diastereomers or enantiomers - THE ANSWER
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,
845 Page Mill Road,
Palo Alto,
CA 94304-1011,
U.S.A.
Tel. +1 (415) 424 9924 x110
FAX +1 (415) 424 9501
E-mail rgab(-(at)-)purisima.molres.org