Insight II [MSI] periodic cell correl. f's

[<mckennam' at \`curie.ml.wpafb.af.mil>]

 	I'm looking for people who are pretty familiar with MSI's
 	Insight II application, especially the Amorphous Cell module,
 	*OR* who are familiar with how correlation functions are
 	computed on periodic systems for chemical research.
 	I am trying to reproduce some Insight output, and failing.
 My Problem (in brief):
 --------------------
     I wrote a program to compute pair and orientational correlation
 functions from molecular conformations (e.g., PDB files.)  To test it,
 I use Insight II to compute the same functions for the same
 conformations.
     When I compare the functions using *NON* periodic systems, I
 get the same answers.
     When I compare them using *PERIODIC* systems, our functions
 agree  FOR SEPARATION DISTANCES (r) LESS THAN SOME RADIUS (r_a)
 (r_a is a bit more than 1/2 the smallest period.) For larger "r"
 values, our functions sometimes agree, but sometimes my pair
 correlation function is larger.  (Mine is never smaller.)
 My program appears to be finding more pairs of atoms than Insight.
 When computing the orientational correlation, the results are
 also consistent with my program finding more pairs than
 Insight for r > r_a.
     I need to know (a) if Insight II is doing something unexpected,
 and/or (b) whether my idea of how to handle periodic systems is
 corect (see below.)
     [Yes, I have contacted MSI about this.  They don't appear eager
     to invest much effort in getting to the bottom of it, which is
     understandable, since it could be my bug or mistake.]
 How I Handle Periodic Systems  (or, "Is This Correct?")
 -----------------------------
     For non-periodic systems, I consider all pairs of atoms with
 one atom chosen from subset A and one from B.
     For periodic systems, I consider subset B to also include
 images of atoms chosen from subset B, i.e., for each "parent" position
 in B, I also consider "image" positions of the form
     (image pos.) = (parent pos.) + i*v1 + j*v2 + k*v3
 where v1, v2, and v3 are the image, or "periodicity" vectors (each has
 the same length and direction as an edge of the periodic cell)
 and i, j, and k are arbitrary integers.
     Since "arbitrary" i, j, and k would produce an infinite number
 of pairs, I use the fact that we are not interested in pairs with
 separation (r) more than some r_max, and compute a crude
 upper bound for |i|, |j|, and |k| , so we start with a finite
 number of pairs.  (Later on, we throw away the remaining pairs that have
 r > r_max.)
     As far as I can see, as long as the upper bounds are large enough,
 I should get all possible pairs with r < r_max.  Any mistakes should
 result in my leaving out a pair I should have.  Such mistakes
 would not have the effect that I see -- me getting more pairs than
 Insight.
 Conclusion
 ----------
     Please send me any specific suggestions, questions, etc., via
 E-mail, and I will summarize what I find out.
 ------------------------------------------------------------------------
 Alan McKenney
 Wright-Patterson AFB, Dayton, OH
 <mckennam' at \`curie.ml.wpafb.af.mil>