start clean up results
This commit is contained in:
parent
ffdd3d89b9
commit
7b0b1b150e
Binary file not shown.
Binary file not shown.
@ -1,13 +1,76 @@
|
|||||||
%% This BibTeX bibliography file was created using BibDesk.
|
%% This BibTeX bibliography file was created using BibDesk.
|
||||||
%% http://bibdesk.sourceforge.net/
|
%% http://bibdesk.sourceforge.net/
|
||||||
|
|
||||||
%% Created for Pierre-Francois Loos at 2020-04-08 14:13:22 +0200
|
%% Created for Pierre-Francois Loos at 2020-04-09 10:05:15 +0200
|
||||||
|
|
||||||
|
|
||||||
%% Saved with string encoding Unicode (UTF-8)
|
%% Saved with string encoding Unicode (UTF-8)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
@article{Woon_1994,
|
||||||
|
Author = {Woon, D. and Dunning, T. H.},
|
||||||
|
Date-Added = {2020-04-09 09:59:19 +0200},
|
||||||
|
Date-Modified = {2020-04-09 10:00:56 +0200},
|
||||||
|
Doi = {10.1063/1.466439},
|
||||||
|
Journal = {J. Chem. Phys.},
|
||||||
|
Pages = {2975--2988},
|
||||||
|
Title = {Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties},
|
||||||
|
Volume = {100},
|
||||||
|
Year = {1994},
|
||||||
|
Bdsk-Url-1 = {https://doi.org/10.1063/1.466439}}
|
||||||
|
|
||||||
|
@article{Kendall_1992,
|
||||||
|
Author = {Kendall, R. A. and Dunning, T. H. and Harisson, R. J.},
|
||||||
|
Date-Added = {2020-04-09 09:58:17 +0200},
|
||||||
|
Date-Modified = {2020-04-09 10:01:10 +0200},
|
||||||
|
Doi = {10.1063/1.462569},
|
||||||
|
Journal = {J. Chem. Phys.},
|
||||||
|
Pages = {6796--6806},
|
||||||
|
Title = {Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions},
|
||||||
|
Volume = {96},
|
||||||
|
Year = {1992},
|
||||||
|
Bdsk-Url-1 = {https://doi.org/10.1063/1.462569}}
|
||||||
|
|
||||||
|
@article{Dunning_1989,
|
||||||
|
Author = {T. H. {Dunning, Jr.}},
|
||||||
|
Date-Added = {2020-04-09 09:55:22 +0200},
|
||||||
|
Date-Modified = {2020-04-09 09:55:22 +0200},
|
||||||
|
Doi = {10.1063/1.456153},
|
||||||
|
Journal = {J. Chem. Phys.},
|
||||||
|
Pages = {1007},
|
||||||
|
Title = {Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen},
|
||||||
|
Volume = {90},
|
||||||
|
Year = {1989},
|
||||||
|
Bdsk-Url-1 = {https://doi.org/10.1063/1.456153}}
|
||||||
|
|
||||||
|
@misc{numgrid,
|
||||||
|
Author = {R. Bast},
|
||||||
|
Date-Added = {2020-04-09 09:23:10 +0200},
|
||||||
|
Date-Modified = {2020-04-09 09:23:10 +0200},
|
||||||
|
Doi = {10.5281/zenodo.2659208},
|
||||||
|
Month = {May},
|
||||||
|
Note = {\url{https://github.com/dftlibs/numgrid}},
|
||||||
|
Publisher = {Zenodo},
|
||||||
|
Title = {numgrid: numerical integration grid for molecules},
|
||||||
|
Url = {https://github.com/dftlibs/numgrid},
|
||||||
|
Year = {2019},
|
||||||
|
Bdsk-Url-1 = {https://github.com/LCPQ/quantum_package},
|
||||||
|
Bdsk-Url-2 = {http://dx.doi.org/10.5281/zenodo.200970}}
|
||||||
|
|
||||||
|
@misc{QuAcK,
|
||||||
|
Author = {P. F. Loos},
|
||||||
|
Date-Added = {2020-04-09 09:19:41 +0200},
|
||||||
|
Date-Modified = {2020-04-09 09:33:32 +0200},
|
||||||
|
Doi = {10.5281/zenodo.3745928},
|
||||||
|
Note = {\url{https://github.com/pfloos/QuAcK}},
|
||||||
|
Publisher = {Zenodo},
|
||||||
|
Title = {{{QuAcK: a software for emerging quantum electronic structure methods}}},
|
||||||
|
Url = {https://github.com/pfloos/QuAcK},
|
||||||
|
Year = {2019},
|
||||||
|
Bdsk-Url-1 = {https://github.com/LCPQ/quantum_package},
|
||||||
|
Bdsk-Url-2 = {http://dx.doi.org/10.5281/zenodo.200970}}
|
||||||
|
|
||||||
@article{Fromager_2020,
|
@article{Fromager_2020,
|
||||||
Archiveprefix = {arXiv},
|
Archiveprefix = {arXiv},
|
||||||
