Next: Parameters
Up: Angular Correlation
Previous: Angular Correlation
  Contents
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
,
,
using the following scheme:
-
where
and
are respectively the normalized vectors along (a1,a2)
and (a1,a3) directions.
is defined as the clockwise normal vector orthogonal to
that belongs to the plane
defined by a1, a2 and a3 atoms
-
Thus, one can define the following autocorrelation functions for the vectors
,
and
defined on triplet t:
 |
(4.34) |
And the angular correlation averaged over all triplets is:
 |
(4.35) |
where
is the number of selected triplets.
Next: Parameters
Up: Angular Correlation
Previous: Angular Correlation
  Contents
pellegrini eric
2009-10-06