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2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
2.2 Chemical Bonds
2.2.1 Concepts of Chemical Bond
Description of chemical bonds is probably most traditional and crucial subject in
chemistry, which makes chemical characteristics and behavior of molecules graspable and understandable at a sight. Even in these days what is called Lewis structure
based on the octet rule is considered tractable for the nature of covalent bonds and
lone pairs in organic and inorganic molecules. But such ideas of chemical bonds actually might be too simple and seem to require a bit more sophisticated consideration
from the quantum chemical viewpoint.
This is because the wavefunction afforded by the usual MO paradigm is not only to
remain in the regions relating to each chemical bond but more or less extends to whole
the molecule giving more complicated pictures than simple chemical bonds. This
feature comes from the difference between the pictures given by the Lewis structure
and by the MO theories. The former is directly based on the concept of the particular
chemical bonds between the atoms but the latter comes from the linear combination
of atomic orbitals (LCAO; AO represents the atomic orbital) formally centered at all
the atoms in the molecule. Considering these situations, it is an interesting problem
to reconcile these contradictory pictures from viewpoints of theoretical chemistry.
In this section, the framework toward proper considerations of the chemical bonds
in terms of quantum chemistry is to be explained.
2.2.2 Description of Chemical Bond
The ordinary MO’s obtained by the usual calculation method, sometimes formally
mentioned as the canonical MO’s (CMO’s), do not necessarily afford the straightforward pictures of chemical bonds in the sense of the Lewis structures. For instance,
patterns of the highest occupied MO (HOMO) and the HOMO-1 of the butane CMO’s
shown in Fig. 2.15a are of the σ-type extending to almost all of the molecule and
do not directly indicate each C–C nor C–H bond. Moreover, those of butadiene in
Fig. 2.15b are of rather familiar delocalized π-type and do not afford the picture of
“each” π-type bond.
In turn it is rather convenient to utilize the concept of the localized MO’s (LMO’s)
obtained from the CMO’s, since the LMO’s are the set of wavefunctions intended
to be localized at each particular interatomic region as much as possible to represent the chemical bonds or lone pairs existing in the molecule in terms of a certain
mathematical manipulation such as unitary transformation of the set of the occupied
CMO’s (Edmiston and Ruedenberg 1963; Foster and Boys 1960). Due to characteristics of the unitary transformation among the occupied MO’s physical meaning of the
CMO’s and the LMO’s are the same in total. Based on similar concept, natural bond
orbitals (NBO’s) being a kind of LMO’s are frequently used in recent years (Reed
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
2.2 Chemical Bonds
2.2.1 Concepts of Chemical Bond
Description of chemical bonds is probably most traditional and crucial subject in
chemistry, which makes chemical characteristics and behavior of molecules graspable and understandable at a sight. Even in these days what is called Lewis structure
based on the octet rule is considered tractable for the nature of covalent bonds and
lone pairs in organic and inorganic molecules. But such ideas of chemical bonds actually might be too simple and seem to require a bit more sophisticated consideration
from the quantum chemical viewpoint.
This is because the wavefunction afforded by the usual MO paradigm is not only to
remain in the regions relating to each chemical bond but more or less extends to whole
the molecule giving more complicated pictures than simple chemical bonds. This
feature comes from the difference between the pictures given by the Lewis structure
and by the MO theories. The former is directly based on the concept of the particular
chemical bonds between the atoms but the latter comes from the linear combination
of atomic orbitals (LCAO; AO represents the atomic orbital) formally centered at all
the atoms in the molecule. Considering these situations, it is an interesting problem
to reconcile these contradictory pictures from viewpoints of theoretical chemistry.
In this section, the framework toward proper considerations of the chemical bonds
in terms of quantum chemistry is to be explained.
2.2.2 Description of Chemical Bond
The ordinary MO’s obtained by the usual calculation method, sometimes formally
mentioned as the canonical MO’s (CMO’s), do not necessarily afford the straightforward pictures of chemical bonds in the sense of the Lewis structures. For instance,
patterns of the highest occupied MO (HOMO) and the HOMO-1 of the butane CMO’s
shown in Fig. 2.15a are of the σ-type extending to almost all of the molecule and
do not directly indicate each C–C nor C–H bond. Moreover, those of butadiene in
Fig. 2.15b are of rather familiar delocalized π-type and do not afford the picture of
“each” π-type bond.
In turn it is rather convenient to utilize the concept of the localized MO’s (LMO’s)
obtained from the CMO’s, since the LMO’s are the set of wavefunctions intended
to be localized at each particular interatomic region as much as possible to represent the chemical bonds or lone pairs existing in the molecule in terms of a certain
mathematical manipulation such as unitary transformation of the set of the occupied
CMO’s (Edmiston and Ruedenberg 1963; Foster and Boys 1960). Due to characteristics of the unitary transformation among the occupied MO’s physical meaning of the
CMO’s and the LMO’s are the same in total. Based on similar concept, natural bond
orbitals (NBO’s) being a kind of LMO’s are frequently used in recent years (Reed