144
S. Tsuzuki
hydrogen bond of water dimer (about −5 kcal/mol). The interaction energy with
parallel adjacent molecule was calculated as −3.62 kcal/mol. These results show that
there exists strong attraction not only between the tilted T-shape adjacent molecules,
but also between the parallel adjacent molecules, although there is no short atom–
atom contact between the parallel adjacent molecules.
The HF level (HF/6-311G**) interaction energies (E HF ) between the tilted Tshape adjacent molecules and between the parallel adjacent molecules are 3.31 and
0.41 kcal/mol, respectively, as summarized in Table 8.2. The HF method cannot
evaluate the dispersion interactions, therefore the contributions of the dispersion
interactions (E disp ) can be estimated approximately by subtracting E HF from E B97D
as shown in Eq. 8.2.
E disp = E B97D −E HF
(8.2)
The contributions of the dispersion interactions (E disp ) calculated for the interactions between the tilted T-shape and parallel adjacent molecules are −8.14 and −
4.03 kcal/mol, respectively (Table 8.2). The contributions of the dispersion interactions are significant. The calculated positive values of E HF suggest that the contributions of the electrostatic interactions to the attractions are not large, since the
attraction by the electrostatic interactions can be evaluated by the HF calculations.
These calculations show that the dispersion interactions are the major source of the
attraction between adjacent naphthalene molecules in the crystal. Although there is
no short atom–atom contact between parallel adjacent molecules, there exists strong
attraction by the dispersion interactions. This indicates that the strong attraction
between parallel adjacent molecules due to the dispersion interactions will be overlooked, if the intermolecular interactions in the crystal are discussed based solely on
the presence of short atom–atom contact in crystals.
8.5 Intermolecular Interactions of Other Polycyclic
Aromatic Molecules
Not only in the crystal of naphthalene, but also in the crystals of other polycyclic
aromatic molecules, there exist strong attraction between adjacent molecules. The
intermolecular interaction energies between parallel adjacent molecules in the crystals of anthracene, tetracene, pentacene, and pyrene (Fig. 8.6) were calculated by
the dispersion-corrected DFT method (B97D/6-311G**) and by HF method (HF/6311G**) The calculated interaction energies (E B97D and E HF ) are summarized in
Table 8.3. Although there is no short atom–atom contact between the parallel adjacent
molecules in these crystals, there exists strong attraction.
As the number of aromatic rings increases, the magnitude of the intermolecular
interaction (E B97D ) increases. The intermolecular interaction energy between parallel
adjacent pentacene molecules is −9.68 kcal/mol, and that for parallel adjacent pyrene
S. Tsuzuki
hydrogen bond of water dimer (about −5 kcal/mol). The interaction energy with
parallel adjacent molecule was calculated as −3.62 kcal/mol. These results show that
there exists strong attraction not only between the tilted T-shape adjacent molecules,
but also between the parallel adjacent molecules, although there is no short atom–
atom contact between the parallel adjacent molecules.
The HF level (HF/6-311G**) interaction energies (E HF ) between the tilted Tshape adjacent molecules and between the parallel adjacent molecules are 3.31 and
0.41 kcal/mol, respectively, as summarized in Table 8.2. The HF method cannot
evaluate the dispersion interactions, therefore the contributions of the dispersion
interactions (E disp ) can be estimated approximately by subtracting E HF from E B97D
as shown in Eq. 8.2.
E disp = E B97D −E HF
(8.2)
The contributions of the dispersion interactions (E disp ) calculated for the interactions between the tilted T-shape and parallel adjacent molecules are −8.14 and −
4.03 kcal/mol, respectively (Table 8.2). The contributions of the dispersion interactions are significant. The calculated positive values of E HF suggest that the contributions of the electrostatic interactions to the attractions are not large, since the
attraction by the electrostatic interactions can be evaluated by the HF calculations.
These calculations show that the dispersion interactions are the major source of the
attraction between adjacent naphthalene molecules in the crystal. Although there is
no short atom–atom contact between parallel adjacent molecules, there exists strong
attraction by the dispersion interactions. This indicates that the strong attraction
between parallel adjacent molecules due to the dispersion interactions will be overlooked, if the intermolecular interactions in the crystal are discussed based solely on
the presence of short atom–atom contact in crystals.
8.5 Intermolecular Interactions of Other Polycyclic
Aromatic Molecules
Not only in the crystal of naphthalene, but also in the crystals of other polycyclic
aromatic molecules, there exist strong attraction between adjacent molecules. The
intermolecular interaction energies between parallel adjacent molecules in the crystals of anthracene, tetracene, pentacene, and pyrene (Fig. 8.6) were calculated by
the dispersion-corrected DFT method (B97D/6-311G**) and by HF method (HF/6311G**) The calculated interaction energies (E B97D and E HF ) are summarized in
Table 8.3. Although there is no short atom–atom contact between the parallel adjacent
molecules in these crystals, there exists strong attraction.
As the number of aromatic rings increases, the magnitude of the intermolecular
interaction (E B97D ) increases. The intermolecular interaction energy between parallel
adjacent pentacene molecules is −9.68 kcal/mol, and that for parallel adjacent pyrene