Nonrigidity parameter

An interesting quantity that characterizes the properties of the two solutions is the nonrigidity parameter R introduced by Berry (1980)... 

The abscissas of the correlation diagrams can be quantified. The quantification is thus far only an ex post facto device with power to classify but not yet to predict. It does not yet have a microscopic interpretation. Nevertheless it satisfies the needs of a theory of the equilibrium behavior of melting and freezing of clusters. Only the existence and not the definition of the nonrigidity parameter or the details of its origins is used in stage 2. However, we make a brief aside here to explain the definition in order to clarify just what information it carries. To understand the order parameter y (not to be confused with the surface tension), it is useful to examine how nonrigidity is traditionally characterized in diatomic and linear, particularly triatomic molecules. For... 

The temperature-dependent PMR spectra of the M(R2Dtc)3 complexes [M = Ga(III), In(III)] show them to be stereochemically nonrigid. Kinetic parameters for the intramolecular metal-centered rearrangement (by a trigonal... 

Variable-temperature PMR studies on the stereochemically nonrigid, (Cl4-n)Ti(R2Dtc) (n = 2, 3, or 4) complexes show the metal-centered rearrangements to be fast on the PMR time scale at temperatures higher than —90°. Hindered rotation about the C-N bonds was observed for R = r -Pr, and activation parameters were determined for this process. 

Similar mixed-ligand complexes of the type (R, R2Dtc)2(MNT)Fe have been synthesized. The complexes were obtained initially as dianions, [(RiR2-Dtc)2(MNT)Fe]J", and were subsequently oxidized either by air or Cu(II) ions in acetonitrile (510). They also exhibit the singlet- triplet equilibrium however, they show a higher population of the triplet state than is found for the TFD analogues. The complexes are stereochemically nonrigid and display the same type of kinetic processes as their TFD counterparts. Thermodynamic activation parameters for inversion of the two complexes (TFD versus MNT) do not differ within experimental error. 

Liquid T (K) A. Fitted Parameters Parameters Relevant to a Rigid Dipole Moment Parameters Relevant to a Nonrigid Dipole Moment ... 

The hat-curved-harmonic oscillator model, unlike other descriptions of the complex permittivity available now for us [17, 55, 56, 64], gives some insight into the mechanisms governing the experimental spectra. Namely, the estimated relaxation time of a nonrigid dipole (xovib 0.2 ps) is close to that determined in the course of very accurate experimental investigations and of their statistical treatment [17, 54-56]. The reduced parameters presented in Tables XIVA and XIVB and the form of the hat-curved potential well (determined by the parameters u, (3, f) do not show marked dependence on the temperature, while the spectra themselves vary with T in greater extent. We shall continue discussion of these results in Section X.A. 

Table 7. Kinetic parameters for rearrangement of nonrigid M(RiR2-(3-dik)3 complexes and mixed 0-diketonate complexes...

Complexes belonging to type 468 (M = Be, Zn, Cd, Hg, Pb) are very important subjects of study in the field of stereochemical nonrigid tetrahedral structures [851,852], Using the method of spin labels (a method in dynamic NMR), it is possible to determine the kinetic parameters, separately as intra- or intermolecular processes, for the stereoisomerization reactions in solution. 

To characterize the geometry of molecules, a model of point nuclear masses with fixed intemuclear distances has proved very useful in many instances. As long as intemuclear distances are not required with an accuracy of better than a few hundredths of an angstrom, this model is quite adequate, and it is possible to speak of the geometrical parameters of a molecule. If greater accuracy is required, however, it becomes necessary to consider the consequences of the nonrigidity of molecules. 

Because of the differing ways in which effects of nonrigidity enter, different experimental techniques do not yield exactly the same values for structural parameters. Furthermore, more than one set of structural parameters may be derivable from the same experimental data, depending on the way in which corrections are made for nonrigidity. As a result, structural parameters reported in the literature have a variety of meanings. In this paper various types of structural parameters commonly reported for gas-phase molecules will be defined and the interrelations among them discussed. A similar discussion has been given by Kuchitsu and Cyvin.1... 

Fig. 5. A schematic representation of the free energy of a cluster as a function of an order parameter for nonrigidity, at a succession of temperatures.

Pig. 6. A schematic representation of the free energy of a clxister as a function of an order parameter for nonrigidity, for a case of a phase that is observable for clusters but not for bulk matter. The reason is that in the range of conditions under which this phase is locally stable and present in observable concentrations for small systems, it is never the most stable phase, and hence, in the bulk limit, is never present in observable concentrations. 

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