20
1 Molecules and Intermolecular Interactions
considering the meaning of σ as an atomic diameter.
In some cases, it is necessary to take electrostatic interactions into account. This
is undoubtedly the case for polar molecules. The electrostatic interactions are also
divided into interatomic contributions by assigning partial charges to atoms. This
way is adequate and more accessible than a sophisticated multipole expansion. The
partial charges may be assigned based on either of the quantum-chemical calculation
of an isolated molecule or kinds of fitting together with other coefficients. The former
poses some difficulty in the transferability of potential functions. Anyway, potential
functions with the contribution of (bare) charges, q i and q j , becomes
v(r i j ) = A
σ
r i j
12
− B
σ
r i j
6
+
1
4ππ 0
q i q j
r i j
(1.71)
or
v(r i j ) = a exp
−
r i j
σ
− b
σ
r i j
6
+
1
4ππ 0
q i q j
r i j
.
(1.72)
The attempt to determine interatomic potentials in this way was initiated by Kitaigorodstky [6], in the 1960s, assuming the Buckingham type of potentials for hydrocarbons and had continued and expanded to include contributions beyond the dispersion
energy and repulsion coming from Pauli’s exclusion principle. Through its history
of the atom–atom potential method, the method has been successfully described
aggregation structure (primarily of crystals) and the dynamics of molecules inside
such structures. The success implies that not only the energy (and structure) but
also its derivatives (up to the second-order) are well approximated by the sum of
interatomic potential functions, at least, around the equilibrium structure with the
minimum energy. Interatomic potential functions with transferability have been proposed for elements composing organic molecules such as carbon, hydrogen, oxygen,
nitrogen, sulfur, and halogens. Detailed description and discussion can be found in
a monograph co-authored by the pioneer of this method [7].
The adoption of isotropic potential functions can express the anisotropy of interatomic interaction arising from the anisotropic molecular shape. However, it cannot
represent the orientational dependence and “valence” saturation of some interactions
between specific atomic pairs such as hydrogen bonds between hydrogen and electronegative (like oxygen) atoms. This fact is not severe for studying crystal properties
but would be for searching stable structures (crystal structure or liquid structure) or
molecular dynamics with significant fluctuation (in liquid).
Note that the resultant potentials determined through a fit to experimental data
are effective ones and dependent on temperatures at which the input data were taken.
In turn, the effect of temperature may be discussed if this aspect is fully utilized. To
this purpose, a fit of lattice vibration frequencies is necessary and promising because
the number of input data on a single compound can be large enough.
Once atom–atom potential functions have been established, it seems natural
to assume their utility not only for intermolecular interaction. Indeed, the interatomic potential functions are also utilized in studying the conformations of flexible
1 Molecules and Intermolecular Interactions
considering the meaning of σ as an atomic diameter.
In some cases, it is necessary to take electrostatic interactions into account. This
is undoubtedly the case for polar molecules. The electrostatic interactions are also
divided into interatomic contributions by assigning partial charges to atoms. This
way is adequate and more accessible than a sophisticated multipole expansion. The
partial charges may be assigned based on either of the quantum-chemical calculation
of an isolated molecule or kinds of fitting together with other coefficients. The former
poses some difficulty in the transferability of potential functions. Anyway, potential
functions with the contribution of (bare) charges, q i and q j , becomes
v(r i j ) = A
σ
r i j
12
− B
σ
r i j
6
+
1
4ππ 0
q i q j
r i j
(1.71)
or
v(r i j ) = a exp
−
r i j
σ
− b
σ
r i j
6
+
1
4ππ 0
q i q j
r i j
.
(1.72)
The attempt to determine interatomic potentials in this way was initiated by Kitaigorodstky [6], in the 1960s, assuming the Buckingham type of potentials for hydrocarbons and had continued and expanded to include contributions beyond the dispersion
energy and repulsion coming from Pauli’s exclusion principle. Through its history
of the atom–atom potential method, the method has been successfully described
aggregation structure (primarily of crystals) and the dynamics of molecules inside
such structures. The success implies that not only the energy (and structure) but
also its derivatives (up to the second-order) are well approximated by the sum of
interatomic potential functions, at least, around the equilibrium structure with the
minimum energy. Interatomic potential functions with transferability have been proposed for elements composing organic molecules such as carbon, hydrogen, oxygen,
nitrogen, sulfur, and halogens. Detailed description and discussion can be found in
a monograph co-authored by the pioneer of this method [7].
The adoption of isotropic potential functions can express the anisotropy of interatomic interaction arising from the anisotropic molecular shape. However, it cannot
represent the orientational dependence and “valence” saturation of some interactions
between specific atomic pairs such as hydrogen bonds between hydrogen and electronegative (like oxygen) atoms. This fact is not severe for studying crystal properties
but would be for searching stable structures (crystal structure or liquid structure) or
molecular dynamics with significant fluctuation (in liquid).
Note that the resultant potentials determined through a fit to experimental data
are effective ones and dependent on temperatures at which the input data were taken.
In turn, the effect of temperature may be discussed if this aspect is fully utilized. To
this purpose, a fit of lattice vibration frequencies is necessary and promising because
the number of input data on a single compound can be large enough.
Once atom–atom potential functions have been established, it seems natural
to assume their utility not only for intermolecular interaction. Indeed, the interatomic potential functions are also utilized in studying the conformations of flexible