Models of spin transition

Spin-state transitions have been studied by the application of numerous physical techniques such as the measurement of magnetic susceptibility, optical and vibrational spectroscopy, the Fe-Mbssbauer effect, EPR, NMR, and EXAFS spectroscopy, the measurement of heat capacity, and others. Most of these studies have been adequately reviewed. The somewhat older surveys [3, 19] cover the complete field of spin-state transitions. Several more recent review articles [20, 21, 22, 23, 24, 25] have been devoted exclusively to spin-state transitions in compounds of iron(II). Two reviews [26, 27] have considered inter alia the available theoretical models of spin-state transitions. Of particular interest is the determination of the X-ray crystal structures of spin transition compounds at two or more temperatures thus approaching the structures of the pure HS and LS electronic isomers. A recent survey [6] concentrates particularly on these studies. 

A pronounced hysteresis of ATC = 9.5 K has been observed (Tc = 181.86 K for rising and Tc = 172.33 K for falling temperature). The authors attempted to describe the results with the thermodynamic model for spin transitions of Slichter and Drickamer 91 Different diffraction patterns were recorded above and below Tc, where only one spin isomer was present (see Fig. 39). This provides evidence that a crystallographic phase change accompanies the abrupt spin phase transition in this compound. The temperature dependence of the peak profiles was found to follow that of the HS fraction as derived from the Mossbauer spectra, which shows that the crystallographic phase change is directly associated with the interconversion of the two spin phases. The Debye-Waller factors were evaluated for the two spin phases they showed at Tc a discontinuity of Af 35% on going from the HS to the LS phase. The shape of the transition curve near Tc and Tc itself, were somewhat different in three independently prepared samples. 

A successful model for the quantitative interpretation of spin transitions should explain all the different types of the temperature dependence of the HS fraction Xhs = 7 as sketched in Fig. 2. 

A successful model of spin-state transitions should... 

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

Many models of phase transitions are based on the Ising lattice (Figure 1.23). E.g. in C2USC of a magnetic, every lattice site (the fth) contains a molecule with two possible directions of its spin ([Pg.95]

Clearly there is need for spin-glass theories beyond mean-field. One approach in this direction is presented by Malozemoff et al. (1983) and Malozemoff and Barbara (1985). They propose a critical fractal cluster model of spin glasses which is able to describe the essential features of the phenomena occurring near the spin-glass transition and to account for the static critical exponents. The basic assumption of this fractal model is the existence of a temperature- and magnetic-field-dependent characteristic cluster size on which all relevant physical quantities depend and which diverges at the transition temperature Tj. It is related to the correlation length and the cluster fractal dimension D by More... 

Spin-pairing model of dioxygen binding and its application to various transition metal systems as well as hemoglobin cooperativity. R. S. Drago and B. B. Corden, Acc. Chem. Res., 1980, 13, 353-360 (39). 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

Several types of spin-lattice relaxation processes have been described in the literature [31]. Here a brief overview of some of the most important ones is given. The simplest spin-lattice process is the direct process in which a spin transition is accompanied by the creation or annihilation of a single phonon such that the electronic spin transition energy, A, is exchanged by the phonon energy, hcoq. Using the Debye model for the phonon spectrum, one finds for k T A that... 

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