SI
This commit is contained in:
parent
08307452e1
commit
2e898d836c
5
Data/DNA_EA.dat
Normal file
5
Data/DNA_EA.dat
Normal file
@ -0,0 +1,5 @@
|
||||
A 73-24-5 1.572302 0.8099 0.4735 0.1725 -0.54
|
||||
C 71-30-7 1.400624 0.6054 0.2638 -0.0257 NA
|
||||
G 73-40-5 1.884993 1.114 0.7487 0.4149 NA
|
||||
T 65-71-4 1.194189 0.3805 0.0564 -0.2136 -0.29
|
||||
U 66-22-8 1.157819 0.3428 0.0124 -0.2832 -0.22
|
||||
20
Data/GW20_HF.dat
Normal file
20
Data/GW20_HF.dat
Normal file
@ -0,0 +1,20 @@
|
||||
He -24.875232 -24.969849 -24.975936 -24.977849
|
||||
Ne -22.642519 -23.004927 -23.101349 -23.137013
|
||||
H2 -16.108487 -16.170252 -16.175638 -16.176321
|
||||
Li2 -4.908093 -4.944398 -4.950660 -4.951012
|
||||
LiH -8.176505 -8.199614 -8.208752 -8.210946
|
||||
FH -17.113217 -17.503471 -17.629239 -17.685456
|
||||
Ar -16.001268 -16.058435 -16.078000 -16.080616
|
||||
H2O -13.418826 -13.726992 -13.826843 -13.877630
|
||||
LiF -12.637075 -12.892094 -12.935669 -12.952391
|
||||
HCl -12.829263 -12.936767 -12.969685 -12.975168
|
||||
BeO -10.482050 -10.508734 -10.535922 -10.562803
|
||||
CO -15.220671 -15.340566 -15.376164 -15.388477
|
||||
N2 -16.548629 -16.653792 -16.687542 -16.701370
|
||||
CH4 -14.784083 -14.838097 -14.842895 -14.843501
|
||||
BH3 -13.506828 -13.564544 -13.567553 -13.568001
|
||||
NH3 -11.404038 -11.599359 -11.659071 -11.689941
|
||||
BF -10.942821 -10.998420 -11.016733 -11.019900
|
||||
BN -11.419979 -11.510472 -11.534256 -11.542202
|
||||
SH2 -10.346702 -10.451184 -10.476043 -10.477999
|
||||
F2 -18.028684 -18.086849 -18.120602 -18.137192
|
||||
Binary file not shown.
Binary file not shown.
@ -1,7 +1,7 @@
|
||||
%% This BibTeX bibliography file was created using BibDesk.
|
||||
%% http://bibdesk.sourceforge.net/
|
||||
|
||||
%% Created for Pierre-Francois Loos at 2019-10-08 22:08:30 +0200
|
||||
%% Created for Pierre-Francois Loos at 2019-10-09 11:44:30 +0200
|
||||
|
||||
|
||||
%% Saved with string encoding Unicode (UTF-8)
|
||||
@ -44,9 +44,9 @@
|
||||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5090983}}
|
||||
|
||||
@article{Johnson_2018,
|
||||
Author = {C. M. Johnson and A. E. Doran and S. L. Ten-no, and S. Hirata},
|
||||
Author = {C. M. Johnson and A. E. Doran and S. L. Ten-no and S. Hirata},
|
||||
Date-Added = {2019-10-08 20:59:18 +0200},
|
||||
Date-Modified = {2019-10-08 21:00:15 +0200},
|
||||
Date-Modified = {2019-10-09 11:44:29 +0200},
|
||||
Doi = {10.1063/1.5054610},
|
||||
Journal = {J. Chem. Phys.},
|
||||
Pages = {174112},
|
||||
|
||||
@ -49,11 +49,11 @@
|
||||
\newcommand{\QP}{\textsc{quantum package}}
|
||||
|
||||
% methods
|
||||
\newcommand{\evGW}{evGW}
|
||||
\newcommand{\qsGW}{qsGW}
|
||||
\newcommand{\GOWO}{G$_0$W$_0$}
|
||||
\newcommand{\GW}{GW}
|
||||
\newcommand{\GnWn}[1]{G$_{#1}$W$_{#1}$}
|
||||
\newcommand{\evGW}{ev$GW$}
|
||||
\newcommand{\qsGW}{qs$GW$}
|
||||
\newcommand{\GOWO}{$G_0W_0$}
|
||||
\newcommand{\GW}{$GW$}
|
||||
\newcommand{\GnWn}[1]{$G_{#1}W_{#1}$}
|
||||
|
||||
% operators
|
||||
\newcommand{\hH}{\Hat{H}}
|
||||
@ -189,11 +189,11 @@ Here, we propose a density-based basis set correction based on short-range corre
|
||||
\section{Introduction}
|
||||
\label{sec:intro}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
The purpose of many-body perturbation theory (MBPT) is to solve the formidable many-body problem by adding the electron-electron Coulomb interaction perturbatively starting from an independent-particle model.
|
||||
In MBPT, the ``screening'' of the Coulomb interaction plays a central role, and is responsible for a rich variety of phenomena that would be otherwise absent (such as quasiparticle satellites and lifetimes).
