Subject: diastereomers or enantiomers - THE ANSWER

From: "R.G.A. Bone" <[email-masked]>
Date: Mon, 25 Apr 94 14:09:34 -0700

On the question of comparing the energies of "diastereomers", I followed
the few publicly-posted answers and then the subsequent summary by Matthew
Stahl.  Although this discussion is now several days old, I believe that 
there is  something else to contribute;  I do not usually post answers
publically but in this case I think there would be interest.

Let us be very careful:

Suppose that our molecule has a single asymmetric centre; if we invert
at that centre and obtain the "enantiomer", then we have an energetically
equivalent structure.  That much we are all agreed upon.  This should
hopefully be irrespective of the force-field. One hopes that the Hamiltonian
is symmetric w.r.t. inversion of all particle coordinates 
[(x,y,z,) -> (-x,-y,-z)] and in any case, as has been pointed out, this
operation preserves inter-particle distances.  [By way of an aside, although
the traditional way of obtaining an enantiomer, is to 'reflect' in a plane,
as is well known, a reflection operation is the composite of inversion through
a center and a 2-fold rotation - neither of which alter the energy.]

But, what happens if 2 chiral centres are present?  (One may refer to a standard
text-book of  organic chemistry, e.g., March, if one is not familiar with the
terms enantiomer and 'diastereomer'.)  There are 4 possible isomers (assuming
that the two centres do not contain identical sets of substituents).

Now,  let us write them schematically:

     V           V                     V             V
     |           |                     |             |
   U-C-W       W-C-U                 U-C-W         W-C-U
     |           |                     |             |
   X-C-Z       Z-C-X                 Z-C-X         X-C-Z
     |           |                     |             |
     Y           Y                     Y             Y
 
     A           A'                    B             B'

Note that A and A' are enantiomers,   as are B and B'.

But the relationship of, say, A and B, is that they are diastereomers.  
"diastereomers are stereoisomers which are not enantiomers."

For all 4 of these structures, the 'bonded' interactions are the same, and 
on that basis they will have identical energies.   But it is the non-bonded
interactions which discriminate.  Note that the molecules A and A', in the
configurations shown all have V---Y, W---Z and U---X  _non-bonded_ interactions,
whereas the pair B and B' have   V---Y, U---Z and W---X non-bonded matches.
(You can 'rotate' each of the C(XYZ) or C(UVW) centres but you can't get the 
same set of triple pair-wise interactions.)

It is thus to be expected that the relative energies of diastereomers will
depend upon the nature of the force-field used.  Thus a very crude model,
which does not contain the longer-range, non-bonded interactions will not
distinguish energetically between diastereomers.

The message is thus that, when more than one chiral centre is present, 
inversion at a single centre introduces changes in long-range pair-wise
interactions which may well bea manifested in changes in the potential
energy.

Richard Bone

================================================================================

R. G. A. Bone.
Molecular Research Institute,
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