
||||
\\[2\p@]%
|
||||
{\fontsize{8\p@}{15\p@}%
|
||||
\ifxetexorluatex
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\@paperfield
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
{\fontsize{18\p@}{23\p@}\bfseries\raggedright\@title\par}
|
||||
\vskip27\p@%
|
||||
\noindent\begin{minipage}{0.8\textwidth}\@author\end{minipage}%
|
||||
\vskip21\p@%
|
||||
\thispagestyle{firstpage}
|
||||
}
|
||||
|
||||
% Affiliation + other metadata
|
||||
\newcommand{\wiley@affilmetadata}{%
|
||||
\AB@affillist\par%
|
||||
\vskip10pt%
|
||||
\textbf{Correspondence}\\
|
||||
\@corraddress\\
|
||||
Email: \@corremail\par
|
||||
\ifx\empty\@presentaddress
|
||||
\else%
|
||||
\vskip10pt%
|
||||
\textbf{Present address}\\
|
||||
\@presentaddress\par
|
||||
\fi%
|
||||
\vskip10pt%
|
||||
\textbf{Funding information}\\
|
||||
\@fundinginfo\par
|
||||
\ifdefempty{\@papereditor}{}
|
||||
{\vskip10pt Editor: \@papereditor\par}
|
||||
}
|
||||
|
||||
%% Abbreviations in the footnote
|
||||
\newcommand{\abbrevs}[1]{\blfootnote{\textbf{Abbreviations:} #1\\[-3\p@]}}
|
||||
|
||||
%% Abstract and affiliation in the margin
|
||||
\RequirePackage{changepage}
|
||||
\RequirePackage{environ}
|
||||
\reversemarginpar
|
||||
\newlength{\wiley@affilmetadataheight}
|
||||
\newlength{\wiley@abstractheight}
|
||||
\NewEnviron{wiley@abstract}{%
|
||||
\newcommand{\keywords}[1]{%
|
||||
\vskip8\p@%
|
||||
\noindent{\bfseries\fontsize{7\p@}{13\p@}\allcaps[\ifxetexorluatex 20\else 200\fi]{keywords}\par}
|
||||
\noindent{\raggedright\fontsize{8\p@}{13\p@}\selectfont ##1\par}
|
||||
}%
|
||||
\strictpagecheck%
|
||||
\begin{adjustwidth*}{\dimexpr 54.9mm-6.5\p@}{}%
|
||||
\setlength{\marginparsep}{-47mm}%
|
||||
\setlength{\marginparwidth}{47mm}%
|
||||
%% Measure the height of the affil metadata in the sidebar
|
||||
\settototalheight{\wiley@affilmetadataheight}{\parbox{\marginparwidth}{\wiley@affilmetadata}}%
|
||||
\newsavebox{\wiley@abstractbox}%
|
||||
%% Save the abstract text in a box
|
||||
\savebox{\wiley@abstractbox}{%
|
||||
\parbox{\linewidth}{%
|
||||
\begin{mdframed}[font=\fontsize{9\p@}{15\p@}\selectfont,
|
||||
topline=false,bottomline=false,
|
||||
leftline=true,rightline=false,
|
||||
backgroundcolor=black!10,
|
||||
middlelinewidth=6\p@,middlelinecolor=white,
|
||||
outerlinewidth=0.5\p@]
|
||||
\BODY
|
||||
\end{mdframed}}%
|
||||
}%
|
||||
\settototalheight{\wiley@abstractheight}{\usebox{\wiley@abstractbox}}%
|
||||
\marginpar{\wiley@affilmetadata}\vskip-1.5em%
|
||||
\begin{mdframed}[font=\fontsize{9\p@}{15\p@}\selectfont,
|
||||
topline=false,bottomline=false,
|
||||
leftline=true,rightline=false,
|
||||
backgroundcolor=black!10,
|
||||
middlelinewidth=6\p@,middlelinecolor=white,
|
||||
outerlinewidth=0.5\p@]%
|
||||
\BODY
|
||||
\end{mdframed}%
|
||||
%% If the affildata is taller than the abstract, add vskip
|
||||
\ifdimgreater
|
||||
{\wiley@affilmetadataheight}
|
||||
{\wiley@abstractheight}
|
||||
{\vskip\dimexpr\wiley@affilmetadataheight-\wiley@abstractheight+\baselineskip\relax}{}
|
||||
}[\end{adjustwidth*}]%
|
||||
|
||||
\renewcommand{\abstract}{\wiley@abstract}
|
||||
\renewcommand{\endabstract}{\endwiley@abstract}
|
||||
|
||||
% quotes and epigraphs
|
||||
\RequirePackage{quoting}
|
||||
\quotingsetup{vskip=\baselineskip,indentfirst=false,font={itshape,RaggedRight,normalsize},leftmargin=26\p@,rightmargin=26\p@}
|
||||
|
||||