|
||||
The purpose of many-body perturbation theory (MBPT) is to solve the formidable many-body problem by adding the electron-electron Coulomb interaction perturbatively starting from an independent-particle model. \cite{MarReiCep-BOOK-16}
|
||||
In MBPT, the \textit{screening} of the Coulomb interaction is a central quantity, and is responsible for a rich variety of phenomena that would be otherwise absent (such as quasiparticle satellites and lifetimes). \cite{Aryasetiawan_1998, Onida_2002, Reining_2017}
|
||||
|
||||
The so-called GW approximation is the workhorse of MBPT and has a long and successful history in the calculation of the electronic structure of solids \cite{Aryasetiawan_1998, Onida_2002, Reining_2017} and is getting increasingly popular in molecular systems \cite{Blase_2011, Faber_2011, Bruneval_2012, Bruneval_2013, Bruneval_2015, Bruneval_2016, Bruneval_2016a, Boulanger_2014, Blase_2016, Li_2017, Hung_2016, Hung_2017, vanSetten_2015, vanSetten_2018, Ou_2016, Ou_2018, Faber_2014} thanks to efficient implementation relying on local basis functions. \cite{Blase_2011, Blase_2018, Bruneval_2016, vanSetten_2013, Kaplan_2015, Kaplan_2016, Krause_2017, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b}
|
||||
The GW approximation stems from the acclaimed Hedin's equations \cite{Hedin_1965}
|
||||
The so-called $GW$ approximation is the workhorse of MBPT and has a long and successful history in the calculation of the electronic structure of solids \cite{Aryasetiawan_1998, Onida_2002, Reining_2017} and is getting increasingly popular in molecular systems \cite{Blase_2011, Faber_2011, Bruneval_2012, Bruneval_2013, Bruneval_2015, Bruneval_2016, Bruneval_2016a, Boulanger_2014, Blase_2016, Li_2017, Hung_2016, Hung_2017, vanSetten_2015, vanSetten_2018, Ou_2016, Ou_2018, Faber_2014} thanks to efficient implementation relying on local basis functions. \cite{Blase_2011, Blase_2018, Bruneval_2016, vanSetten_2013, Kaplan_2015, Kaplan_2016, Krause_2017, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b}
|
||||
The $GW$ approximation stems from the acclaimed Hedin's equations \cite{Hedin_1965}
|
||||
\begin{subequations}
|
||||
\begin{align}
|
||||
\label{eq:G}
|
||||
@ -217,30 +217,31 @@ The GW approximation stems from the acclaimed Hedin's equations \cite{Hedin_1965
|
||||
\end{subequations}
|
||||
which connects the Green's function $G$, its non-interacting version $G_0$, the irreducible vertex function $\Gamma$, the irreducible polarizability $P$, the dynamically-screened Coulomb interaction $W$
|
||||
and the self-energy $\Sigma$, where $v$ is the bare Coulomb interaction, $\delta(12)$ is Dirac's delta function \cite{NISTbook} and $(1)$ is a composite coordinate gathering spin, space and time variables $(\sigma_1,\br{1},t_1)$.
|
||||
Within the GW approximation, one bypasses the calculation of the vertex corrections by setting \cite{Aryasetiawan_1998, Onida_2002, Reining_2017, Blase_2018}
|
||||
Within the $GW$ approximation, one bypasses the calculation of the vertex corrections by setting
|
||||
\begin{equation}
|
||||
\label{eq:GW}
|
||||
\Gamma(123) = \delta(12) \delta(13).
|
||||
\Gamma(123) \stackrel{GW}{\approx} \delta(12) \delta(13).
|
||||
\end{equation}
|
||||
Depending on the degree of self-consistency one is willing to perform, there exists several types of GW calculations. \cite{Loos_2018}
|
||||
The simplest and most popular variant of GW is perturbative GW, or {\GOWO}, \cite{Hybertsen_1985a, Hybertsen_1986} which has been widely used in the literature to study solids, atoms and molecules. \cite{Bruneval_2012, Bruneval_2013, vanSetten_2015, vanSetten_2018}
|
||||
For finite systems such as atoms and molecules, partially or fully self-consistent GW methods have shown great promise. \cite{Ke_2011, Blase_2011, Faber_2011, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b, Koval_2014, Hung_2016, Blase_2018, Jacquemin_2017}
|
||||
Depending on the degree of self-consistency one is willing to perform, there exists several types of $GW$ calculations. \cite{Loos_2018}
|
||||
The simplest and most popular variant of $GW$ is perturbative $GW$, or {\GOWO}. \cite{Hybertsen_1985a, Hybertsen_1986}
|
||||
Although obviously starting-point dependent, it has been widely used in the literature to study solids, atoms and molecules. \cite{Bruneval_2012, Bruneval_2013, vanSetten_2015, vanSetten_2018}
|
||||
For finite systems such as atoms and molecules, partially or fully self-consistent $GW$ methods have shown great promise. \cite{Ke_2011, Blase_2011, Faber_2011, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b, Koval_2014, Hung_2016, Blase_2018, Jacquemin_2017}
|
||||
|
||||
Similarly to other electron correlation methods, MBPT methods suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set.
