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Pierre-Francois Loos 2022-04-11 10:07:03 +02:00
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@ -163,7 +163,7 @@ Finally, our conclusions are drawn in Sec.~\ref{sec:conclusion}.
\subsection{Selected configuration interaction calculations} \subsection{Selected configuration interaction calculations}
\label{sec:SCI} \label{sec:SCI}
For the SCI calculations, we rely on the CIPSI algorithm implemented in QUANTUM PACKAGE, \cite{Garniron_2019} which iteratively select determinants in the FCI space. For the SCI calculations, we rely on the CIPSI algorithm implemented in QUANTUM PACKAGE, \cite{Garniron_2019} which iteratively select determinants in the FCI space.
To treat electronic states on equal footing, we use a state-averaged formalism where the ground and excited states are expanded with the same set of determinants but with different CI coefficients. To treat electronic states on an equal footing, we use a state-averaged formalism where the ground and excited states are expanded with the same set of determinants but with different CI coefficients.
Note that the determinant selection for these states are performed simultaneously via the protocol described in Refs.~\onlinecite{Scemama_2019,Garniron_2019}. Note that the determinant selection for these states are performed simultaneously via the protocol described in Refs.~\onlinecite{Scemama_2019,Garniron_2019}.
For a given size of the variational wave function and for each electronic state, the CIPSI energy is the sum of two terms: the variational energy obtained by diagonalization of the CI matrix in the reference space $E_\text{var}$ and a second-order perturbative correction $E_\text{PT2}$ which estimates the contribution of the external determinants that are not included in the variational space at a given iteration. For a given size of the variational wave function and for each electronic state, the CIPSI energy is the sum of two terms: the variational energy obtained by diagonalization of the CI matrix in the reference space $E_\text{var}$ and a second-order perturbative correction $E_\text{PT2}$ which estimates the contribution of the external determinants that are not included in the variational space at a given iteration.
@ -188,7 +188,7 @@ In some cases, we have also computed (singlet and triplet) excitation energies a
To avoid having to perform multi-reference CC calculations or high-level CC calculations in the restricted open-shell or unrestricted formalisms, it is worth mentioning that, for the {\Dfour} arrangement, we have considered the lowest \textit{closed-shell} singlet state {\Aoneg} as reference. To avoid having to perform multi-reference CC calculations or high-level CC calculations in the restricted open-shell or unrestricted formalisms, it is worth mentioning that, for the {\Dfour} arrangement, we have considered the lowest \textit{closed-shell} singlet state {\Aoneg} as reference.
Hence, the open-shell ground state {\sBoneg} and the {\Btwog} state appear as a de-excitation and an excitation, respectively. Hence, the open-shell ground state {\sBoneg} and the {\Btwog} state appear as a de-excitation and an excitation, respectively.
With respect to {\Aoneg}, {\sBoneg} has a dominant double excitation character, while {\Btwog} have a dominant single excitation character, hence their contrasting convergence behaviors with respect to the order of the CC expansion (see below). With respect to {\Aoneg}, {\sBoneg} has a dominant double excitation character, while {\Btwog} has a dominant single excitation character, hence their contrasting convergence behaviors with respect to the order of the CC expansion (see below).
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