getting there
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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 2019-05-28 13:36:42 +0200
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%% Created for Pierre-Francois Loos at 2019-05-28 23:01:35 +0200
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%% Saved with string encoding Unicode (UTF-8)
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@article{SheLeiVanSch-JCP-98,
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Author = {C. D. Sherrill and M. L. Leininger and T. J. Van Huis and H. F. Schaefer},
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Date-Added = {2019-05-28 22:50:09 +0200},
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Date-Modified = {2019-05-28 22:50:09 +0200},
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Journal = {J. Chem. Phys.},
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Pages = {1040},
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Title = {Structures and vibrational frequencies in the full configuration interaction limit: Predictions for four electronic states of methylene using a triple-zeta plus double polarization (TZ2P) basis.},
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Volume = {108},
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Year = {1998}}
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@article{BauTay-JCP-86,
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Author = {C. W. Bauschlicher and P. R. Taylor},
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Date-Added = {2019-05-28 22:46:11 +0200},
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Date-Modified = {2019-05-28 22:47:25 +0200},
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Journal = {J. Chem. Phys.},
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Pages = {6510-6512},
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Title = {A full CI treatment of the 1A1-3B1 separation in methylene},
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Volume = {85},
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Year = {1986}}
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@article{Sch-Science-86,
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Author = {{H. F. Schaeffer III}},
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Date-Added = {2019-05-28 22:42:40 +0200},
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Date-Modified = {2019-05-28 22:46:09 +0200},
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Pages = {1100-1107},
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Title = {Methylene: A paradigm for computational quantum chemistry},
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Year = {1986}}
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@article{BarDelPerMat-JMS-97,
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Author = {Rodney J. Bartlett and Janet E. Del Bene and S.Ajith Perera and Renee-Peloquin Mattie},
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Date-Added = {2019-05-28 13:34:13 +0200},
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@ -750,11 +778,13 @@
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@article{QP2,
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Author = {Y. Garniron and K. Gasperich and T. Applencourt and A. Benali and A. Fert{\'e} and J. Paquier and B. Pradines and R. Assaraf and P. Reinhardt and J. Toulouse and P. Barbaresco and N. Renon and G. David and J. P. Malrieu and M. V{\'e}ril and M. Caffarel and P. F. Loos and E. Giner and A. Scemama},
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Date-Added = {2019-04-07 13:54:16 +0200},
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Date-Modified = {2019-05-13 21:00:49 +0200},
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Date-Modified = {2019-05-28 22:19:25 +0200},
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Doi = {10.1021/acs.jctc.9b00176},
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Journal = {J. Chem. Theory Comput.},
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Title = {Quantum Package 2.0: A Open-Source Determinant-Driven Suite Of Programs},
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Volume = {submitted},
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Year = {2019}}
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Volume = {in press},
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Year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00176}}
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@article{PerRuzTaoStaScuCso-JCP-05,
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Author = {J. P. Perdew and A. Ruzsinszky and J. Tao and V. N. Staroverov and G. E. Scuseria and G. I. Csonka},
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@ -6442,8 +6472,10 @@
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@article{JenBun-JCP-88,
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Author = {P. Jensen and P. R. Bunker},
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Date-Modified = {2019-05-28 22:43:17 +0200},
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Journal = {J. Chem. Phys.},
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Pages = {1327},
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Title = {The potential surface and stretching frequencies of X3B1 methylene (CH2) determined from experiment using the Morse oscillator-rigid bender internal dynamics Hamiltonian.},
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Volume = {89},
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Year = {1988}}
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@ -10573,12 +10605,14 @@
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Volume = {112},
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Year = {2014}}
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@article{SheLeiVanSch-JCP-98,
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Author = {C. D. Sherrill and M. L. Leininger and T. J. Van Huis and H. F. Schaefer},
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Journal = {J. Chem. Phys.},
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Pages = {1040},
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Volume = {108},
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Year = {1998}}
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@article{SheVanYamSch-JMS-97,
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Author = {C. D. Sherrill and T. J. {Van Huis} and Y. Yamaguchi and H. F. Schaefer},
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Date-Modified = {2019-05-28 22:52:17 +0200},
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Journal = {J. Mol. Struct. (THEOCHEM)},
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Pages = {139-156},
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Title = {Full configuration interaction benchmarks for the states of methylene},
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Volume = {400},
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Year = {1997}}
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@article{SheMenGriBae-JCP-13,
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Author = {X. W. Sheng and {\L}. M. Mentel and O. V. Gritsenko and E. J. Baerends},
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@ -166,7 +166,7 @@
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\affiliation{\LCPQ}
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\begin{abstract}
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By combining extrapolated selected configuration interaction (sCI) calculations performed with the CIPSI algorithm with the recently proposed short-range density-functional functional correction for basis set incompleteness [\href{https://doi.org/10.1063/1.5052714}{Giner et al., \textit{J.~Chem.~Phys.}~\textbf{149}, 194301 (2018)}], we show that one can obtain vertical and adiabatic excitation energies with chemical accuracy with, typically, augmented double-$\zeta$ basis sets.
