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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 , , 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