|
||||
Pioneered by Hyllerras \cite{Hyl-ZP-29} in the 1930's and popularized in the 1990's by Kutzelnigg and coworkers, \cite{NogKut-JCP-94,KutMor-ZPD-96,Kut-TCA-85,KutKlo-JCP-91} (and subsequently others \cite{KonBisVal-CR-12, HatKloKohTew-CR-12, TenNog-WIREs-12, GruHirOhnTen-JCP-17}) this can be tracked down to the lack of explicit electron-electron terms modeling the infamous electron-electron Kato cusp. \cite{Kat-CPAM-57}
|
||||
Pioneered by Hyllerras \cite{Hyl-ZP-29} in the 1930's and popularized in the 1990's by Kutzelnigg and coworkers \cite{NogKut-JCP-94,KutMor-ZPD-96,Kut-TCA-85,KutKlo-JCP-91} (and subsequently others \cite{KonBisVal-CR-12, HatKloKohTew-CR-12, TenNog-WIREs-12, GruHirOhnTen-JCP-17}), this can be tracked down to the lack of explicit electron-electron terms modeling the infamous electron-electron coalescence points also known as Kato cusp. \cite{Kat-CPAM-57}
|
||||
|
||||
The basis-set correction presented here follow a different avenue, and relies on the range-separated density-functional theory (RS-DFT) formalism to capture, thanks to a short-range correlation functional, the missing part of the short-range correlation effects. \cite{GinPraFerAssSavTou-JCP-18, LooPraSceTouGin-JPCL-19}
|
||||
As we shall illustrate later on in this manuscript, it significantly speeds up the convergence of energetics towards the complete basis set (CBS) limit.
|
||||
|
||||
Explicitly correlated F12 correction schemes have been derived for second-order Green's function methods (GF2) \cite{SzaboBook, Casida_1989, Casida_1991, Stefanucci_2013, Ortiz_2013, Phillips_2014, Phillips_2015, Rusakov_2014, Rusakov_2016, Hirata_2015, Hirata_2017, Loos_2018} by Ten-no and coworkers \cite{Ohnishi_2016, Johnson_2018} and Valeev and coworkers. \cite{Pavosevic_2017, Teke_2019}
|
||||
However, to the best of our knowledge, a F12-based correction for GW has not been designed yet.
|
||||
However, to the best of our knowledge, a F12-based correction for $GW$ has not been designed yet.
|
||||
|
||||
In the present manuscript, we illustrate the performance of the density-based basis set correction on ionization potentials (IPs) obtained within {\GOWO}.
|
||||
Note that the the present basis set correction can be straightforwardly applied to other properties (e.g., electron affinities and fundamental gap), as well as other flavours of GW or Green's function-based methods, such as GF2 (and its higher-order variants).
|
||||
Note that the the present basis set correction can be straightforwardly applied to other properties (e.g., electron affinities and fundamental gap), as well as other flavours of $GW$ or Green's function-based methods, such as GF2 (and its higher-order variants).
|
||||
Moreover, we are currently investigating the performances of the present approach for linear response theory, in order to speed up the convergence of excitation energies obtained within the random-phase approximation (RPA) \cite{Dreuw_2005} and Bethe-Salpeter equation (BSE) formalism. \cite{Strinati_1988, Leng_2016, Blase_2018}
|
||||
|
||||
The paper is organised as follows.
|
||||
In Sec.~\ref{sec:theory}, we provide details about the theory behind the present basis set correction and its adaptation to GW methods.
|
||||
In Sec.~\ref{sec:theory}, we provide details about the theory behind the present basis set correction and its adaptation to $GW$ methods.
|
||||
Results are reported and discussed in Sec.~\ref{sec:results}.
|
||||
Finally, we draw our conclusions in Sec.~\ref{sec:conclusion}.
|
||||
Unless otherwise stated, atomic units are used throughout.
|
||||
@ -323,7 +324,7 @@ with $\bar{v}^{\cal B}[n](\b{r}) = \delta \bar{E}^{\cal B}[n] / \delta n(\b{r})$
|
||||
%\end{split}
|
||||
%\end{equation}
|
||||
|
||||
\subsection{The GW Approximation}
|
||||
\subsection{The $GW$ Approximation}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
The Dyson equation can be written with an arbitrary reference
|
||||
@ -341,7 +342,7 @@ For a given (occupied or virtual) orbital $p$, the correlation part of the self-
|
||||
\label{eq:SigC}
|
||||
\SigC{p}(\omega) = \SigCp{p}(\omega) + \SigCh{p}(\omega),
|
||||
\end{equation}
|
||||
which, within the GW approximation, read
|
||||
which, within the $GW$ approximation, read
|
||||
\begin{subequations}
|
||||
\begin{align}
|
||||
\label{eq:SigCh}
|
||||
@ -388,7 +389,7 @@ with
|
||||
B_{ia,jb} & = 2 (ia|bj),
|
||||
\end{align}
|
||||
and $\delta_{pq}$ is the Kronecker delta. \cite{NISTbook}
|
||||
The one-electron energies $\epsilon_p$ in \eqref{eq:SigCh}, \eqref{eq:SigCp} and \eqref{eq:RPA} are either the HF or the GW quasiparticle energies.
|
||||
The one-electron energies $\epsilon_p$ in \eqref{eq:SigCh}, \eqref{eq:SigCp} and \eqref{eq:RPA} are either the HF or the $GW$ quasiparticle energies.
|
||||
Equation \eqref{eq:LR} also provides the neutral excitation energies $\Om{x}$.