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By combining extrapolated selected configuration interaction (sCI) energies obtained with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm with the recently proposed short-range density-functional functional correction for basis set incompleteness [\href{https://doi.org/10.1063/1.5052714}{Giner et al., \textit{J.~Chem.~Phys.}~\textbf{149}, 194301 (2018)}], we show that one can obtain vertical and adiabatic excitation energies with chemical accuracy with, typically, augmented double-$\zeta$ basis sets.
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The present study clearly evidences that special care has to be taken for very diffuse excited states where the present correction might not be enough to catch the radial incompleteness of the one-electron basis set.
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\end{abstract}
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@ -177,19 +177,20 @@ The present study clearly evidences that special care has to be taken for very d
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\label{sec:intro}
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%%%%%%%%%%%%%%%%%%%%%%%%
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One of the most fundamental problems of conventional electronic structure methods is their slow energy convergence with respect to the size of the one-electron basis set.
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The overall basis set incompleteness error can be, qualitatively at least, split in two contributions steaming from the radial and angular incompleteness.
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Although for ground state properties angular incompleteness is by far the main source of error, for excited states, it is definitely not unusual to have a significant radial incompleteness (especially for Rydberg states) which can be alleviated by using additional sets of diffuse basis functions (i.e.~augmented basis sets).
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The overall basis set incompleteness error can be, qualitatively at least, split in two contributions stemming from the radial and angular incompleteness.
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Although for ground-state properties angular incompleteness is by far the main source of error, it is definitely not unusual to have a significant radial incompleteness in the case of excited states (especially for Rydberg states), which can be alleviated by using additional sets of diffuse basis functions (i.e.~augmented basis sets).
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Explicitly-correlated F12 methods \cite{Kut-TCA-85, Kut-TCA-85, KutKlo-JCP-91, NogKut-JCP-94} have been specifically designed to efficiently catch angular incompleteness. \cite{Ten-TCA-12, TenNog-WIREs-12, HatKloKohTew-CR-12, KonBisVal-CR-12, GruHirOhnTen-JCP-17, MaWer-WIREs-18}
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Although they have been extremely successful to speed up convergence of ground state properties, such as correlation and atomization energies, \cite{TewKloNeiHat-PCCP-07} their performances for excited states \cite{FliHatKlo-JCP-06, NeiHatKlo-JCP-06, HanKoh-JCP-09, Koh-JCP-09, ShiWer-JCP-10, ShiKniWer-JCP-11, ShiWer-JCP-11, ShiWer-MP-13} have been much more conflicting. \cite{FliHatKlo-JCP-06, NeiHatKlo-JCP-06}
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Although they have been extremely successful to speed up convergence of ground-state energies and properties, such as correlation and atomization energies, \cite{TewKloNeiHat-PCCP-07} their performances for excited states \cite{FliHatKlo-JCP-06, NeiHatKlo-JCP-06, HanKoh-JCP-09, Koh-JCP-09, ShiWer-JCP-10, ShiKniWer-JCP-11, ShiWer-JCP-11, ShiWer-MP-13} have been much more conflicting. \cite{FliHatKlo-JCP-06, NeiHatKlo-JCP-06}
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Instead of F12 methods, here we propose to follow a different philosophy and investigate the performances of the recently proposed universal density-based basis set
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Instead of F12 methods, here we propose to follow a different route and investigate the performances of the recently proposed universal density-based basis set
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incompleteness correction. \cite{GinPraFerAssSavTou-JCP-18}
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This density-based correction relies on short-range correlation density functionals (with multideterminant reference) from range-separated density-functional theory \cite{TouColSav-PRA-04, AngGerSavTou-PRA-05, GolWerSto-PCCP-05, TouGerJanSavAng-PRL-09,JanHenScu-JCP-09, TouZhuSavJanAng-JCP-11, MusReiAngTou-JCP-15, LeiStoWerSav-CPL-97, FroTouJen-JCP-07, FroCimJen-PRA-10, HedKneKieJenRei-JCP-15, HedTouJen-JCP-18, FerGinTou-JCP-18} (RS-DFT) to estimate the basis-set incompleteness error.
