18
1 Molecules and Intermolecular Interactions
1.2.5 Practical Representation
1.2.5.1 First-Principle Computation
The fundamental physics that describes the behavior of molecules has long been
established as the quantum mechanics, and numerous recipes to numerically solve
the fundamental equations (wave equations) have been proposed. Besides, significant progress in computers was achieved in the past. Intermolecular interaction for
a specific configuration for a molecular pair is an easy task for a modern computer.
The most faithful way to follow quantum mechanics is to perform first-principle
(quantum-chemical) calculations for every configuration upon necessity. Such computation may be possible but impractical in most cases. Alternatively, a prior construction of the intermolecular potential function, i.e., an approximation to the computed
energy using some analytical functions, is more practical. In this case, computation is
also necessary for a large number of configurations, i.e., combinations of molecular
orientations and separations.
1.2.5.2 Atom–Atom Potential Method
Molecules are generally nonspherical. Any model of intermolecular interaction
between them should reflect this anisotropy. Since the anisotropy of molecular shape
is certainly based on atomic arrangements, it is naïve to assume that intermolecular
interaction is expressed as a sum of interatomic interactions. This way of presenting
intermolecular interaction is called the atom–atom potential method. It is, however,
rather evident that the method has some problems for aromatic molecules that bear
π-electrons spreading over many atoms. Indeed, a somewhat stronger interaction
resulting in the stacking of planar aromatic molecules has been identified as the π–π
interaction, though it is essentially the dispersion interaction. Note that atoms in a
molecule are not conceptually straightforward and require theoretical development
in quantum theory [8], in contrast to naïve intuition.
In the atom–atom potential method, the intermolecular interaction between
molecules 1 and 2 is expressed as
V 12 =
(i, j)
v(i, j)
(1.62)
where the summation is over atomic pairs, of which atom i is chosen from molecule
1 and atom j from molecule 2. The interatomic potential is usually assumed as a
function of their distance r i j and atomic species. Taking asymptotic forms of attractive
and repulsive parts of interaction into account, one of the most often assumed forms
of the interatomic potential function is
1 Molecules and Intermolecular Interactions
1.2.5 Practical Representation
1.2.5.1 First-Principle Computation
The fundamental physics that describes the behavior of molecules has long been
established as the quantum mechanics, and numerous recipes to numerically solve
the fundamental equations (wave equations) have been proposed. Besides, significant progress in computers was achieved in the past. Intermolecular interaction for
a specific configuration for a molecular pair is an easy task for a modern computer.
The most faithful way to follow quantum mechanics is to perform first-principle
(quantum-chemical) calculations for every configuration upon necessity. Such computation may be possible but impractical in most cases. Alternatively, a prior construction of the intermolecular potential function, i.e., an approximation to the computed
energy using some analytical functions, is more practical. In this case, computation is
also necessary for a large number of configurations, i.e., combinations of molecular
orientations and separations.
1.2.5.2 Atom–Atom Potential Method
Molecules are generally nonspherical. Any model of intermolecular interaction
between them should reflect this anisotropy. Since the anisotropy of molecular shape
is certainly based on atomic arrangements, it is naïve to assume that intermolecular
interaction is expressed as a sum of interatomic interactions. This way of presenting
intermolecular interaction is called the atom–atom potential method. It is, however,
rather evident that the method has some problems for aromatic molecules that bear
π-electrons spreading over many atoms. Indeed, a somewhat stronger interaction
resulting in the stacking of planar aromatic molecules has been identified as the π–π
interaction, though it is essentially the dispersion interaction. Note that atoms in a
molecule are not conceptually straightforward and require theoretical development
in quantum theory [8], in contrast to naïve intuition.
In the atom–atom potential method, the intermolecular interaction between
molecules 1 and 2 is expressed as
V 12 =
(i, j)
v(i, j)
(1.62)
where the summation is over atomic pairs, of which atom i is chosen from molecule
1 and atom j from molecule 2. The interatomic potential is usually assumed as a
function of their distance r i j and atomic species. Taking asymptotic forms of attractive
and repulsive parts of interaction into account, one of the most often assumed forms
of the interatomic potential function is