CH2
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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 2019-05-29 23:30:47 +0200
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%% Created for Pierre-Francois Loos at 2019-05-30 11:26:43 +0200
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%% Saved with string encoding Unicode (UTF-8)
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@ -12712,9 +12712,9 @@
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Year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00591}}
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@article{LooBogSceCafJAc-JCTC-19,
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@article{LooBogSceCafJac-JCTC-19,
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Author = {Loos, Pierre-Fran{\c c}ois and Boggio-Pasqua, Martial and Scemama, Anthony and Caffarel, Michel and Jacquemin, Denis},
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Date-Modified = {2019-04-07 14:02:34 +0200},
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Date-Modified = {2019-05-30 11:26:43 +0200},
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Doi = {10.1021/acs.jctc.8b01205},
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Journal = {J. Chem. Theory Comput.},
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Number = {3},
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@ -333,11 +333,13 @@ This computationally-lighter functional will be refered to as PBE.
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In the present study, we compute the ground- and excited-state energies, one-electron and on-top densities with a selected CI method known as CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively). \cite{HurMalRan-JCP-73, GinSceCaf-CJC-13, GinSceCaf-JCP-15}
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The total energy of each state is obtained via an efficient extrapolation procedure of the sCI energies designed to reach near-FCI accuracy. \cite{QP2}
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These energies will be labeled exFCI in the following.
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Using near-FCI excitation energies (within a given basis set) has the indisputable advantage to remove the error inherent to the WFT method.
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Indeed, in the present case, the only source of error on the excitation energies is due to basis set incompleteness.
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We refer the interested reader to Refs.~\onlinecite{HolUmrSha-JCP-17, SceGarCafLoo-JCTC-18, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18, LooBogSceCafJac-JCTC-19, QP2} for more details.
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The one-electron and on-top densities are computed from a very large CIPSI expansion containing several million determinants.
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All the RS-DFT and exFCI calculations have been performed with {\QP}. \cite{QP2}
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For the numerical quadratures, we employ the SG-2 grid. \cite{DasHer-JCC-17}
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Except for methylene for which FCI/TZVP geometries have been taken from Ref.~\onlinecite{SheLeiVanSch-JCP-98}, the other geometries have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19} and have been obtained at the CC3/aug-cc-pVTZ level of theory.
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Except for methylene for which FCI/TZVP geometries have been taken from Ref.~\onlinecite{SheLeiVanSch-JCP-98}, the other geometries have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJac-JCTC-19} and have been obtained at the CC3/aug-cc-pVTZ level of theory.
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For the sake of completeness, they are also reported in the {\SI}.
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Frozen-core calculations are systematically performed and defined as such: a \ce{He} core is frozen from \ce{Li} to \ce{Ne}, while a \ce{Ne} core is frozen from \ce{Na} to \ce{Ar}.
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The frozen-core density-based correction is used consistently with the frozen-core approximation in WFT methods.
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@ -365,12 +367,18 @@ We have also computed these adiabatic energies at the exFCI/AV5Z level and used
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\end{equation}
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These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{tab:CH2} alongside reference values from the literature obtained with various approaches. \cite{ChiHolAdaOttUmrShaZim-JPCA-18, SheLeiVanSch-JCP-98, JenBun-JCP-88, SheLeiVanSch-JCP-98, ZimTouZhaMusUmr-JCP-09}
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Figure \ref{fig:CH2} clearly shows that, for the double-$\zeta$ basis, the exFCI adiabatic energies are far from being chemically accurate with errors as high as 0.015 eV.
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From triplet-$\zeta$ onward, the exFCI excitation energies are chemically-accurate though.
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%%% TABLE 1 %%%
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\begin{turnpage}
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\begin{squeezetable}
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\begin{table*}
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\caption{
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Total energies $E$ (in hartree) and adiabatic transition energies $\Ead$ (in eV) of excited states of methylene for various methods and basis sets.}
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Total energies $E$ (in hartree) and adiabatic transition energies $\Ead$ (in eV) of excited states of methylene for various methods and basis sets.
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The value in parenthesis is an estimate on the last digit of the extrapolation error.
