loos/eDFT_FUEG
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

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

Browse Source
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
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

8
Manuscript/eDFT.tex
View File

@ -92,7 +92,7 @@
\newcommand{\manu}[1]{{\textcolor{blue}{ Manu: #1 }} } \newcommand{\manu}[1]{{\textcolor{blue}{ Manu: #1 }} }
\newcommand{\beq}{\begin{eqnarray}} \newcommand{\beq}{\begin{eqnarray}}
\newcommand{\eeq}{\nonumber\end{eqnarray}} \newcommand{\eeq}{\end{eqnarray}}
\newcommand{\bmk}{\bm{\kappa}} % orbital rotation vector \newcommand{\bmk}{\bm{\kappa}} % orbital rotation vector
\newcommand{\bmg}{\bm{\Gamma}} % orbital rotation vector \newcommand{\bmg}{\bm{\Gamma}} % orbital rotation vector
\newcommand{\bfx}{\bf{x}} \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)}} E^{(I)}&=&E^{{\bw}}+\sum_{K>0}\left(\delta_{IK}-w^{(K)}\right)\dfrac{\partial E^{{\bw}}}{\partial w^{(K)}}
\nonumber\\ \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 \eeq
} }