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Theory and implementation

The angular correlation analysis computes the autocorrelation of a set of vectors describing the extent of a molecule in three orthogonal directions. This kind of analysis can be useful when trying to highlight the fact that a molecule is constrainted in a given direction.

For a given triplet of non-colinear atoms g=(a1,a2,a3), one can derive an orthonormal set of three vectors ${\bf v}_1$, ${\bf v}_2$, ${\bf v}_3$ using the following scheme:

Thus, one can define the following autocorrelation functions for the vectors ${\bf v}_1$, ${\bf v}_2$ and ${\bf v}_3$ defined on triplet t:

\begin{displaymath}
AC_{g,i} (t) = \langle {\bf v}_{t,i}(0)\cdot{\bf v}_{t,i}(t)\rangle, \qquad i = 1,2,3
\end{displaymath} (4.34)

And the angular correlation averaged over all triplets is:

\begin{displaymath}
AC_i(t) = \sum_{g=1}^{N_{triplets}} AC_{g,i}(t), \qquad i = 1,2,3
\end{displaymath} (4.35)

where $N_{triplets}$ is the number of selected triplets.


next up previous contents
Next: Parameters Up: Angular Correlation Previous: Angular Correlation   Contents
pellegrini eric 2009-10-06