From f61dc22754c99e1c35fdf824708b34f743c97898 Mon Sep 17 00:00:00 2001 From: Raul QUINTERO MONSEBAIZ Date: Thu, 13 Oct 2022 10:46:52 +0200 Subject: [PATCH] details in the normal order hamiltonian --- CCvsMBPT.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/CCvsMBPT.tex b/CCvsMBPT.tex index 9d9a259..e78745c 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 $\bHN = e^{-\hT} \hH e^{\hT} - E_\text{CCD}$ is the normal-ordered similarity-transformed Hamiltonian, $\Psi_{i}^{a}$ are singly-excited determinants, the one-body terms are +where \textcolor{blue}{ $\bHN = e^{-\hT} \hH_{N} e^{\hT} $} is the normal-ordered similarity-transformed Hamiltonian, $\Psi_{i}^{a}$ are singly-excited determinants, the one-body terms are \begin{subequations} \begin{align} \label{eq:cFab} @@ -503,9 +503,9 @@ where $\be{}{\GW}$ is a diagonal matrix collecting the quasiparticle energies, t \end{subequations} and the corresponding coupling blocks read \begin{align} - V^\text{2h1p}_{p,klc} & = \ERI{pc}{kl} + V^\text{2h1p}_{p,klc} & =\textcolor{blue}{\sqrt{2}}\ERI{pc}{kl} & - V^\text{2p1h}_{p,kcd} & = \ERI{pk}{dc} + V^\text{2p1h}_{p,kcd} & =\textcolor{blue}{\sqrt{2}} \ERI{pk}{dc} \end{align} Going beyond the Tamm-Dancoff approximation is possible, but more cumbersome. \cite{Bintrim_2021}