|
||||
|
||||
In practice, there exist two ways of determining the {\GOWO} QP energies. \cite{Hybertsen_1985a, vanSetten_2013}
|
||||
@ -522,7 +523,7 @@ IPs (in eV) of the 20 smallest molecule of the GW100 set computed at the {\GOWO}
|
||||
\begin{tabular}{lccccccccccccc}
|
||||
& \mc{5}{c}{{\GOWO}@PBE0} & \mc{4}{c}{{\GOWO}@PBE0+srLDA} & \mc{4}{c}{{\GOWO}@PBE0+srPBE} \\
|
||||
\cline{2-6} \cline{7-10} \cline{11-14}
|
||||
Mol. & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & def2-TQZVP & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z \\
|
||||
Mol. & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & CBS & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z \\
|
||||
\hline
|
||||
\ce{He} & 23.99 & 23.98 & 24.03 & 24.04 & 24.06 & 24.26 & 24.09 & 24.09 & 24.07 & 24.29 & 24.10 & 24.08 & 24.07 \\
|
||||
\ce{Ne} & 20.35 & 20.88 & 21.05 & 21.05 & 21.12 & 20.86 & 21.16 & 21.22 & 21.16 & 21.05 & 21.22 & 21.23 & 21.15 \\
|
||||
@ -553,21 +554,31 @@ IPs (in eV) of the 20 smallest molecule of the GW100 set computed at the {\GOWO}
|
||||
\end{table*}
|
||||
\end{squeezetable}
|
||||
|
||||
|
||||
%%% FIG 1 %%%
|
||||
\begin{figure*}
|
||||
\includegraphics[width=0.49\linewidth]{IP_G0W0HF_H2O}
|
||||
\includegraphics[width=0.49\linewidth]{IP_G0W0PBE0_H2O}
|
||||
\caption{
|
||||
IPs (in eV) of the water molecule computed at the {\GOWO} (black circles), {\GOWO}+srLDA (red squares) and {\GOWO}+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) with two different starting points: HF (left) and PBE0 (right).
|
||||
The thick black line represents the CBS value obtained by extrapolation (see text for more details).
|
||||
\label{fig:IP_G0W0_H2O}
|
||||
}
|
||||
\end{figure*}
|
||||
|
||||
%%% TABLE III %%%
|
||||
\begin{table*}
|
||||
\caption{
|
||||
IPs (in eV) of the five canonical nucleobases computed at the {\GOWO}@PBE level of theory for various basis sets.
|
||||
The deviation with respect to the {\GOWO}@PBE/def2-TQZVP extrapolated values are reported in square brackets.
|
||||
The extrapolation error is reported in parenthesis.
|
||||
The CCSD(T)/def2-TZVPP and experimental results are reported for comparison purposes.
|
||||
\label{tab:DNA}
|
||||
\label{tab:DNA_IP}
|
||||
}
|
||||
\begin{ruledtabular}
|
||||
\begin{tabular}{llccccc}
|
||||
& & \mc{5}{c}{IPs of nucleobases (eV)} \\
|
||||
\cline{3-7}
|
||||
Method & Basis & \tabc{Adenine} & \tabc{Cytosine} & \tabc{Thymine} & \tabc{Guanine} & \tabc{Uracil} \\
|
||||
Method & Basis & \tabc{Adenine} & \tabc{Cytosine} & \tabc{Guanine} & \tabc{Thymine} & \tabc{Uracil} \\
|
||||
\hline
|
||||
{\GOWO}@PBE\fnm[1] & def2-SVP & 7.27[-0.88] & 7.53[-0.92] & 6.95[-0.92] & 8.02[-0.85] & 8.38[-1.00] \\
|
||||
{\GOWO}@PBE+srLDA\fnm[1] & def2-SVP & 7.60[-0.55] & 7.95[-0.50] & 7.29[-0.59] & 8.36[-0.51] & 8.80[-0.58] \\
|
||||
@ -576,37 +587,54 @@ The CCSD(T)/def2-TZVPP and experimental results are reported for comparison purp
|
||||
{\GOWO}@PBE+srLDA\fnm[1] & def2-TZVP & 7.92[-0.23] & 8.26[-0.19] & 7.64[-0.23] & 8.67[-0.20] & 9.25[-0.13] \\
|
||||
{\GOWO}@PBE+srPBE\fnm[1] & def2-TZVP & 7.92[-0.23] & 8.27[-0.18] & 7.64[-0.23] & 8.68[-0.19] & 9.27[-0.11] \\
|
||||
{\GOWO}@PBE\fnm[2] & def2-QZVP & 7.98[-0.18] & 8.29[-0.16] & 7.69[-0.18] & 8.71[-0.16] & 9.22[-0.16] \\
|
||||
{\GOWO}@PBE\fnm[3] & def2-TQZVP & 8.15 & 8.45 & 7.87 & 8.87 & 9.38 \\
|
||||
{\GOWO}@PBE\fnm[3] & def2-TQZVP & 8.16(1) & 8.44(1) & 7.87(1) & 8.87(1) & 9.38(1) \\
|
||||
\hline
|
||||
CCSD(T)\fnm[4] & def2-TZVPP & 8.33 & 9.51 & 8.03 & 9.08 & 10.13 \\
|
||||
Experiment\fnm[5] & & 8.48 & 8.94 & 8.24 & 9.2 & 9.68 \\
|
||||
Experiment\fnm[5] & & 8.48 & 8.94 & 8.24 & 9.20 & 9.68 \\
|
||||
\end{tabular}
|
||||
\end{ruledtabular}
|
||||
\fnt[1]{This work.}
|
||||
\fnt[2]{Unpublished data taken from \url{https://gw100.wordpress.com}.}
|
||||
\fnt[2]{Unpublished data taken from \url{https://gw100.wordpress.com} obtained with Turbomole v7.0.}
|
||||
\fnt[3]{Extrapolated values obtained from the def2-TZVP and def2-QZVP values.}
|
||||
\fnt[4]{Reference \onlinecite{Krause_2015}.}
|
||||
\fnt[5]{Experimental values taken from Ref.~\onlinecite{Maggio_2017}.}
|
||||
\fnt[5]{Experimental values are taken from Ref.~\onlinecite{vanSetten_2015} and correspond to vertical ionization energies.}
|
||||
\end{table*}
|
||||
|
||||
\begin{figure*}
|
||||
\includegraphics[width=\linewidth]{IP_G0W0HF}
|
||||
\caption{
|
||||
IPs (in eV) computed at the {\GOWO}@HF (black circles), {\GOWO}@HF+srLDA (red squares) and {\GOWO}@HF+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) for the 20 smallest molecules of the GW100 set.