Author = {Emmanuel Fromager},
|
Author = {Emmanuel Fromager},
|
||||||
@ -27,7 +90,8 @@
|
|||||||
Pages = {L5},
|
Pages = {L5},
|
||||||
Title = {Autoionizing States of the Hydrogen Molecule.},
|
Title = {Autoionizing States of the Hydrogen Molecule.},
|
||||||
Volume = {7},
|
Volume = {7},
|
||||||
Year = {1974}}
|
Year = {1974},
|
||||||
|
Bdsk-Url-1 = {https://doi.org/10.1088/0022-3700/7/1/002}}
|
||||||
|
|
||||||
@article{Mielke_2005,
|
@article{Mielke_2005,
|
||||||
Author = {S. L. Mielke and D. W. Schwenke and K. A. Peterson},
|
Author = {S. L. Mielke and D. W. Schwenke and K. A. Peterson},
|
||||||
@ -92,13 +156,6 @@
|
|||||||
Title = {A weight-dependent local correlation density-functional approximation for ensembles},
|
Title = {A weight-dependent local correlation density-functional approximation for ensembles},
|
||||||
Year = {submitted}}
|
Year = {submitted}}
|
||||||
|
|
||||||
@article{Fromager_2020,
|
|
||||||
title={Individual correlations in ensemble density-functional theory: State-driven/density-driven decomposition without additional Kohn-Sham systems},
|
|
||||||
author={Fromager, Emmanuel},
|
|
||||||
journal={arXiv:2001.08605},
|
|
||||||
year={submitted},
|
|
||||||
url={https://arxiv.org/abs/2001.08605}}
|
|
||||||
|
|
||||||
@article{Lindh_2001,
|
@article{Lindh_2001,
|
||||||
Author = {R. Lindh and P.-A. Malmqvist and L. Gagliardi},
|
Author = {R. Lindh and P.-A. Malmqvist and L. Gagliardi},
|
||||||
Date-Added = {2020-03-30 09:59:22 +0200},
|
Date-Added = {2020-03-30 09:59:22 +0200},
|
||||||
@ -376,7 +433,8 @@
|
|||||||
@article{Perdew_1983,
|
@article{Perdew_1983,
|
||||||
Author = {J. P. Perdew and M. Levy},
|
Author = {J. P. Perdew and M. Levy},
|
||||||
Date-Added = {2019-09-05 12:04:19 +0200},
|
Date-Added = {2019-09-05 12:04:19 +0200},
|
||||||
Date-Modified = {2019-09-05 12:13:34 +0200},
|
Date-Modified = {2020-04-09 10:05:15 +0200},
|
||||||
|
Doi = {10.1103/PhysRevLett.51.1884},
|
||||||
Journal = {Phys. Rev. Lett.},
|
Journal = {Phys. Rev. Lett.},
|
||||||
Pages = {1884},
|
Pages = {1884},
|
||||||
Title = {Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities},
|
Title = {Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities},
|
||||||
|
@ -183,12 +183,12 @@ However, Loos and Gill have recently shown that there exists other UEGs which co
|
|||||||
Electrons restricted to remain on the surface of a $\cD$-sphere (where $\cD$ is the dimensionality of the surface of the sphere) are an example of finite UEGs (FUEGs). \cite{Loos_2011b}
|
Electrons restricted to remain on the surface of a $\cD$-sphere (where $\cD$ is the dimensionality of the surface of the sphere) are an example of finite UEGs (FUEGs). \cite{Loos_2011b}
|
||||||
In particular, we combine these FUEGs with the usual infinite UEG (IUEG) to construct a weigh-dependent LDA correlation functional for ensembles, which is specifically designed to compute double excitations within GOK-DFT, and automatically incorporates the infamous derivative discontinuity contribution to the excitation energies through its explicit ensemble weight dependence. \cite{Levy_1995, Perdew_1983}
|
In particular, we combine these FUEGs with the usual infinite UEG (IUEG) to construct a weigh-dependent LDA correlation functional for ensembles, which is specifically designed to compute double excitations within GOK-DFT, and automatically incorporates the infamous derivative discontinuity contribution to the excitation energies through its explicit ensemble weight dependence. \cite{Levy_1995, Perdew_1983}
|
||||||
|
|
||||||
%The paper is organised as follows.