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RS-DFT combines rigorously density-functional theory (DFT) and wave function theory (WFT) via a decomposition of the electron-electron interaction into a non-divergent long-range part and a (complementary) short-range part treated with WFT and DFT, respectively.
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As the WFT method is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the convergence of these methods with respect to the size of the basis set is significantly improved. \cite{FraMusLupTou-JCP-15}
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This density-based correction relies on short-range correlation density functionals (with multideterminant reference) from range-separated density-functional theory \cite{TouColSav-PRA-04, AngGerSavTou-PRA-05, GolWerSto-PCCP-05, TouGerJanSavAng-PRL-09,JanHenScu-JCP-09, TouZhuSavJanAng-JCP-11, MusReiAngTou-JCP-15, LeiStoWerSav-CPL-97, FroTouJen-JCP-07, FroCimJen-PRA-10, HedKneKieJenRei-JCP-15, HedTouJen-JCP-18, FerGinTou-JCP-18} (RS-DFT) to estimate the basis set incompleteness error.
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Because RS-DFT combines rigorously density-functional theory (DFT) \cite{ParYan-BOOK-89} and wave function theory (WFT) \cite{SzaOst-BOOK-96} via a decomposition of the electron-electron interaction into a non-divergent long-range part and a (complementary) short-range part (treated with WFT and DFT, respectively), the WFT method is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points.
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Consequently, the energy convergence with respect to the size of the basis set is significantly improved, \cite{FraMusLupTou-JCP-15} and chemical accuracy can be obtained even with small basis sets.
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For example, in Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, we have shown that one can recover quintuple-$\zeta$ quality atomization and correlation energies with triple-$\zeta$ basis sets for a much lower computational cost than F12 methods.
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The present basis-set correction relies on the RS-DFT formalism to capture the missing part of the short-range correlation effects, a consequence of the incompleteness of the one-electron basis set.
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The present basis set correction relies on the RS-DFT formalism to capture the missing part of the short-range correlation effects, a consequence of the incompleteness of the one-electron basis set.
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The present methodology is identical to the one described in Ref.~\onlinecite{LooPraSceTouGin-JPCL-19} where the main working equation are reported and discussed.
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Contrary to our recent study on atomization and correlation energies, \cite{LooPraSceTouGin-JPCL-19} the present contribution focuses on vertical and adiabatic excitation energies in molecular electronically-excited systems which is a much tougher test for the reasons mentioned above.
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@ -219,10 +220,10 @@ is the basis-dependent complementary density functional,
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&
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\hWee{} & = \sum_{i<j}^{\Ne} r_{ij}^{-1},
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\end{align}
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are the kinetic and interelectronic repulsion operators, respectively, and $\wf{}{\Bas}$ and $\wf{}{}$ are two general $\Ne$-electron normalized wave functions belonging to the Hilbert space spanned by $\Bas$ and the complete basis set (CBS), respectively.
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are the kinetic and interelectronic repulsion operators, respectively, and $\wf{}{\Bas}$ and $\wf{}{}$ are two general $\Ne$-electron normalized wave functions belonging to the Hilbert space spanned by $\Bas$ and the complete basis set, respectively.
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The notation $\wf{}{} \rightsquigarrow \n{}{}$ states that $\wf{}{}$ yield the density $\n{}{}$.
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Hence, the CBS excitation energy reads
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Hence, the CBS excitation energy associated with the $k$th excited state reads
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\begin{equation}
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\DE{k}{\CBS} = \E{k}{\CBS} - \E{0}{\CBS} = \DE{k}{\Bas} + \DbE{}{\Bas}[\n{0}{\Bas},\n{k}{\Bas}],
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\end{equation}
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@ -237,12 +238,17 @@ is the excitation energy in $\Bas$ and
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\DbE{}{\Bas}[\n{0}{\Bas},\n{k}{\Bas}] = \bE{}{\Bas}[\n{k}{\Bas}] - \bE{}{\Bas}[\n{0}{\Bas}]
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\end{equation}
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its basis set correction.