|
||||
The thick black line represents the CBS value obtained by extrapolation with the three largest basis sets.
|
||||
\label{fig:IP_G0W0HF}
|
||||
}
|
||||
\end{figure*}
|
||||
|
||||
\begin{figure*}
|
||||
\includegraphics[width=\linewidth]{IP_G0W0PBE0}
|
||||
\caption{
|
||||
IPs (in eV) computed at the {\GOWO}@PBE0 (black circles), {\GOWO}@PBE0+srLDA (red squares) and {\GOWO}@PBE0+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) for the 20 smallest molecules of the GW100 set.
|
||||
The thick black line represents the CBS value obtained by extrapolation with the three largest basis sets.
|
||||
\label{fig:IP_G0W0HF}
|
||||
}
|
||||
\end{figure*}
|
||||
%%% TABLE IV %%%
|
||||
%\begin{table*}
|
||||
%\caption{
|
||||
%EAs (in eV) of the five canonical nucleobases computed at the {\GOWO}@PBE level of theory for various basis sets.
|
||||
%The deviation with respect to the {\GOWO}@PBE/def2-TQZVP extrapolated values are reported in square brackets.
|
||||
%The extrapolation error is reported in parenthesis.
|
||||
%The experimental results are reported for comparison purposes.
|
||||
%\label{tab:DNA_EA}
|
||||
%}
|
||||
% \begin{ruledtabular}
|
||||
% \begin{tabular}{llccccc}
|
||||
% & & \mc{5}{c}{EAs of nucleobases (eV)} \\
|
||||
% \cline{3-7}
|
||||
% Method & Basis & \tabc{Adenine} & \tabc{Cytosine} & \tabc{Guanine} & \tabc{Thymine} & \tabc{Uracil} \\
|
||||
% \hline
|
||||
% {\GOWO}@PBE\fnm[1] & def2-SVP & -1.57[-] & -1.40[-] & -1.88[-] & -1.19[-] & -1.16[-] \\
|
||||
% {\GOWO}@PBE+srLDA\fnm[1] & def2-SVP & [-] & [-] & [-] & [-] & [-] \\
|
||||
% {\GOWO}@PBE+srPBE\fnm[1] & def2-SVP & [-] & [-] & [-] & [-] & [-] \\
|
||||
% {\GOWO}@PBE\fnm[2] & def2-TZVP & -0.81[-] & -0.61[-] & -1.11[-] & -0.38[-] & -0.34[-] \\
|
||||
% {\GOWO}@PBE+srLDA\fnm[1] & def2-TZVP & [-] & [-] & [-] & [-] & [-] \\
|
||||
% {\GOWO}@PBE+srPBE\fnm[1] & def2-TZVP & [-] & [-] & [-] & [-] & [-] \\
|
||||
% {\GOWO}@PBE\fnm[2] & def2-QZVP & -0.47[-] & -0.26[-] & -0.75[-] & -0.06[-] & -0.01[-] \\
|
||||
% {\GOWO}@PBE\fnm[3] & def2-TQZVP & -0.21(1) & -0.01(1) & -0.46(2) & +0.18(1) & +0.25(1) \\
|
||||
% \hline
|
||||
% Experiment\fnm[5] & & 0.54 & & & 0.29 & 0.22 \\
|
||||
% \end{tabular}
|
||||
% \end{ruledtabular}
|
||||
% \fnt[1]{This work.}
|
||||
% \fnt[2]{Unpublished data taken from \url{https://gw100.wordpress.com} obtained with MolGW 2.B.}
|
||||
% \fnt[3]{Extrapolated values obtained from the def2-TZVP and def2-QZVP values.}
|
||||
% \fnt[4]{Reference \onlinecite{Krause_2015}.}
|
||||
% \fnt[5]{Experimental values are taken from Ref.~\onlinecite{vanSetten_2015} and correspond to laser photoelectron spectroscopy values.}
|
||||
%\end{table*}
|
||||
|
||||
%%% FIG 2 %%%
|
||||
\begin{figure*}
|
||||
\includegraphics[width=\linewidth]{DNA}
|
||||
\caption{
|
||||
@ -623,7 +651,7 @@ The CCSD(T)/def2-TZVPP and experimental results are reported for comparison purp
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section*{Supporting Information Available}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
Additional graphs reporting the convergence of the ionization potentials of the 20 smallest molecules of the GW100 set.
|
||||
Additional graphs reporting the convergence of the ionization potentials of the GW20 set with respect to the size of the basis set.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\begin{acknowledgements}
|
||||
|
||||
Binary file not shown.
