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Pierre-Francois Loos 2019-05-26 00:05:12 +02:00
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Manuscript/Ex-srDFT.tex
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@ -173,18 +173,18 @@ By combining extrapolated selected configuration interaction (sCI) calculations
\section{Introduction} \section{Introduction}
\label{sec:intro} \label{sec:intro}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
One of the most fundamental problem of conventional electronic structure methods is their slow energy convergence with respect to the size of the one-electron basis set. 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.
Explicitly-correlated F12 methods \cite{Kut-TCA-85, Kut-TCA-85, KutKlo-JCP-91, NogKut-JCP-94} have been specifically designed to cure this problem. \cite{Ten-TCA-12, TenNog-WIREs-12, HatKloKohTew-CR-12, KonBisVal-CR-12, GruHirOhnTen-JCP-17, MaWer-WIREs-18} The overall basis set incompleteness error can be, qualitatively at least, split in two contributions steaming from the radial and angular incompleteness.
Although they have extremely successful to speed up convergence of the ground state properties such as correlation and atomization energies (for example), \cite{TewKloNeiHat-PCCP-07} their performances for excited states \cite{ShiWer-JCP-10, ShiKniWer-JCP-11, ShiWer-JCP-11, ShiWer-MP-13} have been much more conflicting. \cite{FliHatKlo-JCP-06, NeiHatKlo-JCP-06, HanKoh-JCP-09, Koh-JCP-09} 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).
There are two types of basis set completeness: angular and radial completeness. 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}
F12 is good at doing angular basis set correction. 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}
However, radial correction are much harder to design and it is a real test for the present approach.
Instead of F12 methods, here we propose to follow a different philosophy and rely on the recently proposed short-range density-functional functional correction to reduce the basis set incompleteness error. \cite{GinPraFerAssSavTou-JCP-18} 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
incompleteness correction. \cite{GinPraFerAssSavTou-JCP-18}
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.
This choice is motivated by the much faster convergence of these methods with respect to the size of the basis set. \cite{FraMusLupTou-JCP-15} This choice is motivated by the much faster convergence of these methods with respect to the size of the basis set. \cite{FraMusLupTou-JCP-15}
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 systems which is a much tougher test for the reasons mentioned above.
The present method is illustrated on several molecules and singly- and doubly-excited states with diffuse basis sets.
%Contemporary quantum chemistry has developed in two directions --- wave function theory (WFT) \cite{Pop-RMP-99} and density-functional theory (DFT). \cite{Koh-RMP-99} %Contemporary quantum chemistry has developed in two directions --- wave function theory (WFT) \cite{Pop-RMP-99} and density-functional theory (DFT). \cite{Koh-RMP-99}
%Although both spring from the same Schr\"odinger equation, each of these philosophies has its own \textit{pros} and \textit{cons}. %Although both spring from the same Schr\"odinger equation, each of these philosophies has its own \textit{pros} and \textit{cons}.
@ -384,19 +384,19 @@ The FC density-based correction is used consistently with the FC approximation i
& -0.07 & -0.03 & -0.02 & -0.07 & -0.03 & -0.02
\\ \\
& $1\,^{1}A_{1} \ra 1\,^{1}E$ & Ryd. & 8.21 & -0.13 & -0.05 & -0.02 & $1\,^{1}A_{1} \ra 1\,^{1}E$ & Ryd. & 8.21 & -0.13 & -0.05 & -0.02
& 0.01 & 0.00 & -0.03 & 0.01 & 0.00 & 0.01
& -0.03 & -0.01 & 0.00 & -0.03 & -0.01 & 0.00
& -0.03 & 0.00 & -0.01 & -0.03 & 0.00 & 0.00
\\ \\
& $1\,^{1}A_{1} \ra 2\,^{1}A_{1}$ & Ryd. & 8.65 & 1.03 & 0.68 & 0.47 & $1\,^{1}A_{1} \ra 2\,^{1}A_{1}$ & Ryd. & 8.65 & 1.03 & 0.68 & 0.47
& 1.17 & 0.73 & 0.46 & 1.17 & 0.73 & 0.50
& 1.12 & 0.72 & 0.48 & 1.12 & 0.72 & 0.49
& 1.11 & 0.71 & 0.48 & 1.11 & 0.71 & 0.49
\\ \\
& $1\,^{1}A_{1} \ra 2\,^{1}A_{2}$ & Ryd. & 8.65 & 1.22 & 0.77 & 0.59 & $1\,^{1}A_{1} \ra 2\,^{1}A_{2}$ & Ryd. & 8.65 & 1.22 & 0.77 & 0.59
& 1.36 & 0.83 & 0.58 & 1.36 & 0.83 & 0.62
& 1.33 & 0.81 & 0.60 & 1.33 & 0.81 & 0.61
& 1.32 & 0.81 & 0.59 & 1.32 & 0.81 & 0.61
\\ \\
& $1\,^{1}A_{1} \ra 1\,^{3}A_{2}$ & Ryd. & 9.19 & -0.18 & -0.06 & -0.03 & $1\,^{1}A_{1} \ra 1\,^{3}A_{2}$ & Ryd. & 9.19 & -0.18 & -0.06 & -0.03
& -0.03 & 0.00 & -0.02 & -0.03 & 0.00 & -0.02