|
The paper is organised as follows.
|
||||||
%In Sec.~\ref{sec:theo}, the theory behind GOK-DFT is presented.
|
In Sec.~\ref{sec:theo}, the theory behind GOK-DFT is presented.
|
||||||
%Section \ref{sec:func} provides details about the construction of the weight-dependent xc LDA functional.
|
Section \ref{sec:compdet} provides the computational details.
|
||||||
%The results of our calculations for the prototypical \ce{H2} molecule are reported and discussed in Sec.~\ref{sec:resdis}.
|
The results of our calculations for two-electron systems are reported and discussed in Secs.~\ref{sec:res_H2} and \ref{sec:res_He}.
|
||||||
%Finally, we draw our conclusions in Sec.~\ref{sec:ccl}.
|
Finally, we draw our conclusions in Sec.~\ref{sec:ccl}.
|
||||||
%Unless otherwise stated, atomic units are used throughout.
|
Unless otherwise stated, atomic units are used throughout.
|
||||||
|
|
||||||
%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%
|
||||||
%%% THEORY %%%
|
%%% THEORY %%%
|
||||||
@ -248,7 +248,7 @@ is the density matrix operator, $\lbrace \Det{I}{\bw} \rbrace_{0 \le I \le \nEns
|
|||||||
\end{split}
|
\end{split}
|
||||||
\end{equation}
|
\end{equation}
|
||||||
is the ensemble Hartree-exchange-correlation (Hxc) functional.
|
is the ensemble Hartree-exchange-correlation (Hxc) functional.
|
||||||
Note that the weight-independent Hartree functional $\E{\Ha}{}[\n{}{}]$ causes the infamous ghost-interaction error (GIE) \cite{Gidopoulos_2002, Pastorczak_2014, Alam_2016, Alam_2017, Gould_2017} in eDFT, which is supposed to be cancelled by the weight-dependent xc functional $\E{\xc}{\bw}[\n{}{}]$.
|
Note that the weight-independent Hartree functional $\E{\Ha}{}[\n{}{}]$ causes the infamous ghost-interaction error \cite{Gidopoulos_2002, Pastorczak_2014, Alam_2016, Alam_2017, Gould_2017} in eDFT, which is supposed to be cancelled by the weight-dependent xc functional $\E{\xc}{\bw}[\n{}{}]$.
|
||||||
|
|
||||||
From the GOK-DFT ensemble energy expression in Eq.~\eqref{eq:Ew-GOK}, we obtain \cite{Gross_1988b,Deur_2019}
|
From the GOK-DFT ensemble energy expression in Eq.~\eqref{eq:Ew-GOK}, we obtain \cite{Gross_1988b,Deur_2019}
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
@ -312,15 +312,15 @@ where $\e{\ex}{\ew{}}(\n{}{})$ and $\e{\co}{\ew{}}(\n{}{})$ are the weight-depen
|
|||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
\section{Computational details}
|
\section{Computational details}
|
||||||
\label{sec:compdet}
|
\label{sec:compdet}
|
||||||
The self-consistent GOK-DFT calculations have been performed with the \texttt{QuAcK} software, freely available on \texttt{github}, where the present functional has been implemented.
|
The self-consistent GOK-DFT calculations have been performed in a restricted formalism with the \texttt{QuAcK} software, \cite{QuAcK} which is freely available on \texttt{github}, and where the present weight-dependent functionals have been implemented.
