2.1 Molecular Structure
11
Lowest Singlet
Excited State (S 1 )
Photoexcitation
Ground State (S 0 )
Structural Relaxation
(radiationless transition)
E
R (Nuclear Coordinates)
R(S 0 ) opt
R(S 1 ) opt
Fig. 2.9 Illustrative drawing of Franck–Condon principle, where structural relaxation takes place
after the vertical photoexcitation from S 0 to S 1
1.1859
(1.2553)
[1.2557]
1.0907
(1.0854)
[1.0925]
116.29
(118.27)
[112.77]
Bending angle of the
C-H-C plane away from
the molecule plane in the
S 0 state
0.00
(24.89)
[43.14]
O
C
H
H
Fig. 2.10 Principal structural parameters of a formaldehyde molecule in the S 0 , S 1 (in parentheses),
and T 1 (in brackets) states calculated by CIS/6-31+G*. Bond lengths are in Å and bond angles in
degrees. Adapted with permission from Foresman et al. (1992). Copyright 1992 American Chemical
Society
the DFT methods, the latter being called time-dependent DFT (TD-DFT), which are
currently most popular schemes to deal with the electronic structures and properties
of molecules in the comparatively simple excited state (see Sects. 3.1 and 3.2).