Transitions parity-allowed

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. 

Conjugated polymers are centrosymmetric systems where excited states have definite parity of even (A,) or odd (B ) and electric dipole transitions are allowed only between states of opposite parity. The ground state of conjugated polymers is an even parity singlet state, written as the 1A... PM spectroscopy is a linear technique probing dipole allowed one-photon transitions. Non linear spectroscopies complement these measurements as they can couple to dipole-forbidden trail-... 

Excited states formed by light absorption are governed by (dipole) selection rules. Two selection rules derive from parity and spin considerations. Atoms and molecules with a center of symmetry must have wavefunctions that are either symmetric (g) or antisymmetric (u). Since the dipole moment operator is of odd parity, allowed transitions must relate states of different parity thus, u—g is allowed, but not u—u or g—g. Similarly, allowed transitions must connect states of the same multiplicity—that is, singlet—singlet, triplet-triplet, and so on. The parity selection rule is strictly obeyed for atoms and molecules of high symmetry. In molecules of low symmetry, it tends to break down gradually however,... 

Divalent rare earth ions also have an outer electronic configuration of 4f"( including one more electron than for the equivalent trivalent rare earth). However, unlike that of (RE) + ions, the 4f " 5d excited configuration of divalent rare earth ions is not far from the 4f" fundamental configuration. As a result, 4f" 4f " 5d transitions can possibly occur in the optical range for divalent rare earth ions. They lead to intense (parity-allowed transitions) and broad absorption and emission bands. 

Since the Cg orbitals are stabihzed by interaction with the d-orbitals of the central ion, he ascribed the first c.t. transition to the parity-allowed hg- -f. Since neither the hg nor the / level are strongly influenced by the bonding in the complex, the position of the c. t. transition is expected to be host-lattice independent as observed experimentally for six-coordination. 

Rare earth ions (band emission) Ce + 5d-4f Transition is parity allowed and spin selection is not appropriate =y fully allowed (10-100 ns)... 

Transitions onto the levels of mixed 4/ 5d-configuration result in the appearance of broad intensive absorption bands. These specific features are due, first, to the fact that the said transitions occur between states with dissimilar electron configurations and, therefore, are parity-allowed. In these transitions... 

By reference to the MO scheme in Fig. 2, the bands at X < 400 nm have been assigned to sharp and intense parity-allowed transitions between occupied (bonding) and empty (antibonding) MOs. Such excitations include Au(HOMO)— fJg(LUMO + 1) and hg—> Optical transitions between the HOMO(Au) and LUMO(f/u), which are electric dipole forbidden, occur via excitation of a vibronic state with appropriate parity symmetry and account for the broad and low intensity band at X > 400 nm. 

Table 2 lists the selection rules for beta decay the entry A means that for die indicated spin and parity change llie transition is allowed 1, means that it is first forbidden II, second forbidden. .. 

Fig. 3). Note that optical transitions between the two configurations are parity allowed as electric-dipole transitions. The spin-selection rule is relaxed by spin-orbit coupling, the more so the higher the principal quantum number is. Due to selection rules on AJ, the transitions 1S0-3F0 and 1S0-3P2 remain strongly forbidden. The emission is due to the 3P0,i >1 o transition. Whether 3P0 or 3Pj is the initial level depends on their energy difference and the temperature.

The interconfigurational 4/"-4/n 15d transitions are of a different nature. They are parity allowed and can be described with the intermediate-coupling model, i.e. 1 < S < 5. In some cases a beautiful vibrational structure with a short progression has been observed. 

A-jg) transition which is symmetry and parity allowed for an electric dipole transition mechanism the spin selection rule is suspended by the large spin orbit coupling of about Ijp 3T 2 400 cm (j 2). Since analysis of the progressions yields, for both compounds, only eg quanta (240 cm 1 for Cl, 154cm 1 for Br) the excitea state must be distorted by Jahn-Teller forces... 

For the 4f7 configuration of Eu2+, the host sensitive energy levels of the 4f65d states are not far from the metastable 4f7 6P7/2 multiplet near 27 000 cm-1. The strength of crystal field interaction determines whether the lowest 4f65d state is above or below the excited 4f7 multiplet, which is insensitive to host lattice. Because there is no 4f state below 6P7/2, strong blue luminescence arises from the parity allowed 4f55d-4f7 transition. The intensity of the... 

Relaxation of the rules can occur, especially since the selection rules apply strongly only to atoms that have pure Russell-Saunders (I-S) coupling. In heavy atoms such as lanthanides, the Russell-Saunders coupling is not entirely valid as there is the effect of the spin-orbit interactions, or so called j mixing, which will cause a breakdown of the spin selection rule. In lanthanides, the f-f transitions, which are parity-forbidden, can become weakly allowed as electric dipole transitions by admixture of configurations of opposite parity, for example d states, or charge transfer. These f-f transitions become parity-allowed in two-photon absorptions that are g g and u u. These even-parity transitions are forbidden for one photon but not for two photons, and vice versa for g u transitions [46],... 

The selection rules are restrictions imposed on the quantum transitions, because of the laws of conservation of angular momentum and parity [59], In the case of IR spectroscopy, within the frame of the harmonic approximation, the applicable rules are the electric dipole selection rules. That is, when the expression in Equation 4.19 has a finite value, the transition is allowed, and when this expression is zero the transition is forbidden. In the Raman case, when one of the integrals given by Equation 4.23 is different from zero, the normal vibration associated is Raman-active. 

In solutions, the energy of the 4f—> 5d transitions is lowered by about 15000 cm-1 as compared to gaseous ions and the corresponding parity allowed and relatively intense bands are observed in the ultraviolet region in Ce3+, Pr3+ and Tb3+ ions. As shown in Fig. 8.14, the electronic absorption spectra of the majority of the trivalent lanthanides in the UV-vis spectral range involves only f-f transitions. 

Magnetic dipole transitions play a role in the luminescence of some lanthanide ions, specially Eu +, when the local symmetry deviates little from inversion symmetry. They are parity-allowed between states ofthe3d or4f configurations but have a low probability. They are subject to selection rules AL = A5" = 0 and AJ = 0, 1 (0 0 forbidden). 

The opposite effect, the so-called down-conversion was reported in 1974, independently, for YFsiPr [5.230, 5.231]. Here, two photons with lower energy (visible) are emitted per photon absorbed at energy above about 5.7 eV (Figure 5.52). Absorption preferably takes place in the 5d band of Pr, as the underlying 4f-5d optical transition is parity allowed (Figure 5.53). 

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