4
1 Molecules and Intermolecular Interactions
1.1.2 Molecular World
It is evident from Table 1.1 that the energy involved in a nuclear reaction is much
larger than those of other phenomena. The separation of the process from other
processes is almost complete, accordingly. Nuclear synthesis (syntheses of elements
below nickel) proceeds in stars. Indeed, the pressure and temperature at the solar
core are, respectively, 2.5 · 10
11 atm and 1.5 · 10
7 K, the thermal energy of the latter
amounts to ca. 1.3 keV. Although this energy is still smaller than the binding energies
of atomic nuclei, the extreme density caused by the high pressure facilitates the
synthesis of helium nuclei from protons. Under the complete separation in the energy
scale, any low-energy process is almost impossible to affect the nuclear process. This
separation is the basis of the possibility of chemistry, a science of the diversity and
“inhomogeneity” of the materials world.
Note that the relevant energy to be compared with average translational energy,
i.e., thermal energy, is not biding energies but the energy barrier to be overcome
necessary for nuclear reactions. A similar situation is also encountered in molecular
syntheses.
The ignorance of nuclear reaction automatically offers a way of understanding
materials based on atoms. This is the way traditionally developed in condensed
matter physics, and certainly possible. However, for example, in the interpretation of
temperature dependence of heat capacity of crystals, the analysis in this way assuming
the number of atoms in a unit cell yields a high characteristic temperature (Debye
temperature described in Sect. 5.5.1), which is practically useless because of too
high value in comparison with melting temperatures. Although the separation in the
energy scale is not complete in contrast with the above case, the energies of electronic
processes such as ionization and formation of chemical bonds involve larger energy
by, at least, about one order of magnitude than intermolecular interactions. Thus, it
is reasonable and even better to consider this separation for understanding molecular
materials. Indeed, returning to the example of heat capacity, we can readily explain
even an apparent saturation of heat capacity to 6R if the number of degrees of freedom
is adequately assumed (such as 6 for a rigid molecule).
The last case exemplifies the benefit of the understanding of materials based on
the molecular description. In some cases, this is done by replacing “atoms” with
“molecules.” For example, in discussing electronic or magnetic properties of molecular systems (molecular conductor and magnet), their properties are interpreted based
on a complicated (and often anisotropic) arrangement of sites. On the other hand,
such a replacement cannot work for, for example, the issue of melting. The intrinsic
difference between atoms and molecules lies in the necessity to take their anisotropy
into account (except for cases of monatomic molecules, i.e., rare gasses). A partial
melting, e.g., the melting of solely the positional degrees of freedom but the orientational ones, is only possible in cases of crystals consisting of molecules because
atoms have no rotational degrees of freedom detectable from the outside. The possibility of molecular deformation is also an intrinsic difference. The main body of this
1 Molecules and Intermolecular Interactions
1.1.2 Molecular World
It is evident from Table 1.1 that the energy involved in a nuclear reaction is much
larger than those of other phenomena. The separation of the process from other
processes is almost complete, accordingly. Nuclear synthesis (syntheses of elements
below nickel) proceeds in stars. Indeed, the pressure and temperature at the solar
core are, respectively, 2.5 · 10
11 atm and 1.5 · 10
7 K, the thermal energy of the latter
amounts to ca. 1.3 keV. Although this energy is still smaller than the binding energies
of atomic nuclei, the extreme density caused by the high pressure facilitates the
synthesis of helium nuclei from protons. Under the complete separation in the energy
scale, any low-energy process is almost impossible to affect the nuclear process. This
separation is the basis of the possibility of chemistry, a science of the diversity and
“inhomogeneity” of the materials world.
Note that the relevant energy to be compared with average translational energy,
i.e., thermal energy, is not biding energies but the energy barrier to be overcome
necessary for nuclear reactions. A similar situation is also encountered in molecular
syntheses.
The ignorance of nuclear reaction automatically offers a way of understanding
materials based on atoms. This is the way traditionally developed in condensed
matter physics, and certainly possible. However, for example, in the interpretation of
temperature dependence of heat capacity of crystals, the analysis in this way assuming
the number of atoms in a unit cell yields a high characteristic temperature (Debye
temperature described in Sect. 5.5.1), which is practically useless because of too
high value in comparison with melting temperatures. Although the separation in the
energy scale is not complete in contrast with the above case, the energies of electronic
processes such as ionization and formation of chemical bonds involve larger energy
by, at least, about one order of magnitude than intermolecular interactions. Thus, it
is reasonable and even better to consider this separation for understanding molecular
materials. Indeed, returning to the example of heat capacity, we can readily explain
even an apparent saturation of heat capacity to 6R if the number of degrees of freedom
is adequately assumed (such as 6 for a rigid molecule).
The last case exemplifies the benefit of the understanding of materials based on
the molecular description. In some cases, this is done by replacing “atoms” with
“molecules.” For example, in discussing electronic or magnetic properties of molecular systems (molecular conductor and magnet), their properties are interpreted based
on a complicated (and often anisotropic) arrangement of sites. On the other hand,
such a replacement cannot work for, for example, the issue of melting. The intrinsic
difference between atoms and molecules lies in the necessity to take their anisotropy
into account (except for cases of monatomic molecules, i.e., rare gasses). A partial
melting, e.g., the melting of solely the positional degrees of freedom but the orientational ones, is only possible in cases of crystals consisting of molecules because
atoms have no rotational degrees of freedom detectable from the outside. The possibility of molecular deformation is also an intrinsic difference. The main body of this