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Theory and implementation
The SD can be seen as an generalization of the pair distribution function. Indeed, pair distribution functions are defined
as orientionally averaged distribution functions. are in the sense that, Altough these correlation functions reflects many
key features of the short-range order in molecular systems, it should be realized that an average spatial assembly of
non-spherical particles can not be uniquely characterized from these one-dimensionals functions. So, structural models
postulated for the molecular ordering in nonsimple systems based only on one-dimensional PDF will always be somewhat
ambiguous. The goal of SD analysis is to provide greater clarity in the structual analysis of molecular systems by utilizing
distribution function which span both the radial and angular coordinates of the separation vector. This can provide useful
information about the average local structure in a complex system.
nMOLDYN allows one to compute the SD in spherical coordinates on a set of concentrics shells surrounding the centers of
mass of selected triplets of atoms using the formula:
 |
(4.194) |
where
and
are respectively the number of triplets and groups,
,
and
are the spherical coordinates at which the SD is evaluated,
,
and
are respectively the number of discrete r,
and
values and
is the number of group of atoms of type g whose centers of mass is found
to be in the volume element defined by
,
and
in the
spherical coordinates basis centered on the center of mass of triplet t.
So technically, nMOLDYN proceeds more or less on the following way:
- defines the center of mass
for each triplet of atoms,
- defines the center of mass
for each group of atoms,
- constructs an oriented orthonormal basis
centered on each
, this
basis is defined from the three vectors
,
,
,
-
where
and
are respectively the normalized vectors in (a1,a2)
and (a1,a3) directions where (a1,a2,a3) are the three atoms of the triplet t,
is defined as the clockwise normal vector orthogonal to
that belongs to the plane
defined by a1, a2 and a3 atoms,
-
- expresses the cartesian coordinates of each
in each
,
- transforms these coordinates in spherical coordinates,
- discretizes the spherical coordinates in
,
and
,
- does
.
Next: Parameters
Up: Spatial Density
Previous: Spatial Density
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pellegrini eric
2009-10-06