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hmmm ...
author
hackbard
<hackbard>
Thu, 14 Sep 2006 15:27:55 +0000
(15:27 +0000)
committer
hackbard
<hackbard>
Thu, 14 Sep 2006 15:27:55 +0000
(15:27 +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
+++ b/
posic/thesis/basics.tex
@@
-190,14
+190,14
@@
F_n^i & = & - \frac{\partial}{\partial x_n} \sum_{j \neq i} V_{ij} \nonumber\\
The cutoff function $f_C$ derivated with repect to $x^i_n$ is
\begin{equation}
\partial_{x^i_n} f_C(r_{ij}) =
The cutoff function $f_C$ derivated with repect to $x^i_n$ is
\begin{equation}
\partial_{x^i_n} f_C(r_{ij}) =
- \frac{1}{2} \sin \Big( \pi (r_{ij} - R_{ij}) / (S_{ij} - R_{ij}) \Big) \frac{\pi x^i_n}{(S_{ij} - R_{ij}) r_{ij}}
+
-
\frac{1}{2} \sin \Big( \pi (r_{ij} - R_{ij}) / (S_{ij} - R_{ij}) \Big) \frac{\pi x^i_n}{(S_{ij} - R_{ij}) r_{ij}}
\label{eq:d_cutoff}
\end{equation}
for $R_{ij} < r_{ij} < S_{ij}$ and otherwise zero.
The derivations of the repulsive and attractive part are:
\begin{eqnarray}
\label{eq:d_cutoff}
\end{equation}
for $R_{ij} < r_{ij} < S_{ij}$ and otherwise zero.
The derivations of the repulsive and attractive part are:
\begin{eqnarray}
-\partial_{x_n^i} f_R(r_{ij}) & = & - \lambda_{ij} A_{ij} \exp (-\lambda_{ij} r_{ij})\\
-\partial_{x_n^i} f_A(r_{ij}) & = & \mu_{ij} B_{ij} \exp (-\mu_{ij} r_{ij}) \textrm{ .}
+\partial_{x_n^i} f_R(r_{ij}) & = & - \lambda_{ij}
\frac{x_n^i - x_n^j}{r_{ij}}
A_{ij} \exp (-\lambda_{ij} r_{ij})\\
+\partial_{x_n^i} f_A(r_{ij}) & = & \mu_{ij}
\frac{x_n^i - x_n^j}{r_{ij}}
B_{ij} \exp (-\mu_{ij} r_{ij}) \textrm{ .}
\end{eqnarray}
The angle $\theta_{ijk}$ can be expressed by the atom distances with the law of cosines:
\begin{eqnarray}
\end{eqnarray}
The angle $\theta_{ijk}$ can be expressed by the atom distances with the law of cosines:
\begin{eqnarray}