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An important of the present correction is
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An important property of the present correction is
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\begin{equation}
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\label{eq:limitfunc}
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\lim_{\Bas \to \CBS} \DbE{}{\Bas}[\n{0}{\Bas},\n{k}{\Bas}] = 0.
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\end{equation}
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In other words, the correction vanishes in the CBS limit, hence guaranteeing an unaltered CBS limit.
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In other words, the correction vanishes in the CBS limit, hence guaranteeing an unaltered CBS limit. \cite{LooPraSceTouGin-JPCL-19}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Range-separation function}
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\label{sec:rs}
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%%%%%%%%%%%%%%%%%%%%%%%%
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In Ref.~\onlinecite{LooPraSceTouGin-JPCL-19}, we have shown that one can efficiently approximate $\bE{}{\Bas}[\n{}{}]$ by short-range correlation functionals with multi-determinantal (ECMD) reference, \cite{TouGorSav-TCA-05} $\bE{\text{c,md}}{\sr}[\n{}{},\rsmu{}{}]$.
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The ECMD functionals admit, for any $\n{}{}$, the following two limits
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@ -252,9 +258,11 @@ The ECMD functionals admit, for any $\n{}{}$, the following two limits
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&
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\lim_{\mu \to 0} \bE{\text{c,md}}{\sr}[\n{}{},\rsmu{}{}] & = \Ec[\n{}{}],
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\end{align}
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where $\Ec[\n{}{}]$ is the usual universal correlation density functional defined in KS-DFT.
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The key ingredient --- the range-separated function $\rsmu{}{\Bas}(\br{})$ --- is defined such that the long-range interaction of RS-DFT, $\w{}{\lr,\mu}(r_{12}) = \erf( \mu r_{12})/r_{12}$, coincides with the effective interaction at coalescence, i.e.~$\w{}{\lr,\rsmu{}{\Bas}(\br{})}(0) = \W{}{\Bas}(\br{},\br{})$ at any $\br{}$, with \cite{GinPraFerAssSavTou-JCP-18}
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\begin{equation}
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where $\Ec[\n{}{}]$ is the usual universal correlation density functional defined in Kohn-Sham DFT. \cite{HohKoh-PR-64, KohSha-PR-65}
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The key ingredient --- the range-separated function $\rsmu{}{\Bas}(\br{})$ --- automatically adapts to the spatial non-homogeneity of the basis set incompleteness error.
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It is defined such that the long-range interaction of RS-DFT, $\w{}{\lr,\mu}(r_{12}) = \erf( \mu r_{12})/r_{12}$, coincides, at coalescence, with an effective two-electron interaction $\W{}{\Bas}(\br{1},\br{2})$ ``mimicking'' the Coulomb operator in an incomplete basis $\Bas$, i.e.~$\w{}{\lr,\rsmu{}{\Bas}(\br{})}(0) = \W{}{\Bas}(\br{},\br{})$ at any $\br{}$, with \cite{GinPraFerAssSavTou-JCP-18}
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\begin{gather}
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\label{eq:def_weebasis}
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\W{}{\Bas}(\br{1},\br{2}) =
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\begin{cases}
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@ -262,13 +270,11 @@ The key ingredient --- the range-separated function $\rsmu{}{\Bas}(\br{})$ --- i
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\\
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\infty, & \text{otherwise,}
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\end{cases}
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\end{equation}
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and
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\begin{equation}
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\\
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\label{eq:n2basis}
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\n{2}{\Bas}(\br{1},\br{2})
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= \sum_{pqrs \in \Bas} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2},
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\end{equation}
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\end{gather}
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and $\Gam{pq}{rs} = 2 \mel*{\wf{}{\Bas}}{ \aic{r_\downarrow}\aic{s_\uparrow}\ai{q_\uparrow}\ai{p_\downarrow}}{\wf{}{\Bas}}$ are the opposite-spin pair density associated with $\wf{}{\Bas}$ and its corresponding tensor, respectively, $\SO{p}{}$ is a (real-valued) molecular orbital (MO),
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\begin{equation}
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\label{eq:fbasis}
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@ -297,7 +303,8 @@ To go beyond the LDA and cure its over correlation at small $\mu$, some of the a
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\int \n{}{}(\br{}) \be{\text{c,md}}{\sr,\PBE}\qty(\n{}{}(\br{}),s(\br{}),\zeta(\br{}),\rsmu{}{\Bas}(\br{})) \dbr{},
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\end{equation}
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where $s = \abs{\nabla \n{}{}}/\n{}{4/3}$ is the reduced density gradient.
