Electronic spin state

EPR) netic) resonance [218-222] electron spin states in a magnetic field species... 

The negative sign in equation (b 1.15.26) implies that, unlike the case for electron spins, states with larger magnetic quantum number have smaller energy for g O. In contrast to the g-value in EPR experiments, g is an inlierent property of the nucleus. NMR resonances are not easily detected in paramagnetic systems because of sensitivity problems and increased linewidths caused by the presence of unpaired electron spins. 

Stehlik D, Bock C H and Thurnauer M 1989 Transient EPR-spectroscopy of photoinduced electronic spin states in rigid matrices Advanced ERR in Biology and Biochemistry ed A J Hoff (Amsterdam Elsevier) oh 11, pp 371 03... 

Secondly, you must describe the electron spin state of the system to be calcn lated. Electron s with their individual spin s of Sj=l /2 can combine in various ways to lead to a state of given total spin. The second input quantity needed is a description of the total spin... 

Both of these integrals are zero due to the orthogonality of the electron spin states a and fd. 

Secondly, you must describe the electron spin state of the system to be calculated. Electrons with their individual spins of sj=l/2 can combine in various ways to lead to a state of given total spin. The second input quantity needed is a description of the total spin S=Esj. Since spin is a vector, there are various ways of combining individual spins, but the net result is that a molecule can have spin S of 0, 1/2, 1,. These states have a multiplicity of 2S-tl = 1, 2, 3,. ..,that is, there is only one way of orienting a spin of 0, two ways of orienting a spin of 1/2, three ways of orienting a spin of 1, and so on. 

Shannon and Prewitt base their effective ionic radii on the assumption that the ionic radius of (CN 6) is 140 pm and that of (CN 6) is 133 pm. Also taken into consideration is the coordination number (CN) and electronic spin state (HS and LS, high spin and low spin) of first-row transition metal ions. These radii are empirical and include effects of covalence in specific metal-oxygen or metal-fiuorine bonds. Older crystal ionic radii were based on the radius of (CN 6) equal to 119 pm these radii are 14-18 percent larger than the effective ionic radii. 

Oxides and other chalcogenides Table 25.4 Electronic spin-states of iron... 

Iron is notable for the range of electronic spin states to which it gives rise. The values of S which are found include every integral and half-integral value from 0 to i.e. every value possible for a d-block element (Table 25.4). 

The differential cross-section, averaged over the initial electron spin states and summed over the final spin states for the potential... 

Postulate (i) follows from the fact that when two radicals, produced by whatever means, encounter each other, the interaction of the electron spin of one radical with that on the other radical can give rise to two mutually exclusive spin states, triplet and singlet. Random combination of the two possible electron spin states for the two electrons yields the three components of the triplet state, represented as T+i, To, and T i, and the singlet state, S. Throughout this article, S is assumed to be the singlet state of lowest energy. 

Consider a geminate radical pair, its component radicals in close proximity and therefore having correlated electron spins reflecting the electronic spin state of the precursor. Three different situations can be envisaged. 

At time [Case (2)] therefore, the hj rfine energy is approximately equal to the energy difference between the S and T states and can provide the driving force for T-S mixing. Now the h3q>erfine constants and Oj are a function of both nuclear and electronic spin states and thus one particular nuclear spin state for Hj and Hj will induce the T-S mixing more readily than the other. Thus nuclear spin selection occurs during the transition between S and T manifolds. However, this would yield no... 

The spin Hamiltonian is thus generated. In particular it can be used to examine the Tq-S mixing of electron spin states and its relationship to the distributions of populations of nuclear spin states. The total spin Hamiltonian is given in equation (15) which contains both electron and nuclear terms. 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

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... 

Encapsulation of [Co(bpy)3]2+ within zeolite frameworks has also been shown to have a remarkable influence on the electronic spin state of the complex.240 Distortions imparted on the tris-chelate complex by the confines of the zeolite supercage are found to be responsible for stabilizing the unusual low-spin electronic ground state.241,242 The [Co(bpy)3]3+/2+ couple has been measured for the encapsulated complex and it has been found that the complexes remain within the zeolite and do not exchange with the bulk solution.243 Electrochemistry of [Co(bpy)3]3+/2+ immobilized within a sol-gel has also been studied.244... 

The electron spin resonance spectrum of a free radical or coordination complex with one unpaired electron is the simplest of all forms of spectroscopy. The degeneracy of the electron spin states characterized by the quantum number, ms = 1/2, is lifted by the application of a magnetic field, and transitions between the spin levels are induced by radiation of the appropriate frequency (Figure 1.1). If unpaired electrons in radicals were indistinguishable from free electrons, the only information content of an ESR spectrum would be the integrated intensity, proportional to the radical concentration. Fortunately, an unpaired electron interacts with its environment, and the details of ESR spectra depend on the nature of those interactions. The arrow in Figure 1.1 shows the transitions induced by 0.315 cm-1 radiation. 

ESR line widths are also sensitive to processes that modulate the g-value or hyperfine coupling constants or limit the lifetime of the electron spin state. The effects are closely analogous to those observed in NMR spectra of dynamical systems. However, since ESR line widths are typically on the order of 0.1-10 G... 

The spectrum of Mn2+ in zeolites has been used to study the bonding and cation sites in these crystalline materials. This is a 3d5 ion hence, one would expect a zero-field splitting effect. A detailed analysis of this system was carried out by Nicula et al. (170). When the symmetry of the environment is less than cubic, the resonance field for transitions other than those between the + and — electron spin states varies rapidly with orientation, and that portion of the spectrum is spread over several hundred gauss. The energies of the levels are given by the equation... 

Figure 3.10 Removal of degeneracy of the a and P electron spin states by a magnetic field. (Adapted with permission from Figure 2.16 of Cowan, J. A. Inorganic Biochemistry, An Introduction, 2nd ed., Wiley-VCH, New York, 1997. Copyright 1997, Wiley-VCH.)...

This chapter will concentrate on the electronic spin-state crossover observed in the iron and cobalt complexes formed with the HB(pz)3 and HC(pz)3 ligands and their various methyl derivatives. In the majority of cases, the spin-state crossover occurs in the solid state and, as a consequence, solid state studies will be covered first, followed by the more limited studies... 

The long-range cooperative nature of the electronic spin-state crossover in [Fe(HB(pz)3)2] and the accompanying crystallographic phase transition is... 

The electronic spin-state crossover in [Fe(HB(pz)3)2] has also been observed in the fine structure of its fC-edge x-ray absorption spectrum [38]. The changes in the x-ray absorption spectra of [Fe(HB(pz)3)2] are especially apparent between 293 and 450 K at ca. 25 eV, as is shown in Fig. 5. The 293 K x-ray absorption spectral profile observed in Fig. 5 for [Fe(HB(pz)3)2] has been reproduced [39] by a multiple photoelectron scattering calculation, a calculation that indicated that up to 33 atoms at distances of up to 4.19 A are involved in the scattering. As expected, the extended x-ray absorption fine structure reveals [38] no change in the average low-spin iron(II)-nitro-gen bond distance of 1.97 A in [Fe(HB(pz)3)2] upon cooling from 295 to 77 K. 

Excitation between electronic spin states Electron paramagnetic resonance, EPR... 

Thus, for a r.h. rotating field, only nuclei which belong to molecules with an electron spin state ms = 1/2 and which have a hf coupling a, > 2/ NgnB0 will contribute to the ENDOR spectrum. 

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