Vibronic transitions electric-dipole intensity

It is found experimentally that the intensity of both the magnetic dipole and vibronically induced electric dipole allowed transitions are principally determined by the orbital character of the electronic states. That is, transitions that are forbidden in the orbital basis but allowed in the spin-orbit basis in Table 1, are likely to be weak. 

AJ = 1), have a pure magnetic dipole character. The transitions with AJ = 0, 2 have both a magnetic dipole and a vibronically induced electric dipole character. Later, calculations of vibronic intensities based on the model have been reported by the... 

A very weak peak at 348 mn is the 4 origin. Since the upper state here has two quanta of v, its vibrational syimnetry is A and the vibronic syimnetry is so it is forbidden by electric dipole selection rules. It is actually observed here due to a magnetic dipole transition [21]. By magnetic dipole selection rules the A2- A, electronic transition is allowed for light with its magnetic field polarized in the z direction. It is seen here as having about 1 % of the intensity of the syimnetry-forbidden electric dipole transition made allowed by... 

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. 

Crystal field, or d-d, transitions are defined as transitions from levels that are exclusively perturbed d orbitals to levels of the same type. In other words, the electron is originally localized at the central metal ion and remains so in the excited state. When the system has ( symmetry, Laporte s rule says that an electric-dipole allowed transition must be between a g state and an u state, i.e., u - g. Since all the crystal field electronic states are gerade ( g ), no electric-dipole allowed transitions are possible. In short, all d-d transitions are symmetry forbidden and hence have low intensities. The fact that the d-d transitions are observed at all is due to the interaction between the electronic motion and the molecular vibration. We will discuss this (vibronic) interaction later (Section 8.10). 

We therefore developed a much simplified, but mathematically exact, version of a shell model which is particularly suitable for the analysis of cross relaxation in high symmetry systems such as the lanthanide elpasolites. Since the vibronic structure in the emission and absorption spectra of these compounds is both intense and broad (relative to the electronic origins), there are many cases where the vibronic structure of one electronic transition in emission overlaps with the vibronic structure of another electronic transition of a chemically identical ion in absorption. The emission of the excited ion may then be partially quenched by energy transfer. Implicit in this formulation is the assumption that the interionic coupling is weak compared with the vibronic coupling this is certainly true for the lanthanide elpasolites where the lanthanide ions are separated by distances of more than 0.7 nm. We refer to this process as cross relaxation by the electric dipole vibronic-electric dipole vibronic (EDVEDV) mechanism. 

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). 

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