Rotational orientation factor

The macroscopic polarization of the phase is given by equations 1 and 2, where Di is the number density of the ith conformation, jlj is the component of the molecular dipole normal to the tilt plane when the ith conformation of the molecule is oriented in the rotational minimum in the binding site, ROFj is the "rotational orientation factor", a number from zero to one reflecting the degree of rotational order for the ith conformation, and e is a complex and unmeasured dielectric constant of the medium (local field correction). 

This section deals with a single donor-acceptor distance. Let us consider first the case where the donor and acceptor can freely rotate at a rate higher than the energy transfer rate, so that the orientation factor k2 can be taken as 2/3 (isotropic dynamic average). The donor-acceptor distance can then be determined by steady-state measurements via the value of the transfer efficiency (Eq. 9.3) ... 

From presently known structural data, the orientation of the SO2 group in most SP complexes can be rationalized by considering the effect of basal donors and acceptors on the ML4(S02) molecular orbitals. The factors involved in determining the rotational orientation of the bent axial nitrosyl in MNO square-pyramidal complexes have been considered extensively by several authors For convenience, we reproduce two rules, which may be of some utility in rationalizing orientational features of the SO2 complexes discussed here (see especially Ref. 48 for underlying assumptions) (1) (a) In... 

The critical stress intensity factor, Kc, obtained at different loading rates and environmental conditions was then reported as a function of fibre orientation. It was expected that the most evident relationship with the considered mechanical property would have been shown by the orientation factor in the applied stress direction (direction 1 in Fig. 2b). Therefore the orientation factor aj, previously measured on the plane 2 -3 was transformed into the orientation factor a, defined with respect to the applied stress direction 1 (Fig. 2 a and b) by a coordinate axis rotation of an angle a. Further details on such data handling can be found in ref [7, 13]. It is worth reminding here that a, and a go opposite when a increases from 0 to 90 degrees a, decreases from 1 to 2ero. 

FRET efficiency depends on the spectral overlap of the donor and acceptor, their distance from each other, and the relative orientation of the chromophore s transition dipoles. The orientation factor is usually assumed to be 2/S, a value that approximates complete random orientation. In contrast to small fluorophores that rotate fi eely, GFP has slower rotation in comparison with the excited-state lifetime. 

Surface symmetry Substrate Number of rotational orientations of unit mesh Possible number of equivalent translational shifts on a single step Multiplying factor due to possible different steps Total no. of dispositions... 

Often a value of = 2/3 is assumed, which corresponds to the situation when there is rapid, isotropic rotation of the donor and acceptor molecules. Randomly oriented dipoles that remain fixed during the singlet lifetime give = 0.476. When required, the range of values for can be estimated by polarization measurements [139]. A comprehensive discussion on the theory and effects of the orientation factor is given in [140]. 

Ogilvie JF (1995) Electric polarity + BrCl and rotational g factor from analysis of frequencies of pure rotational and vibration-rotational spectra. J Chem Soc Faraday Trans 91 3005-3006 Bazalgette G, White R, Loison J et al (1995) Photodissociation of ICl molecules oriented in an electric-field—direct determination of the sign of the dipole-moment. Chem Phys Lett 244 195-198... 

Identical formulae apply in both cases. When excited molecules do not rotate or transfer excitation energy to differently oriented molecules between the initial absorption event and the later absorption (photoinduced dichroism) or emission (photoluminescence) event, their orientation factors are time independent. Negligible ground-state depletion is assumed in the first step. 

In a similar way to the derivation of equation (14), the orientation factors of the structural unit, possibly of a noncrystalline unit involving the fluorescence, may be related to the above orientation factors using equation (68), where /(<4), m(even numbers. For most of the noncrystalline orientation, it may be assumed that the noncrystalline chain segments are randomly oriented around their own 1/3 axes, Le. random orientation with respect to the rotational angle tj. Thus equation (68) can be rewritten as equation (69), where / = 2 or 4, and m=0, 2 or 4. 

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