|
||||||
For more details about the self-consistent implementation of GOK-DFT, we refer the interested reader to Ref.~\onlinecite{Loos_2020} where additional technical details can be found.
|
For more details about the self-consistent implementation of GOK-DFT, we refer the interested reader to Ref.~\onlinecite{Loos_2020} where additional technical details can be found.
|
||||||
For all calculations, we use a restricted formalism and the aug-cc-pVXZ (X = D, T, and Q) Dunning's family of atomic basis sets.
|
For all calculations, we use the aug-cc-pVXZ (X = D, T, Q, and 5) Dunning family of atomic basis sets. \cite{Dunning_1989,Kendall_1992,Woon_1994}
|
||||||
Numerical quadratures are performed with the \texttt{numgrid} library using 194 angular points (Lebedev grid) and a radial precision of $10^{-6}$. \cite{Becke_1988,Lindh_2001}
|
Numerical quadratures are performed with the \texttt{numgrid} library \cite{numgrid} using 194 angular points (Lebedev grid) and a radial precision of $10^{-6}$. \cite{Becke_1988,Lindh_2001}
|
||||||
This study deals only with spin-unpolarised systems, \ie, $\n{\uparrow}{} = \n{\downarrow}{} = \n{}{}/2$ (where $\n{\uparrow}{}$ and $\n{\downarrow}{}$ are the spin-up and spin-down electron densities).
|
This study deals only with spin-unpolarised systems, \ie, $\n{\uparrow}{} = \n{\downarrow}{} = \n{}{}/2$ (where $\n{\uparrow}{}$ and $\n{\downarrow}{}$ are the spin-up and spin-down electron densities).
|
||||||
Moreover, we restrict our study to the case of a two-state ensemble (\ie, $\nEns = 2$) where both the ground state ($I=0$ with weight $1 - \ew{}$) and the first doubly-excited state ($I=1$ with weight $\ew{}$) are considered.
|
Moreover, we restrict our study to the case of a two-state ensemble (\ie, $\nEns = 2$) where both the ground state ($I=0$ with weight $1 - \ew{}$) and the first doubly-excited state ($I=1$ with weight $\ew{}$) are considered.
|
||||||
Although we should have $0 \le \ew{} \le 1/2$ to ensure the GOK variational principle, we will sometimes ``violate'' this variational constraint.
|
Although one should have $0 \le \ew{} \le 1/2$ to ensure the GOK variational principle, we will sometimes ``violate'' this variational constraint.
|
||||||
Indeed, the limit $\ew{} = 1$ is of particular interest as it corresponds to a genuine saddle point of the KS equations, and match perfectly the results obtained with the maximum overlap method (MOM) developed by Gilbert, Gill and coworkers. \cite{Gilbert_2008,Barca_2018a,Barca_2018b}
|
Indeed, the limit $\ew{} = 1$ is of particular interest as it corresponds to a genuine saddle point of the KS equations, and match perfectly the results obtained with the maximum overlap method (MOM) developed by Gilbert, Gill and coworkers. \cite{Gilbert_2008,Barca_2018a,Barca_2018b}
|
||||||
Moreover, the limits $\ew{} = 0$ and $\ew{} = 1$ are the only two weights for which there is no ghost-interaction error.
|
\titou{Moreover, the limits $\ew{} = 0$ and $\ew{} = 1$ are the only two weights for which there is no ghost-interaction error.}
|
||||||
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
\section{Hydrogen molecule}
|
\section{Hydrogen molecule}
|
||||||
@ -340,9 +340,9 @@ First, we compute the ensemble energy of the \ce{H2} molecule (at equilibrium bo
|
|||||||
In the case of \ce{H2}, the ensemble is composed by the $1\sigma_g^2$ ground state and the lowest doubly-excited state of configuration $1\sigma_u^2$, which has an autoionising resonance nature. \cite{Bottcher_1974}
|
In the case of \ce{H2}, the ensemble is composed by the $1\sigma_g^2$ ground state and the lowest doubly-excited state of configuration $1\sigma_u^2$, which has an autoionising resonance nature. \cite{Bottcher_1974}
|
||||||
The ensemble energy $\E{}{\ew{}}$ is depicted in Fig.~\ref{fig:Ew_H2} as a function of the weight $0 \le \ew{} \le 1$.
