150
3 Fundamentals of the Analysis Tools
all the normal vibration frequencies. A couple of instances are 0.8929 for HF/631G* data (Pople et al. 1993) and 0.989 for DFT/B3LYP/6-311 + G(3df, 2p) data
(Bauschlicher and Partridge 1995), signifying that elaborate DFT generally gives
better frequency values. For the general HF method, the above value (0.8929) is
often used irrespective of the basis sets, and so for the general DFT method (0.989).
Q6: Are there notes for the calculation of excitation energies?
A6: These can be obtained either by MO or by DFT method with an assignment of the
MO’s concerning the electron transition. Although the usual HF method is capable of
enumerating the excitation energy, usage of the configuration interaction (CI) or more
quantitative coupled-cluster (CC) method is generally recommended since these
methods include electron correlation effect, which is of importance in description
of the excited state. In DFT method, the TD-DFT one has been developed for the
calculation of excitation energies. Along with the excitation energy, the oscillator
strength compared to the absorption coefficient is also obtained as has been described
in Sect. 2.5.
Since the experimental absorption spectra are often measured in solution, it is
required to include the solvation effect to the theoretically obtained data. For this
purpose is usually utilized correction using the polarizable continuum model (PCM)
for each solvent, in which the parameters of the conventional solvent species are
included. An example of usage of the PCM has also been given in Sect. 2.5.
Q7: Can one obtain the thermochemical data such as enthalpy, entropy, and
free energy of a molecule?
A7: It is possible that one obtains the data Gibbs free energy G, entropy S, and
enthalpy H of a molecule after the optimization of molecular structure with frequency
analysis of the normal vibrations. This is because the partition function including that
of vibration is indispensable to the calculation of entropy of a molecule. Temperature
T and pressure p are to be given as parameters for the actual calculation of these
data. This process is not so tedious since frequency analysis is normally performed
to carry on the structural optimization of a molecule. Moreover, the subroutine for
the additional calculation of these thermochemical data is often equipped within the
usual software of the MO calculation.
Q8: What is BSSE?
A8: In the calculation of supermolecule A . . . B such as a hydrogen-bonded system,
for instance, one should pay attention to the basis set superposition error (BSSE).
This occurs from that the moiety A automatically utilizes the basis set of the counter
moiety B resulting in excessive stabilization of A, and vice versa to the moiety B.
The BSSE especially tends to take place when the basis set functions of low quality
are employed for the concerning molecule. This kind of error can be eliminated by
the counterpoise method (Boys and Bernardi 1970).
3 Fundamentals of the Analysis Tools
all the normal vibration frequencies. A couple of instances are 0.8929 for HF/631G* data (Pople et al. 1993) and 0.989 for DFT/B3LYP/6-311 + G(3df, 2p) data
(Bauschlicher and Partridge 1995), signifying that elaborate DFT generally gives
better frequency values. For the general HF method, the above value (0.8929) is
often used irrespective of the basis sets, and so for the general DFT method (0.989).
Q6: Are there notes for the calculation of excitation energies?
A6: These can be obtained either by MO or by DFT method with an assignment of the
MO’s concerning the electron transition. Although the usual HF method is capable of
enumerating the excitation energy, usage of the configuration interaction (CI) or more
quantitative coupled-cluster (CC) method is generally recommended since these
methods include electron correlation effect, which is of importance in description
of the excited state. In DFT method, the TD-DFT one has been developed for the
calculation of excitation energies. Along with the excitation energy, the oscillator
strength compared to the absorption coefficient is also obtained as has been described
in Sect. 2.5.
Since the experimental absorption spectra are often measured in solution, it is
required to include the solvation effect to the theoretically obtained data. For this
purpose is usually utilized correction using the polarizable continuum model (PCM)
for each solvent, in which the parameters of the conventional solvent species are
included. An example of usage of the PCM has also been given in Sect. 2.5.
Q7: Can one obtain the thermochemical data such as enthalpy, entropy, and
free energy of a molecule?
A7: It is possible that one obtains the data Gibbs free energy G, entropy S, and
enthalpy H of a molecule after the optimization of molecular structure with frequency
analysis of the normal vibrations. This is because the partition function including that
of vibration is indispensable to the calculation of entropy of a molecule. Temperature
T and pressure p are to be given as parameters for the actual calculation of these
data. This process is not so tedious since frequency analysis is normally performed
to carry on the structural optimization of a molecule. Moreover, the subroutine for
the additional calculation of these thermochemical data is often equipped within the
usual software of the MO calculation.
Q8: What is BSSE?
A8: In the calculation of supermolecule A . . . B such as a hydrogen-bonded system,
for instance, one should pay attention to the basis set superposition error (BSSE).
This occurs from that the moiety A automatically utilizes the basis set of the counter
moiety B resulting in excessive stabilization of A, and vice versa to the moiety B.
The BSSE especially tends to take place when the basis set functions of low quality
are employed for the concerning molecule. This kind of error can be eliminated by
the counterpoise method (Boys and Bernardi 1970).