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

From: <[email-masked]>
Date: Tue, 22 Jul 1997 16:07:27 -0400 (EDT)

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
<[email-masked]>