Allowed /-transitions

If one of the components of this electronic transition moment is non-zero, the electronic transition is said to be allowed if all components are zero it is said to be forbidden. In the case of diatomic molecules, if the transition is forbidden it is usually not observed unless as a very weak band occurring by magnetic dipole or electric quadnipole interactions. In polyatomic molecules forbidden electronic transitions are still often observed, but they are usually weak in comparison with allowed transitions. 

Using the selection rule for allowed transitions the relative intensity for the transition from the state Mg) to Mg+l) is given by... 

Most electronic valence transitions shift to longer wavelengths at higher pressures drat is, the gap between the highest occupied orbital and lowest unoccupied orbital tends to decrease upon compression. The rates of shift usually are larger (1) for pure materials than for solutes in a solvent and (2) for stronger (more allowed) transitions. However, these correlations are not quantitative, and many transitions shift in the opposite... 

Figure C 1.3.4. The real pattern of intennolecular bending energy levels for Ar-HCl (left) compared witli tire pattern expected for a free internal rotor (centre) and a near-rigid bender (right). The allowed transitions are shown in each case. (Taken from 1191.)...

At this point, it is important to note that as the potential energy surfaces are even in the vibrational coordinate (r), the same parity, that is, even even and odd odd transitions should be allowed both for nonreactive and reactive cases but due to the conical intersection, the diabatic calculations indicate that the allowed transition for the reactive case ate odd even and even odd whereas in the case of nomeactive transitions even even and odd odd remain allowed. 

The ordinary BO approximate equations failed to predict the proper symmetry allowed transitions in the quasi-JT model whereas the extended BO equation either by including a vector potential in the system Hamiltonian or by multiplying a phase factor onto the basis set can reproduce the so-called exact results obtained by the two-surface diabatic calculation. Thus, the calculated hansition probabilities in the quasi-JT model using the extended BO equations clearly demonshate the GP effect. The multiplication of a phase factor with the adiabatic nuclear wave function is an approximate treatment when the position of the conical intersection does not coincide with the origin of the coordinate axis, as shown by the results of [60]. Moreover, even if the total energy of the system is far below the conical intersection point, transition probabilities in the JT model clearly indicate the importance of the extended BO equation and its necessity. 

An example of an El forbidden but "vibronically allowed" transition is provided by the singlet n ==> ti transition of H2CO that was discussed earlier in this section. As detailed there, the ground electronic state has Ai symmetry, and the n ==> 71 state is of 1A2 symmetry, so the El transition integral... 

Such vibronically allowed transitions are said to derive their intensity through vibronic borrowing. 

Absorption of a photon is accompanied by the excitation of an electron from a lower-energy atomic orbital to an orbital of higher energy. Not all possible transitions between atomic orbitals are allowed. For sodium the only allowed transitions are those in which there is a change of +1 in the orbital quantum number ) thus transitions from s—orbitals are allowed, but transitions from s d orbitals are forbidden. The wavelengths of electromagnetic radiation that must be absorbed to cause several allowed transitions are shown in Figure 10.18. 

The transition probability R is related to selection mles in spectroscopy it is zero for a forbidden transition and non-zero for an allowed transition. By forbidden or allowed we shall mostly be referring to electric dipole selection mles (i.e. to transitions occurring through interaction with the electric vector of the radiation). 

Using the C2 character table (Table A. 11 in Appendix A) we can immediately write down the allowed transitions involving the zero-point level as... 

For a spherical rotor belonging to the octahedral Of, point group, Table A.43 in Appendix A, in conjunction with the vibrational selection rules of Equation (6.56), show that the only allowed transitions are... 

Cerous salts in general are colorless because Ce " has no absorption bands in the visible. Trivalent cerium, however, is one of the few lanthanide ions in which parity-allowed transitions between 4f and Sd configurations can take place and as a result Ce(III) compounds absorb in the ultraviolet region just outside the visible. 

Ceo samples [66]. At higher photon energies, dipole-allowed transitions ean occur, and the optical absorption increases dramatieally. 

Theoretical predictions must be compared to appropriate high quality experimental results. Allowed transitions (having oscillator strength greater than 0) may be compared to standard one-photon spectroscopic data. However, forbidden transitions must be compared to multi-photon experiments, and both types must be considered before a complete characterization of a system s excited states can be made. 

Singlet oxygen, O2, can readily be generated by irradiating normal triplet oxygen, 2 in the presence of a sensitizer, S, which is usually a fluorescein-type dye, a polycyclic hydrocarbon or other strong absorber of light. A spin-allowed transition then occurs ... 

Figure A Simplified Energy Level diagram for d ions showing possible spin-allowed transitions in complexes of low-spin cobalt(lll).

In a cubic field three spin-allowed transitions are expected because of the splitting of the free-ion, ground term and the presence of the term. In an octahedral field the splitting is the same as for the octahedral d ion and the same energy level diagram (p. 1029) can be used to interpret the spectra as was used for octahedral Cr Spectra of octahedral Ni usually do consist of three bands which are accordingly assigned as ... 

Whilst temperature coefficients suggest modest potential differences, these calculations do not take into account the large potential changes that can occur when thermal effects allow transition from active to passive states. 

Figure 15-3 shows the optical absorption spectrum of a MEH-PPV/C60 film with different C, content compared to the optical absorption spectrum of the components alone. The peak at 2.5 eV is identified as the n-n absorption of MEH-PPV and is clearly observed along with the first dipole-allowed transition in C(l0 (at 3.75 eV). The spectrum is a simple superposition of the two components. Further-... 

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