Regarding the concatenations, my implementation has several differences with respect to your original proposal:

• The real coordinates are normalized by dividing by the cutoff (which is relatively small), and rounded to the next lower integer (i.e., floored). The "concatenation" is numerical; $n = 1000000*$x + 1000*$y + $z + 500500500. Problem here: I'm assuming that the entire system is within +/- 500*$cutoff. I'll have to fix that somehow.
• I use a hash to store the atoms. Each "bucket" ($hash{$n}) may contain more than one atom (usually 1-4), so it's actually an array reference. Atoms are Chemistry::Atom objects, which know their own symbol, name, real coordinates, etc.
• The buckets don't need to be sorted; I just loop for each of them, and then check for bonds with the N^2 algorithm within the bucket (remember N is small), and then check for bonds with the atoms in the neighboring buckets (this requires N*M checks if there are M atoms in the neighbor). "Neighbor" is defined in a way that avoids counting the same pair twice.

Note: the neighbors of $n are $n+1, $n+1000, $n+1000000, etc., for a total of 13 neighbors (a cube is surrounded by 26 cubes, but you only need half of them to avoid counting twice)

When you said "based on your post", you should have prefixed it with "loosely" :)

I'm not sure that I fully understand the details of what you are doing. Maybe I'll pull the module and take a looksee if the code and POD clarifies anything. Note: It's not your description that is lacking, just my knowledge of the actual application.

If the idea adapts to something useful, it's the best reward one can ask for. Thanks for mentioning it:)

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Examine what is said, not who speaks.

"Efficiency is intelligent laziness." -David Dunham
"Think for yourself!" - Abigail