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Pierre-Francois Loos 2022-04-06 09:14:41 +02:00
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Manuscript/CASPT3.tex
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@ -143,7 +143,7 @@ Nonetheless, going against popular beliefs and one step further in the perturbat
Although CASPT3 calculations have been reported in the literature,
\cite{Angeli_2006,Yanai_2007,Grabarek_2016,Li_2017,Li_2018,Li_2021,Bittererova_2001,Bokarev_2009,Frankcombe_2011,Gu_2008,Kerkines_2005,Lampart_2008,Leininger_2000,Maranzana_2020,Papakondylis_1999,Schild_2013,Sun_2018,Takatani_2009,Takatani_2010,Verma_2018,Woywod_2010,Yan_2004,Zhang_2020,Zhu_2005,Zhu_2007,Zhu_2013,Zou_2009}
the present study provides, to the best of our knowledge, the first comprehensive benchmark of CASPT3 and allows assessing its accuracy in the framework of electronically excited states.
%DJ: Ce sont des phrases de ccls, dŽjˆ dans l'abstract, pq aussi dans l'Intro ?
%DJ: Ce sont des phrases de ccls, dŽjˆ dans l'abstract, pq aussi dans l'Intro ?
%Based on the same 284 highly-accurate vertical excitation energies from the QUEST database, we show that CASPT3 only provides a very slight improvement over CASPT2 as far as accuracy is concerned.
%Moreover, as already reported in Ref.~\onlinecite{Grabarek_2016} where CASPT3 excitation energies are reported for retinal chromophore minimal models, we also observe that the accuracy of CASPT3 is much less sensitive to the IPEA shift.
We underline that, although a third-order version of NEVPT has been developed \cite{Angeli_2006} and has been used in some applications \cite{Pastore_2006a,Pastore_2006b,Pastore_2007,Angeli_2007,Camacho_2010,Angeli_2011,Angeli_2012} by Angeli and coworkers, as far as we are aware of, no NEVPT3 implementation are publicly available.
@ -315,7 +315,7 @@ TBEs listed as ``safe'' are assumed to be chemically accurate (\ie, absolute err
94 & &$^1A_1(\pi,\pis)$ &V &91.4 &5.90 &\Y &5.65 &6.21 &5.92 &6.18 &6.13\\
95 & &$^3A_2(\pi,\pis)$ &V &97.7 &2.79 &\Y &3.02 &2.87 &2.67 &2.84 &2.79\\
96 & &$^3A_1(\pi,\pis)$ &V &98.6 &4.05 &\Y &4.27 &4.10 &3.88 &4.06 &4.01\\
97 & &$^3B_1(\pi,3s )$ &R &98.0 &5.35 &\Y &4.45 &5.34 &5.15 &5.33 &5.30\\
97 & &$^3B_1(\pi,3s)$ &R &98.0 &5.35 &\Y &4.45 &5.34 &5.15 &5.33 &5.30\\
98 & &$^3A_1(\pi,3p)$ &R &98.5 &6.82 &\Y &6.34 &7.00 &6.76 &6.96 &6.91\\
99 & &$^1A''[F](\pi,\pis)$ &V &87.4 &0.71 &\Y &0.72 &0.69 &0.52 &0.66 &0.62\\
100 &Formamide &$^1A''(n,\pis)$ &V &90.8 &5.65 &\Y &5.95 &5.66 &5.45 &5.71 &5.67\\
@ -566,12 +566,11 @@ TBEs listed as ``safe'' are assumed to be chemically accurate (\ie, absolute err
\end{table*}
%%% %%% %%% %%%
From the different statistical quantities reported in Table \ref{tab:stat}, one can highlight the two following trends.
First, as previously reported, \cite{Werner_1996,Grabarek_2016} CASPT3 vertical excitation energies are much less sensitive to the IPEA shift, which drastically alters the accuracy of CASPT2.
\hl{Ce sont deux choses differentes: je separerais l'effet de l'IPEA et la precision finale. Donc, quel est le MAD avec/sans IPEA en PT2 et en PT3 sans tenir compte des TBEs, puis aller vers les TBEs}
Interestingly, the MAEs of CASPT3(IPEA) and CASPT3(NOIPEA) are amazingly close (\SI{0.11}{} and \SI{0.09}{\eV}), while the MAEs of CASPT2(IPEA) and CASPT2(NOIPEA) are remarkably different (\SI{0.11}{} and \SI{0.27}{\eV}).
Likewise, the MSEs of CASPT2(IPEA) and CASPT2(NOIPEA), \SI{0.06}{} and \SI{-0.26}{\eV}, clearly evidence the well-known global underestimation of the CASPT2(NOIPEA) excitation energies in molecular systems
when large basis sets are used. For CASPT3, the MSE with IPEA shift is only slightly larger without IPEA (\SI{0.10}{} and \SI{0.05}{\eV}, respectively).
From the different statistical quantities reported in Table \ref{tab:stat}, one can highlight the following trends.
First, as previously reported, \cite{Werner_1996,Grabarek_2016} CASPT3 vertical excitation energies are much less sensitive to the IPEA shift, which drastically alters the accuracy of CASPT2: the mean absolute deviation between the CASPT2(NOIPEA) and CASPT2(IPEA) data is \SI{0.329}{\eV} while it is only \SI{0.051}{\eV} between CASPT3(NOIPEA) and CASPT3(IPEA).
Consequently, the MAEs of CASPT3(IPEA) and CASPT3(NOIPEA) are amazingly close (\SI{0.11}{} and \SI{0.09}{\eV}), while the MAEs of CASPT2(IPEA) and CASPT2(NOIPEA) are remarkably different (\SI{0.11}{} and \SI{0.27}{\eV}).
Likewise, the MSEs of CASPT2(IPEA) and CASPT2(NOIPEA), \SI{0.06}{} and \SI{-0.26}{\eV}, clearly evidence the well-known global underestimation of the CASPT2(NOIPEA) excitation energies in molecular systems when large basis sets are used.
For CASPT3, the MSE with IPEA shift is only slightly larger without IPEA (\SI{0.10}{} and \SI{0.05}{\eV}, respectively).
Importantly, CASPT3 performs slightly better without IPEA shift, which is a nice outcome that holds for each group of transitions and system size (see the MAEs in Table \ref{tab:stat_subset}).
Second, CASPT3 (with or without IPEA) has a similar accuracy as CASPT2(IPEA).