From 31e68ff0d3a8e7babf11031993b40df56f733968 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Thu, 13 Oct 2022 16:13:29 +0200 Subject: [PATCH] corrections Antoine --- CCvsMBPT.tex | 6 +++--- Cover_Letter/CoverLetter.tex | 2 +- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/CCvsMBPT.tex b/CCvsMBPT.tex index e5d5c1e..23d4761 100644 --- a/CCvsMBPT.tex +++ b/CCvsMBPT.tex @@ -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}} diff --git a/Cover_Letter/CoverLetter.tex b/Cover_Letter/CoverLetter.tex index 1c461be..973a831 100644 --- a/Cover_Letter/CoverLetter.tex +++ b/Cover_Letter/CoverLetter.tex @@ -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.}