7 Supramolecular, Hierarchical, and Energetical Interpretation …
131
display by molecular graphics Mercury. Thus, a side-view of a face affords a line. So,
two-fold helical assembly of the faces composes an assembly of the lines. When the
lines in front exhibit right-tilt alignment along the two-fold helical axis, the helical
assembly is right-handed (and vice versa). Now, such a visual and qualitative description has developed to a quantitative one according to three kinds of rotations along
a two-fold helical axis. These rotations bring about position-dependent chirality,
explaining the well-known fact that supramolecular chirality generates in molecular
assemblies composed of achiral molecules [32]. We can say that the conventional idea
focused on molecular chirality, but did not on supramolecular chirality in crystals.
7.6.2 Achiral Assemblies of Enantiomeric
and Diastereomeric Isomers
A combination of racemic (R, r)- and (S, s)-isomers forms an achiral (R, r)(S, s)dimer through inversion, reflection or glide operation. The operations are repeated to
form achiral 1D columns, which align toward achiral 2D layers, and further achiral
3D crystals.
The diastereomeric (R, r)(R, s)- or (S, s)(S, r)-dimer may be observed in organic
crystals. For example, pentacene [39] form crystals which belong to space group
P-1. It can be seen on display by Mercury that their dimers have parallel and Ttype arrangements, indicating the same ω values of the rotations around z-axis in
Fig. 7.5(c). As a result, the two-fold helix operations disappear and only inversion
operations remain. Namely, pentacene employs (ϕ, ψ, ω) = (16, 28, 22) for three
rotation angles and forms four kinds of position-dependent chiral isomers with (Dx,
Dy, Dz) as follows; (−90, 90, −22) for (R, r), (−90, 90, 22) for (R, s), (90, −90, −
22) for (S, r) and (90, −90, 22) for (S, s) (see Fig. 7.7d).
7.6.3 Diverse Diastereomers Regarding Position-Dependent
Chirality
In principle, it is possible that diastereomeric isomers are combined to yield other
achiral dimers, including an enantiomeric (R, s)(S, r)-dimer, a diastereomeric (R,
r)(S, r)- or (S, s)(R, s)-dimer. Symmetry operations do not describe these dimers, and
probably one might observe these dimers as two independent molecules in crystals.
It should be mentioned once more that the tilt rotation along y-axis in Fig. 7.5c
is limited to forward tilt (0° < ψ < 90°) in this article. If necessary, this can be
extended to backward tilt or reclination. This extension would make the discussion
more complex than that mentioned above.
131
display by molecular graphics Mercury. Thus, a side-view of a face affords a line. So,
two-fold helical assembly of the faces composes an assembly of the lines. When the
lines in front exhibit right-tilt alignment along the two-fold helical axis, the helical
assembly is right-handed (and vice versa). Now, such a visual and qualitative description has developed to a quantitative one according to three kinds of rotations along
a two-fold helical axis. These rotations bring about position-dependent chirality,
explaining the well-known fact that supramolecular chirality generates in molecular
assemblies composed of achiral molecules [32]. We can say that the conventional idea
focused on molecular chirality, but did not on supramolecular chirality in crystals.
7.6.2 Achiral Assemblies of Enantiomeric
and Diastereomeric Isomers
A combination of racemic (R, r)- and (S, s)-isomers forms an achiral (R, r)(S, s)dimer through inversion, reflection or glide operation. The operations are repeated to
form achiral 1D columns, which align toward achiral 2D layers, and further achiral
3D crystals.
The diastereomeric (R, r)(R, s)- or (S, s)(S, r)-dimer may be observed in organic
crystals. For example, pentacene [39] form crystals which belong to space group
P-1. It can be seen on display by Mercury that their dimers have parallel and Ttype arrangements, indicating the same ω values of the rotations around z-axis in
Fig. 7.5(c). As a result, the two-fold helix operations disappear and only inversion
operations remain. Namely, pentacene employs (ϕ, ψ, ω) = (16, 28, 22) for three
rotation angles and forms four kinds of position-dependent chiral isomers with (Dx,
Dy, Dz) as follows; (−90, 90, −22) for (R, r), (−90, 90, 22) for (R, s), (90, −90, −
22) for (S, r) and (90, −90, 22) for (S, s) (see Fig. 7.7d).
7.6.3 Diverse Diastereomers Regarding Position-Dependent
Chirality
In principle, it is possible that diastereomeric isomers are combined to yield other
achiral dimers, including an enantiomeric (R, s)(S, r)-dimer, a diastereomeric (R,
r)(S, r)- or (S, s)(R, s)-dimer. Symmetry operations do not describe these dimers, and
probably one might observe these dimers as two independent molecules in crystals.
It should be mentioned once more that the tilt rotation along y-axis in Fig. 7.5c
is limited to forward tilt (0° < ψ < 90°) in this article. If necessary, this can be
extended to backward tilt or reclination. This extension would make the discussion
more complex than that mentioned above.