Here's a simplistic mechanism that would probably benefit from using a GRT. It relies upon having a pre-ordered lookup table, here in the form of a simple space delimited string and the ordering is performed by the simple numerical comparision of the target position within the string.

#! perl -slw
use strict;

my $order = 'N CA C O CB CG CD1 CD2 CE1 CE2 CZ OH 2HB 3HB HD1 HD2 HE1 
+HE2 HH';


my @unordered = qw[ 2HB 3HB C CA CB CG CD1 CD2 CE1 CZ CE2 HE2 HE1 HH H
+D1 HD2 N O OH ];

print join' ', sort{ index( $order, $a ) <=> index( $order, $b ) } @un
+ordered;

__END__
P:\test>295668
N C CA O CB CG CD1 CD2 CE1 CE2 CZ OH 2HB 3HB HD1 HD2 HE1 HE2 HH
[download]

However, I suspect that you would like to not have to pre-construct the ordering of all possible compounds but would prefer their "weight" to be calculated according to your set of rules. That would be possible to do using a lookup hash mapping the symbols to weights and the some math to multiply by the number of hydrogens (terminology?).

To code this would require a clearer set of rules to work with. The only minor problem I see is parsing combined symbols -- do CA, CB, CD, CE, CZ break down into "C & A", "C & B"... etc. or are they intrinsic, but that is easily summountable.