Selection rules for induced electric dipole

Selection rules for induced electric dipole transitions... 

From eq. (143) selection rules for induced electric dipole transitions can be derived ... 

By making use of the selection rules for induced electric dipole (ED) and magnetic dipole (ED) transitions (see Appendix 5), it is in principle possible to discriminate between the different point groups. This has been explored by several authors, like Sinha and Butter (1969). These authors determined the symmetry of europium complexes, but their symmetry discriminating table contains unfortunately many errors. Bunzli (1989) has discussed the use of the Dq,i — luminescent transitions of Eu for the point... 

Appendix 5. Selection rules for induced electric dipole (ED) and magnetic dipole (MD) 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]. 

Perturbations affect the rate of absorption and emission of radiation in a fully understood and exactly calculable manner. They also affect the rates of chemical and collisional population/depopulation processes, but in a less easily estimated way. Perturbation effects on steady-state populations can be very large and level-specific. Although collision-induced transitions and chemical reactions are not governed by rigorous selection rules as are electric dipole transitions and perturbation interactions, some useful propensity rules have been suggested theoretically and confirmed experimentally. Gelbart and Freed (1973) suggested that the cross sections for collision-induced transitions between two different electronic states, E and E, are... 

The selection rules for the Raman spectrum turn out to depend not on the matrix elements of the electric dipole moment, but on the matrix elements of the molecular polarizability, which we now define. The application of an electric field E to a molecule gives rise to an induced electric dipole moment djnd (which is in addition to the permanent dipole moment d). If E= "> 1 + yl+ >zk, then the induced dipole moment has the components... 

It must be stressed that the polarizability gradient da/dQk also appears in the equation for Raman intensities [175], as indicated also by Lambert [176]. Thus, in view of Eq. (25), we can extend the consequences of the static electric field to vibrations which are forbidden by the surface selection rule the high electric field in the double layer can induce a dipole moment component in the direction of the field on permanent dipoles which are parallel to the surface. Thus the effect of orientation due to the electric field is just a manifestation of the Stark effect. 

For excitation by a weak beam of radiation, such that a single photon is involved per absorption event, one is mainly concerned with electric dipole transitions, because they are usually the strongest. Other selection rules will apply if the transitions are not due to an induced electric dipole. 

Due to the mixing of for example p2 and D2 states the transition D2 <— is allowed by the induced electric dipole mechanism, the relevant selection rules being ... 

The mechanism by which the Raman effect occurs can be understood classically, although a quantum mechanical derivation is necessary for understanding the variation in line intensities and developing selection rules for predicting which vibrational modes are Raman active. Both descriptions are based upon an interaction between the oscillating induced polarization or dipole moment of the molecule (P) and the time-dependent electric field vector of the incident radiation (E). 

It turns out that the atom has built into it very good tests to determine if it is in a state of definite parity. A selection rule for electric dipole ( 1) transitions is that the parity of the final state must be opposite from that of the initial state. Therefore, one cannot induce an 1 transition between two electronic energy levels of the same parity. But if these electronic levels have a small admixture of opposite parity state (due, for example, to the... 

A FIGURE 9.5 The dipole selection rule for rotational transitions. A polar molecule can be induced to change its rotational state by interaction with the electric field of a photon, as long as the field vector has some component that is parallel to the dipole moment of the molecule (a). If the electric field vector of the photon is perpendicular to the dipole moment (b), or if the dipole moment is zero (c), there is no allowed interaction. 

Raman spectroscopy also has selection rules. The gross selection rule for a Raman-active vibration is related to the polarizability of the molecule. Polarizability is a measure of how easily an electric field can induce a dipole moment on an atom or molecule. Vibrations that are Raman-active have a changing polarizability during the course of the vibration. Thus, a changing polarizability is what makes a vibration Raman-active. The quantum-mechanical selection rule, in terms of the change in the vibrational quantum number, is based on a transition moment that is similar to the form of M in equation 14.2. For allowed Raman transitions, the transition moment [a] is written in terms of the polarizability a of the molecule ... 

The intensities of the majority of the f-f transitions vary only within a factor of 2-3 from host matrix to host matrix, but some transitions are much more host dependent. These transitions are called hypersensitive transitions. These induced electric dipole transitions obey the selection rules for electric quadrupole transitions and are therefore sometimes called pseudo-quadrupole transitions. In sect. 8, we will discuss hypersensitivity in detail. The dependence of the Qx intensity parameters on the host matrix is the subject of sect. 9. Two-photon spectra (sect. 10) and vibronic transitions (sect. 11) are discussed briefly. On the other hand, chiroptical methods will not be considered. Since the color of the lanthanide ions is related to the spectral intensities of f-f transitions, we want to give attention to the phenomenon of color (sect. 12). Finally, the intensities of actinide ions are reviewed (sect. 13). 

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. 

Judd (1962) and independently Ofelt (1962) worked out the theoretical background for the calculation of the induced electric dipole matrix element. The basic idea of Judd and Ofelt is that the intensity of the forbidden f- f electric dipole transitions can arise from the admixture into the 4f configuration of configurations of opposite parity (e.g., 4f d and 4f " n g ). As already mentioned in the introduction, we will unravel here in detail the theoretical model developed by Judd. Special attention will be given to the dimensions, units and selection rules. Our symbolism is close to Judd s. The difference is that we represent the crystal-field coefficient by (instead of Judd s Atp), the light polarization by p (instead of Judd s q), and the additional quantum number by r (Judd s y). 

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. 

Since both the operator and the/orbitals have u (ungerade, odd) symmetry, electric dipole transitions are forbidden by the parity rule (see section below on Judd-Ofelt theory and induced electric dipole transitions). The selection rales for these transitions are summarised in Table 1.13. 

Raman and IR spectroscopies are complementary to each other because of their different selection rules. Raman scattering occurs when the electric field of light induces a dipole moment by changing the polarizability of the molecules. In Raman spectroscopy the intensity of a band is linearly related to the concentration of the species. IR spectroscopy, on the other hand, requires an intrinsic dipole moment to exist for charge with molecular vibration. The concentration of the absorbing species is proportional to the logarithm of the ratio of the incident and transmitted intensities in the latter technique. 

A rotation of the H2 molecule through 180° creates an identical electric field. In other words, for every full rotation of a H2 molecule, the dipole induced in the collisional partner X oscillates twice through the full cycle. Quadrupole induced lines occur, therefore, at twice the (classical) rotation frequencies, or with selection rules J — J + 2, like rotational Raman lines of linear molecules. Orientational transitions (J — J AM 0) occur at zero frequency and make up the translational line. Besides multipole induction of the lowest-order multipole moments consistent with... 

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