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Manu: derived the hopefully proper expression for the individual Hx energy

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This commit is contained in:
Emmanuel Fromager 2019-09-10 18:35:14 +02:00
parent 0d01c4376d
commit 7ae8c41498
1 changed files with 6 additions and 2 deletions
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8
Manuscript/eDFT.tex
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@ -92,7 +92,7 @@
\newcommand{\manu}[1]{{\textcolor{blue}{ Manu: #1 }} }
\newcommand{\beq}{\begin{eqnarray}}
\newcommand{\eeq}{\nonumber\end{eqnarray}}
\newcommand{\eeq}{\end{eqnarray}}
\newcommand{\bmk}{\bm{\kappa}} % orbital rotation vector
\newcommand{\bmg}{\bm{\Gamma}} % orbital rotation vector
\newcommand{\bfx}{\bf{x}}
@ -322,7 +322,11 @@ Tr}\left[{\bmg}^{(0)}{\bm h}\right]
E^{(I)}&=&E^{{\bw}}+\sum_{K>0}\left(\delta_{IK}-w^{(K)}\right)\dfrac{\partial E^{{\bw}}}{\partial w^{(K)}}
\nonumber\\
&=&
...+\dfrac{1}{2}\Tr(\bmg^{\bw} \, \bG \, \bmg^{\bw})
...+\Tr(\bmg^{(I)} \, \bG \, \bmg^{\bw})
-\dfrac{1}{2}\Tr(\bmg^{\bw} \, \bG \, \bmg^{\bw})+...
\nonumber\\
&=&...+
\Tr\left[\left(\bmg^{(I)}-\dfrac{1}{2}\bmg^{\bw}\right) \, \bG \, \bmg^{\bw}\right]
+...
\eeq
}