4.4 Cohesive Energy
81
4.4.3 Crystal Engineering
The success of the analyses by Kitaigorodskii [29, 30] described in Sect. 4.3.2 suggests that the effect of thermal agitation is not significant in many cases on structures
of molecular crystals, because crystallographic experiments are performed most often
at room temperature. Thus, we may expect that the minimization of intermolecular
interaction energy is a promising strategy to understand and/or even to design crystal
structure. Besides, the crystal structure is effectively the most fundamental basis for
understanding any physical properties of crystals. For example, the electronic properties of crystalline material are basically and well understood through the so-called
band theory. The same is true for molecular conductors [55, 56]. Furthermore, the
effects of thermal agitation are possibly taken into account based on crystal structures. In this respect, designing crystal structure is a key step in materials science not
only for fundamental aspects but also for applications. The term, crystal engineering
[57], is thus used while emphasizing this aspect.
For the search for the most stable crystal structure, the lattice energy is treated
as a function of structural parameters. There is no systematic way to cover all possibilities of arbitrary crystal structures. Usually, the number of atoms (molecules)
in a unit cell and the space group is a priori assumed. For molecular crystals, the
molecular geometries are also assumed when the identity of molecules is utilized in
such cases as the atom-atom potential method. At this point, there are two choices
about the molecular geometry, idealized one vs. one referring experimental data of
known or related compounds. Namely, concerning benzene, for example, which of
the sixfold or the inversion symmetry is more suitable for computation? Although
both have been used in literature, it is necessary to recognize where the assumed
atomic positions come from. The author thinks that the idealized geometry is better
than the experimental one. Finally, we must minimize the “energy” while taking
into account the potential energy for a flexible degree of motion, if the degree is
significantly flexible like the rotation around a single bond.
Once the lattice energy is expressed in terms of structural parameters within some
constraints (such as molecular geometry and space group), numerical minimization
can be performed in a standard way. For this purpose, some care is necessary for the
atom-atom potential of the Buckingham type (Eq. 1.65). Since this potential function
diverges to −∞ at r → +0, naïve and careless minimization of the lattice energy
may reach unphysical results (overlapping of atoms).
Practically, designing crystal packing becomes more manageable if we can identify a small number of strong intermolecular interactions. In this respect, the hydrogen
bonding, which is stronger than dispersion interactions, directional and saturable, is
often utilized.
We must keep in mind the following issues. First, there is no way to cover all
possible crystal structures. The ability of nature (a real molecular system) to search
a stable structure(s) is generally superior to a sophisticated computer, even if it is the
most advanced. Second, one needs to assess the “stability” of found structures unless
81
4.4.3 Crystal Engineering
The success of the analyses by Kitaigorodskii [29, 30] described in Sect. 4.3.2 suggests that the effect of thermal agitation is not significant in many cases on structures
of molecular crystals, because crystallographic experiments are performed most often
at room temperature. Thus, we may expect that the minimization of intermolecular
interaction energy is a promising strategy to understand and/or even to design crystal
structure. Besides, the crystal structure is effectively the most fundamental basis for
understanding any physical properties of crystals. For example, the electronic properties of crystalline material are basically and well understood through the so-called
band theory. The same is true for molecular conductors [55, 56]. Furthermore, the
effects of thermal agitation are possibly taken into account based on crystal structures. In this respect, designing crystal structure is a key step in materials science not
only for fundamental aspects but also for applications. The term, crystal engineering
[57], is thus used while emphasizing this aspect.
For the search for the most stable crystal structure, the lattice energy is treated
as a function of structural parameters. There is no systematic way to cover all possibilities of arbitrary crystal structures. Usually, the number of atoms (molecules)
in a unit cell and the space group is a priori assumed. For molecular crystals, the
molecular geometries are also assumed when the identity of molecules is utilized in
such cases as the atom-atom potential method. At this point, there are two choices
about the molecular geometry, idealized one vs. one referring experimental data of
known or related compounds. Namely, concerning benzene, for example, which of
the sixfold or the inversion symmetry is more suitable for computation? Although
both have been used in literature, it is necessary to recognize where the assumed
atomic positions come from. The author thinks that the idealized geometry is better
than the experimental one. Finally, we must minimize the “energy” while taking
into account the potential energy for a flexible degree of motion, if the degree is
significantly flexible like the rotation around a single bond.
Once the lattice energy is expressed in terms of structural parameters within some
constraints (such as molecular geometry and space group), numerical minimization
can be performed in a standard way. For this purpose, some care is necessary for the
atom-atom potential of the Buckingham type (Eq. 1.65). Since this potential function
diverges to −∞ at r → +0, naïve and careless minimization of the lattice energy
may reach unphysical results (overlapping of atoms).
Practically, designing crystal packing becomes more manageable if we can identify a small number of strong intermolecular interactions. In this respect, the hydrogen
bonding, which is stronger than dispersion interactions, directional and saturable, is
often utilized.
We must keep in mind the following issues. First, there is no way to cover all
possible crystal structures. The ability of nature (a real molecular system) to search
a stable structure(s) is generally superior to a sophisticated computer, even if it is the
most advanced. Second, one needs to assess the “stability” of found structures unless