2.1 Molecular Structure
7
interaction including dispersion force with typical adsorption energy of the order
10–20 kJ/mol. Also note that in the “adsorption science” it is rather usual to use the
energy unit of kJ/mol (= 1.036 × 10
−2 eV = 3.809 × 10
−4 hartree). These analyses
would be useful to obtain the information on H 2 molecule storage for miscellaneous
purposes such as hydrogen source for fuel cells.
Hydrogen bond is universally seen in weakly associated molecules utilizing
hydrogen atoms bonded to electronegative atoms, such as N, O, or F, being particularly crucial in biomolecules. In Fig. 2.4b is shown an example consisting of a
dimeric form of formic acids with a water molecule (Krishnakumar and Maity 2017)
employing the DFT/ωB97X-D/aug-cc-pVDZ scheme. This system is regarded as
the simplest example of microhydrated cluster of carboxylic acids. Calculated free
energy of formation for the association of this cluster consisting of three hydrogen
bonds at 100 K and low pressure (μTorr order) is −16.4 kcal/mol signifying a
hydrogen-bond energy of 5.47 kcal/mol (=22.9 kJ/mol) in average. The hydrogenbond energy is usually slightly larger than the van der Waals interaction energy
mentioned above. For the supermolecules partly consisting of weak interaction such
as van der Waals interactions or hydrogen bonds as mentioned above, one had better
employ the calculation scheme such as ωB97X-D, APF-D, or CCSD(T) also applicable to these weak interactions rather than the HF or DFT/B3LYP method suitable
to the ordinary covalent bonds (see Sects. 3.1 and 3.2).
Case (3) in the above might be rather rare but can happen in the design of unsynthesized molecules or when one deals with molecule the structure of which is completely
unknown. In the former case, one could examine the stability against deformation
of the structure of the target molecule by the structural optimization process. In the
latter case, one ought to collect the experimental (spectroscopic) data such as infrared
(IR) and nuclear magnetic resonance (NMR) data of the actual molecule in order to
infer its structure. For the both cases, one might have to assume more than two plausible molecular structures and to perform the optimization starting from each initial
geometry and compare the total energy values obtained.
In the following several examples of the optimized molecular structures are actually to be given. The optimized structure of a well-known benzene molecule C 6 H 6 is
shown in Fig. 2.5a. However, when one did not know the benzene structure but only
knew the chemical composition C 6 H 6 , there can be several isomers as in Fig. 2.5b–f,
each of whose energy could correspond to the local minimum point on the whole PES.
In the most stable benzene with the D 6h symmetry, its internal degrees of freedom
or, in other words, the numbers of variables are essentially two, signifying the C–C
and the C–H bond lengths.
Similarly, history of clarification of the optimized structure of buckminsterfullerene, C 60 , is somewhat of interest. The original experimental report of preparation of C 60 showed that its mass is 720 and only gave a suggestion that this molecule
would be a cluster-shape polygon with 60 carbon atoms at the vertices of a truncated
icosahedron with I h symmetry (Kroto et al. 1985). This hypothesis has actually
been confirmed by the
13 C NMR measurement showing a single line (Taylor et al.
1990). Hence the early intuitive suggestion was indeed correct and C 60 has the caged
I h symmetry eventually with two kinds of C–C bonds as shown in Fig. 2.6a and
7
interaction including dispersion force with typical adsorption energy of the order
10–20 kJ/mol. Also note that in the “adsorption science” it is rather usual to use the
energy unit of kJ/mol (= 1.036 × 10
−2 eV = 3.809 × 10
−4 hartree). These analyses
would be useful to obtain the information on H 2 molecule storage for miscellaneous
purposes such as hydrogen source for fuel cells.
Hydrogen bond is universally seen in weakly associated molecules utilizing
hydrogen atoms bonded to electronegative atoms, such as N, O, or F, being particularly crucial in biomolecules. In Fig. 2.4b is shown an example consisting of a
dimeric form of formic acids with a water molecule (Krishnakumar and Maity 2017)
employing the DFT/ωB97X-D/aug-cc-pVDZ scheme. This system is regarded as
the simplest example of microhydrated cluster of carboxylic acids. Calculated free
energy of formation for the association of this cluster consisting of three hydrogen
bonds at 100 K and low pressure (μTorr order) is −16.4 kcal/mol signifying a
hydrogen-bond energy of 5.47 kcal/mol (=22.9 kJ/mol) in average. The hydrogenbond energy is usually slightly larger than the van der Waals interaction energy
mentioned above. For the supermolecules partly consisting of weak interaction such
as van der Waals interactions or hydrogen bonds as mentioned above, one had better
employ the calculation scheme such as ωB97X-D, APF-D, or CCSD(T) also applicable to these weak interactions rather than the HF or DFT/B3LYP method suitable
to the ordinary covalent bonds (see Sects. 3.1 and 3.2).
Case (3) in the above might be rather rare but can happen in the design of unsynthesized molecules or when one deals with molecule the structure of which is completely
unknown. In the former case, one could examine the stability against deformation
of the structure of the target molecule by the structural optimization process. In the
latter case, one ought to collect the experimental (spectroscopic) data such as infrared
(IR) and nuclear magnetic resonance (NMR) data of the actual molecule in order to
infer its structure. For the both cases, one might have to assume more than two plausible molecular structures and to perform the optimization starting from each initial
geometry and compare the total energy values obtained.
In the following several examples of the optimized molecular structures are actually to be given. The optimized structure of a well-known benzene molecule C 6 H 6 is
shown in Fig. 2.5a. However, when one did not know the benzene structure but only
knew the chemical composition C 6 H 6 , there can be several isomers as in Fig. 2.5b–f,
each of whose energy could correspond to the local minimum point on the whole PES.
In the most stable benzene with the D 6h symmetry, its internal degrees of freedom
or, in other words, the numbers of variables are essentially two, signifying the C–C
and the C–H bond lengths.
Similarly, history of clarification of the optimized structure of buckminsterfullerene, C 60 , is somewhat of interest. The original experimental report of preparation of C 60 showed that its mass is 720 and only gave a suggestion that this molecule
would be a cluster-shape polygon with 60 carbon atoms at the vertices of a truncated
icosahedron with I h symmetry (Kroto et al. 1985). This hypothesis has actually
been confirmed by the
13 C NMR measurement showing a single line (Taylor et al.
1990). Hence the early intuitive suggestion was indeed correct and C 60 has the caged
I h symmetry eventually with two kinds of C–C bonds as shown in Fig. 2.6a and