Spin Arrhenius parameters

Table 11. Arrhenius parameters for the spin-state transition in rFet2-nicl.irPF 1. at nr siirpe ...

The Arrhenius parameters for the reaction of the persistent (CF3)2NO-radical with n-Bu3SiH also were determined by ESR spectroscopy (Table V).72 It has been suggested that the unusually low preexponential factor is due to geometric constraints on the transition state. The similar reactivities of (CF3)2NO- and PhCMe200- radicals toward n-Bu3SiH and Ph3SiH, respectively, are expected because both the thermochemistries and spin distributions for these two radicals are rather similar.72,73... 

The similar reactivity of peroxyl with (CF3)2NO radicals towards a large variety of substrates has been observed previously and attributed to rather similar thermochemistries and spin density distributions for these two radicals [30]. The Arrhenius parameters for the reaction of the persistent (CF3)2NO radical with n-BusSiH determined by kinetic EPR spectroscopy are logyl/M s = 5.5 and Ea = 32.2kJ/mol, which corresponds to k = 4.3 s- at 73 °C [31]. 

Of the mechanistic issues dealt with in the full study (including kinetic trade-off s between different Co-+ spin states in the reaction product and the role of solvent and conformational fluctuations of the DBA system), we focus here on the activation parameters and related nuclear tunneling and entropy effects which are crucial for establishing meaningful contact with the Arrhenius parameters obtained from the experimental rate data [158]. The theoretical analysis also led to new insights... 

The thermal decomposition of diphenyldiazomethane is first order in aceto-nitrile , xylene and 1-methyl naphthalene and probably leads to the formation of diphenylcarbene . The rate-determining step is the formation of diphenyl-carbene. The nature of the solvent does not affect the rate, but does alter the subsequent reactions of the carbene. At 85°, k = 1.6 x 10 sec" and the Arrhenius parameters give Af/ == 27.2 kcal.mole" and AS = 0 . Diphenylcarbene displays a marked electrophilic character implying a singlet electronic state. In the absence of nucleophiles rapid spin inversion to the ground triplet occurs, and it was suggested that this spin inversion is reversible. 

Muon spin relaxation (/u.SR) has been employed in determining the rate constants and Arrhenius parameters for the addition of the ethyl radical and the t-butyl radical to... 

What can we make of this list of rate constants In view of the complete uncertainty in mechanism, and the considerable variation in the Arrhenius parameters, it is very difficult to assess the situation. The most reassuring aspect is the parallel between nitrogen atom reactivity and H atom reactivity. The substantially lower rates for the nitrogen atom additions probably reflect the spin-forbidden character of the reaction in its ability to produce products in their ground electronic states. 

Unless retarded by repulsion between bulky substituents in the more crowded planar isomer, the tetrahedral-to-planar isomerization has a low enthalpy of activation, AH 10 4 kcal/mol [24]. Its entropy of activation is ordinarily quite negative for a unimolecular isomerization AS < —10 kcal/mol K) but is substantially less so - occasionally approaching zero - in nickel(II) complexes with halogen atoms as coordinating ligands [25]. This pattern of Arrhenius parameters, characteristic of reactions that occur with spin inversion (see Chapter 9), is hardly surprising in view of the fact that the tetrahedral complex is high-spin (5 = 1) whereas the square-planar complex is low-spin S = 0). 

The explanation for this lack of correlation appears to lie in the factor governing the energies of the transition states. Reactions (4) and (13) are overall spin and symmetry allowed and their low rates must be attributed to the higher energies of their respective triplet and quartet transition states as compared with the doublet surfaces over which the other reactions can proceed. In the absence of Arrhenius parameters it carmot be excluded that reaction (10) proceeds non-adiabatically via a doublet surface. Reactions (8) and (9) must pass through intermediate states corresponding to pemitrous acid and chlorine nitrite both of which have been prepared by Knauth at Kiel they therefore go via attractive potential surfaces. 

The effect of a pressure of 80 and 150 MPa on the spin-state transition has been also studied [169], a series of spectra obtained at 150 MPa being shown in Fig. 32. The speetra show relaxation effects as line broadening and linewidth asymmetry. Calculated spectra were obtained in the same way as at ambient pressure. Rate constants for a number of temperatures are listed in Table 12, the parameter values resulting from an Arrhenius plot of the rate constants being listed in Table 13. In Fig. 33, the quantity 5g of Eq. (36) has been plotted as a... 

The spin-lattice relaxation time 7] as a function of temperature T in liquid water has been studied by many researchers [387-393], and in all the experiments the dependence T (T) showed a distinct non-Arrhenius character. Other dynamic parameters also have a non-Arrhenius temperature dependence, and such a behavior can be explained by both discrete and continuous models of the water structure [394]. In the framework of these models the dynamics of separate water molecules is described by hopping and drift mechanisms of the molecule movement and by rotations of water molecules [360]. However, the cooperative effects during the self-diffusion and the dynamics of hydrogen bonds formation have not been practically considered. 

Boum describe their use of the line shape method in the temperature range —24° to — 82°C (deuterium decoupling was used so that only the unperturbed single proton resonance was observed) and of a double-resonance method in the temperature range —97° to — 116°C. This involved the observation of recovery of magnetization of one of the two lines in the spectrum after a saturating r.f. field applied to the other line was removed. Consistent rates of inversion were found from both methods as evidenced by linearity of the Arrhenius plot. The results do not agree with the spin-echo results of Allerhand et al In this type of work, while fairly consistent results of rate constants may be obtained, there is dispute as to how the thermodynamic parameters should be derived, even in the relatively simple case of cyclohexane. ... 

Figure 7.10 Temperature dependence of the longitudinal muon spin relaxation of the slow relaxing component of ferrocene measured at 200 mT (on the left). An Arrhenius plot of inverse correlation time giving the activation parameters of the dynamic process (on the right) [5,6]. Reproduced from U. A. Jayasooriya et al, Appl. Magn. Resonance 13, 165-171 (1997) with permission from Springer-Verlag KG.

Fig. 4. Arrhenius plots of the rotational parameters Rs (+) and Ri (x) in s determined in randomly spin-labeled PMMA in dibutyl phthalate. For the symbols, see Fig. 3. (From Ref. 31, with permission.)...

Fig. 10. Arrhenius plots of rotational parameters/fs (fuU symbols) and/ [ (empty symbols) in determined in the random copolymer of styrene witb spin-labeled methacrylic acid nnits in four solvents and their best fits to Eq. 4. The X-band data for the styrene copolymer with spin-labeled acryhc acid nnits in toluene (TOL ) are given for comparison. (From Ref 43, with permission.)...

Fig. 16. Arrhenius plots of rotational parameters R (empty symbols) and Ri (full symbols) in s determined in spin-labeled PHEMA in methanol for all the concentrations studied. (From...

To optimize force fields for long time scale motions Aliev et al. propose a new robust approach to use NMR spin-lattice relaxation times Ti of both backbone and sidechain carbons. This allows a selective determination of both overall molecular and intramolecular motional time scales. In addition they use motionally averaged experimental/ coupling constants for torsional FF parameters. The force constants in the FFs and the correlation times are fitted in an Arrhenius-type of equation. 

Table 3.5 NMR parameters obtained from the Li NMR experiments in polymer electrolytes. T ax is the temperature at the spin-relaxation rate maximum, to is a pre-exponential factor in the Arrhenius expression, Eq. [3.1], and Ea is the activation energy for the motion causing the relaxation...

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