Binary file not shown.
203
Manuscript/SI/GW-srDFT-SI.tex
Normal file
203
Manuscript/SI/GW-srDFT-SI.tex
Normal file
@ -0,0 +1,203 @@
|
||||
\documentclass[aip,jcp,reprint,noshowkeys]{revtex4-1}
|
||||
\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable,wrapfig}
|
||||
|
||||
\usepackage{natbib}
|
||||
\usepackage[extra]{tipa}
|
||||
\bibliographystyle{achemso}
|
||||
\AtBeginDocument{\nocite{achemso-control}}
|
||||
\usepackage{mathpazo,libertine}
|
||||
|
||||
\usepackage{hyperref}
|
||||
\hypersetup{
|
||||
colorlinks=true,
|
||||
linkcolor=blue,
|
||||
filecolor=blue,
|
||||
urlcolor=blue,
|
||||
citecolor=blue
|
||||
}
|
||||
\urlstyle{same}
|
||||
|
||||
\newcommand{\alert}[1]{\textcolor{red}{#1}}
|
||||
\definecolor{darkgreen}{HTML}{009900}
|
||||
\usepackage[normalem]{ulem}
|
||||
\newcommand{\titou}[1]{\textcolor{red}{#1}}
|
||||
\newcommand{\jt}[1]{\textcolor{purple}{#1}}
|
||||
\newcommand{\manu}[1]{\textcolor{darkgreen}{#1}}
|
||||
\newcommand{\toto}[1]{\textcolor{brown}{#1}}
|
||||
\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}}
|
||||
\newcommand{\trashJT}[1]{\textcolor{purple}{\sout{#1}}}
|
||||
\newcommand{\trashMG}[1]{\textcolor{darkgreen}{\sout{#1}}}
|
||||
\newcommand{\trashAS}[1]{\textcolor{brown}{\sout{#1}}}
|
||||
\newcommand{\MG}[1]{\manu{(\underline{\bf MG}: #1)}}
|
||||
\newcommand{\JT}[1]{\juju{(\underline{\bf JT}: #1)}}
|
||||
\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}}
|
||||
\newcommand{\AS}[1]{\toto{(\underline{\bf TOTO}: #1)}}
|
||||
|
||||
\usepackage{hyperref}
|
||||
\hypersetup{
|
||||
colorlinks=true,
|
||||
linkcolor=blue,
|
||||
filecolor=blue,
|
||||
urlcolor=blue,
|
||||
citecolor=blue
|
||||
}
|
||||
\newcommand{\mc}{\multicolumn}
|
||||
\newcommand{\fnm}{\footnotemark}
|
||||
\newcommand{\fnt}{\footnotetext}
|
||||
\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
|
||||
\newcommand{\SI}{\textcolor{blue}{supporting information}}
|
||||
\newcommand{\QP}{\textsc{quantum package}}
|
||||
|
||||
% methods
|
||||
\newcommand{\evGW}{ev$GW$}
|
||||
\newcommand{\qsGW}{qs$GW$}
|
||||
\newcommand{\GOWO}{$G_0W_0$}
|
||||
\newcommand{\GW}{$GW$}
|
||||
\newcommand{\GnWn}[1]{$G_{#1}W_{#1}$}
|
||||
|
||||
% operators
|
||||
\newcommand{\hH}{\Hat{H}}
|
||||
|
||||
% energies
|
||||
\newcommand{\Ec}{E_\text{c}}
|
||||
\newcommand{\EHF}{E_\text{HF}}
|
||||
\newcommand{\EKS}{E_\text{KS}}
|
||||
\newcommand{\EcK}{E_\text{c}^\text{Klein}}
|
||||
\newcommand{\EcRPA}{E_\text{c}^\text{RPA}}
|
||||
\newcommand{\EcGM}{E_\text{c}^\text{GM}}
|
||||
\newcommand{\EcMP}{E_c^\text{MP2}}
|
||||
\newcommand{\Egap}{E_\text{gap}}
|
||||
\newcommand{\IP}{\text{IP}}
|
||||
\newcommand{\EA}{\text{EA}}
|
||||
\newcommand{\RH}{R_{\ce{H2}}}
|
||||
\newcommand{\RF}{R_{\ce{F2}}}
|
||||
\newcommand{\RBeO}{R_{\ce{BeO}}}
|
||||
|
||||
% orbital energies
|
||||
\newcommand{\nDIIS}{N^\text{DIIS}}
|
||||
\newcommand{\maxDIIS}{N_\text{max}^\text{DIIS}}
|
||||
\newcommand{\nSat}[1]{N_{#1}^\text{sat}}
|
||||
\newcommand{\eSat}[2]{\epsilon_{#1,#2}}
|
||||
\newcommand{\e}[1]{\epsilon_{#1}}
|
||||
\newcommand{\eHF}[1]{\epsilon^\text{HF}_{#1}}
|
||||
\newcommand{\teHF}[1]{\Tilde{\epsilon}^\text{HF}_{#1}}
|
||||
\newcommand{\eKS}[1]{\epsilon^\text{KS}_{#1}}
|
||||
\newcommand{\eQP}[1]{\epsilon^\text{QP}_{#1}}
|
||||