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$\be{\text{c,md}}{\sr,\PBE}\qty(\n{}{},s,\zeta,\rsmu{}{})$ interpolates between the usual PBE correlation functional, \cite{PerBurErn-PRL-96} $\e{\text{c}}{\PBE}(\n{}{},s,\zeta)$, at $\rsmu{}{}=0$ and the exact large-$\rsmu{}{}$ behavior, \cite{TouColSav-PRA-04, GorSav-PRA-06, PazMorGorBac-PRB-06} yielding
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$\be{\text{c,md}}{\sr,\PBE}\qty(\n{}{},s,\zeta,\rsmu{}{})$ interpolates between the usual PBE correlation functional, \cite{PerBurErn-PRL-96} $\e{\text{c}}{\PBE}(\n{}{},s,\zeta)$, at $\rsmu{}{}=0$ and the exact large-$\rsmu{}{}$ behavior. \cite{TouColSav-PRA-04, GorSav-PRA-06, PazMorGorBac-PRB-06}
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It reads
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\begin{subequations}
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\begin{gather}
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\label{eq:epsilon_cmdpbe}
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@ -308,30 +315,27 @@ $\be{\text{c,md}}{\sr,\PBE}\qty(\n{}{},s,\zeta,\rsmu{}{})$ interpolates between
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\end{gather}
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\end{subequations}
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We will refer to this functional as the ``on top'' PBE (PBEot) ECMD functional.
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More recently, we have also proposed a simplified version of the PBEot functional where we replaced the on-top pair density by its UEG version, i.e.~$\n{2}{\Bas}(\br{},\br{}) \approx \n{2}{\UEG}(\n{}{}(\br{}),\zeta(\br{}))$, where $\n{2}{\UEG}(\n{}{},\zeta) \approx \n{}{2} (1-\zeta^2) g_0(n)$ with the parametrization of the UEG on-top pair-distribution function $g_0(n)$ given in Eq.~(46) of Ref.~\citenum{GorSav-PRA-06}.
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This computationally-lighter functional will be refer to as PBE.
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More recently, \cite{LooPraSceTouGin-JPCL-19} we have also proposed a simplified version of the PBEot functional where we replaced the on-top pair density by its UEG version, i.e.~$\n{2}{\Bas}(\br{},\br{}) \approx \n{2}{\UEG}(\n{}{}(\br{}),\zeta(\br{}))$, where $\n{2}{\UEG}(\n{}{},\zeta) \approx \n{}{2} (1-\zeta^2) g_0(n)$ with the parametrization of the UEG on-top pair-distribution function $g_0(n)$ given in Eq.~(46) of Ref.~\citenum{GorSav-PRA-06}.
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This computationally-lighter functional will be refered to as PBE.
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%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Computational details}
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\label{sec:compdetails}
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%%%%%%%%%%%%%%%%%%%%%%%%
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Here, we compute the ground and excited state energies, one-electron and on-top densities with a selected CI methods known as as CIPSI. \cite{HurMalRan-JCP-73, GinSceCaf-CJC-13, GinSceCaf-JCP-15}
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exFCI stands for extrapolated FCI energies computed by increasing the number of determinants in the CI expansion.
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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} for more details.
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The one-electron density and on-top density is computed from a very large CIPSI expansion containing several million determinants.
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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 energies. \cite{QP2}
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These energies will be labeled exFCI in the following.
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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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The 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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They are also reported in the {\SI}.
