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hackbard
<hackbard>
Wed, 16 Aug 2006 15:22:14 +0000
(15:22 +0000)
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hackbard
<hackbard>
Wed, 16 Aug 2006 15:22:14 +0000
(15:22 +0000)
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
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posic/thesis/basics.tex
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-184,7
+184,7
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This is gradually done in the following.
The $n$th component of the force acting on atom $i$ is
\begin{eqnarray}
F_n^i & = & - \frac{\partial}{\partial x_n} \sum_{j \neq i} V_{ij} \nonumber\\
The $n$th component of the force acting on atom $i$ is
\begin{eqnarray}
F_n^i & = & - \frac{\partial}{\partial x_n} \sum_{j \neq i} V_{ij} \nonumber\\
- & = & \sum_{j \neq i} \Big( \partial_{x_n^i} f_C(r_{ij}) \big[ f_R(r_{ij}) + b_
ij
f_A(r_{ij}) \big] + \nonumber\\
+ & = & \sum_{j \neq i} \Big( \partial_{x_n^i} f_C(r_{ij}) \big[ f_R(r_{ij}) + b_
{ij}
f_A(r_{ij}) \big] + \nonumber\\
& & + f_C(r_{ij}) \big[ \partial_{x_n^i} f_R(r_{ij}) + b_{ij} \partial_{x_n^i} f_A(r_{ij}) + f_A(r_{ij}) \partial_{x_n^i} b_{ij} \big] \Big)
\end{eqnarray}
The cutoff function $f_C$ derivated with repect to $x^i_n$ is
& & + f_C(r_{ij}) \big[ \partial_{x_n^i} f_R(r_{ij}) + b_{ij} \partial_{x_n^i} f_A(r_{ij}) + f_A(r_{ij}) \partial_{x_n^i} b_{ij} \big] \Big)
\end{eqnarray}
The cutoff function $f_C$ derivated with repect to $x^i_n$ is