Dimers, rotational strength

In the dimeric case, the coupled oscillator equation predicts the rotational strengths R for the symmetric +) and antisymmetric -) combination states of two interacting vibrations according to... 

The predicted features of the dichroic spectra are in good agreement with observations for the adenylate oligomers in neutral solution. Taking the simplest case, the dimer, we see that there should be two bands of opposite sign, spaced above and below the position of the monomer band their rotational strength should be given by... 

Each of these bands will be of half-width comparable to that of the monomer band. Thus, while the difference in sign allows resolution in the circular dichroic spectrum, the bands cannot be resolved in the absorption spectrum. If we algebraically add two bands of appropriate width and intensity, the series of points shown in Figure 1 is obtained this accurately represents the observed circular dichroic spectrum of the dimer. A calculation (25) of the rotational strength to be observed in either half of the curve leads to values in good agreement with experiment, if Z is assumed to be 3-4 A., and a is between 30° and 45°. 

Before moving further to the multimer case we should outline one further significant feature of a dimer. Dimer excited states have a well defined rotational strength [33, 34] ... 

V mon is simply the sum of the intrinsic rotational strengths of the individual molecules, with the contribution of each subunit weighted by the square of the corresponding coefficient in Pb - This term, sometimes called the one-electron contribution, is independent of how the two molecules are arranged with respect to each other in the dimer, assuming that the intermolecular interactions do not affect the magnetic and electronic transition dipoles of the individual molecules. However, it could reflect perturbations of or by the electrostatic environment in the dimer. 

Fig. 9.7 SHex contributes opposite rotational strengths to the exciton bands of a dimer. The dashed lines in (A) show the exciton absorption bands of a dimer the solid curve is the total absorption spectrum. In (B), the dashed lines are the circular dichroism (CD) of the two bands and the solid curve Is the total CD spectrum. The spectra are for a homodimer with = Di,a 2) =10 D, I/ 2iI = 7 A, 9 = 71°, a = P = 90° (Fig. 7.2) and ba = 4,444 A. This geometry makes H21 positive (7 21 = 50 cm in the point-dipole approximation) and gives the exciton band the higher transition energy, the larger dipole strength, and a positive rotational strength. For purposes of Illustration, the exciton bands were assigned Gaussian shapes with arbitrary widths...

What are the exciton rotational strengths ( ex) of the two exciton bands of the dimer discussed in Exercise 8.1 Explain your answer. 

Molecules a and 6 in the dimer shown in Fi. E.3 are the same as those of Fig. E.2, and also lie in planes separated by 4 A in the z direction. Axes and Xb again project out toward the viewer, (a) What is the stereochemical relation between this structure and that of Fig. E.2 (b) Calculate the contributions of ilfex to the rotational strengths of the two exciton bands of this dimer, (c) Sketch the predicted absorption and CD spectra, assuming again that dominates the rotational strengths. 

The eight dipolar and rotational strengths have been calculated for a Bchla dimer whose structure is similar to P-860 and a Bchl6 dimer whose structure is similar to P-960 (table 4). The calculated spectra of these dimers using the appropriate log normal curves (15) are shown in Figure 2. 

These calculations show that the lower-energy Qy transition s energies, dipolar and rotational strengths are in fairly good agreement with those of P-860 and P-960 measured at room temperature. They also predict that the two dimer s higher-energy Qy excitonic... 

The effects in this reaction may be explained by the vdW bond strength and by the structure of the complex. In the reaction of (CF3l)2 the dimeric bond contributes six additional degrees of freedom to the reaction complex. Because of their very low frequencies, they behave like phonons in the condensed phase. Therefore they contribute greatly to the density of states in the reaction complex, and a significant portion of the energy is deposited in them. Since these modes correspond to translational or rotational motion, once the dimer dissociates, much less energy remains in the vibrational of the Bal. 

The structures of VdW dimers, considered as weakly bounded complexes in which each monomer maintains its original structure (Buckingham, 1982), are studied at low temperatures by sophisticated experimental techniques, such as far infrared spectra, high-resolution rotational spectroscopy in the microwave region, and molecular beams. Distances Re between the centres of mass and bond strengths De at the VdW minimum for some homodimers of atoms and molecules taken from Literature are collected in Table 4.4. 

The energy and oscillator strength of the PIC dimer at the rotation of the molecules divided on distance 7.8 A were calculated using the ZINDO/S method, including 3 orbitals in configuration interactions (Cl). The results of the calculation for two first allowed singlet transitions are shown in fig. 37. 

Fig. 37. The values of the wavelengths (a) and asciUator strength (b) for the two allowed singlet transitions in the PIC dimer depending on the rotation angle in ZX plane...

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