\newcommand{\eGOWO}[1]{\epsilon^\text{\GOWO}_{#1}}
|
||||
\newcommand{\eGW}[1]{\epsilon^\text{\GW}_{#1}}
|
||||
\newcommand{\eGnWn}[2]{\epsilon^\text{\GnWn{#2}}_{#1}}
|
||||
\newcommand{\de}[1]{\Delta\epsilon_{#1}}
|
||||
\newcommand{\deHF}[1]{\Delta\epsilon^\text{HF}_{#1}}
|
||||
\newcommand{\Om}[1]{\Omega_{#1}}
|
||||
\newcommand{\eHOMO}{\epsilon_\text{HOMO}}
|
||||
\newcommand{\eLUMO}{\epsilon_\text{LUMO}}
|
||||
\newcommand{\HOMO}{\text{HOMO}}
|
||||
\newcommand{\LUMO}{\text{LUMO}}
|
||||
|
||||
% Matrix elements
|
||||
\newcommand{\A}[1]{A_{#1}}
|
||||
\newcommand{\B}[1]{B_{#1}}
|
||||
\newcommand{\tA}{\Tilde{A}}
|
||||
\newcommand{\tB}{\Tilde{B}}
|
||||
\renewcommand{\S}[1]{S_{#1}}
|
||||
\newcommand{\G}[1]{G_{#1}}
|
||||
\newcommand{\Po}[1]{P_{#1}}
|
||||
\newcommand{\W}[1]{W_{#1}}
|
||||
\newcommand{\Wc}[1]{W^\text{c}_{#1}}
|
||||
\newcommand{\vc}[1]{v_{#1}}
|
||||
\newcommand{\SigX}[1]{\Sigma^\text{x}_{#1}}
|
||||
\newcommand{\SigC}[1]{\Sigma^\text{c}_{#1}}
|
||||
\newcommand{\tSigC}[1]{\Tilde{\Sigma}^\text{c}_{#1}}
|
||||
\newcommand{\SigCp}[1]{\Sigma^\text{p}_{#1}}
|
||||
\newcommand{\SigCh}[1]{\Sigma^\text{h}_{#1}}
|
||||
\newcommand{\SigGW}[1]{\Sigma^\text{\GW}_{#1}}
|
||||
\newcommand{\Z}[1]{Z_{#1}}
|
||||
|
||||
% Matrices
|
||||
\newcommand{\bG}{\boldsymbol{G}}
|
||||
\newcommand{\bW}{\boldsymbol{W}}
|
||||
\newcommand{\bvc}{\boldsymbol{v}}
|
||||
\newcommand{\bSig}{\boldsymbol{\Sigma}}
|
||||
\newcommand{\bSigX}{\boldsymbol{\Sigma}^\text{x}}
|
||||
\newcommand{\bSigC}{\boldsymbol{\Sigma}^\text{c}}
|
||||
\newcommand{\bSigGW}{\boldsymbol{\Sigma}^\text{\GW}}
|
||||
\newcommand{\be}{\boldsymbol{\epsilon}}
|
||||
\newcommand{\bDelta}{\boldsymbol{\Delta}}
|
||||
\newcommand{\beHF}{\boldsymbol{\epsilon}^\text{HF}}
|
||||
\newcommand{\beGW}{\boldsymbol{\epsilon}^\text{\GW}}
|
||||
\newcommand{\beGnWn}[1]{\boldsymbol{\epsilon}^\text{\GnWn{#1}}}
|
||||
\newcommand{\bdeGnWn}[1]{\Delta\boldsymbol{\epsilon}^\text{\GnWn{#1}}}
|
||||
\newcommand{\bde}{\boldsymbol{\Delta\epsilon}}
|
||||
\newcommand{\bdeHF}{\boldsymbol{\Delta\epsilon}^\text{HF}}
|
||||
\newcommand{\bdeGW}{\boldsymbol{\Delta\epsilon}^\text{GW}}
|
||||
\newcommand{\bOm}{\boldsymbol{\Omega}}
|
||||
\newcommand{\bA}{\boldsymbol{A}}
|
||||
\newcommand{\bB}{\boldsymbol{B}}
|
||||
\newcommand{\bX}{\boldsymbol{X}}
|
||||
\newcommand{\bY}{\boldsymbol{Y}}
|
||||
\newcommand{\bZ}{\boldsymbol{Z}}
|
||||
|
||||
\newcommand{\fc}{f_\text{c}}
|
||||
\newcommand{\Vc}{V_\text{c}}
|
||||
|
||||
\newcommand{\MO}[1]{\phi_{#1}}
|
||||
|
||||
% coordinates
|
||||
\newcommand{\br}[1]{\mathbf{r}_{#1}}
|
||||
\renewcommand{\b}[1]{\mathbf{#1}}
|
||||
\renewcommand{\d}{\text{d}}
|
||||
\newcommand{\dbr}[1]{d\br{#1}}
|
||||
\renewcommand{\bra}[1]{\ensuremath{\langle #1 \vert}}
|
||||
\renewcommand{\ket}[1]{\ensuremath{\vert #1 \rangle}}
|
||||
\renewcommand{\braket}[2]{\ensuremath{\langle #1 \vert #2 \rangle}}
|
||||
|
||||
|
||||
\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France}
|
||||
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
|
||||
\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\title{Supplementary Materials for ``A Density-Based Basis Set Correction for GW Methods''}
|
||||
|
||||
\author{Pierre-Fran\c{c}ois Loos}
|
||||
\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
|
||||
\affiliation{\LCPQ}
