Forbidden transition intensity borrowing

Forbidden Transitions Intensity Borrowing by Mixing with a Remote Perturber 406... 

The azido group affects the spectrum of the hydrocarbon itself in two ways it causes a red shift of the L -band and a smaller red shift of the other bands (the size of the aromatic system is increased) it also reduces the symmetry of the molecule, thus enhancing the extinction of the symmetry forbidden transition at the expense of the associated B-transition (intensity borrowing ). From the size of the effect it can be inferred that the inductive interaction of the azido group with the ring is comparable with, if somewhat weaker than, that of the amino group For the spectra of aromatic diazides see reference 40. 

In the picture of spin-orbit perturbed Russell-Saunders states, the dipole transition moment of a spin-forbidden radiative transition is thus a sum of spin-allowed dipole transitions weighted by spin-orbit coupling coefficients (e.g., the expansion coefficients in Eq. [218]). The fact that the transition dipole moment of a spin-forbidden radiative transition is a weighted sum of spin-allowed dipole transition moments is exactly what experimentalists mean when they speak of intensity borrowing. The contribution of perturbing states to the oscillator strength can be positive or negative. In other words, per-turbers can not only lend intensity to a spin-forbidden transition, they can also take it away. 

The first term in Equation (1.47) is identical with the expression derived in the last section for electronically allowed transitions. It is presently assumed to be very small or zero. (A/o f - 0 for symmetry-forbidden transitions.) The second term results from vibronic mixing and represents a first-order vibronic contribution to the transition moment. It is seen that in this description the forbidden transition 0->f steals or borrows intensity from the allowed transition 0- b. If A/o f is exactly zero all observed components of the electronic transition will be polarized along the direction of the transition dipole moment A o b. The 0- 0 transition (v = v = 0) will have zero intensity and only vibrational levels of overall symmetry given by the direct product of symmetries of the states % and % will appear. 

The position of the 0 O band defines the energy of the excited state relative to that of the ground state, E0 0 = hv0 0. It can usually be located accurately in gas-phase spectra, especially in high-resolution spectra that can be obtained in low-temperature molecular beams. In solution, however, many molecules do not exhibit any vibrational fine structure in their electronic absorption spectra, so that it is difficult to determine v0 0. Moreover, the intensity dependence illustrated in Figure 2.10 holds only for symmetry-allowed transitions (see Section 4.4). That symmetry-forbidden transitions are observable at all as weak absorptions is due to vibrational borrowing vibronic transitions to upper (non-totally symmetric) vibrational levels become weakly allowed when the total symmetry of the vibronic transition is considered. Forbidden 0 0 bands are sometimes (barely) detectable in solution spectra due to symmetry perturbations induced by the solvent, but possible contributions from hot bands (Section 2.1.4) must be taken into account. 

If the intensity of the forbidden transition, into the vr vibrational level is borrowed from several vibrational levels, vm, of the main state, then... 

Thus the dipole-forbidden transition to the state can become vibrationally allowed, borrowing intensity from the interfering Bj state via modes of b2 symmetry. 

For allowed electric dipole transitions, the contributions from vibrational coupling can be neglected. In the case of a forbidden electric or a magnetic dipole transition there should be contributions from the vi-bronic coupling and intensity-borrowing from other transitions via vibrations of the molecules. 

Because of the importance of intensity borrowing, a forbidden electric and magnetic dipole transition of a compound of symmetry D2 will be analysed as an example. For the transition j N) —> R) between an electronic and vibrational ground and an electronic and vibrational excited state A —> A, only the coefficient R(2) ] in Equation [46] is different from zero. With Equation [50], the frequency dependence of the CD and ACD is determined by a progression starting on false origins of one vibration = v = 1,2... of an... 

The quality of the SOC calculation in O2 can be checked by estimation of the fc Sj" — A3E transition probability. The transition is forbidden by selection rules for electric dipole radiation with account of SOC, and occurs as magnetic dipole spin-current borrowing intensity from microwave transitions between spin-sublevels of the ground state [41]. 

---