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Pierre-Francois Loos 2020-01-22 23:18:55 +01:00
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BSE-PES.tex
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@ -176,11 +176,12 @@
%\end{wrapfigure}
The many-body Green's function Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative to time-dependent density-functional theory (TD-DFT) in order to compute vertical transition energies for medium and large molecular systems.
In particular, BSE@\textit{GW} faithfully treats charge-transfer states and avoids the delicate choice of the exchange-correlation functional from an ever-growing zoo of functionals.
However, contrary to TD-DFT, there is no clear definition of the ground- and excited-state energies within BSE, which makes the development of analytical nuclear gradients a particularly tricky task.
Here, we provide an unambiguous definition of the ground-state BSE energy, and we calculate the excited-state BSE energy of a given state by adding the corresponding BSE excitation energy to the ground-state BSE energy.
Embracing this definition which treats on equal footing ground and excited states at the BSE level, we study the topological features of the ground- and (singlet and triplet) excited-state potential energy surfaces (PES) for several diatomic molecules.
However, contrary to TD-DFT, there is no clear definition of the ground- and excited-state energies within BSE.
This makes the development of analytical nuclear gradients a particularly tricky task.
Here, we provide an unambiguous definition of the ground-state BSE energy, and we calculate the excited-state BSE energy of a given state by adding the corresponding BSE excitation energy to the ground-state BSE energy which is calculated in the framework of the adiabatic-connection fluctuation-dissipation theorem.
Embracing this definition which treats on equal footing ground and excited states at the BSE level, we study the topological features of the ground- and singlet excited-state potential energy surfaces (PES) for several diatomic molecules.
Our aim is to know whether or not the BSE formalism is able to reproduce faithfully the main features of these PES near equilibrium, and, in particular, the location of the minima on the ground- and excited-state PES.
\titou{Thanks to comparison with both similar and state-of-art computational approaches, we show that ...}
\titou{Thanks to comparison with both similar and state-of-art computational approaches, we show that the present approach is surprisingly accurate.}
\end{abstract}
\maketitle
@ -430,18 +431,18 @@ Equilibrium distances (in bohr) of the ground state of diatomic molecules obtain
MP2 & cc-pVDZ & 1.426 & 3.041 & 3.010 & 2.133 & 2.166 & 2.431 & 2.681 & 2.426 \\
& cc-pVTZ & 1.393 & 3.004 & 2.968 & 2.095 & 2.144 & 2.383 & 2.636 & 2.405 \\
& cc-pVQZ & 1.391 & 3.008 & 2.970 & 2.091 & 2.137 & 2.382 & 2.634 & 2.395 \\
BSE@{\GOWO}@HF & cc-pVDZ & 1.437 & 3.042 & 2.999 & 2.107 & 2.153 & 2.416 & & 2.437 \\
& cc-pVTZ & 1.404 & 3.023 & glitch & & & 2.437 & & \\
& cc-pVQZ & 1.399 & & & & & & & \\
RPA@{\GOWO}@HF & cc-pVDZ & 1.426 & 3.019 & 2.994 & 2.083 & 2.144 & 2.403 & & 2.436 \\
& cc-pVTZ & 1.388 & 3.013 & glitch & & & <2.420 & & \\
& cc-pVQZ & 1.382 & & & & & & & \\
RPAx@HF & cc-pVDZ & 1.428 & 3.040 & 2.998 & 2.077 & 2.130 & 2.417 & & 2.424 \\
& cc-pVTZ & 1.395 & 3.003 & <2.990 & & & <2.420 & & \\
& cc-pVQZ & 1.394 & & & & & & & \\
RPA@HF & cc-pVDZ & 1.431 & 3.021 & 2.999 & 2.083 & 2.134 & & & 2.424 \\
& cc-pVTZ & 1.388 & 2.978 & <2.990 & & & 2.416 & & \\
& cc-pVQZ & 1.386 & & & & & <2.420 & & \\
BSE@{\GOWO}@HF & cc-pVDZ & 1.437 & 3.042 & 3.000 & 2.107 & 2.153 & 2.407 & 2.700 & >2.440 \\
& cc-pVTZ & 1.404 & 3.023 & glitch & & & <2.420 & & <2.410 \\
& cc-pVQZ & 1.399 & & & & & & & \\
RPA@{\GOWO}@HF & cc-pVDZ & 1.426 & 3.019 & 2.994 & 2.083 & 2.144 & 2.403 & 2.691 & 2.436 \\
& cc-pVTZ & 1.388 & 3.013 & glitch & & & <2.420 & & <2.410 \\
& cc-pVQZ & 1.382 & & & & & & & \\
RPAx@HF & cc-pVDZ & 1.428 & 3.040 & 2.998 & 2.077 & 2.130 & 2.417 & NaN & 2.424 \\
& cc-pVTZ & 1.395 & 3.003 & <2.990 & & & <2.420 & & <2.410 \\
& cc-pVQZ & 1.394 & & & & & & & \\
RPA@HF & cc-pVDZ & 1.431 & 3.021 & 2.999 & 2.083 & 2.134 & & 2.623 & 2.424 \\
& cc-pVTZ & 1.388 & 2.978 & <2.990 & & & 2.416 & & <2.410 \\
& cc-pVQZ & 1.386 & & & & & <2.420 & & \\
% FROZEN CORE VERSION
% Method & Basis & \ce{H2} & \ce{LiH}& \ce{LiF}& \ce{N2} & \ce{CO} & \ce{BF} & \ce{F2} & \ce{HCl}\\
% \hline
@ -487,7 +488,7 @@ Equilibrium distances (in bohr) of the ground state of diatomic molecules obtain
\includegraphics[width=0.45\linewidth]{HCl_GS_VTZ}
\caption{
PES of the ground state of diatomic molecules around their respective equilibrium geometry obtained at various levels of theory with the cc-pVTZ basis set.
Graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}.
Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}.
\label{fig:PES}
}
\end{figure*}