48
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
interest to the experimental chemists. Moreover, calculations related to the circular
dichroism (CD) behavior of optically active molecules are to be described as well.
2.5.1 Absorption Spectrum
The most popular excited state to the experimental chemists would be the first singlet
(S 1 ) and the triplet (T 1 ) excited states. Higher excited states like S 2 and T 2 are also
getting to be familiar with more sophisticated purposes utilizing higher excited states.
An idea of the most popular optical UV-visible (UV-vis) absorption (or electronic
transition) to yield the S 1 state is schematically shown in the left side of Fig. 2.38.
The single-electron excitation energy to the S n states (n = 1, 2, …) with the oscillator
strengths accompanied is frequently estimated by the following scheme related to
either the post HF or the DFT framework as in what follows:
(1) Related to the post HF: Configuration interaction singles (CI-singles or CIS)
(see Sect. 3.1.2)
(2) Related to the DFT: TD-DFT (see Sect. 3.2).
In the CIS or the TD-DFT methods, the wavefunction corresponding to the S n
state is generally given by linear combination of several electronic configurations
combined with multiple electron transitions employing the original MO’s as, for
instance,
Ψ S n = c 1 Ψ HO→LU + c 2 Ψ HO - 1→LU + c 2 Ψ HO→LU + 1 + · · ·
(2.38)
where Ψ HO→LU stands for the configuration with the electron transition from the
HOMO to the LUMO and so on. Equation (2.38) signifies that the wavefunction of
the excited state described by the above CIS or TD-DFT automatically includes the
electron correlation to a certain extent. A simple example of this representation for
S 1 state is illustrated in the right side of Fig. 2.38. The most fundamental estimation
LU
HO-1
HO
LU+1
HO
LU
= c 1
+ c 2
+ c 3
+ …
S 0
S 1
E
Nuclear coordinate
Fig. 2.38 An example of description of the single-electron excitation from S 0 to S 1 state expressed
by linear combination of multiple electronic configurations
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
interest to the experimental chemists. Moreover, calculations related to the circular
dichroism (CD) behavior of optically active molecules are to be described as well.
2.5.1 Absorption Spectrum
The most popular excited state to the experimental chemists would be the first singlet
(S 1 ) and the triplet (T 1 ) excited states. Higher excited states like S 2 and T 2 are also
getting to be familiar with more sophisticated purposes utilizing higher excited states.
An idea of the most popular optical UV-visible (UV-vis) absorption (or electronic
transition) to yield the S 1 state is schematically shown in the left side of Fig. 2.38.
The single-electron excitation energy to the S n states (n = 1, 2, …) with the oscillator
strengths accompanied is frequently estimated by the following scheme related to
either the post HF or the DFT framework as in what follows:
(1) Related to the post HF: Configuration interaction singles (CI-singles or CIS)
(see Sect. 3.1.2)
(2) Related to the DFT: TD-DFT (see Sect. 3.2).
In the CIS or the TD-DFT methods, the wavefunction corresponding to the S n
state is generally given by linear combination of several electronic configurations
combined with multiple electron transitions employing the original MO’s as, for
instance,
Ψ S n = c 1 Ψ HO→LU + c 2 Ψ HO - 1→LU + c 2 Ψ HO→LU + 1 + · · ·
(2.38)
where Ψ HO→LU stands for the configuration with the electron transition from the
HOMO to the LUMO and so on. Equation (2.38) signifies that the wavefunction of
the excited state described by the above CIS or TD-DFT automatically includes the
electron correlation to a certain extent. A simple example of this representation for
S 1 state is illustrated in the right side of Fig. 2.38. The most fundamental estimation
LU
HO-1
HO
LU+1
HO
LU
= c 1
+ c 2
+ c 3
+ …
S 0
S 1
E
Nuclear coordinate
Fig. 2.38 An example of description of the single-electron excitation from S 0 to S 1 state expressed
by linear combination of multiple electronic configurations