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The relative difference with respect to the exFCI/CBS result is reported in square brackets.}
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\label{tab:CH2}
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\begin{ruledtabular}
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\begin{tabular}{llddddddd}
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@ -386,64 +394,64 @@ These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{t
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& \tabc{$E$ (a.u.)} & \tabc{$\Ead$ (eV)} \\
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\hline
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exFCI & AVDZ & -39.04846(1)
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& -39.03225(1) & 0.441
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& -38.99203(1) & 1.536
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& -38.95076(1) & 2.659 \\
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& -39.03225(1) & 0.441 [+0.053]
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& -38.99203(1) & 1.536 [+0.146]
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& -38.95076(1) & 2.659 [+0.154] \\
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& AVTZ & -39.08064(3)
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& -39.06565(2) & 0.408
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& -39.02833(1) & 1.423
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& -38.98709(1) & 2.546 \\
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& -39.06565(2) & 0.408 [+0.020]
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& -39.02833(1) & 1.423 [+0.034]
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& -38.98709(1) & 2.546 [+0.042] \\
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& AVQZ & -39.08854(1)
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& -39.07402(2) & 0.395
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& -39.03711(1) & 1.399
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& -38.99607(1) & 2.516 \\
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& -39.07402(2) & 0.395 [+0.007]
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& -39.03711(1) & 1.399 [+0.010]
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& -38.99607(1) & 2.516 [+0.012] \\
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& AV5Z & -39.09079(1)
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& -39.07647(1) & 0.390
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& -39.03964(3) & 1.392
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& -38.99867(1) & 2.507 \\
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& CBS & -39.09111
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& -39.07682 & 0.388
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& -39.04000 & 1.390
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& -38.99904 & 2.504 \\
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\\
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exFCI+LDA & AVDZ & -39.07450(1)
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& -39.06213(1) & 0.337
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& -39.02233(1) & 1.420
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& -38.97946(1) & 2.586 \\
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& AVTZ & -39.09099(3)
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& -39.07779(2) & 0.359
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& -39.04051(1) & 1.374
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& -38.99859(1) & 2.514 \\
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& AVQZ & -39.09319(1)
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& -39.07959(2) & 0.370
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& -39.04267(1) & 1.375
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& -39.00135(1) & 2.499 \\
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\\
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exFCI+PBE & AVDZ & -39.07282(1)
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& -39.06150(1) & 0.308
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& -39.02181(1) & 1.388
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& -38.97873(1) & 2.560 \\
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& AVTZ & -39.08948(3)
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& -39.07639(2) & 0.356
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& -39.03911(1) & 1.371
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& -38.99724(1) & 2.510 \\
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& AVQZ & -39.09247(1)
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& -39.07885(2) & 0.371
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& -39.04193(1) & 1.375
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& -39.00066(1) & 2.498 \\
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& -39.07647(1) & 0.390 [+0.001]
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& -39.03964(3) & 1.392 [+0.002]
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& -38.99867(1) & 2.507 [+0.003] \\
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& CBS & -39.09141
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& -39.07715 & 0.388
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& -39.04034 & 1.390
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& -38.99939 & 2.504 \\
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\\
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exFCI+PBEot & AVDZ & -39.06924(1)
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& -39.05651(1) & 0.347
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& -39.01777(1) & 1.401
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& -38.97698(1) & 2.511 \\
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& -39.05651(1) & 0.347 [-0.042]
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& -39.01777(1) & 1.401 [+0.011]
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& -38.97698(1) & 2.511 [+0.007] \\
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& AVTZ & -39.08805(3)
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& -39.07430(2) & 0.374
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& -39.03742(1) & 1.378
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& -38.99652(1) & 2.491 \\
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& -39.07430(2) & 0.374 [-0.014]
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& -39.03742(1) & 1.378 [-0.012]
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& -38.99652(1) & 2.491 [-0.013] \\
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& AVQZ & -39.09189(1)
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& -39.07795(2) & 0.379
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& -39.04124(1) & 1.378
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& -39.00044(1) & 2.489 \\
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& -39.07795(2) & 0.379 [-0.009]
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& -39.04124(1) & 1.378 [-0.011]
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& -39.00044(1) & 2.489 [-0.016] \\
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\\
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exFCI+PBE & AVDZ & -39.07282(1)
