74
4 Molecular Crystals
ing good packing. In this respect, close packing is the most important guideline for
understanding the structure of molecular crystals [29, 30].
Kitaigorodskii [29] performed analyses of possible space groups suitable for the
close packing (sixfold coordination within a layer) of a physically reasonable range
of molecular shape. He classified close-packed layers into closest-packed, limitingly
close-packed, and permissible ones. Here, the terminology for layers is: Closestpacked layers are layers that can be made no denser at a given molecular volume.
Limitingly close-packed layers (for a given symmetry) are closest-packed ones in
which a molecule occupies a special position, i.e., one in which the molecule retains
its inherent symmetry. Permissible layers are those that, while close-packed, are
neither closest-packed nor limitingly close-packed. Although his analyses are not
rigorous, the result is useful as a general background of understanding the structures
of molecular crystals. A full list can be found in his old book published originally in
1955.
Kitaigorodskii showed that molecular symmetry crucially affects the range of
available space groups. According to his analysis [29], the closest packing is allowed
only for P1, P2 1 , P2 1 /c, Pca, Pna, and P2 1 2 1 2 1 , if the molecule to crystallize has
no special symmetry (C 1 ). Note that the molecular symmetry under discussion is
one in the crystal but not of an isolated molecule. Thus, all space groups are available to achiral molecules. If the molecule is a chiral enantiomer, on the other hand,
only non-centrosymmetric space groups (P2 1 and P2 1 2 1 2 1 ) are allowed. The counterpart is necessary for a chiral molecule to complete the crystal packing for centrosymmetric space groups (P1, P2 1 /c, Pca, and Pna). Namely, only the racemic
mixture can crystallize with the closest packing. It is interesting to see that two
(P1, P2 1 /c) of centrosymmetric space groups are also favorable for centrosymmetric molecules. Reflecting this fact, these occupy significant parts in reported crystal
structures recorded in the Cambridge Crystallographic Data Centre [31], as seen in
Fig. 4.2. Not only them, all space groups in Fig. 4.2 were identified as favorable ones
by Kitaigorodskii. This fact indicates that his analyses caught some of the essential
features of structures of molecular crystals.
4.3.3 Polymorphism
When a molecule is merely a sphere as an argon atom, the only variable to characterize their relative geometry is the distance. In contrast, necessary for anisotropic
molecules are additional six variables, i.e., three Euler angles for each. Thus, a
possible “space” for a variety of molecular packing is vast for molecular crystals.
Some of these possible crystal structures really occur often. When plural crystalline
phases can exist under the same condition in equilibrium (typically at room temperature under the ambient pressure), each phase with a different crystal structure from
other(s) is called polymorph. The phenomenon of the presence of plural polymorphs
is termed as polymorphism. There is no limit on the number of possible polymorphs.
4 Molecular Crystals
ing good packing. In this respect, close packing is the most important guideline for
understanding the structure of molecular crystals [29, 30].
Kitaigorodskii [29] performed analyses of possible space groups suitable for the
close packing (sixfold coordination within a layer) of a physically reasonable range
of molecular shape. He classified close-packed layers into closest-packed, limitingly
close-packed, and permissible ones. Here, the terminology for layers is: Closestpacked layers are layers that can be made no denser at a given molecular volume.
Limitingly close-packed layers (for a given symmetry) are closest-packed ones in
which a molecule occupies a special position, i.e., one in which the molecule retains
its inherent symmetry. Permissible layers are those that, while close-packed, are
neither closest-packed nor limitingly close-packed. Although his analyses are not
rigorous, the result is useful as a general background of understanding the structures
of molecular crystals. A full list can be found in his old book published originally in
1955.
Kitaigorodskii showed that molecular symmetry crucially affects the range of
available space groups. According to his analysis [29], the closest packing is allowed
only for P1, P2 1 , P2 1 /c, Pca, Pna, and P2 1 2 1 2 1 , if the molecule to crystallize has
no special symmetry (C 1 ). Note that the molecular symmetry under discussion is
one in the crystal but not of an isolated molecule. Thus, all space groups are available to achiral molecules. If the molecule is a chiral enantiomer, on the other hand,
only non-centrosymmetric space groups (P2 1 and P2 1 2 1 2 1 ) are allowed. The counterpart is necessary for a chiral molecule to complete the crystal packing for centrosymmetric space groups (P1, P2 1 /c, Pca, and Pna). Namely, only the racemic
mixture can crystallize with the closest packing. It is interesting to see that two
(P1, P2 1 /c) of centrosymmetric space groups are also favorable for centrosymmetric molecules. Reflecting this fact, these occupy significant parts in reported crystal
structures recorded in the Cambridge Crystallographic Data Centre [31], as seen in
Fig. 4.2. Not only them, all space groups in Fig. 4.2 were identified as favorable ones
by Kitaigorodskii. This fact indicates that his analyses caught some of the essential
features of structures of molecular crystals.
4.3.3 Polymorphism
When a molecule is merely a sphere as an argon atom, the only variable to characterize their relative geometry is the distance. In contrast, necessary for anisotropic
molecules are additional six variables, i.e., three Euler angles for each. Thus, a
possible “space” for a variety of molecular packing is vast for molecular crystals.
Some of these possible crystal structures really occur often. When plural crystalline
phases can exist under the same condition in equilibrium (typically at room temperature under the ambient pressure), each phase with a different crystal structure from
other(s) is called polymorph. The phenomenon of the presence of plural polymorphs
is termed as polymorphism. There is no limit on the number of possible polymorphs.