H2 stretch
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FarDFT.nb
554
FarDFT.nb
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|
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|
||||
@ -314,7 +314,7 @@ where $\e{\ex}{\ew{}}(\n{}{})$ and $\e{\co}{\ew{}}(\n{}{})$ are the weight-depen
|
||||
\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.
|
||||
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 the aug-cc-pVXZ (X = D, T, and Q) Dunning's family of atomic basis sets.
|
||||
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.
|
||||
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}
|
||||
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.
|
||||
@ -633,6 +633,8 @@ MOM excitation energies can then be obtained via GOK-DFT ensemble calculations b
|
||||
The results gathered in Table \ref{tab:BigTab_H2} show that the GOK-DFT excitation energies obtained with the GIC-SeVWN5 functional at zero weight are the most accurate with an improvement of $0.25$ eV as compared to GIC-SVWN5, which is due to the ensemble derivative contribution of the eVWN5 functional.
|
||||
The GIC-SeVWN5 excitation energies at equi-weights (\ie, $\ew{} = 1/2$) are less satisfactory, but still remains in good agreement with FCI, with again a small improvement as compared to GIC-SVWN5.
|
||||
|
||||
The GIC-S functional does not alter the MOM excitation energy as the correction vanishes accordingly for $\ew{} = 1$.
|
||||
|
||||
%%% TABLE I %%%
|
||||
\begin{table*}
|
||||
\caption{
|
||||
@ -657,6 +659,10 @@ Excitation energies (in eV) associated with the lowest double excitation of \ce{
|
||||
& & aug-cc-pVTZ & 38.54 & 27.81 & 24.46 & 27.17 \\
|
||||
& & aug-cc-pVQZ & 38.81 & 27.81 & 24.46 & 27.17 \\
|
||||
\\
|
||||
S & eVWN5 & aug-cc-pVDZ & 21.28 & 27.92 & 24.49 & 27.27 \\
|
||||
& & aug-cc-pVTZ & 21.39 & 27.98 & 24.55 & 27.34 \\
|
||||
& & aug-cc-pVQZ & 21.38 & 27.97 & 24.55 & 27.34 \\
|
||||
\\
|
||||
GIC-S & & aug-cc-pVDZ & 26.83 & 26.51 & 26.53 & 26.60 \\
|
||||
& & aug-cc-pVTZ & 26.88 & 26.59 & 26.61 & 26.67 \\
|
||||
& & aug-cc-pVQZ & 26.82 & 26.60 & 26.62 & 26.67 \\
|
||||
@ -682,12 +688,60 @@ Excitation energies (in eV) associated with the lowest double excitation of \ce{
|
||||
\end{table*}
|
||||
%%% %%% %%% %%%
|
||||
|
||||
|
||||
%%% TABLE I %%%
|
||||
\begin{table*}
|
||||
\caption{
|
||||
Excitation energies (in eV) associated with the lowest double excitation of \ce{H2} with $\RHH = 3.7$ bohr for various methods, combinations of xc functionals, and basis sets.
|
||||
\label{tab:BigTab_H2}
|
||||
}
|
||||
\begin{ruledtabular}
|
||||
\begin{tabular}{llccccc}
|
||||
\mc{2}{c}{xc functional} & & \mc{2}{c}{GOK} \\
|
||||
\cline{1-2} \cline{4-5}
|
||||
exchange & correlation & Basis & $\ew{} = 0$ & $\ew{} = 1/2$ & LIM & MOM \\
|
||||
\hline
|
||||
HF & & aug-cc-pVDZ & 19.08 & 6.58 & 12.92 & \\
|
||||
& & aug-cc-pVTZ & 19.09 & 6.59 & 12.92 & \\
|
||||
\\
|
||||
S & & aug-cc-pVDZ & 5.31 & 5.60 & 5.46 & 5.56 \\
|
||||
& & aug-cc-pVTZ & 5.31 & 5.60 & 5.46 & 5.56 \\
|
||||
\\
|
||||
S & VWN5 & aug-cc-pVDZ & 5.34 & 5.57 & 5.46 & 5.53 \\
|
||||
& & aug-cc-pVTZ & 5.34 & 5.57 & 5.46 & 5.52 \\
|
||||
\\
|
||||
S & eVWN5 & aug-cc-pVDZ & 5.53 & 5.76 & 5.56 & 5.72 \\
|
||||
& & aug-cc-pVTZ & 5.53 & 5.76 & 5.56 & 5.72 \\
|
||||
& & aug-cc-pVQZ & & & & \\
|
||||
\\
|
||||
GIC-S & & aug-cc-pVDZ & 10.54 & 5.61 & 8.47 & 5.56 \\
|
||||
& & aug-cc-pVTZ & 10.53 & 5.61 & 8.47 & 5.56 \\
|
||||
\\
|
||||
GIC-S & VWN5 & aug-cc-pVDZ & 10.67 & 5.59 & 8.55 & 5.53 \\
|
||||
& & aug-cc-pVTZ & 10.67 & 5.59 & 8.55 & 5.52 \\
|
||||
\\
|
||||
GIC-S & eVWN5 & aug-cc-pVDZ & 10.86 & 5.77 & 8.64 & 5.72 \\
|
||||
& & aug-cc-pVTZ & 10.86 & 5.77 & 8.64 & 5.72 \\
|
||||
\\
|
||||
% HF & FCI & aug-cc-pVDZ & & & & 8.78 \\
|
||||
% HF & FCI & aug-cc-pVTZ & & & & 8.71 \\
|
||||
% HF & FCI & aug-cc-pVQZ & & & & 8.70 \\
|
||||
HF & FCI & aug-cc-pV5Z & & & & 8.69 \\
|
||||
\end{tabular}
|
||||
\end{ruledtabular}
|
||||
\fnt[1]{Reference \onlinecite{Mielke_2005}.}
|
||||
\fnt[2]{Reference \onlinecite{Barca_2018a}.}
|
||||
\end{table*}
|
||||
%%% %%% %%% %%%
|
||||
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%
|
||||
%%% CONCLUSION %%%
|
||||
%%%%%%%%%%%%%%%%%%
|
||||
\section{Conclusion}
|
||||
\label{sec:ccl}
|
||||
As concluding remarks, we would like to say that what we have done, we think, is awesome.
|
||||
We have studied the weight dependence of the ensemble energy in the framework of GOK-DFT.
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
%%% ACKNOWLEDGEMENTS %%%
|
||||
|
||||
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Block a user