62
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
2.6 Mechanical Properties
Theoretical-chemistry calculation also works as a kind of valuable probe for the
mechanical phenomena occurring in molecules. Furthermore, theoretical analyses
of quantities related to elastic constant of linear polymers are of use toward essential
understanding of the response of 1D-polymers to the stress caused by the external
force field such as tensile strength along the main-chain axis. In this section, some
examples of application to mechanical properties of molecules and regular 1D polymers are to be afforded for comprehension of efficiency of theoretical calculation on
this theme.
2.6.1 Strains in Molecules
Some molecules can store strain energies inside them and they often show higher
chemical reactivity or spontaneous isomerization to release strain energies compared
with less strained ones. There can be a couple of patterns to store molecular strains: (1)
bond-angle strain, (2) steric strain, and (3) torsional strain, each of which is connected
to the peculiar molecular structure. The bond-angle strain causes the deviation from
the normal hybridization angles, that is, 109.5° for sp
3 , 120° for sp
2 , and 180° for sp
hybridizations. The steric strain comes from “too close” atoms in molecule causing
severe interelectron repulsions and, hence, is also referred to as steric repulsions.
The torsional strain can happen in association with eclipsed or gauche interactions.
All of these strains can be estimated by theoretical calculations on the total energy
or heat of formation of the concerning molecule.
In this subsection, theoretical calculation dealing with the bond-angle strain taking
as the example of interest is to be described. Small-ring molecules with three or
four membered rings usually possess high strains inside them or, in other words,
they automatically store mechanical energy in themselves. This is because the bond
angles largely change from the normal bond angles such as those for sp
3 (109.5°) and
sp
2 (120°) hybridizations. For instance, cyclopropane and cyclobutane have the bond
angles of 60° and 90°, respectively, being considerably smaller than 109.5°, that is,
they are out of the normal sp
3 hybridization. This situation causes rather peculiar
electronic structures compared with those of the strain-free molecules. For instance,
in Fig. 2.56a there is seen an electron-deficient hollow inside the triangle formed by
the three C–C bonds with the electron density rather tending to direct outside the
molecular skeleton of cyclopropane. On the other hand, such behavior is not seen in
the normal propane molecule.
More quantitative way of describing magnitude of the strain is to examine the
strain energy based on the MO calculation scheme in an adequate manner. There
can be several ways of definition of strain energies in theoretical chemistry, and
perhaps the most popular one would employ the concept of homodesmotic reaction.
This belongs to isodesmic reactions, in which the total numbers of each bond type
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
2.6 Mechanical Properties
Theoretical-chemistry calculation also works as a kind of valuable probe for the
mechanical phenomena occurring in molecules. Furthermore, theoretical analyses
of quantities related to elastic constant of linear polymers are of use toward essential
understanding of the response of 1D-polymers to the stress caused by the external
force field such as tensile strength along the main-chain axis. In this section, some
examples of application to mechanical properties of molecules and regular 1D polymers are to be afforded for comprehension of efficiency of theoretical calculation on
this theme.
2.6.1 Strains in Molecules
Some molecules can store strain energies inside them and they often show higher
chemical reactivity or spontaneous isomerization to release strain energies compared
with less strained ones. There can be a couple of patterns to store molecular strains: (1)
bond-angle strain, (2) steric strain, and (3) torsional strain, each of which is connected
to the peculiar molecular structure. The bond-angle strain causes the deviation from
the normal hybridization angles, that is, 109.5° for sp
3 , 120° for sp
2 , and 180° for sp
hybridizations. The steric strain comes from “too close” atoms in molecule causing
severe interelectron repulsions and, hence, is also referred to as steric repulsions.
The torsional strain can happen in association with eclipsed or gauche interactions.
All of these strains can be estimated by theoretical calculations on the total energy
or heat of formation of the concerning molecule.
In this subsection, theoretical calculation dealing with the bond-angle strain taking
as the example of interest is to be described. Small-ring molecules with three or
four membered rings usually possess high strains inside them or, in other words,
they automatically store mechanical energy in themselves. This is because the bond
angles largely change from the normal bond angles such as those for sp
3 (109.5°) and
sp
2 (120°) hybridizations. For instance, cyclopropane and cyclobutane have the bond
angles of 60° and 90°, respectively, being considerably smaller than 109.5°, that is,
they are out of the normal sp
3 hybridization. This situation causes rather peculiar
electronic structures compared with those of the strain-free molecules. For instance,
in Fig. 2.56a there is seen an electron-deficient hollow inside the triangle formed by
the three C–C bonds with the electron density rather tending to direct outside the
molecular skeleton of cyclopropane. On the other hand, such behavior is not seen in
the normal propane molecule.
More quantitative way of describing magnitude of the strain is to examine the
strain energy based on the MO calculation scheme in an adequate manner. There
can be several ways of definition of strain energies in theoretical chemistry, and
perhaps the most popular one would employ the concept of homodesmotic reaction.
This belongs to isodesmic reactions, in which the total numbers of each bond type