3.6 Hints for Calculations
149
afford considerably precise molecular structures consisting of atoms of less than
several hundreds. For large molecules such as polymeric, biological, and catalytic
systems, MM method is rather effective than the elaborate MO methods. Care should
be taken to the selection of the molecular force field in the MM depending on the
target molecule. The ONIOM method (QM/MM) would also be applicable to those
huge systems.
For the molecules in the excited state (S 1 or T 1 ), the CIS or the TD-DFT method
can be applicable. Also, it is noted that, even in the ground state, anionic species
ought to be dealt with the diffuse basis sets into the MO calculations.
Q4: Are there notes for the calculation of the electronic structure of a molecule?
A4: The MM method is not appropriate to obtain the electronic structure since this
does not contain the information of electrons. Empirical MO and the semiempirical
HF methods give only qualitative and/or partial results on the electronic structures but,
on one hand, can supply considerably enough information for chemical reactivity
analyses. For instance, early frontier orbital theory (Fukui et al. 1952, 1971) and
Woodward-Hoffmann’s rule (Woodward and Hoffmann 1965, 1969) came out based
on the empirical MO methods. This comes from that the MO patterns and the order
of MO energies are rather insensitive to the degree of the approximation employed
in the MO theory. Incidentally, it is noted that in the CO patterns of the 1D polymers
the graspable ones are only obtained at the center and the boundaries of the Brillouin
zone (see Sect. 3.3) since the CO’s is obtained as complex functions in other zone
points.
More general electronic structures and properties such as atomic net charges,
bond-order indices, dipole moment, polarizability, NMR shift (or NICS (see
Sect. 2.8.2)), and so on should be enumerated by the non-empirical HF or the recent
DFT method used in quantum chemistry. Care should be taken, however, that atomic
net charges are rather sensitive to not only the MO method but selected basis sets
due to the tendency of delocalization of electrons depending on those conditions as
described in Sect. 2.3. It is mentioned that high quality of the basis set such as 6-311
+ G(2d, p) or more should be employed to obtain a plausible result for the NMR
shift.
Q5: Is it possible to get the IR vibration and Raman scattering data?
A5: One can obtain this kind of information out of the MM and the MO method,
which can perform the optimization of molecular structure in Q3. This is because the
normal vibration data can be obtained by the frequency analysis usually performed
for the confirmation of the local minimum of the energy of the molecule. The vibration intensities are also enumerated if the electronic structure of the molecule is
available and, in this sense, the MM method cannot afford these data. The zero-point
frequency is also derived along with each normal vibration, as a matter of course,
which is important for zero-point energy correction particularly in obtaining the
thermochemical data concerning with Q7.
It is noted that, in particular, the frequencies tend to be overestimated by the usual
MO method and a frequency scale factor is to be multiplied to the original data of
149
afford considerably precise molecular structures consisting of atoms of less than
several hundreds. For large molecules such as polymeric, biological, and catalytic
systems, MM method is rather effective than the elaborate MO methods. Care should
be taken to the selection of the molecular force field in the MM depending on the
target molecule. The ONIOM method (QM/MM) would also be applicable to those
huge systems.
For the molecules in the excited state (S 1 or T 1 ), the CIS or the TD-DFT method
can be applicable. Also, it is noted that, even in the ground state, anionic species
ought to be dealt with the diffuse basis sets into the MO calculations.
Q4: Are there notes for the calculation of the electronic structure of a molecule?
A4: The MM method is not appropriate to obtain the electronic structure since this
does not contain the information of electrons. Empirical MO and the semiempirical
HF methods give only qualitative and/or partial results on the electronic structures but,
on one hand, can supply considerably enough information for chemical reactivity
analyses. For instance, early frontier orbital theory (Fukui et al. 1952, 1971) and
Woodward-Hoffmann’s rule (Woodward and Hoffmann 1965, 1969) came out based
on the empirical MO methods. This comes from that the MO patterns and the order
of MO energies are rather insensitive to the degree of the approximation employed
in the MO theory. Incidentally, it is noted that in the CO patterns of the 1D polymers
the graspable ones are only obtained at the center and the boundaries of the Brillouin
zone (see Sect. 3.3) since the CO’s is obtained as complex functions in other zone
points.
More general electronic structures and properties such as atomic net charges,
bond-order indices, dipole moment, polarizability, NMR shift (or NICS (see
Sect. 2.8.2)), and so on should be enumerated by the non-empirical HF or the recent
DFT method used in quantum chemistry. Care should be taken, however, that atomic
net charges are rather sensitive to not only the MO method but selected basis sets
due to the tendency of delocalization of electrons depending on those conditions as
described in Sect. 2.3. It is mentioned that high quality of the basis set such as 6-311
+ G(2d, p) or more should be employed to obtain a plausible result for the NMR
shift.
Q5: Is it possible to get the IR vibration and Raman scattering data?
A5: One can obtain this kind of information out of the MM and the MO method,
which can perform the optimization of molecular structure in Q3. This is because the
normal vibration data can be obtained by the frequency analysis usually performed
for the confirmation of the local minimum of the energy of the molecule. The vibration intensities are also enumerated if the electronic structure of the molecule is
available and, in this sense, the MM method cannot afford these data. The zero-point
frequency is also derived along with each normal vibration, as a matter of course,
which is important for zero-point energy correction particularly in obtaining the
thermochemical data concerning with Q7.
It is noted that, in particular, the frequencies tend to be overestimated by the usual
MO method and a frequency scale factor is to be multiplied to the original data of