From: hackbard <hackbard>
Date: Thu, 14 Sep 2006 15:27:55 +0000 (+0000)
Subject: hmmm ...
X-Git-Url: https://hackdaworld.org/gitweb/?a=commitdiff_plain;h=08f9c1435f017ec1f9202e0632cfb8989613e308;p=lectures%2Flatex.git

hmmm ...
---

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index 6d292e8..d3c91aa 100644
--- 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}) =
-  \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}
-\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}