\renewenvironment{quote}{\begin{quoting}}{\end{quoting}}
|
||||
|
||||
\renewenvironment{quotation}{\begin{quoting}}{\end{quoting}}
|
||||
|
||||
\newenvironment{epigraph}[1]
|
||||
{\begin{quoting}\def\@quotesource{#1}}
|
||||
{\par\hfill\@quotesource\end{quoting}}
|
||||
|
||||
\newenvironment{pullquote}
|
||||
{\begin{quoting}[vskip=\dimexpr 39\p@-23\p@\relax,leftmargin=12\p@,rightmargin=12\p@,font+={raggedright},begintext={\fontsize{18\p@}{23\p@}\selectfont\color{black!50}}]}
|
||||
{\end{quoting}}
|
||||
|
||||
% Enum/itemized
|
||||
\RequirePackage[inline]{enumitem}
|
||||
\setlist{nosep,font=\bfseries,leftmargin=*,align=left}
|
||||
\setlist[1]{topsep=\baselineskip,leftmargin=\parindent,labelsep=*,labelwidth=*}
|
||||
\setlist[enumerate,2]{label={\alph*.},}
|
||||
|
||||
% Space above/below equations
|
||||
\g@addto@macro\normalsize{%
|
||||
\setlength\abovedisplayskip{\baselineskip}%
|
||||
\setlength\belowdisplayskip{\baselineskip}%
|
||||
\setlength\abovedisplayshortskip{\baselineskip}%
|
||||
\setlength\belowdisplayshortskip{\baselineskip}%
|
||||
}
|
||||
|
||||
% All the popular math environments
|
||||
\newtheorem{theorem}{Theorem}
|
||||
\newtheorem{lemma}[theorem]{Lemma}
|
||||
\newtheorem{proposition}[theorem]{Proposition}
|
||||
\newtheorem{corollary}[theorem]{Corollary}
|
||||
|
||||
\newenvironment{proof}[1][Proof]{\begin{trivlist}
|
||||
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
|
||||
\newenvironment{definition}[1][Definition]{\begin{trivlist}
|
||||
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
|
||||
\newenvironment{example}[1][Example]{\begin{trivlist}
|
||||
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
|
||||
\newenvironment{remark}[1][Remark]{\begin{trivlist}
|
||||
\item[\hskip \labelsep {\bfseries #1}]}{\end{trivlist}}
|
||||
|
||||
\newcommand{\qed}{\nobreak \ifvmode \relax \else
|
||||
\ifdim\lastskip<1.5em \hskip-\lastskip
|
||||
\hskip1.5em plus0em minus0.5em \fi \nobreak
|
||||
\vrule height0.75em width0.5em depth0.25em\fi}
|
||||
|
||||
% Captions
|
||||
\RequirePackage[tableposition=top]{caption}
|
||||
\DeclareCaptionFont{captionfont}{\fontsize{8\p@}{11\p@}\selectfont}
|
||||
\DeclareCaptionFont{boxcaption}{\fontsize{9\p@}{13\p@}\selectfont}
|
||||
\ifxetexorluatex
|
||||
\DeclareCaptionFont{heavy}{\fontspec{Lato Black}}
|
||||
\DeclareCaptionLabelFormat{allcaps}{\addfontfeature{LetterSpace=15.0}{\MakeTextUppercase{#1}~#2}}
|
||||
\else
|
||||
\DeclareCaptionFont{heavy}{\fontseries{eb}}
|
||||
\ifpdf
|
||||
\DeclareCaptionLabelFormat{allcaps}{\textls[150]{\MakeTextUppercase{#1}~#2}}
|
||||
\else
|
||||
\DeclareCaptionLabelFormat{allcaps}{\MakeTextUppercase{#1}~#2}
|
||||
\fi
|
||||
\fi
|
||||
\captionsetup*{justification=raggedright,singlelinecheck=false,font=captionfont,labelformat=allcaps,labelfont={heavy},labelsep=quad}
|
||||
\captionsetup*[table]{skip=0.5ex}
|
||||
|
||||
% Tables
|
||||
\AtBeginEnvironment{table}{%
|
||||
\fontsize{7.5\p@}{10.5\p@}\selectfont%
|
||||
\rowcolors*{3}{black!10}{}%
|
||||
\renewcommand{\arraystretch}{1.25}%
|
||||
\arrayrulecolor{black!20}%
|
||||
\setlength{\arrayrulewidth}{1\p@}%
|
||||
}
|
||||
|
||||
\RequirePackage{threeparttable}
|
||||
\renewcommand{\TPTnoteSettings}{\leftmargin=0pt}
|
||||
\newcommand{\headrow}{\rowcolor{black!20}}
|
||||
\newcommand{\thead}[1]{\multicolumn{1}{l}{\bfseries #1\rule[-1.2ex]{0pt}{2em}}}
|
||||
|
||||
%% Boxes!
