Partially relaxed rotation model

Fig. 14. Curve of rotation about the Ru-N-N-Ru axis of C -symmetric (S,S)-8, which produces two stable conformers in which the two phosphines are in orthogonal positions (the phosphine has been modeled by PMe3, the upper PMe3 is marked by an open circle and the position of the lower PMe3 by a closed circle). The curve was calculated with BP86/RI/SV(P) under partially relaxation of the structure at each point (139) (some structural parameters were kept frozen in order to map the rotation coordinate on a dihedral angle).

A tentative interpretation of these results may be based on the assumption that in this laser high rotational levels (J > 10) are indeed populated initially 71>. It should also be mentioned that two peaks in the rotational energy distribution are similarly observed in HC1 chemiluminescence experiments under conditions of partial rotational relaxation 9>. A simple rotational relaxation model suggested by Polanyi and Woodall 72) has been applied to fit these observations. In this model the probability P of the relaxation process J + AJ) / is given as... 

We first consider the A contribution. Equation 1, and an explanation in terms of a two-site model i.e., a model in which a water molecule exchanges between solution and sites (or class of sites) on or near a protein molecule such that at least one direction fixed in the water molecule is constrained to move rigidly with the protein molecule. In the simplest case, a water molecule attaches rigidly to the protein, moves with it for a while, and then leaves. In a somewhat more complex case, the attachment may be less rigid so that the water molecule is free to rotate about an axis fixed with respect to the protein. Additionally, a situation in which water molecules partially orient in the electric fields near the protein surface because of their electric dipole moments would also be a two-site model. Characteristic of a two site-model is that a time Tj, or a distribution of such times, can be defined that measures the mean lifetime of a water molecule in the protein-associated state. Moreover, such a time is in principle a measurable quantity, and its value must satisfy two criteria it must be at least comparable to if not longer than Tj, otherwise the nuclei of the bound water molecules could not sense the rotational motion of the protein molecules and it must be comparable to or shorter than the nuclear relaxation time of a bound water molecule, else it could not communi-... 

A pioneer effort to the account for electrostatic interaction effects in dipole reorientations and correlation functions was made by Brot and Darmon (39) in their Monte Carlo simulations for the partially ordered solid phase of 1 2 3 trichloro 4 5 6 trimethyl benzene (TCTMB) using the point charge model already mentioned in 2.4. Calculations of transition rates between 6 fold rotational wells of fluctuating depth as a result of changing neighbor orientations resulted in essentially Debye relaxation at 300 Kt but a second simulation at 186 K for which considerable rotational ordering is present produced very nearly a circular arc with od = 0.28 as compared to the experimental Ad = 0.39. 

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