|
The ensemble energy $\E{}{\ew{}}$ is depicted in Fig.~\ref{fig:Ew_H2} as a function of the weight $0 \le \ew{} \le 1$.
|
||||||
Because this exchange functional does not depend on the ensemble weight, there is no contribution from the ensemble derivative term [last term in Eq.~\eqref{eq:dEdw}].
|
Because this exchange functional does not depend on the ensemble weight, there is no contribution from the ensemble derivative term [last term in Eq.~\eqref{eq:dEdw}].
|
||||||
As anticipated, $\E{}{\ew{}}$ is far from being linear, which means that the excitation energy obtained via the derivative of the local energy varies significantly with the weight of the double excitation (see Fig.~\ref{fig:Om_H2}).
|
As anticipated, $\E{}{\ew{}}$ is far from being linear, which means that the excitation energy obtained via the derivative of the ensemble energy varies significantly with the weight of the double excitation (see Fig.~\ref{fig:Om_H2}).
|
||||||
Taking as a reference the full configuration interaction (FCI) value of $28.75$ eV obtained with the aug-mcc-pV8Z basis set, \cite{Barca_2018a} one can see that the excitation energy varies by more than $8$ eV from $\ew{} = 0$ to $1/2$.
|
Taking as a reference the full configuration interaction (FCI) value of $28.75$ eV obtained with the aug-mcc-pV8Z basis set, \cite{Barca_2018a} one can see that the excitation energy varies by more than $8$ eV from $\ew{} = 0$ to $1/2$.
|
||||||
Note that the exact xc correlation ensemble functional would yield a perfectly linear energy and, hence, the same value of the excitation energy independently of $\ew{}$.
|
Note that the exact xc ensemble functional would yield a perfectly linear energy and, hence, the same value of the excitation energy independently of $\ew{}$.
|
||||||
|
|
||||||
\begin{figure}
|
\begin{figure}
|
||||||
\includegraphics[width=\linewidth]{Ew_H2}
|
\includegraphics[width=\linewidth]{Ew_H2}
|
||||||
@ -365,8 +365,8 @@ Note that the exact xc correlation ensemble functional would yield a perfectly l
|
|||||||
\subsection{Weight-dependent exchange functional}
|
\subsection{Weight-dependent exchange functional}
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
Second, in order to remove this spurious curvature of the ensemble energy (which is mostly due to the ghost-interaction error, but not only), one can easily reverse-engineer (for this particular system and basis set) a local exchange functional to make $\E{}{\ew{}}$ as linear as possible for $0 \le \ew{} \le 1$.
|
Second, in order to remove this spurious curvature of the ensemble energy (which is mostly due to the ghost-interaction error, but not only), one can easily reverse-engineer (for this particular system, geometry, and basis set) a local exchange functional to make $\E{}{\ew{}}$ as linear as possible for $0 \le \ew{} \le 1$.
|
||||||
Doing so, we have found that the present weight-dependent exchange functional (denoted as GIC-S in the following as its main purpose is to correct for the ghost-interaction error), represented in Fig.~\ref{fig:Cx_H2},
|
Doing so, we have found that the present weight-dependent exchange functional (denoted as GIC-S in the following as its main purpose is to correct for the ghost-interaction error)
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\e{\ex}{\ew{},\text{GIC-S}}(\n{}{}) = \Cx{\ew{}} \n{}{1/3},
|
\e{\ex}{\ew{},\text{GIC-S}}(\n{}{}) = \Cx{\ew{}} \n{}{1/3},
|
||||||
\end{equation}
|
\end{equation}
|
||||||
@ -379,22 +379,23 @@ and
|
|||||||
\begin{subequations}
|
\begin{subequations}
|
||||||
\begin{align}
|
\begin{align}
|
||||||
\alpha & = + 0.575\,178,
|
\alpha & = + 0.575\,178,
|
||||||
\\
|
&
|
||||||
\beta & = - 0.021\,108,
|
\beta & = - 0.021\,108,
|
||||||
\\
|
&
|
||||||
\gamma & = - 0.367\,189,
|
\gamma & = - 0.367\,189,
|
||||||
\end{align}
|
\end{align}
|
||||||
\end{subequations}
|
\end{subequations}
|
||||||
makes the ensemble almost perfectly linear (see Fig.~\ref{fig:Ew_H2}), and the excitation energy much more stable and closer to the FCI reference (see Fig.~\ref{fig:Om_H2}).
