From 20aa963400a7a22e40fccafd992204b011f988f5 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Tue, 11 Feb 2020 16:20:32 +0100 Subject: [PATCH] eq 7 8 9 --- BSE-PES.tex | 8 ++++---- Data/H2_GS_VDZ.pdf | Bin 64984 -> 64724 bytes 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/BSE-PES.tex b/BSE-PES.tex index e53e424..6ac610f 100644 --- a/BSE-PES.tex +++ b/BSE-PES.tex @@ -146,7 +146,7 @@ \newcommand{\bB}[1]{\mathbf{B}^{#1}} \newcommand{\bX}[1]{\mathbf{X}^{#1}} \newcommand{\bY}[1]{\mathbf{Y}^{#1}} -\newcommand{\bZ}[1]{\mathbf{Z}^{#1}} +\newcommand{\bZ}[2]{\mathbf{Z}_{#1}^{#2}} \newcommand{\bK}{\mathbf{K}} \newcommand{\bP}[1]{\mathbf{P}^{#1}} @@ -302,14 +302,14 @@ In the following, the index $m$ labels the $\Nocc \Nvir$ single excitations, $i$ In the absence of instabilities (\ie, when $\bA{\IS} - \bB{\IS}$ is positive-definite), \cite{Dreuw_2005} Eq.~\eqref{eq:LR} is usually transformed into an Hermitian eigenvalue problem of smaller dimension \begin{equation} \label{eq:small-LR} - (\bA{\IS} - \bB{\IS})^{1/2} (\bA{\IS} + \bB{\IS}) (\bA{\IS} - \bB{\IS})^{1/2} \bZ{\IS}_m = (\Om{m}{\IS})^2 \bZ{\IS}_m, + (\bA{\IS} - \bB{\IS})^{1/2} (\bA{\IS} + \bB{\IS}) (\bA{\IS} - \bB{\IS})^{1/2} \bZ{m}{\IS} = (\Om{m}{\IS})^2 \bZ{m}{\IS}, \end{equation} where the excitation amplitudes are \begin{subequations} \begin{align} - \bX{\IS} + \bY{\IS} = (\bOm{\IS})^{-1/2} (\bA{\IS} - \bB{\IS})^{+1/2} \bZ{\IS}, + (\bX{\IS} + \bY{\IS})_m = (\Om{m}{\IS})^{-1/2} (\bA{\IS} - \bB{\IS})^{+1/2} \bZ{m}{\IS}, \\ - \bX{\IS} - \bY{\IS} = (\bOm{\IS})^{+1/2} (\bA{\IS} - \bB{\IS})^{-1/2} \bZ{\IS}. + (\bX{\IS} - \bY{\IS})_m = (\Om{m}{\IS})^{+1/2} (\bA{\IS} - \bB{\IS})^{-1/2} \bZ{m}{\IS}. \end{align} \end{subequations} Introducing the so-called Mulliken notation for the bare two-electron integrals diff --git a/Data/H2_GS_VDZ.pdf b/Data/H2_GS_VDZ.pdf index ef20f3e2cb61d741f29a81ee4649f463dad3ebd7..3d6e0fbdd2b16288e29fdb32fc54817f753f7eee 100644 GIT binary patch delta 54479 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