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& -39.06150(1) & 0.308 [-0.080]
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& -39.02181(1) & 1.388 [-0.002]
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& -38.97873(1) & 2.560 [+0.056] \\
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& AVTZ & -39.08948(3)
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& -39.07639(2) & 0.356 [-0.032]
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& -39.03911(1) & 1.371 [-0.019]
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& -38.99724(1) & 2.510 [+0.006] \\
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& AVQZ & -39.09247(1)
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& -39.07885(2) & 0.371 [-0.017]
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& -39.04193(1) & 1.375 [-0.015]
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& -39.00066(1) & 2.498 [-0.006] \\
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\\
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exFCI+LDA & AVDZ & -39.07450(1)
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& -39.06213(1) & 0.337 [-0.051]
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& -39.02233(1) & 1.420 [+0.030]
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& -38.97946(1) & 2.586 [+0.082] \\
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& AVTZ & -39.09099(3)
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& -39.07779(2) & 0.359 [-0.029]
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& -39.04051(1) & 1.374 [-0.016]
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& -38.99859(1) & 2.514 [+0.010] \\
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& AVQZ & -39.09319(1)
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& -39.07959(2) & 0.370 [-0.018]
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& -39.04267(1) & 1.375 [-0.015]
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& -39.00135(1) & 2.499 [-0.005] \\
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\\
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SHCI\fnm[1] & AVQZ & -39.08849(1)
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& -39.07404(1) & 0.393
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@ -473,13 +481,14 @@ These results are illustrated in Fig.~\ref{fig:CH2} and reported in Table \ref{t
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\fnt[5]{References \onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.}
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\end{table*}
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\end{squeezetable}
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\end{turnpage}
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%%% %%% %%%
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%%% FIG 1 %%%
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\begin{figure}
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\includegraphics[width=\linewidth]{CH2}
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\caption{Error in adiabatic excitation energies $\Ead$ (in eV) of methylene for various basis sets and methods.
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The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
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The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
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See Table \ref{tab:CH2} for raw data.}
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\label{fig:CH2}
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\end{figure}
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@ -497,7 +506,7 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
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\begin{table*}
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\caption{
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Vertical absorption energies $\Eabs$ (in eV) of excited states of ammonia, carbon dimer, water and ethylene for various methods and basis sets.
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The TBEs have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJAc-JCTC-19} on the same geometries.
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The TBEs have been extracted from Refs.~\onlinecite{LooSceBloGarCafJac-JCTC-18, LooBogSceCafJac-JCTC-19} on the same geometries.
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See the {\SI} for raw data.}
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\begin{ruledtabular}{}
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\begin{tabular}{lllddddddddddddd}
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@ -553,33 +562,6 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
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& 0.11 & 0.02 & 0.00
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\\
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\\
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% Hydrogen chloride& ${}^1\Sigma \ra {}^1\Pi$ & CT\fnm[2] & 7.86 & -0.04 & -0.02 & 0.02
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% & 0.13 & 0.06 & 0.06
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% & 0.11 & 0.04 & 0.05
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% & 0.10 & 0.05 & 0.06
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% \\
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% \\
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% Hydrogen sulfide & $1\,^{1}A_1 \ra 1\,^{1}A_2$ & Ryd. & 6.10 & 0.00 & 0.08 & 0.05
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% & 0.15 & 0.12 & 0.07
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% & 0.14 & 0.11 & 0.07
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% & 0.14 & 0.11 & 0.07
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% \\
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% & $1\,^{1}A_1 \ra 1\,^{1}B_1$ & Ryd. & 6.29 & 0.00 & -0.05 & 0.00
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% & -0.12 & 0.01 & 0.03
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% & -0.14 & 0.00 & 0.03
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% & -0.14 & 0.01 & 0.03
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% \\
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% & $1\,^{1}A_1 \ra 1\,^{3}A_2$ & Ryd. & 5.74 & 0.01 & 0.07 & 0.05
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% & 0.18 & 0.12 & 0.08
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% & 0.20 & 0.13 & 0.08
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% & 0.19 & 0.13 & 0.08
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% \\
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% & $1\,^{1}A_1 \ra 1\,^{3}B_1$ & Ryd. & 5.94 & -0.04 & -0.05 & -0.01
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% & 0.07 & 0.02 & 0.03
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% & 0.09 & 0.03 & 0.03
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% & 0.07 & 0.04 & 0.04
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% \\
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% \\
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Water & $1\,^{1}A_1 \ra 1\,^{1}B_1$ & Ryd. & 7.70 & -0.17 & -0.07 & -0.02
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& 0.01 & 0.00 & 0.02