|
||||
\RequirePackage{newfloat}
|
||||
\DeclareFloatingEnvironment[placement=bt,name=box]{featurebox}
|
||||
\captionsetup*[featurebox]{skip=1em,labelformat={default},font={heavy,boxcaption},labelfont={sc,color=black!75}}
|
||||
\AtBeginEnvironment{featurebox}{%
|
||||
\setlist*{topsep=0pt}%
|
||||
}
|
||||
\apptocmd{\featurebox}{%
|
||||
\begin{mdframed}[linewidth=5\p@,linecolor=black!20,
|
||||
innerleftmargin=12\p@,innerrightmargin=12\p@,
|
||||
innertopmargin=12\p@,innerbottommargin=12\p@]
|
||||
}{}{}
|
||||
\pretocmd{\endfeaturebox}{\end{mdframed}}{}{}
|
||||
|
||||
|
||||
% Skips for floats
|
||||
\setlength{\floatsep}{1.5\baselineskip}
|
||||
\setlength{\intextsep}{\baselineskip}
|
||||
\setlength{\textfloatsep}{1.5\baselineskip}
|
||||
|
||||
% The endnotes
|
||||
\RequirePackage{enotez}
|
||||
\newlist{enotezlist}{itemize}{1}
|
||||
\setlist[enotezlist,1]{leftmargin=*,label=\arabic*,labelsep=0.25em,itemsep=0pt,topsep=0.5\baselineskip}
|
||||
\EditInstance{enotez-list}{itemize}
|
||||
{list-type=enotezlist}
|
||||
\setenotez{list-name={endnotes},list-style=itemize}
|
||||
\EditInstance{enotez-list}{itemize}{
|
||||
format=\fontsize{7.5\p@}{10.5\p@}\selectfont,
|
||||
number = \textsuperscript{#1}
|
||||
}
|
||||
|
||||
% References
|
||||
\if@numrefs
|
||||
\RequirePackage[numbers]{natbib}
|
||||
\bibliographystyle{vancouver-authoryear}
|
||||
\fi
|
||||
\if@alpharefs
|
||||
\RequirePackage{natbib}
|
||||
\bibliographystyle{rss}
|
||||
\fi
|
||||
\if@amsrefs
|
||||
\RequirePackage{amsrefs}
|
||||
\let\citep\cite
|
||||
\let\citet\ocite
|
||||
\renewcommand{\biblistfont}{\fontsize{7.5\p@}{10.5\p@}\selectfont}
|
||||
\fi
|
||||
|
||||
\AtBeginDocument{
|
||||
\@ifpackageloaded{natbib}{
|
||||
\setlength{\bibhang}{1.5em}
|
||||
\renewcommand{\bibfont}{\fontsize{7.5\p@}{10.5\p@}\selectfont}
|
||||
\renewcommand{\refname}{references}
|
||||
\renewcommand{\bibname}{references}
|
||||
}{}
|
||||
|
||||
\@ifpackageloaded{amsrefs}{
|
||||
\renewcommand{\biblistfont}{\fontsize{7.5\p@}{10.5\p@}\selectfont}
|
||||
\renewcommand{\refname}{references}
|
||||
\renewcommand{\bibname}{references}
|
||||
}{}
|
||||
}
|
||||
|
||||
% Author biography
|
||||
\RequirePackage{lettrine}
|
||||
\newenvironment{biography}[2][]
|
||||
{\begin{mdframed}
|
||||
[linewidth=0.5\p@,skipabove=1.5\baselineskip,%nobreak,
|
||||
innerleftmargin=6\p@,innerrightmargin=6\p@,
|
||||
innertopmargin=6\p@,innerbottommargin=6\p@]
|
||||
\ifstrequal{#1}{}{}
|
||||
{\lettrine[image,lines=5,findent=1em,nindent=0pt]{#1}{}}%
|
||||
{\bfseries\scshape #2}}
|
||||
{\end{mdframed}}
|
||||
|
||||
\newcommand{\otherinfo}[2][]{%
|
||||
\backmatter%
|
||||
\ifstrequal{#1}{suppinfo}
|
||||
{\section{Supporting Information}
|
||||
Additional Supporting Information may be found online in the supporting information for this article.}
|
||||
{}
|
||||
|
||||
\begin{mdframed}
|
||||
[linewidth=1\p@,linecolor=black!40,nobreak,
|
||||
innerleftmargin=12\p@,innerrightmargin=12\p@,
|
||||
innertopmargin=12\p@,innerbottommargin=12\p@,
|
||||
skipabove=\baselineskip]
|
||||
\textbf{How to cite this article:} #2
|
||||
\end{mdframed}
|
||||
}
|
||||
|
||||
\newenvironment{graphicalabstract}[1]{%
|
||||
\backmatter
|
||||
\section{graphical abstract}
|
||||
\lettrine[image,lines=10,findent=1em,nindent=0pt]{#1}{}%
|
||||
}{}
|
||||
|
||||
% Here we go!
|
||||
\normalsize
|
||||
\pagestyle{fancy}
|
||||
Binary file not shown.
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Reference in New Issue