Transition moment rotational

In their 1978 analysis, Pearlstein and Hemenger [16] presented two sets of theoretical results, one of which is remembered and the other not. The former comes from a nonstandard approach in which each Qy dipole is assumed to be rotated 90° in the plane of its BChl macrocycle relative to the direction assigned [27] by molecular orbital theory. This single assumption virtually solves all of the anomalies just noted, except for the overall red-shift. However, this striking finding has not led anywhere, because so far no physical basis for such a rotation of electronic transition moments has been proven. Nonetheless, there may be a kernel of truth in the transition-moment-rotation hypothesis (see below). 

Hollenstein H, Marquardt R, Quack M and Suhm M A 1994 Dipole moment function and equilibrium structure of methane In an analytical, anharmonic nine-dimenslonal potential surface related to experimental rotational constants and transition moments by quantum Monte Carlo calculations J. Chem. Phys. 101 3588-602... 

In a molecule such as the asymmetric rotor formaldehyde, shown in Figure 5.1(f), the a, b and c inertial axes, of lowest, medium and highest moments of inertia, respectively, are defined by symmetry, the a axis being the C2 axis, the b axis being in the yz plane and the c axis being perpendicular to the yz plane. Vibrational transition moments are confined to the a, b or c axis and the rotational selection mles are characteristic. We call them... 

This general behaviour is characteristic of type A, B and C bands and is further illustrated in Figure 6.34. This shows part of the infrared spectrum of fluorobenzene, a prolate asymmetric rotor. The bands at about 1156 cm, 1067 cm and 893 cm are type A, B and C bands, respectively. They show less resolved rotational stmcture than those of ethylene. The reason for this is that the molecule is much larger, resulting in far greater congestion of rotational transitions. Nevertheless, it is clear that observation of such rotational contours, and the consequent identification of the direction of the vibrational transition moment, is very useful in fhe assignmenf of vibrational modes. 

The three bands in Figure 9.46 show resolved rotational stmcture and a rotational temperature of about 1 K. Computer simulation has shown that they are all Ojj bands of dimers. The bottom spectmm is the Ojj band of the planar, doubly hydrogen bonded dimer illustrated. The electronic transition moment is polarized perpendicular to the ring in the — Ag, n — n transition of the monomer and the rotational stmcture of the bottom spectmm is consistent only with it being perpendicular to the molecular plane in the dimer also, as expected. 

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. 

The Brownian rotation of the emission transition moment is characterized by the angle co(t ) through which the molecule rotates between time zero (b-pulsc excitation) and time t, as shown in Figure 5.11. 

Using the same method that led to Eq. (5.27), it is easy to establish the rule of multiplication of depolarization factors when several processes inducing successive rotations of the transition moments (each being characterized by cos2 C,) are independent random relative azimuths, the emission anisotropy is the product of the depolarization factors (3 cos2 c, — l)/2 ... 

Fig. 5.9. Rotational motions inducing depolarization of fluorescence. The absorption and emission transition moments are assumed to be parallel.

We have considered spherical molecules so far, but it should be noted that isotropic rotations can also be observed in the case of molecules with cylindrical symmetry and whose absorption and emission transition moments are parallel and oriented along the symmetry axis. In fact, any rotation around this axis has no effect on the fluorescence polarization. Only rotations perpendicular to this axis have an effect. A typical example is diphenylhexatriene whose transition moment is very close to the molecular axis (see Chapter 8). 

In most cases, fluorescent molecules undergo anisotropic rotations because of their asymmetry. A totally asymmetric rotor has three different rotational diffusion coefficients, and in cases where the absorption and emission transition moments are not directed along one of the principal diffusion axes, the decay of r(t) is a sum of five exponentials (see Box 5.3). 

For a rod-like probe with its absorption transition moment direction coinciding with the long molecular axis, the rotational motion in this potential well is described by the diffusion coefficient D. The decay of the autocorrelation functions is then shown to be an infinite sum of exponential terms ... 

Otherwise, depolarization would also be a result of energy transfer between probe molecules. Because the transition moments of two interacting probes are unlikely to be parallel, this effect is indeed formally equivalent to a rotation. Moreover, artefacts may arise from scattering light that is not totally rejected in the detection system. 

Figure 3.34. Photochromism of azo dyes under irradiation with polarized light. In an amorphous matrix, trans-cis isomerizations are coupled to rotational diffusion. After many isomerization cycles, the molecules are trapped in an orientation with the transition moment M perpendicular to the polarization direction of the light P.

The calculated state energies, the transition moments, and the symmetry classification are given in Table 3. The symmetry species of the triplet functions is obtained by taking the direct product of irreducible representation of the space and the spin functions Fx, Fy, Fz, which transform as the rotations Rx, Ry, and Rz-... 

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)... 

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