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entered brakets to hf forces, still need to modify final result!
author
hackbard
<hackbard@hackdaworld.org>
Mon, 12 Sep 2011 13:26:42 +0000
(15:26 +0200)
committer
hackbard
<hackbard@hackdaworld.org>
Mon, 12 Sep 2011 13:26:42 +0000
(15:26 +0200)
posic/thesis/basics.tex
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diff --git
a/posic/thesis/basics.tex
b/posic/thesis/basics.tex
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--- a/
posic/thesis/basics.tex
+++ b/
posic/thesis/basics.tex
@@
-558,9
+558,9
@@
However, moving an ion, i.e.\ altering its position, changes the wave functions
Writing down the derivative of the total energy $E$ with respect to the position $\vec{R}_i$ of ion $i$
\begin{equation}
\frac{dE}{d\vec{R_i}}=
Writing down the derivative of the total energy $E$ with respect to the position $\vec{R}_i$ of ion $i$
\begin{equation}
\frac{dE}{d\vec{R_i}}=
- \sum_j \
Phi_j^* \frac{\partial H}{\partial \vec{R}_i} \Phi_j
-+\sum_j \
frac{\partial \Phi_j^*}{\partial \vec{R}_i} H \Phi_j
-+\sum_j \
Phi_j^* H \frac{\partial \Phi_j}{\partial \vec{R}_i}
+ \sum_j \
langle \Phi_j | \frac{\partial H}{\partial\vec{R}_i} | \Phi_j \rangle
++\sum_j \
langle \frac{\partial \Phi_j}{\partial\vec{R}_i} | H \Phi_j \rangle
++\sum_j \
langle \Phi_j H | \frac{\partial \Phi_j}{\partial \vec{R}_i} \rangle
\text{ ,}
\end{equation}
indeed reveals a contribution to the change in total energy due to the change of the wave functions $\Phi_j$.
\text{ ,}
\end{equation}
indeed reveals a contribution to the change in total energy due to the change of the wave functions $\Phi_j$.