4.1. The insufficiency of scalar measures for determining
chirality and distinguishing stereoisomers
Note we use the subscript “a” for the S and R
stereoisomers of glycine because glycine is formally achiral and the
stereoisomers are produced by the symmetry breaking effects of the
introduction of the D and T isotopomers to the alpha carbon (C1), where
the CIP rules were used to allocate the Sa and
Ra designations, see Scheme 1 . The variation of
the (scalar) energies ∆E, BPL and ellipticity values ε relative
to θ = 0.0º, corresponding to the relaxed geometry of glycine, of the CW
(-180.0º ≤ θ ≤ 0.0º) and CCW (0.0º ≤ θ ≤ 180.0º) torsions associated
with the C1-C2 BCP for the pure glycine and singly deuterated and
triterated glycine do not distinguish the isotopomers, seeFigure 1(a-b) . The corresponding results for the C1-N7BCP display a high degree of asymmetry with respect to the
torsion θ, but do not distinguish between the isotopomers, seeFigure 1(c-d) . The variation of the energies ∆E relative
to θ = 0.0º, associated with the C1-N7 BCP and C1-C2 BCP ,
demonstrates the greater strength of interaction of the C1-N7 BCPcompared to the C1-C2 BCP , compare the left panels ofFigure 1(a-b) with those of Figure 1(c-d) . These
include the distance measures for a torsion θ = 0.0º that indicate that
the C1-N7 BCP is closer to the C1 atom (1.198 a.u.) than the
C1-C2 BCP (1.393 a.u.). This asymmetry in the location of theBCP along the C1-N7 BCP bond-path leads to an asymmetry of
the variation of the BPL, see the middle panels of Figure
1(c-d) and the BCP ellipticity ε, see the rights panels ofFigure 1(c-d) with the CCW and CW torsions. In particular, the
lower values of the C1-N7 BCP ellipticity ε for the CCW (0.0º ≤ θ
≤ 180.0º) torsion compared to the CW (-180.0º ≤ θ ≤ 0.0º) torsion
indicate a preference for the CCW torsion over the CW torsion. This is
because a bond with lower ellipticity ε values, e.g. single bonds, will
undergo a torsion deformation more readily than bonds with a higher
ellipticity ε value, as is the case for double bonds. The symmetrical
location of the C1-C2 BCP mid-way along the associated bond-path
results in symmetrical variations of the BPL and the ellipticity ε with
the CCW and CW torsions and hence no preferred direction of torsion, CCW
or CW, is indicated.
Considering the limitations of the scalar BCP ellipticity ε in
determining preferences of CCW over CW for the C1-C2 BCP , we now
proceed to examine the directional differences between the CCW and CW
torsions of the torsional C1-N7 BCP and C1-C2 BCP with the
vector-based stress tensor trajectories Tσ(s), seeFigure 1(c) and Figure 1(d) respectively. TheBCP ellipticity ε does not take into account the bond-path
eigenvector (e3σ ) and therefore cannot
quantify torsional CCW vs. CW preferences for a symmetrically positioned
C1-C2 BCP , see Figure 1(a-d) .