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Single Gaussian restraint

The pdf for a geometric feature $f$ (, distance, angle, dihedral angle) is

\begin{displaymath}
p = \frac{1}{\sigma \sqrt{2 \pi}} \exp \left[-\frac{1}{2}
\left(\frac{f-\bar{f}}{\sigma}\right)^2\right] \; .
\end{displaymath} (7.38)

A corresponding restraint $c$ in the sum that defines the objective function $F$ is
\begin{displaymath}
c = -\ln p = \frac{1}{2} \left(\frac{f-\bar{f}}{\sigma}\right)^2 -
\ln \frac{1}{\sigma \sqrt{2 \pi}}
\end{displaymath} (7.39)

The first derivatives with respect to feature $f$ are:

\begin{displaymath}
\frac{ \; {d}c}{ \; {d}f} = \frac{f-\bar{f}}{\sigma} \; \frac{1}{\sigma} \; .
\end{displaymath} (7.40)



Bozidar BJ Jerkovic 2001-12-21