Dipole strength of transition

The strength or intensity of absorption is related to the dipole strength of transition D or square of the transition moment integral M m , and is pressed in terms of oscillator strength / or integrated molar extinction jfe Jv. A transition with /= 1, is known as totally allowed transition. But the transitions between all the electronic, vibrational or rotational states are not equally permitted. Some are forbidden which can become allowed under certain conditions and then appear as weak absorption bands. The rules which govern such transitions are known as selection rules. For atomic energy levels, these selection rules have been empirically obtained from a comparison between the number of lines theoretically... 

Since the dipole strength of/-/ transitions are formally forbidden, typically, these extinction coefficients are of the order of 1 M cm an alternative path has to be used which is called luminescence sensitization or antenna effect, that is when the luminescent ion is coordinated with an organic ligand or imbedded into a matrix, then the energy absorbed will be transferred from the surrounding onto the luminescent ion and subsequently the ion emits characteristic light. 

The quantity [Xed/ (2J + 1)] ed is sometimes denoted as and can be compared directly with the experimental dipole strength of transition i. The root mean square deviation error RMS is a measure for the goodness of the fit ... 

A parameter that has proven useful in the interpretation of experimental MCD spectra is the dipole strength. The dipole strength of a transition to state J, Dj, can be derived from an absorption spectrum. Dj is defined as... 

Mm I2 is sometimes written as R m 2, where R is known as the Imatrix element of the electric dipole moment and has the same meaning as Vie transition moment integral. There are a few other related quantities which are used forexpressing the strength of an electronic transition. f)ipole strength of transition... 

Unfortunately the calculation of transition probabilities has not been attempted in many instances and the results are not encouraging. Apart from a valiant early attempt by Davies173 for Na2 in a calculation where not all electrons were specifically considered, the first serious attempt to compute transition probabilities from ab initio wavefunctions was due to La Paglia.174 In this important paper La Paglia considered the dipole strengths of various 1 -iE transitions for some first-row diatomic molecules. 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

The eight-coordinate tetrakis(diethyldithiocarbamate) lanthanide complexes are isomor-phous and the lanthanum complex has a quasi-tetrahedral configuration of the four CS2 chelate groups. The transition frequencies and dipole strengths of these complexes available over the accessible f-f manifold allowed the extraction of the Judd-Ofelt intensity parameters Qx for k = 2, 4, 6 by standard least squares methods [112,113]. The values of observed Qx and calculated Q, values are given in Table 8.10. The three components of f2() are... 

Figure 7. Rotational and dipole strengths of the transitions of the model compound of naphthalene-diene (12bS)-26 calculated by the Tc-electron SCF-CI-DV MO method. 18...

The square of the first-order electric dipole moment [Eq. (5)] represents the dipole strength of the metal ion transition in the complex, Dq, which in turn is related through universal constants to the corresponding oscillator strength, foa,... 

Table 2. The mean wavenumber (ircm ), from the first moment of the integrated band area, and the observed and the calculated [Eqs. (5) and (6)] oscillator strength (f/10 ) of the d-d transitions to the Ti (F) and Ti (P) excited state of the cobalt(II) tetrahalides from the A2 ground state, together with the temperature coefficient (C/10 ) of the summed dipole strengths of the two transitions [Eq. (IS)] from X The theoretical f-values are minimal, calculated from the expectation value, tr ) = 0.3661 A, appropriate for a dipositively charged metal ion in the complex...

Optical rotation is a general term which is used to include both circular dichroism and optical rotatory dispersion. These are closely related phenomena in the same way that absorption and ordinary dispersion (refractive index) are related. They can be interconverted by mathematical transforms. Whereas the common element in absorption and ordinary dispersion is the dipole strength of the transition, the common quantity in circular dichroism and optical rotatory dispersion is rotational strength. And, as will be seen below, the rotational strength of a transition may be obtained from either measurement. 

Figure 5. Slick" molecules in the possible modes of interaction during an optical transition, with transition density represented by vertical displacement from the horizontal sticks. Right, the transition densities cancel each other and are silent, and left, the transition densities add so that the dimer becomes a supermolecule with a single allowed optical transition having the combined dipole strength of the two participating molecules. (Reproduced, with permission, from Ref. 30. Copyright J973, Society of Photographic Scientists and Engineers.)...

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