|
makes the ensemble almost perfectly linear (see Fig.~\ref{fig:Ew_H2}), and the excitation energy much more stable and closer to the FCI reference (see Fig.~\ref{fig:Om_H2}).
|
||||||
As readily seen from Eq.~\eqref{eq:Cxw}, $\Cx{\ew{}}$ reduces to $\Cx{}$ for $\ew{} = 0$.
|
As readily seen from Eq.~\eqref{eq:Cxw} and graphically illustrated in Fig.~\ref{fig:Cx_H2}, the weight-dependent correction does not affect the two ghost-interaction-free limits at $\ew{} = 0$ and $\ew{} = 1$, as $\Cx{\ew{}}$ reduces to $\Cx{}$ in these two limits.
|
||||||
Note that we are not only using data from $\ew{} = 0$ to $\ew{} = 1/2$, but we also consider ensemble energies for $1/2 < \ew{} \le 1$, which is strictly forbidden by the GOK variational principle. \cite{Gross_1988a}
|
Note that we are not only using data from $0 \le \ew{} \le 1/2$, but we also consider ensemble energies for $1/2 < \ew{} \le 1$, which is strictly forbidden by the GOK variational principle. \cite{Gross_1988a}
|
||||||
However, it is important to ensure that the weight-dependent functional does not affect the two ghost-interaction-free limits at $\ew{} = 0$ and $\ew{} = 1$.
|
However, it is important to ensure that the weight-dependent functional does not alter the $\ew{} = 1$, which corresponds to a genuine saddle point of the KS equations, as mentioned above.
|
||||||
Therefore, by construction, the weight-dependent correction vanishes for these two limiting weight values (see Fig.~\ref{fig:Cx_H2}).
|
|
||||||
Finally, let us mention that, around $\ew{} = 0$, the behaviour of Eq.~\eqref{eq:Cxw} is linear.
|
Finally, let us mention that, around $\ew{} = 0$, the behaviour of Eq.~\eqref{eq:Cxw} is linear.
|
||||||
|
|
||||||
\begin{figure}
|
\begin{figure}
|
||||||
\includegraphics[width=0.8\linewidth]{Cx_H2}
|
\includegraphics[width=0.8\linewidth]{Cx_H2}
|
||||||
\caption{
|
\caption{
|
||||||
$\Cx{\ew{}}/\Cx{\ew{}=0}$ as a function of $\ew{}$ [see Eq.~\eqref{eq:Cxw}].
|
$\Cx{\ew{}}/\Cx{\ew{}=0}$ as a function of $\ew{}$ [see Eq.~\eqref{eq:Cxw}] for the \ce{H2} molecule at equilibrium bond length and the aug-cc-pVTZ basis set.
|
||||||
|
\titou{T2: Add the same curve for He and stretch H2.}
|
||||||
\label{fig:Cx_H2}
|
\label{fig:Cx_H2}
|
||||||
}
|
}
|
||||||
\end{figure}
|
\end{figure}
|
||||||
@ -733,8 +734,6 @@ Excitation energies (in eV) associated with the lowest double excitation of \ce{
|
|||||||
HF & FCI & aug-cc-pV5Z & & & & 8.69 \\
|
HF & FCI & aug-cc-pV5Z & & & & 8.69 \\
|
||||||
\end{tabular}
|
\end{tabular}
|
||||||
\end{ruledtabular}
|
\end{ruledtabular}
|
||||||
\fnt[1]{Reference \onlinecite{Mielke_2005}.}
|
|
||||||
\fnt[2]{Reference \onlinecite{Barca_2018a}.}
|
|
||||||
\end{table*}
|
\end{table*}
|
||||||
%%% %%% %%% %%%
|
%%% %%% %%% %%%
|
||||||
|
|
||||||
|
Binary file not shown.
Loading…
Reference in New Issue
Block a user