Transitions parity forbidden

Both absorption and emission spectra have been recorded for a variety of octahedral chromium(III) complexes. For the systems of interest here, A/B 2. Inspection of Figure 2 leads to the expectation of three spin-allowed, parity-forbidden transitions between the iA2g and the other quartet states and two spin- and parity-forbidden transitions between the iA2g and the 2Eg and 2T2g states. Aqueous solutions of Cr(H20)s3+ display three bands with e 15 at 17,400, 24,500, and 38,000 cm-1, assigned respectively to the transitions iA2g- iT2g,... 

Recently the observation of Fano antiresonance in the excitation spectra of the luminescence of Eu was reported (82). The two-photon absorption experiments by Downer et al. [37,38], for example, revealed the presence of sharp absorption lines due to transitions from the 87/2 ground state to the Pj, Ij and Dj states within the Af configuration of Eu ". These parity-forbidden transitions are overlapped by the broad 4/ 5d absorption bands of Eu. For this situation the appearance of Fano antiresonance in the vicinity of the sharp absorption lines is to be expected. 

Since f-cis-butadiene belongs to the point group C, which has no center of symmetry, it has no parity-forbidden transitions. 0 for the transition... 

The intrinsic E A2 luminescence (R-line) has a lower intensity, as typical for strictly octahedral symmetry, than the Cr(III) luminescence close to inverted sites l This is not surprising, since the parity-forbidden transitions become partially allowed when the high symmetry is lowered. The R-line intensity increases when Cr(III) is... 

Since the experimental discovery of TPA, multiphoton excitation has become a popular tool in the photochemical sciences to determine the excitation energy of states with parity forbidden transition [3-54], Transitions that are parity forbidden by one-photon (OP) excitation can thus become allowed by two-photon (TP) excitation. TP excitation spectroscopy localizes the energetic position of TP excited states, which cannot be observed by OP excitation. These pioneering works confirmed many quantum chemical studies predicting the existence of TP excited states and therefore experimentally completed the pattern of electronic transitions in organic compounds. In general, TP excitation had been mainly limited to academic interest until the end of the 1980s [2-24, 26-45, 47-52, 55-69]. 

In the above discussion of the electronic structure of the donor levels, the electron spin has been neglected. It has been, however, proven necessary to introduce the spin-orbit coupling to explain the observation of parity-forbidden transitions for donors with relatively deep ls(Ai) ground states. Using the double group representation of Td, it is found (see Table B.4 of appendix B) that the simple representations Ai and E transform into the T6 and Tg double representations, respectively and that T2 transforms into T7 + Eg. Electric-dipole transitions are symmetry-allowed between A (Tg) and the two T2 (Ty) and T2 (r8) levels. 

The Ch-related donor spectra differ on that point as several parity-forbidden transitions are observed. They start with symmetry-allowed transitions from the Is ground state to the valley-orbit split Is excited states, and are supplemented with 2s (T2) and 3s (T2) lines and Fano resonances within the photoionization spectrum. This is shown in Fig. 6.13 for Se°. Compared to group-V donors, this extends the energy span of the Ch°-related spectra to the ionization energy of the Is (T2) level (35-40 meV in isolated chalcogens) and it can even increase to 40-48 meV when singlet-triplet spin-forbidden transitions are observed. 

Considering the He-like ionization energies of the TDDs and their electronic degeneracy, no parity-forbidden transition equivalent to the ls(T2) line is observed in the TDD spectra. 

In P-compensated In-doped silicon, an absorption line at 1213 cm-1 (150.4meV) is observed at LHeT under TEC [135]. The vanishing of this line1 when the compensating donor is neutralized suggests that it could be a parity-forbidden transition. Its excited-state binding energy of 6.5 meV makes the attribution to a 2T7+ level plausible. 

The Judd-Ofelt theory explains how the observation of strictly parity forbidden transitions results from non-centro-symmetric interactions that lead to a mixing of states of opposite parity. One of the most obvious mechanisms is simply the coupling of states of opposite parity by the odd terms of the crystal field expansion. The transition, giving a... 

Transitions occur mainly by an electric dipole mechanism. Such transitions are allowed if the initial and final states are made up of orbitals of opposite parity (A/ =1,3,... / orbital angular momentum quantum number) and if the spin remains unchanged AS = 0) (Laporte rules, see Ligand Field Theory Spectra. However parity-forbidden transitions can occur as a result of mixing with states of opposite parity. Mixing of states by the crystal field requires that the cationic site lacks an inversion center. If the site is centrosymmetric, transitions can nevertheless be observed owing to vibronic coupling. Their probability is low and increases with temperature. 

Finally Figure 3.16 gives the decay time of the Eu emission in SrB407. At low temperatures it is 4 /is (parity forbidden transition), but at higher... 

The first selection rule is related to all molecules with centers of symmetry and deals with the parity-forbidden transitions. The second rule states that singlet-triplet transitions are forbidden. The third rule applies to forbidden transitions that arise... 

The second point above deserves particular attention. It is obvious that calculated transition energies always correspond to differences between the potential curves of the excited state and the ground state taken at a fixed molecular configuration. The spin-allowed and parity-forbidden transitions within the partly filled shell of transition metal ions considered here are associated with changes in electron configuration, e.g., h2t g) ig t%g eg). Consequently, ground and excited state... 

Experimentally, free-ion spectra (both neutral and ionic species) are usually observed in emission, and the energy level structure is deduced from coincidences of energy differences of pairs of spectral lines, subject to verification by isotope shift, hyperfine structure and magnetic gf-factor tests. In condensed phases, spectra are more commonly measured in absorption. Relative intensities associated with parity-allowed and forbidden transitions are reflected in the nature of two processes transitions in which the initial and final states belong to electronic configurations of different parity (parity-allowed transitions, e.g. 5f - 5f 6d) and those in which both states belong to the same configuration (parity-forbidden transitions, e.g. 5f 5f ). The latter are weak and sharp. The... 

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