Forced dipole selection rules

Accordingly, the selection rules for Raman and IR spectroscopy are different. In Raman spectroscopy, there must be a change in the molecule s polarizability upon excitation, whereas a change in dipole moment is required for IR. A dipole moment is the magnitude of the electronic force vector between the negative and positive charges or partial charges on a molecule. A permanent dipole moment exists in all polar mol-... 

Forced electric dipole emission occurs if it is possible to mix even functions into the uneven 4/ functions, so that the parity selection rule is relaxed. It is usually assumed that this occurs by 4f—5d mixing. For Eu +, however, the 4/ 5high energy (see Table 3). Since the electric-dipole emission dominates for Eu3+ on sites without inversion S5unmetry, it seems obvious to assume that another state is used to relax the parity selection rule. This must occur by mixing the 4/ configuration with the levels of opposite parity of the c.t. state. 

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... 

The model which has been most widely applied to the calculation of vibronic intensities of the Cs2NaLnCl6 systems is the vibronic coupling model of Faulkner and Richardson [67]. Prior to the introduction of this model, it was customary to analyse one-phonon vibronic transitions using Judd closure theory, Fig. 7d, [117] (see, for example, [156]) with the replacement of the Tfectromc (which is proportional to the above Q2) parameters by T bromc, which include the vibrational integral and the derivative of the CF with respect to the relevant normal coordinate. The selection rules for vibronic transitions under this scheme therefore parallel those for forced electric dipole transitions (e.g. A/ <6 and in particular when the initial or final state is /=0, then A/ =2, 4, 6). 

Our next step is to further examine selection rules for "forced eleetric dipole" transitions. We need to account for the actual energy observed, in terms of the two terminal states possible, i.e.- yellow = [17560 cm i Hi3/2l VS [green = 21,020 em 6H15/2]. We can see that if an excitation energy of 40,000 cm were to be used, the 2Hh/2 level would be... 

In NaGd02 Eu " the Dd- I 2 emission transition dominates, but other lines are also present. The Eu case is so illustrative, because the theory of forced electric-dipole transitions [8] yields a selection rule in case the initial level has J - 0. Transitions to levels with uneven J are forbidden. Further J = O->J = 0is forbidden, because the total orbital momentum does not change. This restricts the spectrum to D()- Fi, present as magnetic-dipolc emission, but overruled by the forced electric-dipole emission,... 

Fig. 7 Use of Do — Fj Eu luminescence as a probe of site symmetry in crystals. The transitions p3, are forbidden under Judd selection rules and are usually very weak so they are not included. The scheme refers to forced electric dipole-allowed transitions except for the case of the transition, which is allowed by the magnetic dipole mechanism (adapted from [102])...

However it also follows that if there were only dipole forces all the even terms in Zp would be zero for the dipole-allowed transitions. Each term in the Bom series progresses from the initial state to the final by a series of transitions between virtual intermediate states. There are as many transitions as there are orders in the Born term. Each transition changes the parity of the state. Thus an odd number of transitions are required for a dipole-allowed state and therefore only the odd order Born terms contribute. In reality though we only have dipole dominance, not a pure selection rule. Also, first order Born terms are usually not negligible even when forbidden. In any case in the example shown in fig. 5.3, when the sign of Zp is reversed, the cross section 1S-2P remains the same but this is not true of the forbidden transition 1S-2S. 

However, /-/ transitions are formally electric dipole forbidden by the Laporte selection rule, (a change in orbital angular momentum of 1 is required to accommodate the loss of photon spin upon absorption), although they are allowed by electric quadrupole, magnetic dipole and forced electric dipole mechanisms to some extent. Direct excitation of the Ln " ion is therefore not easily achieved, due to the low molar absorption coefficients associated with these transitions... 

Generally, the room temperature emission spectra of Ln species show incompletely resolved stmcture within the peaks. However, an advantageous attribute of luminescent Ln complexes is the dependence of this emission spectral form on the specific coordination environment of the ion. This sensitivity arises from the selection rules associated with intraconfigurational (4f-4f) electronic transitions the selection rules for forced electric dipole transitions are relaxed due to 5d and 4/orbital mixing. In reality the majority of the complexes included for discussion here are non-centrosymmetric, low symmetry species and the relative intensities of the 4/-4/transitions are generally determined by the induced electric dipole transition selection rules. It should also be noted that visibly emissive Eu also possesses a magnetic dipole transition, F, whose intensity is relatively independent of the coordination environment [1,9]. 

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