|
||||
\author{Bath\'elemy Pradines}
|
||||
\affiliation{\LCT}
|
||||
\affiliation{\ISCD}
|
||||
\author{Anthony Scemama}
|
||||
\affiliation{\LCPQ}
|
||||
\author{Emmanuel Giner}
|
||||
\affiliation{\LCT}
|
||||
\author{Julien Toulouse}
|
||||
\email[Corresponding author: ]{toulouse@lct.jussieu.fr}
|
||||
\affiliation{\LCT}
|
||||
|
||||
\begin{abstract}
|
||||
\end{abstract}
|
||||
|
||||
\maketitle
|
||||
|
||||
\begin{figure*}
|
||||
\includegraphics[width=\linewidth]{IP_G0W0HF}
|
||||
\caption{
|
||||
IPs (in eV) computed at the {\GOWO}@HF (black circles), {\GOWO}@HF+srLDA (red squares) and {\GOWO}@HF+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) for the 20 smallest molecules of the GW100 set.
|
||||
The thick black line represents the CBS value obtained by extrapolation with the three largest basis sets.
|
||||
\label{fig:IP_G0W0HF}
|
||||
}
|
||||
\end{figure*}
|
||||
|
||||
\begin{figure*}
|
||||
\includegraphics[width=\linewidth]{IP_G0W0PBE0}
|
||||
\caption{
|
||||
IPs (in eV) computed at the {\GOWO}@PBE0 (black circles), {\GOWO}@PBE0+srLDA (red squares) and {\GOWO}@PBE0+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) for the 20 smallest molecules of the GW100 set.
|
||||
The thick black line represents the CBS value obtained by extrapolation with the three largest basis sets.
|
||||
\label{fig:IP_G0W0HF}
|
||||
}
|
||||
\end{figure*}
|
||||
|
||||
|
||||
\bibliography{../GW-srDFT,../GW-srDFT-control,../biblio}
|
||||
|
||||
\end{document}
|
||||
BIN
Manuscript/SI/IP_G0W0HF.pdf
Normal file
BIN
Manuscript/SI/IP_G0W0HF.pdf
Normal file
Binary file not shown.
BIN
Manuscript/SI/IP_G0W0PBE0.pdf
Normal file
BIN
Manuscript/SI/IP_G0W0PBE0.pdf
Normal file
Binary file not shown.
@ -1,7 +1,7 @@
|
||||
%% This BibTeX bibliography file was created using BibDesk.
|
||||
%% http://bibdesk.sourceforge.net/
|
||||
|
||||
%% Created for Pierre-Francois Loos at 2019-10-08 22:10:37 +0200
|
||||
%% Created for Pierre-Francois Loos at 2019-10-09 11:44:04 +0200
|
||||
|
||||
|
||||
%% Saved with string encoding Unicode (UTF-8)
|
||||
@ -2934,8 +2934,8 @@
|
||||
Year = {1991}}
|
||||
|
||||
@article{DahLeeBar-IJQC-05,
|
||||
Author = {N. E. Dahlen, R. {van Leeuwen}, and U. {von Barth}},
|
||||
Date-Modified = {2019-10-04 21:21:06 +0200},
|
||||
Author = {N. E. Dahlen and R. {van Leeuwen} and U. {von Barth}},
|
||||
Date-Modified = {2019-10-09 11:43:57 +0200},
|
||||
Journal = {Int. J. Quantum Chem.},
|
||||
Pages = {512-519},
|
||||
Title = {Variational energy functionals of the Green function tested on molecules},
|
||||
@ -2943,8 +2943,8 @@
|
||||
Year = {2005}}
|
||||
|
||||
@article{DahLeeBar-PRA-06,
|
||||
Author = {N. E. Dahlen, R. {van Leeuwen}, and U. {von Barth}},
|
||||
Date-Modified = {2019-10-04 21:20:31 +0200},
|
||||
Author = {N. E. Dahlen and R. {van Leeuwen} and U. {von Barth}},
|
||||
Date-Modified = {2019-10-09 11:43:43 +0200},
|
||||
Journal = {Phys. Rev. A},
|
||||
Pages = {012511},
|
||||
Volume = {73},
|
||||
|
||||
160033
Notebooks/GW100.nb
160033
Notebooks/GW100.nb
File diff suppressed because it is too large
Load Diff
BIN
References/Yang_2013_SI.pdf
Normal file
BIN
References/Yang_2013_SI.pdf
Normal file
Binary file not shown.
File diff suppressed because it is too large
Load Diff
Loading…
Reference in New Issue
Block a user