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& -0.02 & -0.01 & 0.00
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@ -611,32 +593,6 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
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& 0.06 & 0.03 & 0.04
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\\
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\\
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% Acetylene & $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{1}\Sigma_{u}^{-}$ & Val. & 7.10 & 0.10 & 0.00
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% & 0.07 & 0.00
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% & 0.11 & 0.00
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% & 0.11 & 0.00
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% \\
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% & $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{1}\Delta_{u}$ & Val. & 7.44 & 0.07 & 0.00
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% & 0.04 & -0.01
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% & 0.12 & 0.02
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% & 0.11 & 0.02
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% \\
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% & $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Sigma_{u}^{+}$ & Val. & 5.56 & -0.06 & -0.03
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% & 0.07 & 0.02
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% & 0.04 & 0.00
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% & 0.02 & 0.00
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% \\
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% & $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Delta_{u}$ & Val. & 6.40 & 0.06 & 0.00
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% & 0.10 & 0.02
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% & 0.14 & 0.03
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% & 0.12 & 0.03
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% \\
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% & $1\,^{1}\Sigma_{g}^{+} \ra 1\,^{3}\Sigma_{u}^{-}$ & Val. & 7.09 & 0.05 & -0.01
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% & 0.08 & 0.00
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% & 0.16 & 0.04
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% & 0.14 & 0.04
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% \\
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% \\
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Ethylene & $1\,^{1}A_{1g} \ra 1\,^{1}B_{3u}$ & Ryd. & 7.43 & -0.12 & -0.04 &
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& -0.05 & -0.01 &
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& -0.04 & -0.01 &
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@ -668,55 +624,9 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
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& 0.05 & 0.04 &
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\\
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\\
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% Formaldehyde& $1\,^{1}A_{1} \ra 1\,^{1}A_{2}$ & Val. & 3.97 & 0.02 & 0.01 &
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% & 0.05 & 0.02 &
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% & 0.03 & 0.02 &
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% & 0.02 & 0.01 &
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% \\
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% & $1\,^{1}A_{1} \ra 1\,^{1}B_{2}$ & Ryd. & 7.30 & -0.19 & -0.07 &
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% & 0.00 & 0.00 &
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% & -0.02 & 0.00 &
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% & -0.04 & 0.00 &
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% \\
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% & $1\,^{1}A_{1} \ra 2\,^{1}B_{2}$ & Ryd. & 8.14 & -0.10 & -0.01 &
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% & 0.09 & 0.07 &
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% & 0.08 & 0.06 &
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% & 0.05 & 0.06 &
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% \\
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% & $1\,^{1}A_{1} \ra 2\,^{1}A_{1}$ & Ryd. & 8.27 & -0.15 & -0.04 &
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% & 0.03 & 0.04 &
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% & 0.02 & 0.03 &
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% & 0.00 & 0.03 &
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% \\
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% & $1\,^{1}A_{1} \ra 1\,^{3}A_{2}$ & Val. & 3.58 & 0.00 & 0.00 &
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% & 0.09 & 0.05 &
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% & 0.11 & 0.06 &
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% & 0.07 & 0.04 &
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% \\
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% & $1\,^{1}A_{1} \ra 1\,^{3}A_{1}$ & Val. & 6.07 & 0.03 & 0.01 &
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% & 0.13 & 0.04 &
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% & 0.15 & 0.05 &
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% & 0.11 & 0.04 &
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% \\
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% & $1\,^{1}A_{1} \ra 1\,^{3}B_{2}$ & Ryd. & 7.14 & -0.19 & -0.08 &
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% & 0.01 & 0.01 &
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% & 0.02 & 0.01 &
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% & -0.01 & 0.00 &
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% \\
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% & $1\,^{1}A_{1} \ra 2\,^{3}B_{2}$ & Ryd. & 7.96 & -0.09 & -0.02 &
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% & 0.13 & 0.08 &
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% & 0.14 & 0.08 &
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% & 0.10 & 0.07 &
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% \\
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% & $1\,^{1}A_{1} \ra 1\,^{3}A_{1}$ & Ryd. & 8.15 & -0.14 & -0.05 &
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% & 0.07 & 0.05 &
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% & 0.07 & 0.04 &
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% & 0.04 & 0.04 &
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% \\
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\end{tabular}
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\end{ruledtabular}
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\fnt[1]{Doubly-excited states of $(\pi,\pi) \ra (\si,\si)$ character.}
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% \fnt[2]{CT stands for charge transfer.}
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||||
\end{table*}
|
||||
\end{squeezetable}
|
||||
%%% %%% %%%
|
||||
@ -725,7 +635,7 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
|
||||
\begin{figure}
|
||||
\includegraphics[width=\linewidth]{H2O}
|
||||
\caption{Error in vertical excitation energies (in eV) of water for various basis sets and methods.