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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}.
|
||||
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}.
|
||||
The FC density-based correction is used consistently with the FC approximation in WFT methods.
|
||||
We refer the interested reader to Ref.~\onlinecite{LooPraSceTouGin-JPCL-19} for detailed explanations on how the previous equations have to be modified within the FC approximation.
|
||||
|
||||
%The most computationally intensive task of the present approach is the evaluation of $\W{}{\Bas}(\br{},\br{})$ at each quadrature grid point.
|
||||
%In the general case (i.e.~$\wf{}{\Bas}$ is a multi-determinant expansion), we compute this embarrassingly parallel step in $\order*{\Ng \Nb^4}$ computational cost with a memory requirement of $\order*{ \Ng \Nb^2}$, where $\Nb$ is the number of basis functions in $\Bas$.
|
||||
%In our current implementation, the computational bottleneck is the four-index transformation to get the two-electron integrals in the MO basis which appear in Eqs.~\eqref{eq:n2basis} and \eqref{eq:fbasis}.
|
||||
%Nevertheless, this step usually has to be performed for most correlated WFT calculations.
|
||||
The frozen-core density-based correction is used consistently with the frozen-core approximation in WFT methods.
|
||||
We refer the interested reader to Ref.~\onlinecite{LooPraSceTouGin-JPCL-19} for an explicit derivation of the equations associated with the frozen-core version of the present density-based basis set correction.
|
||||
Compared to the exFCI calculations performed to compute energies and densities, the basis set correction represents, in any case, a marginal computational cost.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Results}
|
||||
@ -343,7 +347,7 @@ We refer the interested reader to Ref.~\onlinecite{LooPraSceTouGin-JPCL-19} for
|
||||
\label{sec:CH2}
|
||||
%=======================
|
||||
|
||||
As a first test of the present basis set correction, we consider the adiabatic transitions of methylene which have been thourhoughly studied in the literature with high-level ab initio methods. \cite{AbrShe-JCP-04, AbrShe-CPL-05, ZimTouZhaMusUmr-JCP-09, ChiHolAdaOttUmrShaZim-JPCA-18}
|
||||
As a first test of the present basis set correction, we consider the adiabatic transitions of methylene which have been thourhoughly studied in the literature with high-level ab initio methods. \cite{Sch-Science-86, BauTay-JCP-86, JenBun-JCP-88, SheVanYamSch-JMS-97, SheLeiVanSch-JCP-98, AbrShe-JCP-04, AbrShe-CPL-05, ZimTouZhaMusUmr-JCP-09, ChiHolAdaOttUmrShaZim-JPCA-18}
|
||||
|
||||
%%% TABLE 1 %%%
|
||||
\begin{squeezetable}
|
||||
@ -423,27 +427,32 @@ As a first test of the present basis set correction, we consider the adiabatic t
|
||||
& -39.04124(1) & 1.378
|
||||
& -39.00044(1) & 2.489 \\
|
||||
\\
|
||||
SHCI & AVQZ & -39.08849(1)
|
||||
SHCI\fnm[1] & AVQZ & -39.08849(1)
|
||||
& -39.07404(1) & 0.393
|
||||
& -39.03711(1) & 1.398
|
||||
& -38.99603(1) & 2.516 \\
|
||||
CR-EOMCC (2,3)D& AVQZ & -39.08817
|
||||
CR-EOMCC (2,3)D\fnm[2]& AVQZ & -39.08817
|
||||
& -39.07303 & 0.412
|
||||
& -39.03450 & 1.460
|
||||
& -38.99457 & 2.547 \\
|
||||
FCI & TZ2P & -39.066738
|
||||
FCI\fnm[3] & TZ2P & -39.066738
|
||||
& -39.048984 & 0.483
|
||||
& -39.010059 & 1.542
|
||||
& -38.968471 & 2.674 \\
|
||||
DMC & &
|
||||
DMC\fnm[4] & &
|
||||
& & 0.406
|
||||
& & 1.416
|
||||
& & 2.524 \\
|
||||
Exp. & &
|
||||
Exp.\fnm[5] & &
|
||||
& & 0.400
|
||||
& & 1.411
|
||||
\end{tabular}
|
||||
\end{ruledtabular}
|
||||
\fnt[1]{Reference \onlinecite{ChiHolAdaOttUmrShaZim-JPCA-18}.}
|
||||
\fnt[2]{References \onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.}
|
||||
\fnt[3]{Reference \onlinecite{SheLeiVanSch-JCP-98}.}
|
||||
\fnt[4]{Reference \onlinecite{ZimTouZhaMusUmr-JCP-09}.}
|
||||
\fnt[5]{References \onlinecite{SheLeiVanSch-JCP-98, JenBun-JCP-88}.}
|
||||
\end{table*}
|
||||
\end{squeezetable}
|
||||
%%% %%% %%%
|
||||
|
||||
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Reference in New Issue
Block a user