Pseudo-quadrupolar transitions

The forced electric dipole mechanism was treated in detail for the first time by Judd (1962) through the powerful technique of irreducible tensor operators. Two years later it was proposed by Jorgensen and Judd (1964) that an additional mechanism of 4/-4/ transitions, originally referred to as the pseudo-quadrupolar mechanism due to inhomogeneities of the dielectric constant, could be as operative as, or, for some transitions, even more relevant than, the forced electric dipole one. 

The electric quadrupole transition arises from a displacement of charge that has a quadrupolar nature. An electric quadrupole consists of four point charges with overall zero charge and zero dipole moment. It may be pictured as two dipoles arranged so that their dipole moments cancel. An electric quadrupole has even parity. Electric quadrupole transitions are much weaker than magnetic dipole and induced electric dipole transitions. At this moment no experimental evidence exists for the occurrence of quadrupole transitions in lanthanide spectra, although some authors have claimed the existence of such transitions (e.g. Chrysochoos and Evers 1973). However, the so-called hypersensitive transitions (see sect. 8) are eonsidered as pseudo-quadrupole transitions, because these transitions obey the selection rules of quadrupole transitions. 

The intensities of the induced electric dipole transitions in lanthanide ions are not much affected by the environment. The dipole strength of a particular transition of a lanthanide ion in different matrices will not vary more than a factor two or three. However, a few transitions are very sensitive to the environment, and these are usually more intense for a complexed lanthanide ion than for the lanthanide ion in aqueous solution. The intensity increases up to a factor 200 (Gruen and DeKock 1966, Gruen et al. 1967). Only in a few cases has a lower intensity than in the aqueous solution been reported for these transitions (e.g. Krupke 1966). Jorgensen and Judd (1964) have called such transitions hypersensitive transitions. They noted that all known hypersensitive transitions obey the selection rules A5 = 0, AI 2 and jAJj 2. These selection rules are the same as the selection rules of a pure quadrupole transition, but calculations have revealed that the intensities of hypersensitive transitions are several orders of magnitude too large for these transitions to have a quadrupole character. Therefore, hypersensitive transitions have been called also pseudo-quadrupole transitions. No quadrupole transitions have been observed for lanthanide ions, although Chrysochoos and Evers (1973) stated that the intensity of the hypersensitive transitions D2 Fq (in the absorption spectrum) and Do Fi (in the luminescence spectrum) of Eu " are mainly quadrupolar in nature. 

CS tensors for complex spectra, 1, 463 dicyclopentadienylberyllium compounds, 2, 74 tj4-diene and rf-allyl pseudo-rotations, 1, 416 half-integer quadrupolar nuclei, central transition, 1, 457 half-integer spin quadrupolar nuclei central transition,... 

MQCs are not excited uniformly and the efficiency with which the various orders of MQC are excited depends specifically on the parameters of the spin system (dipolar couplings, scalar couplings, quadrupolar couplings, chemical shifts) in the spin system and the choice of the preparation time t. Many researchers have co-added spectra acquired with different preparation times to ensure that all transitions are observed with reasonable intensity. A number of broadband excitation techniques have been developed,13-15 where the value of t in the preparation sequence has been varied either in a pseudo-random or systematic fashion to achieve a more uniform excitation in the multiple quantum domain. An experimental search method has been used to optimise the delays in the preparation period of the MQ excitation sequence16 and Wimperis17 used average Hamiltonian theory to propose... 

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