Coupled spin systems conformer dependence

The detectable signal in the time intervals between the moments of exchanges can be determined by solving the time-dependent Schrodinger equation for the specific conformer however, in this case, the Hamiltonian is independent of time.18 The advantage of this method is its smaller memory requirement its disadvantage is the longer computational time because of the Monte Carlo simulation and that it was not possible to apply it to coupled spin systems so far. 

The pure basis states of the spin sets lead to mixed eigenstates in coupled spin systems, the extent of mixing is defined by the conformer-dependent probabilities ... 

If the molecule has dynamic motions on the timescale of the EPR experiment, this motion will lead to relaxation effects on the EPR line. Depending on the timescale and size of these motions, these effects may be observable directly in the cw-EPR spectrum or indirectly by pulsed EPR measurements of the relaxation times. In many cases, different dynamics may simultaneously contribute to the relaxation behavior of the electron spin system, as, for example, vibrational and rotational motion, conformational dynamics, phonon coupling to the frozen solvent, and nuclear spin dynamics. In these cases, it will be difficult to obtain specific information from these relaxation measurements. On the other hand, it is possible to highlight a specific time-scale window by the selection of pulse sequences and microwave frequencies that can lead, in favourable cases, to a direct relation between measured relaxation times and interesting molecular dynamics at the paramagnetic site. In these cases, very interesting molecular dynamical aspects of electron-transfer, catalytic, or photo-reactions, unobservable by other structural methods, can be studied directly by pulse-EPR techniques. 

The material in this chapter is largely organized around the molecular properties that contribute to electron transfer processes in simple transition metal complexes. To some degree these molecular properties can be classified as functions of either (i) the nuclear coordinates (i.e., properties that depend on the spatial orientation and separation, and the vibrational characteristics) of the electron transfer system or (ii) the electronic coordinates of the system (orbital and spin properties). This partitioning of the physical parameters of the system into nuclear and electronic contributions, based on the Born-Oppenheimer approximation, is not rigorous and even in this approximation the electronic coordinates are a function of the nuclear coordinates. The types of systems that conform to expectation at the weak coupling limit will be discussed after some necessary preliminaries and discussion of formalisms. Applications to more complex, extended systems are mentioned at the end of the chapter. 

By the study of 12 isotopomers of protoadamantane, the stereochemical dependence of isotope effects was also observed. A Karplus-type relationship similar to that for spin-spin coupling constants was proposed Recently, the first quantitative stereochemical dependence between isotope effects and dihedral angle was reported for a series of deuteriated norbornanes, as shown in Figure Observations of the influence of substitution with deuterium on conformational equilibria led to a new method in physical organic chemistry called isotopic perturbation of equilibrium. Details can be found in a recent review The effect was first observed for the chair-tO"Chair interconversion of deuteriated 1,3-dimethylcyclohexane 43 and later in 4-ethyl-l-methylcyclohexane " as well as in 1,1,4,4-tetramethylcyclohexane. In contrast, the isotope effect on conformational equilibrium in related systems turned out to be too small to be observable... 

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