|
||||
The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
|
||||
The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
|
||||
See the {\SI} for raw data.}
|
||||
\label{fig:H2O}
|
||||
\end{figure}
|
||||
@ -735,7 +645,7 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
|
||||
\begin{figure}
|
||||
\includegraphics[width=\linewidth]{NH3}
|
||||
\caption{Error in vertical excitation energies (in eV) of ammonia for various basis sets and methods.
|
||||
The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
|
||||
The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
|
||||
See the {\SI} for raw data.}
|
||||
\label{fig:NH3}
|
||||
\end{figure}
|
||||
@ -746,13 +656,13 @@ Water \cite{CaiTozRei-JCP-00, RubSerMer-JCP-08, LiPal-JCP-11, LooSceBloGarCafJac
|
||||
\label{sec:C2}
|
||||
%=======================
|
||||
It is also interesting to study doubly-excited states. \cite{AbrShe-JCP-04, AbrShe-CPL-05, Var-JCP-08, PurZhaKra-JCP-09, AngCimPas-MP-12, BooCleThoAla-JCP-11, Sha-JCP-15, SokCha-JCP-16, VarRoc-PTRSMPES-18}
|
||||
In the carbon dimer, these valence states are of $(\pi,\pi) \ra (\si,\si)$ character and they have been recently studied with state-of-the-art methods. \cite{LooBogSceCafJAc-JCTC-19}
|
||||
In the carbon dimer, these valence states are of $(\pi,\pi) \ra (\si,\si)$ character and they have been recently studied with state-of-the-art methods. \cite{LooBogSceCafJac-JCTC-19}
|
||||
|
||||
%%% FIG 4 %%%
|
||||
\begin{figure}
|
||||
\includegraphics[width=\linewidth]{C2}
|
||||
\caption{Error in vertical excitation energies $\Eabs$ (in eV) for two doubly-excited states of the carbon dimer for various basis sets and methods.
|
||||
The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
|
||||
The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
|
||||
See the {\SI} for raw data.}
|
||||
\label{fig:C2}
|
||||
\end{figure}
|
||||
@ -766,26 +676,14 @@ In the carbon dimer, these valence states are of $(\pi,\pi) \ra (\si,\si)$ chara
|
||||
|
||||
Ethylene is an interesting molecules as it contains both valence and Rydberg excited states. \cite{SerMarNebLinRoo-JCP-93, WatGwaBar-JCP-96, WibOliTru-JPCA-02, BarPaiLis-JCP-04, Ang-JCC-08, SchSilSauThi-JCP-08, SilSchSauThi-JCP-10, SilSauSchThi-MP-10, Ang-IJQC-10, DadSmaBooAlaFil-JCTC-12, FelPetDav-JCP-14, ChiHolAdaOttUmrShaZim-JPCA-18}
|
||||
|
||||
%\begin{figure}
|
||||
% \includegraphics[width=\linewidth]{C2H2}
|
||||
% \caption{Error in vertical excitation energies (in eV) of acetylene for various basis sets and methods.}
|
||||
% \label{fig:C2H2}
|
||||
%\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=\linewidth]{C2H4}
|
||||
\caption{Error in vertical excitation energies $\Eabs$ (in eV) of ethylene for various basis sets and methods.
|
||||
The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal}).
|
||||
The green region corresponds to chemical accuracy (i.e., error below 1 {\kcal} or 0.043 eV).
|
||||
See the {\SI} for raw data.}
|
||||
\label{fig:C2H4}
|
||||
\end{figure}
|
||||
|
||||
%\begin{figure}
|
||||
% \includegraphics[width=\linewidth]{CH2O}
|
||||
% \caption{Error in vertical excitation energies $\Eabs$ (in eV) of formaldehyde for various basis sets and methods.}
|
||||
% \label{fig:CH2O}
|
||||
%\end{figure}
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Conclusion}
|
||||
\label{sec:ccl}
|
||||
@ -796,7 +694,7 @@ We are currently investigating the performance of the present basis set correcti
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section*{Supporting Information Available}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
See {\SI} for geometries and additional information (including total energies).
|
||||
See {\SI} for geometries and additional information (including energetic correction of the various functionals).
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{acknowledgements}
|
||||
|
||||
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Reference in New Issue
Block a user