Rotational strengths transitional

The planar C2h and C2V geometries of the 1,3-butadiene moiety are achiral structures and obviously they cannot show optical activity (i.e. ORD and CD). This has, of course, a spectroscopic origin. The optical activity of a transition Pq — Pi is determined by its Rotational Strength (R)1 defined as the scalar product... 

The main interest of this molecule resides in the fact that the principal source of rotational strength of the it - it lowest energy transition has been attributed40 to the twist of one of the two double bonds (a = —136°, as in fraws-cyclooctene) rather than to the twist of the 1,3-butadiene moiety (6 = +50.2°)... 

In the skewed form, instead, the transition is allowed both electrically and magnetically, with parallel transition moments. The product in equation 1 is hence non-vanishing, implying that this transition has finite rotational strength. This observation leads to the conclusion that skewed 1,3-butadiene is an intrinsically dissymmetric chromophore. 

As detailed in Section 2, we have derived and programmed the expression for line strengths of individual rotation-vibration transitions of XY3 molecules the line strengths depend on the vibronic transition moments entering into equation (70). With the theory of Section 2, we can simulate rotation-vibration absorption spectra of XY3 molecules. In computing the transition wavenumbers, line strengths, and intensities we use rovibronic wavefunctions generated as described in Ref. [1]. 

Vibrational circular dichroism arises from the interference of the electric dipole transition moment (p joi and the magnetic dipole transition moment (m )io and is proportional to the rotational strength, / ,o, where... 

Denoting the electric and magnetic dipole transition moments of oscillators a and b as p, lUg and m, lUb, respectively, the rotational strength of the coupled oscillator is given by (34)... 

An optically active transition is one that causes the plane of polarization of a light wave to rotate upon passage through a sample. The rotational strength of a transihon will be zero if the following quanhty is zero ... 

The crystal structure and absolute configuration of l-( - )-[Cr(acac)3] has been reported.772 The circular dichroism of D-[Cr(acac)3] has been studied in the solid state and in solution.773 The rotational strengths of the d-d transitions are extensively discussed competing rather than reinforcing effects lead to the smaller rotational strengths observed for tris(acetylacetonates) as compared to tris-(ethylenediamine) or -oxalate complexes. 

For the optical activity of achiral chromophores with a dissymmetric environment, two types of theoretical treatments have been proposed coupled oscillator treatment and one-electron treatment. The charge distribution of the magnetic dipole transition correlates Coulombically with an electric dipole induced in the substituents, and the colinear component of the induced dipole provides, with the zero-th order magnetic moment, a non-vanishing rotational strength. 

As shown in Eq. (35), the quantum mechanical foundation expresses the following equation for rotational strength of 0 - a transition ... 

Equations (54) and (55) correspond to the rotational strengths of the A and B symmetry, respectively. Thus, the rotational strengths of the two resultant transitions are equal in magnitude and opposite in sign (see Table 2). 

Next, consider the simplest model in which jL(l) and (1(2) are perpendicular to the line joining them. The only geometric variables are the distance between the dipoles, d, and the dihedral angle between the dipoles, a. The rotational strength R and dipole strength D, for a given transition of 0 -> a with the wave-number v0a are given as ... 

Now lets consider the rotational strength of the n-n transition for one example generating the optical activity through the mechanism. Thus the rotational strength is given by ... 

The zero- and first-order moments give the first-order rotational strength and the second-order rotational strength which are induced for the given transition Aa <- A0 of the achiral molecule ... 

Assuming the symmetry considerations, we can obtain the final form of the rotational strength of the transition i from the ground state 0 to the excited state a in an aromatic compound Rl(ia, expressed as ... 

In the numerous octahedral bis- and tris-bidentate complexes of this type, the configurational chirality can be associated simply with the array of chelate-spanned edges, and is designated A or A, as in (19a) and (19b), as discussed previously. The nature of the donor atoms is immaterial in this regard, although their consideration is necessary in the analysis of diastereomers with unsymmetrical bidentate ligands and in the assessment of any quantitative measures of chirality, such as the rotational strengths of electronic transitions.121,149... 

Fig. 11.14 Field ionization signal when the Xe 27f state is populated as a function of ionizing field strength (a) without NH3, (b) with 10 5 Torr NH3. The resonant rotational NH3 transitions are indicated beneath each field ionization feature (from ref. 63).

Chromophores which are asymmetric by nature are characterized by the absence of a center and plane of symmetry in the group of atoms participating in the optical transition. The rotational strength of these are usually larger when compared with chromophores that become optically active due to substitution. This is demonstrated in Mason and Schnepp s8 study of trans-cyclooctene, a-pinene and /1-pi none. They pointed out that the g (anisotropy factor, g = Ae/e) value of the major bands in trans -cyclooctene is relatively high as expected for an intrinsically asymmetric chromophore when compared with the other two olefins. 

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