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corrections Antoine

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Pierre-Francois Loos 2022-10-13 16:13:29 +02:00
parent 50b30b1969
commit 31e68ff0d3
2 changed files with 4 additions and 4 deletions
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6
CCvsMBPT.tex
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@ -292,7 +292,7 @@ To be more specific, restricting ourselves to CCD, \ie, $\hT = \hT_2$, the eleme
\begin{equation}
\mel*{ \Psi_{i}^{a} }{ \bHN}{ \Psi_{j}^{b} } = \cF_{ab} \delta_{ij} - \cF_{ij} \delta_{ab} + \cW_{jabi}
\end{equation}
where $\bHN = e^{-\hT} \hH_{N} e^{\hT} - \ECC $ is the (shifted) similarity-transformed Hamiltonian, $\Psi_{i}^{a}$ are singly-excited determinants, the one-body terms are
where $\bHN = e^{-\hT} \hH_{N} e^{\hT} - \ECC $ is the (shifted) similarity-transformed normal-ordered Hamiltonian, $\Psi_{i}^{a}$ are singly-excited determinants, the one-body terms are
\begin{subequations}
\begin{align}
\label{eq:cFab}
@ -574,7 +574,7 @@ Substituting Eq.~\eqref{eq:R} into Eqs.~\eqref{eq:T1R} and \eqref{eq:T2R}, one g
\end{split}
\end{align}
\end{subequations}
In the CC language, in order to determine the 2h1p and 2p1h amplitudes, $t_{ija,p}^{\text{2h1p}}$ and $t_{iab,p}^{\text{2p1h}} $, one must solve the following coupled residual equations
that can be converted to the following CC-like residual equations
\begin{subequations}
\begin{align}
\label{eq:r_2h1p}
@ -603,7 +603,7 @@ In the CC language, in order to determine the 2h1p and 2p1h amplitudes, $t_{ija,
\end{align}
\end{subequations}
with $\Delta_{ija,p}^{\text{2h1p}} = \e{i}{} + \e{j}{} - \e{a}{} - \e{p}{}$ and $\Delta_{iab,p}^{\text{2p1h}} = \e{a}{} + \e{b}{} - \e{i}{} - \e{p}{}$.
One can then employed the usual quasi-Newton iterative procedure to solve these quadratic equations by updating the amplitudes via
To determine the 2h1p and 2p1h amplitudes, $t_{ija,p}^{\text{2h1p}}$ and $t_{iab,p}^{\text{2p1h}} $, one can then rely on the usual quasi-Newton iterative procedure to solve these quadratic equations by updating the amplitudes via
\begin{subequations}
\begin{align}
t_{ija,p}^{\text{2h1p}} & \leftarrow t_{ija,p}^{\text{2h1p}} - \qty( \Delta_{ija,p}^{\text{2h1p}} )^{-1} r_{ija,p}^{\text{2h1p}}

2
Cover_Letter/CoverLetter.tex
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@ -26,7 +26,7 @@ The present work provides a clear path for the computation of ground- and excite
It also broaden the applicability of Green's function methods in the electronic structure community and beyond.
Because of the novelty of this work and its potential impact in quantum chemistry and condensed matter physics, we expect it to be of interest to a wide audience within the chemistry and physics communities.
We suggest Timothy Berkelbach, Gustavo Scuseria, George Booth, Stefano Evangelista, Xavier Blase, and Weitao Yang as potential referees.
We suggest Timothy Berkelbach, Gustavo Scuseria, George Booth, and Lucia Reining as potential referees.
We look forward to hearing from you soon.
\closing{Sincerely, the authors.}