Ring Torsional Modes

Nomenclatu re of bicyclic systems. Note that, if we define m as the sum of the numbers within the brackets, there are m + 1 atoms in the ring system for spiro compounds, and m + 2 atoms in the ring system for bicyclic compounds. 

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Here, S is the Huang-Rhys factor [63], which is related to the intensity of the 0-n vibronic transition, Io-n = e sSn/n, and reflects the time-dependent Stokes shift associated with a given type of vibrational mode (e.g., S 0.6 for the high-frequency C=C stretch modes [61,64,65]). For the class of systems studied here, two types of phonon modes are considered per monomer unit, i.e., high-frequency C=C stretch modes and low-frequency ring-torsional modes. 

In the examples addressed below, for a two-band phonon distribution, the HEP scheme willl be shown to yield essential insight into the interplay between high-frequency (C=C stretch) and low-frequency (ring-torsional) modes of the polymer heterojunction model of Eq. (7). 

In the following, we summarize the pertinent results of our analysis of Refs. [50-53] where we applied the LVC Hamiltonian Eq. (1) in conjunction with a 20-30 mode phonon distribution composed of a high-frequency branch corresponding to C=C stretch modes and a low-frequency branch corresponding to ring-torsional modes. In all cases, the parametrization of the vibronic coupling models is based on the lattice model of Sec. 3.1 and the complementary diabatic representation of Sec. 3.2. 

While the vibrations (stretching, bending, torsion) in high symmetrical rings (Ss, Ss, S12) are almost uncoupled [80], the vibrations in the low symmetrical Sy ring are heavily mixed, especially the bending and torsional modes [81]. 

Fig. 8. Tyrosine coordination modes in galactose oxidase-copper complex. Tyrosine phenolate bond angles (0) and ring torsion angles (t) are indicated. (Based on protein coordinates PDB ID IGOG.)...

Fluorescence excitation of jet-cooled triptycene. Vibrational structure above the Sj — Sj, origin assigned to torsional modes of the phenyl rings Vibrational energy transfer within the... 

Present calculations performed at B3LYP/6-311++G(d,p) computational level. Values taken from Reference 244 with permission. Frequencies in cm IR intensities in kmmol L Glossary of vibrational mode acronyms v, sfretch in-plane bend y, out-of-plane bend r, torsion rg, ring and 63, ring deformations and ri, X2 and TT3, ring torsions. PED elements 10% only are included. 

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