long-wavelength band is explained by the fact that a contribution to it comes for
transitions from vibrational levels with an extensive range of internuclear distances
falling on a small range of change of the transition frequency.
The features described above occur if the overlap integral has a maximum near
m min . Vibrational wave functions of the states AB*ðv
0
Þ, AB*ðv
00
Þ, which at some
distance from the classical turning points are the de Broglie wavelengths
(see (3.1.11) must have the same values k
0
¼ k
00
and be in phase or antiphase. Mulliken has shown [35] that for heavy atoms and
high values v
0 , v
00 for which there is great anharmonicity and, consequently, the
density of vibrational levels, these conditions can be met, since in a small frequency
and energy range one can find regions, where the v v 0 , v v 00 wave functions, depending
on v
0 , v
00 , coincide. Therefore, k
0
¼ k
00 since T
0
¼ T
00 at R = R 3 . The effects
described above occur if the PECs of the states combined in the transition are
sufficiently far apart, and the e m
3 value does not depend too much on v
0 , v
00 .
There is the extremum at the Mulliken difference potential in Fig. 4.7a, and there
are couple of points r
Ã
1 ; r
Ã
2 for each energy values lying higher than the horizontal
dotted line on the potential and corresponding to the same e m value. It is obvious that
the R-centroid approximation is invalid in this energy range, and one has to use the
trial-and-error procedure to simulate a spectrum (see [36] and references).
J. Tellinghuisen has called a band structure in this energy range as interference
structure since contributions of the integrand v v 0 Á v v 00 near r
Ã
1 ; r
Ã
2 to the accumulated
overlap integral
R r
0 v v 0 Á v v 00 dr ‘can add constructively or destructively’ [33, 37].
The PEC positions similar to shown in Fig. 4.7a are typical for the halogen
ion-pair and valence states (see Fig. 4.8 as an example).
4.6 Intramolecular Perturbations. Selection Rules
and Franck–Condon Principle for Intramolecular
Perturbation. Perturbations Between Bound States
Perturbations in diatomic molecules are described in detail in monographs [31, 38],
and the author has used them for writing this section.
Unlike diatomic molecules, an interaction of the states of different species of a
polyatomic molecule can occur due to electronic and vibrational motion coupling.
Therefore, we consider perturbations in di- and polyatomic molecules separately.
4.5 Franck–Condon Principle for Bound–Bound …
105
transitions from vibrational levels with an extensive range of internuclear distances
falling on a small range of change of the transition frequency.
The features described above occur if the overlap integral has a maximum near
m min . Vibrational wave functions of the states AB*ðv
0
Þ, AB*ðv
00
Þ, which at some
distance from the classical turning points are the de Broglie wavelengths
(see (3.1.11) must have the same values k
0
¼ k
00
and be in phase or antiphase. Mulliken has shown [35] that for heavy atoms and
high values v
0 , v
00 for which there is great anharmonicity and, consequently, the
density of vibrational levels, these conditions can be met, since in a small frequency
and energy range one can find regions, where the v v 0 , v v 00 wave functions, depending
on v
0 , v
00 , coincide. Therefore, k
0
¼ k
00 since T
0
¼ T
00 at R = R 3 . The effects
described above occur if the PECs of the states combined in the transition are
sufficiently far apart, and the e m
3 value does not depend too much on v
0 , v
00 .
There is the extremum at the Mulliken difference potential in Fig. 4.7a, and there
are couple of points r
Ã
1 ; r
Ã
2 for each energy values lying higher than the horizontal
dotted line on the potential and corresponding to the same e m value. It is obvious that
the R-centroid approximation is invalid in this energy range, and one has to use the
trial-and-error procedure to simulate a spectrum (see [36] and references).
J. Tellinghuisen has called a band structure in this energy range as interference
structure since contributions of the integrand v v 0 Á v v 00 near r
Ã
1 ; r
Ã
2 to the accumulated
overlap integral
R r
0 v v 0 Á v v 00 dr ‘can add constructively or destructively’ [33, 37].
The PEC positions similar to shown in Fig. 4.7a are typical for the halogen
ion-pair and valence states (see Fig. 4.8 as an example).
4.6 Intramolecular Perturbations. Selection Rules
and Franck–Condon Principle for Intramolecular
Perturbation. Perturbations Between Bound States
Perturbations in diatomic molecules are described in detail in monographs [31, 38],
and the author has used them for writing this section.
Unlike diatomic molecules, an interaction of the states of different species of a
polyatomic molecule can occur due to electronic and vibrational motion coupling.
Therefore, we consider perturbations in di- and polyatomic molecules separately.
4.5 Franck–Condon Principle for Bound–Bound …
105