2.1 Molecular Structure
13
Table 2.2 Absorption and irradiation wavelengths of 1,2-diphenylvinylene (DPV) and 1,2diphenyldisilenylene (DPDSi) between S 0 and S 1 states a
Compound Absorption
Irradiation
Wavelength (nm) Oscillator strength Wavelength (nm) Oscillator strength
DPV
309.75
0.9842
357.98
0.9792
DPDSi
400.34
0.5762
486.21
0.3978
a The S 0 geometry was optimized by DFT/B3LYP/6-31G** and the S 1 by CIS/6-31G**. The
absorption and the irradiation wavelengths were calculated by TD-DFT/B3LYP/6-31G**
2.1.3 Stationary Points on the Potential Energy Surface
(PES)
Let us mention here a simple but a bit detailed outlook of the optimization process
so as to promote comprehension of relationship between the optimized structure
and the normal-vibration analysis. It is currently possible to obtain the most stable
molecular structure with use of many softwares by what is called the energy gradient
method. Calculation based on the MM (see Sect. 3.4) is much easier and less expensive to access a plausible initial structure used in the formal optimization. The MM
method, however, has a drawback in that it cannot deal with the electronic structure
of molecules. Hence, in this subsection, we rather confine ourselves to the quantum
chemical scheme to explicate this subject.
Finding of the optimized structure of molecule in both the ground and the excited
states implies to access the “stationary point” on the PES E(R) of each state where
R collectively represents the 3N variables representing all the nuclei coordinates
in the molecule consisting of N atoms. The transition state (TS) during chemical
reactions is another important stationary point on the PES and will be mentioned
in Sect. 2.7. Note that the degrees of freedom of the translation and rotation of
the whole molecule should be removed and hence R essentially consists of 3N–
6 or 3N–5 variables as has been described above. As a matter of course, 3N–6
variables correspond to the vibrational motions of a non-linear molecule whereas
3N–5 variables to those for linear case. But we normally include all of these degrees
of freedom into the calculation for simplicity with some care. That is, the vibrational
frequencies corresponding to these degrees of freedom become quite small (ideally
zero) and we normally omit those. Note that combination of all the bond lengths, bond
angles, dihedral angles, and so on inside the molecule can be another representative
variables R as the “internal coordinates” for E(R) apart from the Cartesian ones of
the nuclei in the molecule.
The PES E(R) is expressed by summation of the total electronic and the total
internuclear energies of a molecule, both of which are functions of the nuclear position represented by R. In association with the process to find out the stationary points
illustrated in Fig. 2.3 on the PES, it is necessary for principle to get all the points
on the PES, which clearly takes huge time and efforts. Instead, obviously from the
present purpose, it is not necessary to obtain the whole PES but is enough to get
13
Table 2.2 Absorption and irradiation wavelengths of 1,2-diphenylvinylene (DPV) and 1,2diphenyldisilenylene (DPDSi) between S 0 and S 1 states a
Compound Absorption
Irradiation
Wavelength (nm) Oscillator strength Wavelength (nm) Oscillator strength
DPV
309.75
0.9842
357.98
0.9792
DPDSi
400.34
0.5762
486.21
0.3978
a The S 0 geometry was optimized by DFT/B3LYP/6-31G** and the S 1 by CIS/6-31G**. The
absorption and the irradiation wavelengths were calculated by TD-DFT/B3LYP/6-31G**
2.1.3 Stationary Points on the Potential Energy Surface
(PES)
Let us mention here a simple but a bit detailed outlook of the optimization process
so as to promote comprehension of relationship between the optimized structure
and the normal-vibration analysis. It is currently possible to obtain the most stable
molecular structure with use of many softwares by what is called the energy gradient
method. Calculation based on the MM (see Sect. 3.4) is much easier and less expensive to access a plausible initial structure used in the formal optimization. The MM
method, however, has a drawback in that it cannot deal with the electronic structure
of molecules. Hence, in this subsection, we rather confine ourselves to the quantum
chemical scheme to explicate this subject.
Finding of the optimized structure of molecule in both the ground and the excited
states implies to access the “stationary point” on the PES E(R) of each state where
R collectively represents the 3N variables representing all the nuclei coordinates
in the molecule consisting of N atoms. The transition state (TS) during chemical
reactions is another important stationary point on the PES and will be mentioned
in Sect. 2.7. Note that the degrees of freedom of the translation and rotation of
the whole molecule should be removed and hence R essentially consists of 3N–
6 or 3N–5 variables as has been described above. As a matter of course, 3N–6
variables correspond to the vibrational motions of a non-linear molecule whereas
3N–5 variables to those for linear case. But we normally include all of these degrees
of freedom into the calculation for simplicity with some care. That is, the vibrational
frequencies corresponding to these degrees of freedom become quite small (ideally
zero) and we normally omit those. Note that combination of all the bond lengths, bond
angles, dihedral angles, and so on inside the molecule can be another representative
variables R as the “internal coordinates” for E(R) apart from the Cartesian ones of
the nuclei in the molecule.
The PES E(R) is expressed by summation of the total electronic and the total
internuclear energies of a molecule, both of which are functions of the nuclear position represented by R. In association with the process to find out the stationary points
illustrated in Fig. 2.3 on the PES, it is necessary for principle to get all the points
on the PES, which clearly takes huge time and efforts. Instead, obviously from the
present purpose, it is not necessary to obtain the whole PES but is enough to get