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Pierre-Francois Loos 2021-07-31 22:25:52 +02:00
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Manuscript/Ec.tex
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@ -124,6 +124,16 @@ In most molecular calculations, a set of one-electron, atom-centered Gaussian ba
The third and most relevant approximation in the present context is the ansatz (or form) of the electronic wave function $\Psi$.
For example, in configuration interaction (CI) methods, the wave function is expanded as a linear combination of Slater determinants, while in (single-reference) coupled-cluster (CC) theory, \cite{Cizek_1966,Paldus_1972,Crawford_2000,Piecuch_2002b,Bartlett_2007,Shavitt_2009} a reference Slater determinant $\PsiO$ [usually taken as the Hartree-Fock (HF) wave function] is multiplied by a wave operator defined as the exponentiated excitation operator $\hT = \sum_{k=1}^\Nel \hT_k$ (where $\Nel$ is the number of electrons and $\hT_k$ is $k$th-degree excitation operator).
%%% FIG 1 %%%
\begin{figure*}
\includegraphics[width=0.8\linewidth]{ring5}
\includegraphics[width=\linewidth]{ring6}
\caption{
Five-membered rings (top) and six-membered rings (bottom) considered in this study.
\label{fig:mol}}
\end{figure*}
%%% %%% %%%
The truncation of $\hT$ allows to define a hierarchy of non-variational and size-extensive methods with increasing levels of accuracy:
CC with singles and doubles (CCSD), \cite{Cizek_1966,Purvis_1982} CC with singles, doubles, and triples (CCSDT), \cite{Noga_1987a,Scuseria_1988} CC with singles, doubles, triples, and quadruples (CCSDTQ), \cite{Oliphant_1991,Kucharski_1992} with corresponding formal computational scalings of $\order*{\Norb^{6}}$, $\order*{\Norb^{8}}$, and $\order*{\Norb^{10}}$, respectively (where $\Norb$ denotes the number of orbitals).
Parallel to the ``complete'' CC series presented above, an alternative family of approximate iterative CC models has been developed by the Aarhus group in the context of CC response theory \cite{Christiansen_1998} where one skips the most expensive terms and avoids the storage of the higher-excitation amplitudes: CC2, \cite{Christiansen_1995a} CC3, \cite{Christiansen_1995b,Koch_1997} and CC4. \cite{Kallay_2005,Matthews_2021}
@ -158,16 +168,6 @@ In addition to CIPSI, the performance and convergence properties of several seri
In particular, we study i) the MP perturbation series up to fifth-order (MP2, MP3, MP4, and MP5), ii) the CC2, CC3, and CC4 approximate series, and ii) the ``complete'' CC series up to quadruples (\ie, CCSD, CCSDT, and CCSDTQ).
The performance of the ground-state gold standard CCSD(T) as well as the completely renormalized (CR) CC model, CR-CC(2,3), \cite{Kowalski_2000a,Kowalski_2000b,Piecuch_2002a,Piecuch_2002b,Piecuch_2005} are also investigated.
%%% FIG 1 %%%
\begin{figure*}
\includegraphics[width=0.8\linewidth]{ring5}
\includegraphics[width=\linewidth]{ring6}
\caption{
Five-membered rings (top) and six-membered rings (bottom) considered in this study.
\label{fig:mol}}
\end{figure*}
%%% %%% %%%
The present manuscript is organized as follows.
In Sec.~\ref{sec:OO-CIPSI}, we provide theoretical details about the CIPSI algorithm and the orbital optimization procedure employed here.
Section \ref{sec:compdet} deals with computational details concerning geometries, basis sets, and methods.
@ -728,6 +728,8 @@ This project has received funding from the European Research Council (ERC) under
%%%%%%%%%%%%%%%%%%%%%%%%%
The data that support the findings of this study are openly available in Zenodo at \url{http://doi.org/10.5281/zenodo.5150663}.
\clearpage
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\bibliography{Ec}
%%%%%%%%%%%%%%%%%%%%%%%%%