J-manifolds

We have seen earlier that Eu3+ possess two resonance levels, Do mid 5Z>i, from which fluorescence transitions to the J manifold of 1F takes place. The 5Do - 7Fo transition is strictly forbidden for regular octahedral symmetry but is observed in some complexes due to the lack of centro-symmetry. The intensity of the fluorescence transition is not directly dependent only on the amount of T 4f energy transfer, but mainly on the transition probabilities from a particular resonance level to the various J manifolds. However, the transition probabilities are sensitive functions depending on the ligand. A schematic representation of the... 

Ligand field effects split the J manifold in a way that is not easily predicted without specific calculations. However, the overall splitting is such that many of the levels are appreciably populated at room temperature. An elegant procedure that takes such effects into account in a general way with respect to pseudocontact shifts of metal-centered origin has been provided by Bleaney [79]. 

Numerical calculations of (Sz) at 300 K obtained with eq. (22) for all /((III) free ions are collected in table 3 (Golding and Halton, 1972). Pinkerton et al. (1985) have demonstrated that (Sz) are relatively insensitive to the choice of various sets of reported spin-orbit coupling constants. Moreover, except for R = Sm and Eu, (Sz) displays a minor dependence on the temperature and the data calculated at 300 K (table 3) are amenable for a reliable treatment of contact shifts in solution around room temperature. The close proximity of excited states possessing different J manifolds for Sm(III) requires a precise calculation of (Sz) at each temperature as is the case for R = Eu. However, the latter metal brings some specific complications associated with the absence of a well-defined gj value for its 7 = 0 ground state. Golding... 

Zeeman shift required a careful analysis, so that also the 23P, Gj was measured. V. Hughes and collaborators measured all the three intervals separately, since the mixing of FS levels induced by the magnetic fields allowed even J = 2 to J = 0 transitions (we note as J a level that connect to the J manifold at zero magnetic field). Their published results have been recently modified by taking into account better the systematic effects due to the strong magnetic fields [12]. 

The Hartree—Fock basis has a particular significance. The eigenstate n) of the j manifold is represented by the configuration sum... 

Very recently, de Lange et al.30 carefully studied the intensities of the low J manifold of pyrazine with a nanosecond laser, which averages reasonably well over the quantum yields of the MEs. Taking a clue from the beautiful results obtained on benzene by Riedle et al.,31 they fitted the intensities to a quantum yield determined by Coriolis coupling of S, to S0. They assumed a Boltzmann distribution in the ground state, except for the J" = 0, K" = 0 state, which for nuclear symmetry reasons can only be reached by a A J" = — 2 transition. 

Judd (29), in his classic paper of 1962, used the odd parity terms of the ligand field to accomplish this admixture. After applying second order perturbation theory and several simplifying assumptions, he showed that the electric dipole line strength between J-manifolds may be expressed as the sum of three terms, each being the product of an intensity parameter and a reduced matrix element of the tensor operator U of rank X. The electric dipole line strength, Se(j, can be written in the form... 

B. Current Status of An3+ Ion Line Strengths. As with the lanthanides, solution spectra were the first to be investigated in terms of the Judd parameterization scheme. The light actinides U +, Np3+, and Pu3+ have a rather high density of states in the optical region, therefore the free-ion J-manifolds overlap and analysis is difficult. Am + is a special case. 

Only transitions between the ground J = 0 and even J-manifolds are allowed in the context of the free-ion approximation. For Cm + and the heavier actinides Bk +, Cf +, and Es + a number... 

A. Electron-Phonon Interaction Parameterization Scheme. In observing the fluorescence decay rate from a given J-manifold, it is generally found that the decay rate is independent of both the crystal-field level used to excite the system and the level used to monitor the fluorescence decay. This observation indicates that the crystal-field levels within a manifold attain thermal equilibrium within a time short compared to the fluorescence decay time. To obtain this equilibrium, the electronic states must interact with the host lattice which induces transitions between the various crystal-field levels. The interaction responsible for such transitions is the electron-phonon interaction. This interaction produces phonon-induced electric-dipole transitions, phonon side-band structure, and temperature-dependent line widths and fluorescence decay rates. It is also responsible for non-resonant, or more specifically, phonon-assisted energy transfer between both similar and different ions. Studies of these and other dynamic processes have been the focus of most of the spectroscopic studies of the transition metal and lanthanide ions over the past decade. An introduction to the lanthanide work is given by Hiifner (39). 

Multiphonon relaxation processes are usually studied by determining both the transition rates for the process, and the phonon spectrum of the host crystal. Total transition rates (reciprocals of fluorescent lifetimes) are measured and multiphonon (MP) decay rates are extracted from these. In practice, one does not observe the MP transition rate between two energy levels, but that between two J- manifolds, i.e.- the sets of Stark States The decay rate, W, obeys the relation ... 

This evolution will be modified in the presence of colhsions by what was previously defined as primary processes vibrational and rotational relaxation within the i> and j/) manifolds, dephasing of initially prepared coherent states and (in principle) coherence-transfer effects. The basis of zero-order states (pure-spin states in the case of intersystem crossing) has been chosen for this discussion, because it provides clear separation of intramolecular and intermolecular effects the j) and /> states are mutually coupled by the intramolecular (spin-orbit) coupling u, while collisions may uniquely couple 5> and j > ( /> and / >) states within each manifold. 

The rates k/ and k correspond to any nonradiative decay channel, which couple to the levels /) and /n). It should be kept in mind, however, that reverse collisionally induced electronic transitions may follow vibrational relaxation in the /) manifold, thus leading to further emission. This effect must be taken into account when the jj) level is not the lowest one in the j>) manifold (see Section III.B). 

These calculations were carried out for various sets of parameters e i,V i, k, kjj and y, . In addition, the number of relevant levels in the ( j) and (j/) manifolds was accounted for by assigning to the levels w) and m> statistical weights N and N respectively, thus considering them as sets of N (N ) degenerated levels. 

As shown above, the electronic relaxation in small molecules may be more efficient than the vibrational relaxation within the same electronic state. If, moreover, one of interacting electronic states is nonradiative, that is, if the lifetime of molecules transferred to the /> state is much longer than that of the 5> state, new specific deactivation chaimels may play an important role. The usual path of vibrational relaxation within the j manifold collision-induced transitions from initially excited nth to (o— l)th vibronic level may be less efficient than a many-step process involving... 

On the other hand, if the initial excitation prepares one of higher vibronic states in the (j) manifold, this state will be coupled to the lower (s ) levels as well, as to the / levels. The vibrational relaxation within the... 

Table 2 contains corrected energies of Pr + obtained by multiplication of the 2 values by the averaged ratio X — l/iVX)ili Eu/E2i = 0.75 (where N is the total number of J manifolds, Eli and 2 are the (th energies obtained by the semiempirical and first principles calculations, respectively). Inclusion of this correction significantly improves the agreement of the first principles results with semiempirical ones as well as with the Dieke diagram (fig. 1). 

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